Abstract

We investigate the acousto-optic coupling rates between different acoustic resonance modes and a specified optical resonance mode in a one-dimensional phoxonic crystal fishbone nanobeam formed by periodically arranging semi-cylinders of air on both sides of a suspended silicon waveguide. The gradually tapered unit cells form optical and acoustic resonators. In acousto-optic coupling rate calculation, the acoustic fields and optical fields are obtained by steady state monochromatic analysis and eigen-mode computation, respectively. Results showed that the acoustic polarizations and symmetries of the acoustic resonance modes are dominant factors in the acousto-optic coupling efficiency, and appropriate selection of these parameters can prevent cancellation of acousto-optic interactions, thereby enhancing acousto-optic coupling rates. This study provides important insights that can be applied to acousto-optic device designs.

© 2017 Optical Society of America

1. Introduction

Photonic crystal structures are known to be highly dispersive media for optical wave propagation. The spatial distribution of the refractive index in a photonic crystal is periodic. This type of structure can exhibit a photonic band gap, and light cannot propagate within a photonic crystal when the light frequency falls within the photonic band gap. Photonic crystals can be used to design optical waveguides [1], filters, optical cavities [2], and detectors [3,4]. Similarly, a phononic crystal is an artificial structure that has spatially periodic acoustic properties, such as elastic constant and mass density, and elastic wave propagation is prevented in phononic crystals when the acoustic wave frequency falls within the phononic band gap [5]. Many novel acoustic devices have been developed based on phononic crystal structures [6–10]. In recent years, numerous studies have investigated structures that exhibit simultaneous photonic and phononic band gaps [11–15]. For example, Mohammadi et al. showed that a silicon slab with a periodic array of air holes can exhibit simultaneous two-dimensional phononic and photonic band gaps [11]. Rolland et al. demonstrated the existence of dual photonic and phononic bandgaps in an LiNbO3 slab containing an air-hole array [16]. These structures are called phoxonic crystals or optomechanical crystals. The phoxonic crystal structure can control, guide, or confine optical and acoustic waves within the same area. Thus, these structures show considerable potential to enhance acousto-optic (AO) interactions [17–31].

An AO interaction can be enhanced by confining the photons and phonons within the phoxonic crystal. In general, confinement can be achieved by introducing a specific defect into the periodic structure to act as a cavity or waveguide. For example, photons and phonons can be trapped simultaneously by a linear defect in a 2D phoxonic crystal slab with a snowflake structure [30]. Zheng et al. demonstrated that L3-nanobeam cavities in 2D phoxonic crystal slabs with highly confined photonic and phononic resonance modes enhanced the AO interaction [31]. Pennec et al. demonstrated that photons and phonons could also be simultaneously trapped in strip waveguides [32].

High AO interaction devices have been used in various applications, including optical information conversion [33–36], light pulse storage, and phonon lasers [37–40]. Phoxonic crystal sensors have also been reported for simultaneous determination of the optical and acoustic properties of analytes [41–44]. Some researchers have indicated that nanoscale AO coupling elements could be used in quantum information applications [45–47]. Stannigel et al. proposed that a spin qubit could be coupled with the vibration mode of a mechanical resonator; a vibration mode could be coupled to an optical resonance mode using nano-scale AO coupling elements, and the state of the spin qubit can be transferred to the optical mode [48]. For these types of applications, high-quality optical and acoustic resonances are required to provide favorable coupling efficiency, and the phoxonic crystal structure can provide the required high-quality-factor simultaneous optical and acoustic resonators.

Phoxonic crystal structures can be classified into several geometric types, including one-dimensional (1D) nanobeams [17–19,49], two-dimensional (2D) periodic air-hole arrays in silicon [15,50,51], 2D periodic arrays of pillars deposited on thin plates [12], and 2D periodic arrays of holes in a slab [11,52]. Among the various types, the 1D phoxonic crystal nanobeam structure has attracted significant attention. Two types of 1D nanobeams exist: in the first type, the air holes are located in the center of the nanobeam [53], and in the second type, semi-cylinders of air are arranged on both sides of the nanobeam (this is known as a fishbone structure) [20,54]. Owing to the respective acoustic properties of these two types, generating a complete phononic band gap in the fishbone structure is easy [20]. The performance of optical cavities based on fishbone structure is also better than that of the first type of structure [54].

Most previous studies have focused on increasing the quality factors (Q-factors) of the acoustic and optical modes or modifying the overlapping acoustic and optical modes [16,20,26,27,54]. However, few studies have focused on the relationship between the acoustic mode polarization and the AO interaction. In this study, we theoretically investigate the AO interaction between the acoustic resonance modes and the optical resonance modes in 1D phoxonic crystal fishbone nanobeam cavities. We calculated the AO interaction strengths of a specific optical resonance mode coupled with several acoustic modes. In this calculation, the total AO coupling rate is the sum of the contributions from each nanobeam cavity portion to the AO coupling. Thus, the acoustic mode polarizations and symmetries determine whether the AO coupling contributions from each portion will be in-phase or out-of-phase.

2. 1D phoxonic crystal fishbone nanobeam cavity configuration

Figure 1(a) shows a schematic of the 1D fishbone phoxonic crystal nanobeam cavity. The nanobeam is formed using a suspended silicon waveguide with semicircular air-hole pillar arrays on both sides; this structure can be formed within the layers of silicon-on-insulator (SOI) chips. The fishbone nanobeam structure has several advantages. Compared with the nanobeam cavities with air-hole pillars at the center of the nanobeam, the total etched surface of the fishbone nanobeam cavity is significantly reduced [54]. The footprint size of the fishbone nanobeam cavity is smaller than that of the 2D slab structure. We modified the geometric parameters at several periods along the nanobeam center to form the optical and acoustic cavities. These non-uniformly periodic cavity regions are sandwiched between two uniformly periodic regions that mirror each other and extend to their respective nanobeam terminals. Figure 1(b) shows a unit mirror cell in which the lattice constant is denoted by a, the air-hole radius is denoted by r, the thickness is denoted by h, and the nanobeam width is denoted by w. In the mirror region established for this study, a is 440 nm, r/a ratio is 0.32, h is 220 nm, and w is 440 nm. In this study, we investigated two cavity types: even symmetric cavity and odd symmetric cavity. Figure 1(c) shows the first type. The mirrors on each side contain five unit cells; the linearly tapered defect consists of 10 periods of gradually reduced unit cells; in the defect region, the r/a ratio is fixed at 0.32, and the lattice constants from the center to both sides are given by an = a1 + (n − 1) × (aa1) / (N/2), where a1 = 350 nm, a = 440 nm, and N is the total number of periods in the defect region, i.e., 10. In this type, the nanobeam center point is between the two smallest unit cells. Figure 1(d) shows the second type in which the mirror regions are the same as those of the even symmetric cavity; the linearly tapered defect consists of nine periods of gradually varied unit cells; r/a is fixed at 0.32; and the lattice constants from the central unit cell to both sides are an = a1 + (n − 1) × (aa1) / ((N + 1)/2), where a1 = 350 nm, a = 440 nm, and N is 9. In this type, the nanobeam center point is at the center of the smallest unit cell. In both types, the acoustic and optical resonance modes are confined by the mirror regions.

 

Fig. 1 Schematic of (a) 1D phoxonic crystal nanobeam cavity, (b) unit cell, (c) even symmetric cavity, and (d) odd symmetric cavity.

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3. Optical and acoustic resonance modes in 1D phoxonic crystal fishbone nanobeam cavity

The AO interactions and optical and acoustic transmission spectra were simulated using the finite element method (FEM) [55]. The FEM is suitable for mode analysis calculations, and it has also proven efficient in determining field distributions in photonic and phononic crystals [10–14,16,20–31,53,56,57]. In this study, optical transmission simulations are performed by applying the FEM to the steady-state monochromatic analysis. For this purpose, the light source is considered to launch from one waveguide terminal into the cavity, and the transmitted signal is detected at the other terminal. Thus, the light propagates in the Z-direction in Fig. 1(a). The acoustic transmission simulations are performed by applying the FEM to steady state monochromatic analyses. For this purpose, the acoustic wave is also considered to propagate in the Z-direction in Fig. 1(a).

The blue line in Fig. 2(a) indicates the optical transmission spectrum of the even symmetric cavity, which is shown in comparison with the optical transmission spectrum of a reference fishbone structure containing 19 unit cells of the mirror type without defect, as indicated by the red line. In each subfigure, the green blocks mark the optically prohibited transmission bands. Comparing the blue line with the red line shows that one resonance peak exists in the defective region of the even symmetric structure at approximately 1408.5 nm (marked OR1). We adopted the eigen-mode computation of FEM to calculate the resonance wavelength, Q-factor, and resonance mode shape of OR1. The resonance wavelength is 1408.64 nm, and the simulated radiation-limited optical Q-factor is approximately 9.3 × 105. The Q-factor is defined as ω0 × (cavity energy stored / power loss) [53], where ω0 is the angular frequency of resonance. In terms of the resonance mode shape, the integral of each component of the electric field within the defect was calculated. We found that more than 63% of the electric field is in the X-direction component, and therefore the OR1 mode is considered to be a quasi-TE mode, i.e., the electric field is perpendicular to the axes of the air cylinders. Figure 2(c) shows this dominant X-direction component of OR1’s normalized electric field, which is anti-symmetric with respect to the X-Y plane at the center of the structure. In Fig. 2(b), the acoustic transmission spectrum is indicated by the blue line, and the red line indicates the acoustic transmission spectrum of the same reference fishbone structure as in Fig. 1(a). In these simulations, the level of the input strain field is 10−3, which is experimentally achievable. The green blocks in the subfigures mark the acoustic band gap induced by the mirrors. Comparing the blue and red lines in Fig. 2(b) shows eight acoustic resonance peaks labeled ϕ1, κ, α, β, δ, γ, ϕ2, and η at frequencies of 6.16, 6.25, 6.34, 6.52, 6.53, 6.72, 6.84, and 7.08 GHz, respectively.

 

Fig. 2 Simulation results for even symmetric cavity (blue) and a reference with no defective region (red): (a) optical transmission spectra, (b) acoustic transmission spectra, and (c) X-direction component of normalized electric field of optical resonance mode (OR1).

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In Fig. 3(a), the blue line indicates the optical transmission spectrum of the odd symmetric cavity, with the same reference spectrum in Fig. 2(a) in red. The blue line shows a transmission peak within the prohibited optical transmission band at approximately 1414 nm (marked OR2). The eigen-mode computation shows that the simulated OR2 mode exhibited a radiation-limited optical Q-factor of 3 × 105 at 1414.06 nm.

 

Fig. 3 Simulation results for odd symmetric cavity (blue) and a reference with no defective region (red): (a) optical and transmission spectra, (b) acoustic transmission spectra, and (c) X-direction component of normalized electric field of optical resonance mode (OR2).

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The resonance mode shape of OR2 is also calculated by the eigen-mode computation. The integral of each component of the electric field shows that more than 90% of the electric field is in the X-direction. Thus, the electric field mode of OR2 is also considered to be a quasi-TE mode because the dominant electric field component is perpendicular to the axes of the air cylinders. Figure 3(c) shows this dominant X-direction component of the OR2’s normalized electric field, which is symmetrical with respect to the X-Y plane at the center of the structure. In Fig. 3(b), the acoustic transmission spectrum of the odd symmetric cavity is shown by the blue line and the red line is the acoustic transmission spectrum of the same reference structure. Comparing the blue and red lines in Fig. 3(b) shows seven acoustic resonance peaks labeled A, F, B, C, D, G, and E at frequencies of 6.18, 6.24, 6.36, 6.44, 6.65, 6.67, and 6.92 GHz, respectively.

We also perform a FEM calculation for the photonic and phononic band structures of the mirrors in our phoxonic fishbone nanobeam. Figure 4(a) shows the optical band structure of the mirrors. The blue block denotes the light cone, which disperses in the manner of light in a vacuum. The light cone is defined by ck / ω < 1, where c is the speed of light in vacuum, k is the wave vector, and ω is the angular frequency. The corresponding frequencies of the OR1 and OR2 modes are marked by blue dotted lines, and the corresponding frequency ranges of the prohibited optical transmission bands in Figs. 2(a) and 3(a) are marked by the green blocks. Figures 4(b) and 4(c) indicate the phononic band structure of the mirrors. The green blocks mark the phononic band gaps, which extend from 6.12 to 7.25 GHz as shown in Figs. 2(b) and 3(b). Upon close analysis, the band structures in Figs. 4(b) and 4(c) are found to be the same, and the black dotted lines in these figures mark the frequencies of the acoustic resonance peaks exhibited by the even and odd symmetric structures, respectively.

 

Fig. 4 Simulation results for odd symmetric cavity (blue) and a reference with no defective region (red): (a) Optical photonic band structures of mirror. Blue dotted lines mark the frequencies of OR1 and OR2. Phononic band structure of mirror with corresponding acoustic resonance peaks (marked by black dotted lines) in (b) even symmetric structure and (c) odd symmetric structure.

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4. AO coupling rate calculations

The AO coupling rates are obtained from a first-order perturbation [58]. We consider two effects in the AO coupling rate calculations: the photo-elastic (PE) effect and the moving boundary (MB) effect, which is also known as the moving interface (MI) effect in several previous studies [23,24,26,29]. The PE effect causes an inhomogeneous refractive index change resulting from the presence of a strain field in the structure [23,24,26,30,56–58]. The MB effect is related to the structural deformation induced by the acoustic waves [23,24,26,30,56–58].

The AO coupling rate can be represented by the optical resonance mode frequency shift induced by zero-point motion of the mechanical field created by the acoustic waves. This shift can be calculated based on known acoustic and optical field distributions inside the structure. Equations for the PE and MB effect contributions are given as follows:

gPE=ω02E|εα|EEDdV2meffΩm
gMB=ω02(Qn^)(ΔεE||2Δε1D2)dSEDdV2meffΩm

In Eq. (3), Q is the normalized displacement field (max{|Q| = 1}); n^ is the normal vector at the boundary (pointing outward); E is the electric field; D is the electric displacement field; and the subscripts || and represent parallel and perpendicular structure surfaces, respectively. In Eqs. (1) and (2), Sij is the strain tensor; α is the general coordinate parameter for Q amplitude; ω0 is the optical resonance frequency; pij is the PE coefficient; Δε is the difference between the silicon and air permittivities; meff is the effective mass of the acoustic wave mode; Ωm is the acoustic wave mode frequency; and2meffΩm is the zero-point motion of the resonator. The total AO coupling rate g is then given by

g=gMB+gPE

In our AO coupling rate calculations, the displacement fields and strain fields are obtained from acoustic steady state monochromatic analyses. This method is the same as that used to determine acoustic transmissions, as described in Section 2. By using monochromatic analysis, we can calculate the AO coupling rate between a specific optical mode and an acoustic wave with any frequency, not only acoustic waves with resonance frequencies. The perturbed and unperturbed electric fields and electric displacement fields are obtained by eigen-mode computations.

5. Relationship between AO coupling rates and vibration behavior

Figure 5 shows absolute values of the AO coupling rates between the OR1 mode and the different acoustic frequencies, including the eight acoustic resonance frequencies, in an even symmetric cavity structure. We focus on acoustic frequencies ranging between 6.1 and 7.16 GHz, which is within the phononic band gap. The results show that the AO coupling rates of some acoustic resonance modes (κ, δ, ϕ2, and η) are significantly higher than those of the other modes; however, not all resonance modes show strong AO coupling rates, a phenomenon that will be discussed further at the end of this section. Table 1 lists the total AO coupling rates, including gPE, gMB, and g, between the OR1 mode and the eight acoustic resonance modes: gPE is smaller than gMB for all acoustic modes, i.e., the MB effect is dominant. The highest AO coupling rate is that of mode δ at 1.89 MHz.

 

Fig. 5 AO coupling rates in even symmetric cavity between optical resonance mode OR1 mode and all acoustic resonance modes from 6.10 to 7.16 GHz.

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Tables Icon

Table 1. Total AO coupling rates (in MHz) between optical resonance mode OR1 and phononic resonance modes in even symmetric cavity when both PE and MB effects are considered.

Figure 6 shows the displacement fields of the eight acoustic resonance modes in the even symmetric cavity structure. According to their polarizations of the acoustic modes, these resonance modes can be classified into shear-horizontal (SH) and shear-vertical (SV) modes. Those with polarizations of the acoustic modes in the X-Y plane (ϕ1, α, β, and γ) are regarded as SV modes, whereas those with polarizations of the acoustic modes in the X-Z plane (κ, δ, ϕ2, and η) are regarded as SH modes. We further classified these acoustic resonance modes according to their displacement field symmetries. In the following classifications, we abbreviate symmetrical as S and anti-symmetrical as A: modes ϕ1, β, and η are symmetrical with respect to the Φ plane and anti-symmetrical with respect to the Γ plane (SA); modes κ and ϕ2 are anti-symmetrical with respect to the Φ plane and symmetrical with respect to the Γ plane (AS); modes α and γ are symmetrical with respect to both the Φ plane and the Γ plane (SS); and mode δ is anti-symmetrical with respect to both the Φ plane and the Γ plane (AA). As an example, mode κ is denoted by SH-AS: the SH notation represents polarizations of the acoustic modes in the X-Z plane, and AS represents anti-symmetry with respect to the Φ plane and symmetry with respect to the Γ plane.

 

Fig. 6 Displacement fields of acoustic resonance modes ϕ1, κ, α, β, δ, γ, ϕ2, and η: black dashed lines mark the defect centers, and Γ and Φ indicate the reference planes of symmetry.

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With reference to the odd symmetric cavity, Fig. 7 shows the absolute values of the AO coupling rates between the optical resonance mode OR2 and the different acoustic frequencies, including the seven acoustic resonance modes. The AO coupling rates of some acoustic resonance modes (B and G) are significantly higher than those of other modes, but not all acoustic resonance modes show strong AO coupling rates. Table 2 lists gPE, gMB, and g for the seven acoustic resonance modes and optical resonance mode OR2. These AO coupling rates are also dominated by MB effects. Figure 8 shows the displacement fields of the seven acoustic resonance modes. Modes A, B, E, and G are SH modes; and modes C, D, and F are SV modes. For the mode symmetries, modes A and C are SA modes; mode G is an AS mode; modes D, E, and F are SS modes; and mode B is an AA.

 

Fig. 7 AO coupling rates in the odd symmetric cavity between optical resonance mode OR2 mode and all acoustic resonance modes from 6.10 to 7.16 GHz.

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Tables Icon

Table 2. Total AO coupling rates (in MHz) between optical resonance mode OR2 and acoustic resonance modes in odd symmetric cavity when both PE and MB effects are considered.

 

Fig. 8 Displacement fields of acoustic resonance modes A, F, B, C, D, G, and E. Black dashed lines indicate defect centers. Γ and Φ indicate reference planes of symmetry.

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Considering that the MB effect is dominant in the AO coupling of our structures, we focus solely on the MB effect in investigating the relationship between vibration behavior and the AO coupling rate. Applying the perturbative method to the AO coupling calculations allows us to calculate the densities of the AO coupling rates on the surfaces of the structures [56]. The AO coupling density is given by

gdensity=14(Qn^)[Δε|E|||2Δ(ε1)(D)2]

This AO coupling density can be divided into the following acoustic part:

Θacoustic=Qn^

and the following optical part:

Θoptical=Δε|E|||2Δ(ε1)|D|2

The acoustic resonance modes in the odd symmetric cavity can be classified into SH-AS, SH-AA, SH-SS, SH-SA, SV-AS and SV-SS types. We use modes A, B, E, G, C, and F to represent these six mode types and investigate the AO coupling density. The eight subfigures in Fig. 9(a)-9(f) show the normalized Θacoustic, Θoptical, and g density plots on the odd symmetric cavity surface for optical mode OR2 and acoustic modes A, B, E, G, C, and F. The Θoptical color maps indicate values from 0 (blue) to 1 (red), and the g density and Θacoustic color maps indicate values from −1 (blue) to 1 (red). The figures also show the contributions to the AO coupling rate, g, from each unit cell in the odd cavity for each mode.

 

Fig. 9 Θacoustic, Θoptical, and g density plots on the odd symmetrical cavity surface, with individual unit cell contributions to the total g density, for acoustic resonance modes (a) A, (b) B, (c) E, (d) G, (e) C, and (f) F.

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In Fig. 9(a)–9(f), the Θacoustic plots relate significantly to the vibration behavior of each acoustic mode. On the other hand, the Θoptical plots show concentrations at the semi-cylinder surfaces for all six cases. As the g density is proportional to the product of Θacoustic and Θoptical, the g density distributions are also concentrated on the semi-cylinder surfaces. In Fig. 9(a)–9(f), the contributions to the AO coupling rate from each unit cell in the SH cases (modes A, B, E, and G) are significantly higher than those in the SV cases (modes C and F). This result can be explained using the g density distributions: the g density distribution color map in the SV case on the same semi-cylinder surface of a specific unit cell contains both red (indicating a positive value) and blue (indicating a negative value); therefore, as long as the acoustic energy is confined within the defective region, the net contribution to the AO coupling rate of the unit cell is insignificant. By contrast, the g density distributions of the SH cases on the same semi-cylinder surface of a specific unit cell are either all positive or all negative. Thus, the net contribution to the AO coupling rate of the unit cell is stronger in the SH case than in the SV case.

For the SH case, the vibrations of modes A and E are symmetrical with respect to the Φ plane. Adjacent unit cells have opposing vibrations, which cause the contributions to the AO coupling rates from adjacent unit cells to have different signs; thus, the adjacent unit cell contributions cancel each other. By contrast, for modes B and G, the vibrations are anti-symmetrical with respect to the Φ plane, and consequently, the vibrations of adjacent unit cells are almost identical. In these cases, significantly fewer cancellations occur between the adjacent unit cell contributions to the AO coupling rates.

Comparing mode B with mode G shows that the vibrations with respect to the Γ plane of modes B and G are anti-symmetric and symmetric, respectively. Therefore, the corresponding contributions to the AO coupling rate from the upper and lower parts of the defective region have the same sign for mode B, whereas the contributions from the upper and lower parts cancel each other for mode G. The results for the relationships among the g density, polarizations, and symmetries of the acoustic modes in the even cavity structure (not presented in this paper) show the same behavior.

Previous studies indicate that acoustic modes with even–even symmetry exhibit larger AO coupling rates because the asymmetric acoustic modes lead to opposite signs of the g values on each half of the unit cell [26]. However, our study shows that acoustic modes with anti-symmetry have higher AO coupling rates. This result can be explained by the difference between the displacement fields of each unit cell. For example, in Fig. 8, we marked three “wings” of the fishbone as W1, W2, and W3 in mode B. In comparison with the structure with no deformation, all three wings twisted along the Y-axis with the same orientation but with different displacement fields. Therefore, these three wings are no longer parallel to each other after deformation. Although the integral of the g value takes opposite signs on each half of the unit cells, their absolute values are not the same. The integral over the entire unit cell does not completely vanish; therefore, the g values of individual unit cells in Fig. 9(b) do not equal 0.

In summary, the SH modes have higher AO coupling rates than SV modes. The SH-AA modes show the strongest AO coupling rates. Among the remaining modes, the AO coupling rates are diminished because of cancellation between the semi-cylinder surfaces in SV modes, between adjacent unit cells in the SH-SS and SH-SA modes, and between the two halves of the defect regions in the SH–AS modes.

6. Effects of optical Q-factors, acoustic Q-factors, gMB, and gPE

To understand the relationship between AO coupling rates and Q-factors for both optical and acoustic resonances, we varied the numbers of periods in the cavities and calculated the AO coupling rates in those cavities. The acoustic Q-factor is defined as 2π × (cavity energy stored / energy dissipated per cycle) [59]. Results for the even and odd cavities are listed in Tables 3 and 4, respectively. To investigate the MB and PE effects on the AO coupling rates, the gPE and gMB of each of the cavities are also listed.

Tables Icon

Table 3. AO interactions and Qacoustic for five phononic modes (α, β, γ, δ, and η) in even symmetric cavity phoxonic crystal nanobeams with different cavity designs.

Tables Icon

Table 4. AO interactions and Qacoustic for six phononic modes in odd symmetric cavity phoxonic crystal nanobeams with different cavity designs.

The even cavities have five different structures characterized by 6, 8, 10, 12, and 14 gradually varying periods. Table 3 lists the corresponding optical resonance wavelengths and Q-factors (Qoptical) for these structures. Although the optical resonance wavelengths and Q-factors shift with the number of periods in the defective cavity, the optical resonance mode distributions are similar to those of the OR1 mode. In the acoustic resonance modes, the variation in the number of periods in the defective area results in resonance frequency shifts, changes in the acoustic Q-factors (Qacoustic), and disappearance (or appearance) of modes. However, five types of acoustic resonance modes, which are classified on the basis of polarizations and symmetries of the acoustic modes, are observed in each cavity structure. These acoustic modes (α, β, γ,δ, and η) and the resonance mode distributions are presented in Section 5. Table 3 lists the AO coupling rates between these acoustic modes and optical resonance modes in each structure. In Table 3, all the AO coupling rates for the SH modes are higher than those for the SV modes. The highest AO coupling rates occur for mode δ (SH-AA) in all structures (marked by the yellow background). However, the AO coupling rates are not entirely proportional to the optical and acoustic Q-factors. These Q-factors represent the ability of each cavity to confine acoustic and optical energies. However, the AO coupling rate relates not only to the acoustic and optical energy confinement but also to the overlap between acoustic and optical modes.

Table 4 shows the results for five odd symmetric cavity types with different numbers of periods in the defective regions, as well as the optical resonance wavelengths and Q-factors for each structure. These optical modes have similar distributions to those of OR2. The highest AO coupling rates occur for mode B (SH-AA) in all structures (marked by the yellow background). Based on their polarizations and symmetries of the acoustic modes, six acoustic resonance mode types are present in these structures (two types of acoustic resonance modes disappear in Odd 15). These results indicate that the highest AO coupling rates still occur in the SH-AA modes; therefore, the SH modes are considered to have higher AO coupling rates than the SV modes.

In terms of gPE and gMB, the values of gMB are at least one order of magnitude larger than those of gPE for mode δ in Table 3 and mode B in Table 4. These two modes exhibit the largest AO coupling rates. For the rest of the cases, the values of gMB are mostly larger than those of gPE. However, the ratios of gMB and gPE are not as large as that of mode δ in Table 3 and mode B in Table 4. In some cases, the values of gMB are even the same as or less than those of gPE (for example, mode β in Even 6 and mode α in Even 12).

7. Conclusions

We investigated AO interactions among acoustic and optical resonance modes in 1D phoxonic crystal fishbone nanobeam cavities, which were formed using periodically arranged semicircular air cylinders on both sides of the waveguide. Optical and acoustic resonance cavities were formed by tapering specific odd and even numbers of periods at the nanobeam center. Such structures can be realized using SOI technology.

We calculated the AO coupling rates from first-order perturbation. The displacement fields and strain fields were obtained by acoustic steady state monochromatic analysis; meanwhile, the optical fields were obtained by eigen-mode computation. We considered both MB and PE effects in AO coupling, and the MB effect was found to be dominant. Further analysis of the g density in the MB effect showed that the AO coupling rate is significantly related to the polarization and symmetry of the acoustic resonance modes. Although the acoustic and optical energies are effectively confined within the cavity regions with high Q-factors, different polarizations and symmetries of the acoustic modes produce different g density cancellation effects. These cancellations occur within each unit cell, between adjacent unit cells, and between the two halves of the defective regions. The strongest AO coupling occurs in the SH-AA acoustic mode because the g density cancellation is minimized. In our structures, the polarizations and symmetries of the acoustic resonance modes are more important than the Q-factors in AO coupling. The enlargement of the AO coupling rate is predominantly due to the MB effect.

This study offers insights into a method to enhance the AO coupling rate in phoxonic crystal structures by tailoring the polarization and symmetry of the acoustic modes, and this method is useful in the design of high-efficiency AO coupling devices. The largest observed AO coupling rate was −5.14 MHz, which is comparable with recent results in the literature [23,24,26,30,56–58]. In terms of experiments, photonic crystal nanobeam cavities can be measured by waveguide coupling [60], vertical excitation [61], and evanescent coupling [62]. Although the optical transmission simulation of phoxonic crystal fishbone nanobeam cavities in our study is similar to waveguide coupling, the optical resonance can also be excited by vertical excitation or evanescent coupling. As the optical resonance transmission peaks in our simulations were confirmed by eigen-mode computations, the optical resonances could be excited by the aforementioned procedures as long as the excitation wavelength corresponds to the resonance wavelength. The excitation of the acoustic resonance modes and measurement of the AO coupling rate can be performed through the procedure in reference [47]. As the resonance frequencies differ among all acoustic resonance modes, a specific acoustic resonance (frequency, ωm) can be excited by a laser with a frequency equal to ωo + ωm, where ωo is the optical resonance frequency. Each acoustic resonance mode can be excited by adjusting the value of ωo.

Funding

Ministry of Science and Technology (MOST) of Taiwan under contract number MOST 105-2221-E-018-008.

References and links

1. A. I. Rahachou and I. V. Zozoulenko, “Waveguiding properties of surface states in photonic crystals,” J. Opt. Soc. Am. B 23(8), 1679–1683 (2006). [CrossRef]  

2. K. Ishizaki and S. Noda, “Manipulation of photons at the surface of three-dimensional photonic crystals,” Nature 460(7253), 367–370 (2009). [CrossRef]   [PubMed]  

3. T. W. Lu, Y. H. Hsiao, W. D. Ho, and P. T. Lee, “High-index sensitivity of surface mode in photonic crystal hetero-slab-edge microcavity,” Opt. Lett. 35(9), 1452–1454 (2010). [CrossRef]   [PubMed]  

4. S. Y. Su, L. Tang, and T. Yoshie, “Optical surface Bloch modes of complete photonic bandgap materials as a basis of optical sensing,” Opt. Lett. 36(12), 2266–2268 (2011). [CrossRef]   [PubMed]  

5. J. C. Hsu and T. T. Wu, “Efficient formulation for band-structure calculations of two-dimensional phononic- crystal plates,” Phys. Rev. B 74(14), 144303 (2006). [CrossRef]  

6. A. Khelif, B. Aoubiza, S. Mohammadi, A. Adibi, and V. Laude, “Complete band gaps in two-dimensional phononic crystal slabs,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 74(4), 046610 (2006). [CrossRef]   [PubMed]  

7. C. Charles, B. Bonello, and F. Ganot, “Propagation of guided elastic waves in 2D phononic crystals,” Ultrasonics 44(Suppl 1), e1209–e1213 (2006). [CrossRef]   [PubMed]  

8. J. O. Vasseur, P. A. Deymier, B. Djafari-Rouhani, Y. Pennec, and A. C. Hladky-Hennion, “Absolute forbidden bands and waveguiding in two-dimensional phononic crystal plates,” Phys. Rev. B 77(8), 085415 (2008). [CrossRef]  

9. Y. Pennec, B. Djafari-Rouhani, H. Larabi, J. O. Vasseur, and A. C. Hladky-Hennion, “Low-frequency gaps in a phononic crystal constituted of cylindrical dots deposited on a thin homogeneous plate,” Phys. Rev. B 78(10), 104105 (2008). [CrossRef]  

10. T. T. Wu, Z. G. Huang, T. C. Tsai, and T. C. Wu, “Evidence of complete band gap and resonances in a plate with periodic stubbed surface,” Appl. Phys. Lett. 93(11), 111902 (2008). [CrossRef]  

11. S. Mohammadi, A. A. Eftekhar, A. Khelif, and A. Adibi, “Simultaneous two-dimensional phononic and photonic band gaps in opto-mechanical crystal slabs,” Opt. Express 18(9), 9164–9172 (2010). [CrossRef]   [PubMed]  

12. Y. El Hassouani, C. Li, Y. Pennec, E. H. El Boudouti, H. Larabi, A. Akjouj, O. Bou Matar, V. Laude, N. Papanikolaou, A. Martínez, and B. Djafari Rouhani, “Dual phononic and photonic band gaps in a periodic array of pillars deposited on a thin plate,” Phys. Rev. B 82(15), 155405 (2010). [CrossRef]  

13. T. X. Ma, Y. S. Wang, Y. F. Wang, and X. X. Su, “Three-dimensional dielectric phoxonic crystals with network topology,” Opt. Express 21(3), 2727–2732 (2013). [CrossRef]   [PubMed]  

14. T. X. Ma, Y. S. Wang, and C. Zhang, “Investigation of dual photonic and phononic bandgaps in two- dimensional phoxonic crystals with veins,” Opt. Commun. 312, 68–72 (2014). [CrossRef]  

15. S. Sadat-Saleh, S. Benchabane, F. I. Baida, M. P. Bernal, and V. Laude, “Tailoring simultaneous photonic and phononic band gaps,” J. Appl. Phys. 106(7), 074912 (2009). [CrossRef]  

16. Q. Rolland, S. Dupont, J. Gazalet, J. C. Kastelik, Y. Pennec, B. Djafari-Rouhani, and V. Laude, “Simultaneous bandgaps in LiNbO3 phoxonic crystal slab,” Opt. Express 22(13), 16288–16297 (2014). [CrossRef]   [PubMed]  

17. I. E. Psarobas, N. Papanikolaou, N. Stefanou, B. Djafari-Rouhani, B. Bonello, and V. Laude, “Enhanced acousto-optic interactions in a one-dimensional phoxonic cavity,” Phys. Rev. B 82(17), 174303 (2010). [CrossRef]  

18. N. Papanikolaou, I. E. Psarobas, N. Stefanou, B. Djafari-Rouhani, B. Bonello, and V. Laude, “Light modulation in phoxonic nanocavities,” Microelectron. Eng. 90, 155–158 (2012). [CrossRef]  

19. E. Almpanis, N. Papanikolaou, G. Gantzounis, and N. Stefanou, “Tuning the spontaneous light emission in phoxonic cavities,” J. Opt. Soc. Am. B 29(9), 2567–2574 (2012). [CrossRef]  

20. F. L. Hsiao, C. Y. Hsieh, H. Y. Hsieh, and C. C. Chiu, “High-efficiency acousto-optical interaction in phoxonic nanobeam waveguide,” Appl. Phys. Lett. 100(17), 171103 (2012). [CrossRef]  

21. Q. Rolland, M. Oudich, S. El-Jallal, S. Dupont, Y. Pennec, J. Gazalet, J. C. Kastelik, G. Lévêque, and B. Djafari-Rouhani, “Acousto-optic couplings in two-dimensional phoxonic crystal cavities,” Appl. Phys. Lett. 101(6), 061109 (2012). [CrossRef]  

22. T. R. Lin, C. H. Lin, and J. C. Hsu, “Enhanced acousto-optic interaction in two-dimensional phoxonic crystals with a line defect,” J. Appl. Phys. 113(5), 053508 (2013). [CrossRef]  

23. S. El-Jallal, M. Oudich, Y. Pennec, B. Djafari-Rouhani, V. Laude, J. C. Beugnot, A. Martínez, J. M. Escalante, and A. Makhoute, “Analysis of optomechanical coupling in two-dimensional square lattice phoxonic crystal slab cavities,” Phys. Rev. B 88(20), 205410 (2013). [CrossRef]  

24. S. El-Jallal, M. Oudich, Y. Pennec, B. Djafari-Rouhani, A. Makhoute, Q. Rolland, S. Dupont, and J. Gazalet, “Optomechanical interactions in two-dimensional Si and GaAs phoXonic cavities,” J. Phys. Condens. Matter 26(1), 015005 (2014). [CrossRef]   [PubMed]  

25. L. Kipfstuhl, F. Guldner, J. Riedrich-Möller, and C. Becher, “Modeling of optomechanical coupling in a phoxonic crystal cavity in diamond,” Opt. Express 22(10), 12410–12423 (2014). [CrossRef]   [PubMed]  

26. M. Oudich, S. El-Jallal, Y. Pennec, B. Djafari-Rouhani, J. Gomis-Bresco, D. Navarro-Urrios, C. M. Sotomayor Torres, A. Martínez, and A. Makhoute, “Optomechanic interaction in a corrugated phoxonic nanobeam cavity,” Phys. Rev. B 89(24), 245122 (2014). [CrossRef]  

27. Y. Pennec, V. Laude, N. Papanikolaou, B. Djafari-Rouhani, M. Oudich, S. El-Jallal, J. C. Beugnot, J. M. Escalante, and A. Martínez, “Modeling light-sound interaction in nanoscale cavities and waveguides,” Nanophotonics 3(6), 413–440 (2014). [CrossRef]  

28. M. Eichenfield, J. Chan, R. M. Camacho, K. J. Vahala, and O. Painter, “Optomechanical crystals,” Nature 462(7269), 78–82 (2009). [CrossRef]   [PubMed]  

29. J. Gomis-Bresco, D. Navarro-Urrios, M. Oudich, S. El-Jallal, A. Griol, D. Puerto, E. Chavez, Y. Pennec, B. Djafari-Rouhani, F. Alzina, A. Martínez, and C. M. Torres, “A one-dimensional optomechanical crystal with a complete phononic band gap,” Nat. Commun. 5, 4452 (2014). [CrossRef]   [PubMed]  

30. A. H. Safavi-Naeini and O. Painter, “Design of optomechanical cavities and waveguides on a simultaneous bandgap phononic-photonic crystal slab,” Opt. Express 18(14), 14926–14943 (2010). [CrossRef]   [PubMed]  

31. J. Zheng, X. Sun, Y. Li, M. Poot, A. Dadgar, N. N. Shi, W. H. P. Pernice, H. X. Tang, and C. W. Wong, “Femtogram dispersive L3-nanobeam optomechanical cavities: design and experimental comparison,” Opt. Express 20(24), 26486–26498 (2012). [CrossRef]   [PubMed]  

32. Y. Pennec, B. Djafari Rouhani, C. Li, J. M. Escalante, A. Martínez, S. Benchabane, V. Laude, and N. Papanikolaou, “Band gaps and cavity modes in dual phononic and photonic strip waveguides,” AIP Adv. 1(4), 041901 (2011). [CrossRef]  

33. R. W. Andrews, R. W. Peterson, T. P. Purdy, K. Cicak, R. W. Simmonds, C. A. Regal, and K. W. Lehnert, “Bidirectional and efficient conversion between microwave and optical light,” Nat. Phys. 10(4), 321–326 (2014). [CrossRef]  

34. Y. D. Wang and A. A. Clerk, “Using dark modes for high-fidelity optomechanical quantum state transfer,” New J. Phys. 14(10), 105010 (2012). [CrossRef]  

35. J. T. Hill, A. H. Safavi-Naeini, J. Chan, and O. Painter, “Coherent optical wavelength conversion via cavity optomechanics,” Nat. Commun. 3, 1196 (2012). [CrossRef]   [PubMed]  

36. C. Dong, V. Fiore, M. C. Kuzyk, L. Tian, and H. Wang, “Optical wavelength conversion via optomechanical coupling in a silica resonator,” Ann. Phys. 527(1-2), 100–106 (2015). [CrossRef]  

37. D. Razansky, M. Distel, C. Vinegoni, R. Ma, N. Perrimon, R. W. Köster, and V. Ntziachristos, “Multispectral opto-acoustic tomography of deep-seated fluorescent proteins in vivo,” Nat. Photonics 3(7), 412–417 (2009). [CrossRef]  

38. Z. Zhu, D. J. Gauthier, and R. W. Boyd, “Stored light in an optical fiber via stimulated Brillouin scattering,” Science 318(5857), 1748–1750 (2007). [CrossRef]   [PubMed]  

39. I. S. Grudinin, H. Lee, O. Painter, and K. J. Vahala, “Phonon laser action in a tunable two-level system,” Phys. Rev. Lett. 104(8), 083901 (2010). [CrossRef]   [PubMed]  

40. B. S. Williams, H. Callebaut, S. Kumar, Q. Hu, and J. L. Reno, “3.4-THz quantum cascade laser based on longitudinal-optical-phonon scattering for depopulation,” Appl. Phys. Lett. 82(7), 1015–1017 (2003). [CrossRef]  

41. R. Lucklum, M. Zubtsov, and A. Oseev, “Phoxonic crystals--a new platform for chemical and biochemical sensors,” Anal. Bioanal. Chem. 405(20), 6497–6509 (2013). [CrossRef]   [PubMed]  

42. S. Amoudache, Y. Pennec, B. Djafari Rouhani, A. Khater, R. Lucklum, and R. Tigrine, “Simultaneous sensing of light and sound velocities of fluids in a two-dimensional phoXonic crystal with defects,” J. Appl. Phys. 115(13), 134503 (2014). [CrossRef]  

43. S. Amoudache, R. Moiseyenko, Y. Pennec, B. Djafari Rouhani, A. Khater, R. Lucklum, and R. Tigrine, “Optical and acoustic sensing using Fano-like resonances in dual phononic and photonic crystal plate,” J. Appl. Phys. 119(11), 114502 (2016). [CrossRef]  

44. T. X. Ma, Y. S. Wang, C. Zhang, and X. X. Su, “Theoretical research on a two-dimensional phoxonic crystal liquid sensor by utilizing surface optical and acoustic waves,” Sens. Actuators A Phys. 242, 123–131 (2016). [CrossRef]  

45. P. Rabl, P. Cappellaro, M. V. Gurudev Dutt, L. Jiang, J. R. Maze, and M. D. Lukin, “Strong magnetic coupling between an electronic spin qubit and a mechanical resonator,” Phys. Rev. B 79(4), 041302 (2009). [CrossRef]  

46. D. A. Fuhrmann, S. M. Thon, H. Kim, D. Bouwmeester, P. M. Petroff, A. Wixforth, and H. J. Krenner, “Dynamic modulation of photonic crystal nanocavities using gigahertz acoustic phonons,” Nat. Photonics 5(10), 605–609 (2011). [CrossRef]  

47. J. Chan, T. P. Alegre, A. H. Safavi-Naeini, J. T. Hill, A. Krause, S. Gröblacher, M. Aspelmeyer, and O. Painter, “Laser cooling of a nanomechanical oscillator into its quantum ground state,” Nature 478(7367), 89–92 (2011). [CrossRef]   [PubMed]  

48. K. Stannigel, P. Rabl, A. S. Sørensen, P. Zoller, and M. D. Lukin, “Optomechanical transducers for long-distance quantum communication,” Phys. Rev. Lett. 105(22), 220501 (2010). [CrossRef]   [PubMed]  

49. J. Manzanares-Martinez, D. Moctezuma-Enriquez, Y. J. Rodriguez-Viveros, B. Manzanares-Martinez, and P. Castro-Garay, “Non-perpendicular hypersonic and optical stop-bands in porous silicon multilayers,” Appl. Phys. Lett. 101(26), 261902 (2012). [CrossRef]  

50. M. Maldovan and E. L. Thomas, “Simultaneous localization of photons and phonons in two-dimensional periodic structures,” Appl. Phys. Lett. 88(25), 251907 (2006). [CrossRef]  

51. D. Bria, M. B. Assouar, M. Oudich, Y. Pennec, J. Vasseur, and B. Djafari-Rouhani, “Opening of simultaneous photonic and phononic band gap in two-dimensional square lattice periodic structure,” J. Appl. Phys. 109(1), 014507 (2011). [CrossRef]  

52. Y. Pennec, B. Djafari Rouhani, E. H. El Boudouti, C. Li, Y. El Hassouani, J. O. Vasseur, N. Papanikolaou, S. Benchabane, V. Laude, and A. Martínez, “Simultaneous existence of phononic and photonic band gaps in periodic crystal slabs,” Opt. Express 18(13), 14301–14310 (2010). [CrossRef]   [PubMed]  

53. P. B. Deotare, M. W. McCutcheon, I. W. Frank, M. Khan, and M. Lončar, “High quality factor photonic crystal nanobeam cavities,” Appl. Phys. Lett. 94(12), 121106 (2009). [CrossRef]  

54. T. W. Lu and P. T. Lee, “Photonic crystal nanofishbone nanocavity,” Opt. Lett. 38(16), 3129–3132 (2013). [CrossRef]   [PubMed]  

55. COMSOL Multiphysics 3.5 (2009).

56. M. Eichenfield, J. Chan, A. H. Safavi-Naeini, K. J. Vahala, and O. Painter, “Modeling dispersive coupling and losses of localized optical and mechanical modes in optomechanical crystals,” Opt. Express 17(22), 20078–20098 (2009). [CrossRef]   [PubMed]  

57. T. Yu, Z. Wang, W. Liu, T. Wang, N. Liu, and Q. Liao, “Simultaneous large band gaps and localization of electromagnetic and elastic waves in defect-free quasicrystals,” Opt. Express 24(8), 7951–7959 (2016). [CrossRef]   [PubMed]  

58. S. G. Johnson, M. Ibanescu, M. A. Skorobogatiy, O. Weisberg, J. D. Joannopoulos, and Y. Fink, “Perturbation theory for Maxwell’s equations with shifting material boundaries,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 65(6), 066611 (2002). [CrossRef]   [PubMed]  

59. D. Goettler, M. Su, Z. Leseman, Y. Soliman, R. Olsson, and I. El-Kady, “Realizing the frequency quality factor product limit in silicon via compact phononic crystal resonators,” J. Appl. Phys. 108(8), 084505 (2010). [CrossRef]  

60. P. Seidler, K. Lister, U. Drechsler, J. Hofrichter, and T. Stöferle, “Slotted photonic crystal nanobeam cavity with an ultrahigh quality factor-to-mode volume ratio,” Opt. Express 21(26), 32468–32483 (2013). [CrossRef]   [PubMed]  

61. T. W. Lu, W. C. Tsai, T. Y. Wu, and P. T. Lee, “Laser emissions from one-dimensional photonic crystal rings on silicon-dioxide,” Appl. Phys. Lett. 102(5), 051103 (2013). [CrossRef]  

62. S. P. Anderson and P. M. Fauchet, “Experimental demonstration of evanescent coupling and photon confinement in oxide-clad silicon microcavities,” Opt. Lett. 36(14), 2698–2700 (2011). [CrossRef]   [PubMed]  

References

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  • |
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  • |

  1. A. I. Rahachou and I. V. Zozoulenko, “Waveguiding properties of surface states in photonic crystals,” J. Opt. Soc. Am. B 23(8), 1679–1683 (2006).
    [Crossref]
  2. K. Ishizaki and S. Noda, “Manipulation of photons at the surface of three-dimensional photonic crystals,” Nature 460(7253), 367–370 (2009).
    [Crossref] [PubMed]
  3. T. W. Lu, Y. H. Hsiao, W. D. Ho, and P. T. Lee, “High-index sensitivity of surface mode in photonic crystal hetero-slab-edge microcavity,” Opt. Lett. 35(9), 1452–1454 (2010).
    [Crossref] [PubMed]
  4. S. Y. Su, L. Tang, and T. Yoshie, “Optical surface Bloch modes of complete photonic bandgap materials as a basis of optical sensing,” Opt. Lett. 36(12), 2266–2268 (2011).
    [Crossref] [PubMed]
  5. J. C. Hsu and T. T. Wu, “Efficient formulation for band-structure calculations of two-dimensional phononic- crystal plates,” Phys. Rev. B 74(14), 144303 (2006).
    [Crossref]
  6. A. Khelif, B. Aoubiza, S. Mohammadi, A. Adibi, and V. Laude, “Complete band gaps in two-dimensional phononic crystal slabs,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 74(4), 046610 (2006).
    [Crossref] [PubMed]
  7. C. Charles, B. Bonello, and F. Ganot, “Propagation of guided elastic waves in 2D phononic crystals,” Ultrasonics 44(Suppl 1), e1209–e1213 (2006).
    [Crossref] [PubMed]
  8. J. O. Vasseur, P. A. Deymier, B. Djafari-Rouhani, Y. Pennec, and A. C. Hladky-Hennion, “Absolute forbidden bands and waveguiding in two-dimensional phononic crystal plates,” Phys. Rev. B 77(8), 085415 (2008).
    [Crossref]
  9. Y. Pennec, B. Djafari-Rouhani, H. Larabi, J. O. Vasseur, and A. C. Hladky-Hennion, “Low-frequency gaps in a phononic crystal constituted of cylindrical dots deposited on a thin homogeneous plate,” Phys. Rev. B 78(10), 104105 (2008).
    [Crossref]
  10. T. T. Wu, Z. G. Huang, T. C. Tsai, and T. C. Wu, “Evidence of complete band gap and resonances in a plate with periodic stubbed surface,” Appl. Phys. Lett. 93(11), 111902 (2008).
    [Crossref]
  11. S. Mohammadi, A. A. Eftekhar, A. Khelif, and A. Adibi, “Simultaneous two-dimensional phononic and photonic band gaps in opto-mechanical crystal slabs,” Opt. Express 18(9), 9164–9172 (2010).
    [Crossref] [PubMed]
  12. Y. El Hassouani, C. Li, Y. Pennec, E. H. El Boudouti, H. Larabi, A. Akjouj, O. Bou Matar, V. Laude, N. Papanikolaou, A. Martínez, and B. Djafari Rouhani, “Dual phononic and photonic band gaps in a periodic array of pillars deposited on a thin plate,” Phys. Rev. B 82(15), 155405 (2010).
    [Crossref]
  13. T. X. Ma, Y. S. Wang, Y. F. Wang, and X. X. Su, “Three-dimensional dielectric phoxonic crystals with network topology,” Opt. Express 21(3), 2727–2732 (2013).
    [Crossref] [PubMed]
  14. T. X. Ma, Y. S. Wang, and C. Zhang, “Investigation of dual photonic and phononic bandgaps in two- dimensional phoxonic crystals with veins,” Opt. Commun. 312, 68–72 (2014).
    [Crossref]
  15. S. Sadat-Saleh, S. Benchabane, F. I. Baida, M. P. Bernal, and V. Laude, “Tailoring simultaneous photonic and phononic band gaps,” J. Appl. Phys. 106(7), 074912 (2009).
    [Crossref]
  16. Q. Rolland, S. Dupont, J. Gazalet, J. C. Kastelik, Y. Pennec, B. Djafari-Rouhani, and V. Laude, “Simultaneous bandgaps in LiNbO3 phoxonic crystal slab,” Opt. Express 22(13), 16288–16297 (2014).
    [Crossref] [PubMed]
  17. I. E. Psarobas, N. Papanikolaou, N. Stefanou, B. Djafari-Rouhani, B. Bonello, and V. Laude, “Enhanced acousto-optic interactions in a one-dimensional phoxonic cavity,” Phys. Rev. B 82(17), 174303 (2010).
    [Crossref]
  18. N. Papanikolaou, I. E. Psarobas, N. Stefanou, B. Djafari-Rouhani, B. Bonello, and V. Laude, “Light modulation in phoxonic nanocavities,” Microelectron. Eng. 90, 155–158 (2012).
    [Crossref]
  19. E. Almpanis, N. Papanikolaou, G. Gantzounis, and N. Stefanou, “Tuning the spontaneous light emission in phoxonic cavities,” J. Opt. Soc. Am. B 29(9), 2567–2574 (2012).
    [Crossref]
  20. F. L. Hsiao, C. Y. Hsieh, H. Y. Hsieh, and C. C. Chiu, “High-efficiency acousto-optical interaction in phoxonic nanobeam waveguide,” Appl. Phys. Lett. 100(17), 171103 (2012).
    [Crossref]
  21. Q. Rolland, M. Oudich, S. El-Jallal, S. Dupont, Y. Pennec, J. Gazalet, J. C. Kastelik, G. Lévêque, and B. Djafari-Rouhani, “Acousto-optic couplings in two-dimensional phoxonic crystal cavities,” Appl. Phys. Lett. 101(6), 061109 (2012).
    [Crossref]
  22. T. R. Lin, C. H. Lin, and J. C. Hsu, “Enhanced acousto-optic interaction in two-dimensional phoxonic crystals with a line defect,” J. Appl. Phys. 113(5), 053508 (2013).
    [Crossref]
  23. S. El-Jallal, M. Oudich, Y. Pennec, B. Djafari-Rouhani, V. Laude, J. C. Beugnot, A. Martínez, J. M. Escalante, and A. Makhoute, “Analysis of optomechanical coupling in two-dimensional square lattice phoxonic crystal slab cavities,” Phys. Rev. B 88(20), 205410 (2013).
    [Crossref]
  24. S. El-Jallal, M. Oudich, Y. Pennec, B. Djafari-Rouhani, A. Makhoute, Q. Rolland, S. Dupont, and J. Gazalet, “Optomechanical interactions in two-dimensional Si and GaAs phoXonic cavities,” J. Phys. Condens. Matter 26(1), 015005 (2014).
    [Crossref] [PubMed]
  25. L. Kipfstuhl, F. Guldner, J. Riedrich-Möller, and C. Becher, “Modeling of optomechanical coupling in a phoxonic crystal cavity in diamond,” Opt. Express 22(10), 12410–12423 (2014).
    [Crossref] [PubMed]
  26. M. Oudich, S. El-Jallal, Y. Pennec, B. Djafari-Rouhani, J. Gomis-Bresco, D. Navarro-Urrios, C. M. Sotomayor Torres, A. Martínez, and A. Makhoute, “Optomechanic interaction in a corrugated phoxonic nanobeam cavity,” Phys. Rev. B 89(24), 245122 (2014).
    [Crossref]
  27. Y. Pennec, V. Laude, N. Papanikolaou, B. Djafari-Rouhani, M. Oudich, S. El-Jallal, J. C. Beugnot, J. M. Escalante, and A. Martínez, “Modeling light-sound interaction in nanoscale cavities and waveguides,” Nanophotonics 3(6), 413–440 (2014).
    [Crossref]
  28. M. Eichenfield, J. Chan, R. M. Camacho, K. J. Vahala, and O. Painter, “Optomechanical crystals,” Nature 462(7269), 78–82 (2009).
    [Crossref] [PubMed]
  29. J. Gomis-Bresco, D. Navarro-Urrios, M. Oudich, S. El-Jallal, A. Griol, D. Puerto, E. Chavez, Y. Pennec, B. Djafari-Rouhani, F. Alzina, A. Martínez, and C. M. Torres, “A one-dimensional optomechanical crystal with a complete phononic band gap,” Nat. Commun. 5, 4452 (2014).
    [Crossref] [PubMed]
  30. A. H. Safavi-Naeini and O. Painter, “Design of optomechanical cavities and waveguides on a simultaneous bandgap phononic-photonic crystal slab,” Opt. Express 18(14), 14926–14943 (2010).
    [Crossref] [PubMed]
  31. J. Zheng, X. Sun, Y. Li, M. Poot, A. Dadgar, N. N. Shi, W. H. P. Pernice, H. X. Tang, and C. W. Wong, “Femtogram dispersive L3-nanobeam optomechanical cavities: design and experimental comparison,” Opt. Express 20(24), 26486–26498 (2012).
    [Crossref] [PubMed]
  32. Y. Pennec, B. Djafari Rouhani, C. Li, J. M. Escalante, A. Martínez, S. Benchabane, V. Laude, and N. Papanikolaou, “Band gaps and cavity modes in dual phononic and photonic strip waveguides,” AIP Adv. 1(4), 041901 (2011).
    [Crossref]
  33. R. W. Andrews, R. W. Peterson, T. P. Purdy, K. Cicak, R. W. Simmonds, C. A. Regal, and K. W. Lehnert, “Bidirectional and efficient conversion between microwave and optical light,” Nat. Phys. 10(4), 321–326 (2014).
    [Crossref]
  34. Y. D. Wang and A. A. Clerk, “Using dark modes for high-fidelity optomechanical quantum state transfer,” New J. Phys. 14(10), 105010 (2012).
    [Crossref]
  35. J. T. Hill, A. H. Safavi-Naeini, J. Chan, and O. Painter, “Coherent optical wavelength conversion via cavity optomechanics,” Nat. Commun. 3, 1196 (2012).
    [Crossref] [PubMed]
  36. C. Dong, V. Fiore, M. C. Kuzyk, L. Tian, and H. Wang, “Optical wavelength conversion via optomechanical coupling in a silica resonator,” Ann. Phys. 527(1-2), 100–106 (2015).
    [Crossref]
  37. D. Razansky, M. Distel, C. Vinegoni, R. Ma, N. Perrimon, R. W. Köster, and V. Ntziachristos, “Multispectral opto-acoustic tomography of deep-seated fluorescent proteins in vivo,” Nat. Photonics 3(7), 412–417 (2009).
    [Crossref]
  38. Z. Zhu, D. J. Gauthier, and R. W. Boyd, “Stored light in an optical fiber via stimulated Brillouin scattering,” Science 318(5857), 1748–1750 (2007).
    [Crossref] [PubMed]
  39. I. S. Grudinin, H. Lee, O. Painter, and K. J. Vahala, “Phonon laser action in a tunable two-level system,” Phys. Rev. Lett. 104(8), 083901 (2010).
    [Crossref] [PubMed]
  40. B. S. Williams, H. Callebaut, S. Kumar, Q. Hu, and J. L. Reno, “3.4-THz quantum cascade laser based on longitudinal-optical-phonon scattering for depopulation,” Appl. Phys. Lett. 82(7), 1015–1017 (2003).
    [Crossref]
  41. R. Lucklum, M. Zubtsov, and A. Oseev, “Phoxonic crystals--a new platform for chemical and biochemical sensors,” Anal. Bioanal. Chem. 405(20), 6497–6509 (2013).
    [Crossref] [PubMed]
  42. S. Amoudache, Y. Pennec, B. Djafari Rouhani, A. Khater, R. Lucklum, and R. Tigrine, “Simultaneous sensing of light and sound velocities of fluids in a two-dimensional phoXonic crystal with defects,” J. Appl. Phys. 115(13), 134503 (2014).
    [Crossref]
  43. S. Amoudache, R. Moiseyenko, Y. Pennec, B. Djafari Rouhani, A. Khater, R. Lucklum, and R. Tigrine, “Optical and acoustic sensing using Fano-like resonances in dual phononic and photonic crystal plate,” J. Appl. Phys. 119(11), 114502 (2016).
    [Crossref]
  44. T. X. Ma, Y. S. Wang, C. Zhang, and X. X. Su, “Theoretical research on a two-dimensional phoxonic crystal liquid sensor by utilizing surface optical and acoustic waves,” Sens. Actuators A Phys. 242, 123–131 (2016).
    [Crossref]
  45. P. Rabl, P. Cappellaro, M. V. Gurudev Dutt, L. Jiang, J. R. Maze, and M. D. Lukin, “Strong magnetic coupling between an electronic spin qubit and a mechanical resonator,” Phys. Rev. B 79(4), 041302 (2009).
    [Crossref]
  46. D. A. Fuhrmann, S. M. Thon, H. Kim, D. Bouwmeester, P. M. Petroff, A. Wixforth, and H. J. Krenner, “Dynamic modulation of photonic crystal nanocavities using gigahertz acoustic phonons,” Nat. Photonics 5(10), 605–609 (2011).
    [Crossref]
  47. J. Chan, T. P. Alegre, A. H. Safavi-Naeini, J. T. Hill, A. Krause, S. Gröblacher, M. Aspelmeyer, and O. Painter, “Laser cooling of a nanomechanical oscillator into its quantum ground state,” Nature 478(7367), 89–92 (2011).
    [Crossref] [PubMed]
  48. K. Stannigel, P. Rabl, A. S. Sørensen, P. Zoller, and M. D. Lukin, “Optomechanical transducers for long-distance quantum communication,” Phys. Rev. Lett. 105(22), 220501 (2010).
    [Crossref] [PubMed]
  49. J. Manzanares-Martinez, D. Moctezuma-Enriquez, Y. J. Rodriguez-Viveros, B. Manzanares-Martinez, and P. Castro-Garay, “Non-perpendicular hypersonic and optical stop-bands in porous silicon multilayers,” Appl. Phys. Lett. 101(26), 261902 (2012).
    [Crossref]
  50. M. Maldovan and E. L. Thomas, “Simultaneous localization of photons and phonons in two-dimensional periodic structures,” Appl. Phys. Lett. 88(25), 251907 (2006).
    [Crossref]
  51. D. Bria, M. B. Assouar, M. Oudich, Y. Pennec, J. Vasseur, and B. Djafari-Rouhani, “Opening of simultaneous photonic and phononic band gap in two-dimensional square lattice periodic structure,” J. Appl. Phys. 109(1), 014507 (2011).
    [Crossref]
  52. Y. Pennec, B. Djafari Rouhani, E. H. El Boudouti, C. Li, Y. El Hassouani, J. O. Vasseur, N. Papanikolaou, S. Benchabane, V. Laude, and A. Martínez, “Simultaneous existence of phononic and photonic band gaps in periodic crystal slabs,” Opt. Express 18(13), 14301–14310 (2010).
    [Crossref] [PubMed]
  53. P. B. Deotare, M. W. McCutcheon, I. W. Frank, M. Khan, and M. Lončar, “High quality factor photonic crystal nanobeam cavities,” Appl. Phys. Lett. 94(12), 121106 (2009).
    [Crossref]
  54. T. W. Lu and P. T. Lee, “Photonic crystal nanofishbone nanocavity,” Opt. Lett. 38(16), 3129–3132 (2013).
    [Crossref] [PubMed]
  55. COMSOL Multiphysics 3.5 (2009).
  56. M. Eichenfield, J. Chan, A. H. Safavi-Naeini, K. J. Vahala, and O. Painter, “Modeling dispersive coupling and losses of localized optical and mechanical modes in optomechanical crystals,” Opt. Express 17(22), 20078–20098 (2009).
    [Crossref] [PubMed]
  57. T. Yu, Z. Wang, W. Liu, T. Wang, N. Liu, and Q. Liao, “Simultaneous large band gaps and localization of electromagnetic and elastic waves in defect-free quasicrystals,” Opt. Express 24(8), 7951–7959 (2016).
    [Crossref] [PubMed]
  58. S. G. Johnson, M. Ibanescu, M. A. Skorobogatiy, O. Weisberg, J. D. Joannopoulos, and Y. Fink, “Perturbation theory for Maxwell’s equations with shifting material boundaries,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 65(6), 066611 (2002).
    [Crossref] [PubMed]
  59. D. Goettler, M. Su, Z. Leseman, Y. Soliman, R. Olsson, and I. El-Kady, “Realizing the frequency quality factor product limit in silicon via compact phononic crystal resonators,” J. Appl. Phys. 108(8), 084505 (2010).
    [Crossref]
  60. P. Seidler, K. Lister, U. Drechsler, J. Hofrichter, and T. Stöferle, “Slotted photonic crystal nanobeam cavity with an ultrahigh quality factor-to-mode volume ratio,” Opt. Express 21(26), 32468–32483 (2013).
    [Crossref] [PubMed]
  61. T. W. Lu, W. C. Tsai, T. Y. Wu, and P. T. Lee, “Laser emissions from one-dimensional photonic crystal rings on silicon-dioxide,” Appl. Phys. Lett. 102(5), 051103 (2013).
    [Crossref]
  62. S. P. Anderson and P. M. Fauchet, “Experimental demonstration of evanescent coupling and photon confinement in oxide-clad silicon microcavities,” Opt. Lett. 36(14), 2698–2700 (2011).
    [Crossref] [PubMed]

2016 (3)

S. Amoudache, R. Moiseyenko, Y. Pennec, B. Djafari Rouhani, A. Khater, R. Lucklum, and R. Tigrine, “Optical and acoustic sensing using Fano-like resonances in dual phononic and photonic crystal plate,” J. Appl. Phys. 119(11), 114502 (2016).
[Crossref]

T. X. Ma, Y. S. Wang, C. Zhang, and X. X. Su, “Theoretical research on a two-dimensional phoxonic crystal liquid sensor by utilizing surface optical and acoustic waves,” Sens. Actuators A Phys. 242, 123–131 (2016).
[Crossref]

T. Yu, Z. Wang, W. Liu, T. Wang, N. Liu, and Q. Liao, “Simultaneous large band gaps and localization of electromagnetic and elastic waves in defect-free quasicrystals,” Opt. Express 24(8), 7951–7959 (2016).
[Crossref] [PubMed]

2015 (1)

C. Dong, V. Fiore, M. C. Kuzyk, L. Tian, and H. Wang, “Optical wavelength conversion via optomechanical coupling in a silica resonator,” Ann. Phys. 527(1-2), 100–106 (2015).
[Crossref]

2014 (9)

S. Amoudache, Y. Pennec, B. Djafari Rouhani, A. Khater, R. Lucklum, and R. Tigrine, “Simultaneous sensing of light and sound velocities of fluids in a two-dimensional phoXonic crystal with defects,” J. Appl. Phys. 115(13), 134503 (2014).
[Crossref]

T. X. Ma, Y. S. Wang, and C. Zhang, “Investigation of dual photonic and phononic bandgaps in two- dimensional phoxonic crystals with veins,” Opt. Commun. 312, 68–72 (2014).
[Crossref]

Q. Rolland, S. Dupont, J. Gazalet, J. C. Kastelik, Y. Pennec, B. Djafari-Rouhani, and V. Laude, “Simultaneous bandgaps in LiNbO3 phoxonic crystal slab,” Opt. Express 22(13), 16288–16297 (2014).
[Crossref] [PubMed]

S. El-Jallal, M. Oudich, Y. Pennec, B. Djafari-Rouhani, A. Makhoute, Q. Rolland, S. Dupont, and J. Gazalet, “Optomechanical interactions in two-dimensional Si and GaAs phoXonic cavities,” J. Phys. Condens. Matter 26(1), 015005 (2014).
[Crossref] [PubMed]

L. Kipfstuhl, F. Guldner, J. Riedrich-Möller, and C. Becher, “Modeling of optomechanical coupling in a phoxonic crystal cavity in diamond,” Opt. Express 22(10), 12410–12423 (2014).
[Crossref] [PubMed]

M. Oudich, S. El-Jallal, Y. Pennec, B. Djafari-Rouhani, J. Gomis-Bresco, D. Navarro-Urrios, C. M. Sotomayor Torres, A. Martínez, and A. Makhoute, “Optomechanic interaction in a corrugated phoxonic nanobeam cavity,” Phys. Rev. B 89(24), 245122 (2014).
[Crossref]

Y. Pennec, V. Laude, N. Papanikolaou, B. Djafari-Rouhani, M. Oudich, S. El-Jallal, J. C. Beugnot, J. M. Escalante, and A. Martínez, “Modeling light-sound interaction in nanoscale cavities and waveguides,” Nanophotonics 3(6), 413–440 (2014).
[Crossref]

J. Gomis-Bresco, D. Navarro-Urrios, M. Oudich, S. El-Jallal, A. Griol, D. Puerto, E. Chavez, Y. Pennec, B. Djafari-Rouhani, F. Alzina, A. Martínez, and C. M. Torres, “A one-dimensional optomechanical crystal with a complete phononic band gap,” Nat. Commun. 5, 4452 (2014).
[Crossref] [PubMed]

R. W. Andrews, R. W. Peterson, T. P. Purdy, K. Cicak, R. W. Simmonds, C. A. Regal, and K. W. Lehnert, “Bidirectional and efficient conversion between microwave and optical light,” Nat. Phys. 10(4), 321–326 (2014).
[Crossref]

2013 (7)

T. R. Lin, C. H. Lin, and J. C. Hsu, “Enhanced acousto-optic interaction in two-dimensional phoxonic crystals with a line defect,” J. Appl. Phys. 113(5), 053508 (2013).
[Crossref]

S. El-Jallal, M. Oudich, Y. Pennec, B. Djafari-Rouhani, V. Laude, J. C. Beugnot, A. Martínez, J. M. Escalante, and A. Makhoute, “Analysis of optomechanical coupling in two-dimensional square lattice phoxonic crystal slab cavities,” Phys. Rev. B 88(20), 205410 (2013).
[Crossref]

T. X. Ma, Y. S. Wang, Y. F. Wang, and X. X. Su, “Three-dimensional dielectric phoxonic crystals with network topology,” Opt. Express 21(3), 2727–2732 (2013).
[Crossref] [PubMed]

R. Lucklum, M. Zubtsov, and A. Oseev, “Phoxonic crystals--a new platform for chemical and biochemical sensors,” Anal. Bioanal. Chem. 405(20), 6497–6509 (2013).
[Crossref] [PubMed]

T. W. Lu and P. T. Lee, “Photonic crystal nanofishbone nanocavity,” Opt. Lett. 38(16), 3129–3132 (2013).
[Crossref] [PubMed]

P. Seidler, K. Lister, U. Drechsler, J. Hofrichter, and T. Stöferle, “Slotted photonic crystal nanobeam cavity with an ultrahigh quality factor-to-mode volume ratio,” Opt. Express 21(26), 32468–32483 (2013).
[Crossref] [PubMed]

T. W. Lu, W. C. Tsai, T. Y. Wu, and P. T. Lee, “Laser emissions from one-dimensional photonic crystal rings on silicon-dioxide,” Appl. Phys. Lett. 102(5), 051103 (2013).
[Crossref]

2012 (8)

J. Manzanares-Martinez, D. Moctezuma-Enriquez, Y. J. Rodriguez-Viveros, B. Manzanares-Martinez, and P. Castro-Garay, “Non-perpendicular hypersonic and optical stop-bands in porous silicon multilayers,” Appl. Phys. Lett. 101(26), 261902 (2012).
[Crossref]

Y. D. Wang and A. A. Clerk, “Using dark modes for high-fidelity optomechanical quantum state transfer,” New J. Phys. 14(10), 105010 (2012).
[Crossref]

J. T. Hill, A. H. Safavi-Naeini, J. Chan, and O. Painter, “Coherent optical wavelength conversion via cavity optomechanics,” Nat. Commun. 3, 1196 (2012).
[Crossref] [PubMed]

J. Zheng, X. Sun, Y. Li, M. Poot, A. Dadgar, N. N. Shi, W. H. P. Pernice, H. X. Tang, and C. W. Wong, “Femtogram dispersive L3-nanobeam optomechanical cavities: design and experimental comparison,” Opt. Express 20(24), 26486–26498 (2012).
[Crossref] [PubMed]

N. Papanikolaou, I. E. Psarobas, N. Stefanou, B. Djafari-Rouhani, B. Bonello, and V. Laude, “Light modulation in phoxonic nanocavities,” Microelectron. Eng. 90, 155–158 (2012).
[Crossref]

E. Almpanis, N. Papanikolaou, G. Gantzounis, and N. Stefanou, “Tuning the spontaneous light emission in phoxonic cavities,” J. Opt. Soc. Am. B 29(9), 2567–2574 (2012).
[Crossref]

F. L. Hsiao, C. Y. Hsieh, H. Y. Hsieh, and C. C. Chiu, “High-efficiency acousto-optical interaction in phoxonic nanobeam waveguide,” Appl. Phys. Lett. 100(17), 171103 (2012).
[Crossref]

Q. Rolland, M. Oudich, S. El-Jallal, S. Dupont, Y. Pennec, J. Gazalet, J. C. Kastelik, G. Lévêque, and B. Djafari-Rouhani, “Acousto-optic couplings in two-dimensional phoxonic crystal cavities,” Appl. Phys. Lett. 101(6), 061109 (2012).
[Crossref]

2011 (6)

Y. Pennec, B. Djafari Rouhani, C. Li, J. M. Escalante, A. Martínez, S. Benchabane, V. Laude, and N. Papanikolaou, “Band gaps and cavity modes in dual phononic and photonic strip waveguides,” AIP Adv. 1(4), 041901 (2011).
[Crossref]

S. Y. Su, L. Tang, and T. Yoshie, “Optical surface Bloch modes of complete photonic bandgap materials as a basis of optical sensing,” Opt. Lett. 36(12), 2266–2268 (2011).
[Crossref] [PubMed]

D. A. Fuhrmann, S. M. Thon, H. Kim, D. Bouwmeester, P. M. Petroff, A. Wixforth, and H. J. Krenner, “Dynamic modulation of photonic crystal nanocavities using gigahertz acoustic phonons,” Nat. Photonics 5(10), 605–609 (2011).
[Crossref]

J. Chan, T. P. Alegre, A. H. Safavi-Naeini, J. T. Hill, A. Krause, S. Gröblacher, M. Aspelmeyer, and O. Painter, “Laser cooling of a nanomechanical oscillator into its quantum ground state,” Nature 478(7367), 89–92 (2011).
[Crossref] [PubMed]

D. Bria, M. B. Assouar, M. Oudich, Y. Pennec, J. Vasseur, and B. Djafari-Rouhani, “Opening of simultaneous photonic and phononic band gap in two-dimensional square lattice periodic structure,” J. Appl. Phys. 109(1), 014507 (2011).
[Crossref]

S. P. Anderson and P. M. Fauchet, “Experimental demonstration of evanescent coupling and photon confinement in oxide-clad silicon microcavities,” Opt. Lett. 36(14), 2698–2700 (2011).
[Crossref] [PubMed]

2010 (9)

D. Goettler, M. Su, Z. Leseman, Y. Soliman, R. Olsson, and I. El-Kady, “Realizing the frequency quality factor product limit in silicon via compact phononic crystal resonators,” J. Appl. Phys. 108(8), 084505 (2010).
[Crossref]

Y. Pennec, B. Djafari Rouhani, E. H. El Boudouti, C. Li, Y. El Hassouani, J. O. Vasseur, N. Papanikolaou, S. Benchabane, V. Laude, and A. Martínez, “Simultaneous existence of phononic and photonic band gaps in periodic crystal slabs,” Opt. Express 18(13), 14301–14310 (2010).
[Crossref] [PubMed]

K. Stannigel, P. Rabl, A. S. Sørensen, P. Zoller, and M. D. Lukin, “Optomechanical transducers for long-distance quantum communication,” Phys. Rev. Lett. 105(22), 220501 (2010).
[Crossref] [PubMed]

I. S. Grudinin, H. Lee, O. Painter, and K. J. Vahala, “Phonon laser action in a tunable two-level system,” Phys. Rev. Lett. 104(8), 083901 (2010).
[Crossref] [PubMed]

T. W. Lu, Y. H. Hsiao, W. D. Ho, and P. T. Lee, “High-index sensitivity of surface mode in photonic crystal hetero-slab-edge microcavity,” Opt. Lett. 35(9), 1452–1454 (2010).
[Crossref] [PubMed]

S. Mohammadi, A. A. Eftekhar, A. Khelif, and A. Adibi, “Simultaneous two-dimensional phononic and photonic band gaps in opto-mechanical crystal slabs,” Opt. Express 18(9), 9164–9172 (2010).
[Crossref] [PubMed]

Y. El Hassouani, C. Li, Y. Pennec, E. H. El Boudouti, H. Larabi, A. Akjouj, O. Bou Matar, V. Laude, N. Papanikolaou, A. Martínez, and B. Djafari Rouhani, “Dual phononic and photonic band gaps in a periodic array of pillars deposited on a thin plate,” Phys. Rev. B 82(15), 155405 (2010).
[Crossref]

I. E. Psarobas, N. Papanikolaou, N. Stefanou, B. Djafari-Rouhani, B. Bonello, and V. Laude, “Enhanced acousto-optic interactions in a one-dimensional phoxonic cavity,” Phys. Rev. B 82(17), 174303 (2010).
[Crossref]

A. H. Safavi-Naeini and O. Painter, “Design of optomechanical cavities and waveguides on a simultaneous bandgap phononic-photonic crystal slab,” Opt. Express 18(14), 14926–14943 (2010).
[Crossref] [PubMed]

2009 (7)

M. Eichenfield, J. Chan, R. M. Camacho, K. J. Vahala, and O. Painter, “Optomechanical crystals,” Nature 462(7269), 78–82 (2009).
[Crossref] [PubMed]

S. Sadat-Saleh, S. Benchabane, F. I. Baida, M. P. Bernal, and V. Laude, “Tailoring simultaneous photonic and phononic band gaps,” J. Appl. Phys. 106(7), 074912 (2009).
[Crossref]

K. Ishizaki and S. Noda, “Manipulation of photons at the surface of three-dimensional photonic crystals,” Nature 460(7253), 367–370 (2009).
[Crossref] [PubMed]

D. Razansky, M. Distel, C. Vinegoni, R. Ma, N. Perrimon, R. W. Köster, and V. Ntziachristos, “Multispectral opto-acoustic tomography of deep-seated fluorescent proteins in vivo,” Nat. Photonics 3(7), 412–417 (2009).
[Crossref]

P. Rabl, P. Cappellaro, M. V. Gurudev Dutt, L. Jiang, J. R. Maze, and M. D. Lukin, “Strong magnetic coupling between an electronic spin qubit and a mechanical resonator,” Phys. Rev. B 79(4), 041302 (2009).
[Crossref]

P. B. Deotare, M. W. McCutcheon, I. W. Frank, M. Khan, and M. Lončar, “High quality factor photonic crystal nanobeam cavities,” Appl. Phys. Lett. 94(12), 121106 (2009).
[Crossref]

M. Eichenfield, J. Chan, A. H. Safavi-Naeini, K. J. Vahala, and O. Painter, “Modeling dispersive coupling and losses of localized optical and mechanical modes in optomechanical crystals,” Opt. Express 17(22), 20078–20098 (2009).
[Crossref] [PubMed]

2008 (3)

J. O. Vasseur, P. A. Deymier, B. Djafari-Rouhani, Y. Pennec, and A. C. Hladky-Hennion, “Absolute forbidden bands and waveguiding in two-dimensional phononic crystal plates,” Phys. Rev. B 77(8), 085415 (2008).
[Crossref]

Y. Pennec, B. Djafari-Rouhani, H. Larabi, J. O. Vasseur, and A. C. Hladky-Hennion, “Low-frequency gaps in a phononic crystal constituted of cylindrical dots deposited on a thin homogeneous plate,” Phys. Rev. B 78(10), 104105 (2008).
[Crossref]

T. T. Wu, Z. G. Huang, T. C. Tsai, and T. C. Wu, “Evidence of complete band gap and resonances in a plate with periodic stubbed surface,” Appl. Phys. Lett. 93(11), 111902 (2008).
[Crossref]

2007 (1)

Z. Zhu, D. J. Gauthier, and R. W. Boyd, “Stored light in an optical fiber via stimulated Brillouin scattering,” Science 318(5857), 1748–1750 (2007).
[Crossref] [PubMed]

2006 (5)

M. Maldovan and E. L. Thomas, “Simultaneous localization of photons and phonons in two-dimensional periodic structures,” Appl. Phys. Lett. 88(25), 251907 (2006).
[Crossref]

A. I. Rahachou and I. V. Zozoulenko, “Waveguiding properties of surface states in photonic crystals,” J. Opt. Soc. Am. B 23(8), 1679–1683 (2006).
[Crossref]

J. C. Hsu and T. T. Wu, “Efficient formulation for band-structure calculations of two-dimensional phononic- crystal plates,” Phys. Rev. B 74(14), 144303 (2006).
[Crossref]

A. Khelif, B. Aoubiza, S. Mohammadi, A. Adibi, and V. Laude, “Complete band gaps in two-dimensional phononic crystal slabs,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 74(4), 046610 (2006).
[Crossref] [PubMed]

C. Charles, B. Bonello, and F. Ganot, “Propagation of guided elastic waves in 2D phononic crystals,” Ultrasonics 44(Suppl 1), e1209–e1213 (2006).
[Crossref] [PubMed]

2003 (1)

B. S. Williams, H. Callebaut, S. Kumar, Q. Hu, and J. L. Reno, “3.4-THz quantum cascade laser based on longitudinal-optical-phonon scattering for depopulation,” Appl. Phys. Lett. 82(7), 1015–1017 (2003).
[Crossref]

2002 (1)

S. G. Johnson, M. Ibanescu, M. A. Skorobogatiy, O. Weisberg, J. D. Joannopoulos, and Y. Fink, “Perturbation theory for Maxwell’s equations with shifting material boundaries,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 65(6), 066611 (2002).
[Crossref] [PubMed]

Adibi, A.

S. Mohammadi, A. A. Eftekhar, A. Khelif, and A. Adibi, “Simultaneous two-dimensional phononic and photonic band gaps in opto-mechanical crystal slabs,” Opt. Express 18(9), 9164–9172 (2010).
[Crossref] [PubMed]

A. Khelif, B. Aoubiza, S. Mohammadi, A. Adibi, and V. Laude, “Complete band gaps in two-dimensional phononic crystal slabs,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 74(4), 046610 (2006).
[Crossref] [PubMed]

Akjouj, A.

Y. El Hassouani, C. Li, Y. Pennec, E. H. El Boudouti, H. Larabi, A. Akjouj, O. Bou Matar, V. Laude, N. Papanikolaou, A. Martínez, and B. Djafari Rouhani, “Dual phononic and photonic band gaps in a periodic array of pillars deposited on a thin plate,” Phys. Rev. B 82(15), 155405 (2010).
[Crossref]

Alegre, T. P.

J. Chan, T. P. Alegre, A. H. Safavi-Naeini, J. T. Hill, A. Krause, S. Gröblacher, M. Aspelmeyer, and O. Painter, “Laser cooling of a nanomechanical oscillator into its quantum ground state,” Nature 478(7367), 89–92 (2011).
[Crossref] [PubMed]

Almpanis, E.

Alzina, F.

J. Gomis-Bresco, D. Navarro-Urrios, M. Oudich, S. El-Jallal, A. Griol, D. Puerto, E. Chavez, Y. Pennec, B. Djafari-Rouhani, F. Alzina, A. Martínez, and C. M. Torres, “A one-dimensional optomechanical crystal with a complete phononic band gap,” Nat. Commun. 5, 4452 (2014).
[Crossref] [PubMed]

Amoudache, S.

S. Amoudache, R. Moiseyenko, Y. Pennec, B. Djafari Rouhani, A. Khater, R. Lucklum, and R. Tigrine, “Optical and acoustic sensing using Fano-like resonances in dual phononic and photonic crystal plate,” J. Appl. Phys. 119(11), 114502 (2016).
[Crossref]

S. Amoudache, Y. Pennec, B. Djafari Rouhani, A. Khater, R. Lucklum, and R. Tigrine, “Simultaneous sensing of light and sound velocities of fluids in a two-dimensional phoXonic crystal with defects,” J. Appl. Phys. 115(13), 134503 (2014).
[Crossref]

Anderson, S. P.

Andrews, R. W.

R. W. Andrews, R. W. Peterson, T. P. Purdy, K. Cicak, R. W. Simmonds, C. A. Regal, and K. W. Lehnert, “Bidirectional and efficient conversion between microwave and optical light,” Nat. Phys. 10(4), 321–326 (2014).
[Crossref]

Aoubiza, B.

A. Khelif, B. Aoubiza, S. Mohammadi, A. Adibi, and V. Laude, “Complete band gaps in two-dimensional phononic crystal slabs,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 74(4), 046610 (2006).
[Crossref] [PubMed]

Aspelmeyer, M.

J. Chan, T. P. Alegre, A. H. Safavi-Naeini, J. T. Hill, A. Krause, S. Gröblacher, M. Aspelmeyer, and O. Painter, “Laser cooling of a nanomechanical oscillator into its quantum ground state,” Nature 478(7367), 89–92 (2011).
[Crossref] [PubMed]

Assouar, M. B.

D. Bria, M. B. Assouar, M. Oudich, Y. Pennec, J. Vasseur, and B. Djafari-Rouhani, “Opening of simultaneous photonic and phononic band gap in two-dimensional square lattice periodic structure,” J. Appl. Phys. 109(1), 014507 (2011).
[Crossref]

Baida, F. I.

S. Sadat-Saleh, S. Benchabane, F. I. Baida, M. P. Bernal, and V. Laude, “Tailoring simultaneous photonic and phononic band gaps,” J. Appl. Phys. 106(7), 074912 (2009).
[Crossref]

Becher, C.

Benchabane, S.

Y. Pennec, B. Djafari Rouhani, C. Li, J. M. Escalante, A. Martínez, S. Benchabane, V. Laude, and N. Papanikolaou, “Band gaps and cavity modes in dual phononic and photonic strip waveguides,” AIP Adv. 1(4), 041901 (2011).
[Crossref]

Y. Pennec, B. Djafari Rouhani, E. H. El Boudouti, C. Li, Y. El Hassouani, J. O. Vasseur, N. Papanikolaou, S. Benchabane, V. Laude, and A. Martínez, “Simultaneous existence of phononic and photonic band gaps in periodic crystal slabs,” Opt. Express 18(13), 14301–14310 (2010).
[Crossref] [PubMed]

S. Sadat-Saleh, S. Benchabane, F. I. Baida, M. P. Bernal, and V. Laude, “Tailoring simultaneous photonic and phononic band gaps,” J. Appl. Phys. 106(7), 074912 (2009).
[Crossref]

Bernal, M. P.

S. Sadat-Saleh, S. Benchabane, F. I. Baida, M. P. Bernal, and V. Laude, “Tailoring simultaneous photonic and phononic band gaps,” J. Appl. Phys. 106(7), 074912 (2009).
[Crossref]

Beugnot, J. C.

Y. Pennec, V. Laude, N. Papanikolaou, B. Djafari-Rouhani, M. Oudich, S. El-Jallal, J. C. Beugnot, J. M. Escalante, and A. Martínez, “Modeling light-sound interaction in nanoscale cavities and waveguides,” Nanophotonics 3(6), 413–440 (2014).
[Crossref]

S. El-Jallal, M. Oudich, Y. Pennec, B. Djafari-Rouhani, V. Laude, J. C. Beugnot, A. Martínez, J. M. Escalante, and A. Makhoute, “Analysis of optomechanical coupling in two-dimensional square lattice phoxonic crystal slab cavities,” Phys. Rev. B 88(20), 205410 (2013).
[Crossref]

Bonello, B.

N. Papanikolaou, I. E. Psarobas, N. Stefanou, B. Djafari-Rouhani, B. Bonello, and V. Laude, “Light modulation in phoxonic nanocavities,” Microelectron. Eng. 90, 155–158 (2012).
[Crossref]

I. E. Psarobas, N. Papanikolaou, N. Stefanou, B. Djafari-Rouhani, B. Bonello, and V. Laude, “Enhanced acousto-optic interactions in a one-dimensional phoxonic cavity,” Phys. Rev. B 82(17), 174303 (2010).
[Crossref]

C. Charles, B. Bonello, and F. Ganot, “Propagation of guided elastic waves in 2D phononic crystals,” Ultrasonics 44(Suppl 1), e1209–e1213 (2006).
[Crossref] [PubMed]

Bou Matar, O.

Y. El Hassouani, C. Li, Y. Pennec, E. H. El Boudouti, H. Larabi, A. Akjouj, O. Bou Matar, V. Laude, N. Papanikolaou, A. Martínez, and B. Djafari Rouhani, “Dual phononic and photonic band gaps in a periodic array of pillars deposited on a thin plate,” Phys. Rev. B 82(15), 155405 (2010).
[Crossref]

Bouwmeester, D.

D. A. Fuhrmann, S. M. Thon, H. Kim, D. Bouwmeester, P. M. Petroff, A. Wixforth, and H. J. Krenner, “Dynamic modulation of photonic crystal nanocavities using gigahertz acoustic phonons,” Nat. Photonics 5(10), 605–609 (2011).
[Crossref]

Boyd, R. W.

Z. Zhu, D. J. Gauthier, and R. W. Boyd, “Stored light in an optical fiber via stimulated Brillouin scattering,” Science 318(5857), 1748–1750 (2007).
[Crossref] [PubMed]

Bria, D.

D. Bria, M. B. Assouar, M. Oudich, Y. Pennec, J. Vasseur, and B. Djafari-Rouhani, “Opening of simultaneous photonic and phononic band gap in two-dimensional square lattice periodic structure,” J. Appl. Phys. 109(1), 014507 (2011).
[Crossref]

Callebaut, H.

B. S. Williams, H. Callebaut, S. Kumar, Q. Hu, and J. L. Reno, “3.4-THz quantum cascade laser based on longitudinal-optical-phonon scattering for depopulation,” Appl. Phys. Lett. 82(7), 1015–1017 (2003).
[Crossref]

Camacho, R. M.

M. Eichenfield, J. Chan, R. M. Camacho, K. J. Vahala, and O. Painter, “Optomechanical crystals,” Nature 462(7269), 78–82 (2009).
[Crossref] [PubMed]

Cappellaro, P.

P. Rabl, P. Cappellaro, M. V. Gurudev Dutt, L. Jiang, J. R. Maze, and M. D. Lukin, “Strong magnetic coupling between an electronic spin qubit and a mechanical resonator,” Phys. Rev. B 79(4), 041302 (2009).
[Crossref]

Castro-Garay, P.

J. Manzanares-Martinez, D. Moctezuma-Enriquez, Y. J. Rodriguez-Viveros, B. Manzanares-Martinez, and P. Castro-Garay, “Non-perpendicular hypersonic and optical stop-bands in porous silicon multilayers,” Appl. Phys. Lett. 101(26), 261902 (2012).
[Crossref]

Chan, J.

J. T. Hill, A. H. Safavi-Naeini, J. Chan, and O. Painter, “Coherent optical wavelength conversion via cavity optomechanics,” Nat. Commun. 3, 1196 (2012).
[Crossref] [PubMed]

J. Chan, T. P. Alegre, A. H. Safavi-Naeini, J. T. Hill, A. Krause, S. Gröblacher, M. Aspelmeyer, and O. Painter, “Laser cooling of a nanomechanical oscillator into its quantum ground state,” Nature 478(7367), 89–92 (2011).
[Crossref] [PubMed]

M. Eichenfield, J. Chan, A. H. Safavi-Naeini, K. J. Vahala, and O. Painter, “Modeling dispersive coupling and losses of localized optical and mechanical modes in optomechanical crystals,” Opt. Express 17(22), 20078–20098 (2009).
[Crossref] [PubMed]

M. Eichenfield, J. Chan, R. M. Camacho, K. J. Vahala, and O. Painter, “Optomechanical crystals,” Nature 462(7269), 78–82 (2009).
[Crossref] [PubMed]

Charles, C.

C. Charles, B. Bonello, and F. Ganot, “Propagation of guided elastic waves in 2D phononic crystals,” Ultrasonics 44(Suppl 1), e1209–e1213 (2006).
[Crossref] [PubMed]

Chavez, E.

J. Gomis-Bresco, D. Navarro-Urrios, M. Oudich, S. El-Jallal, A. Griol, D. Puerto, E. Chavez, Y. Pennec, B. Djafari-Rouhani, F. Alzina, A. Martínez, and C. M. Torres, “A one-dimensional optomechanical crystal with a complete phononic band gap,” Nat. Commun. 5, 4452 (2014).
[Crossref] [PubMed]

Chiu, C. C.

F. L. Hsiao, C. Y. Hsieh, H. Y. Hsieh, and C. C. Chiu, “High-efficiency acousto-optical interaction in phoxonic nanobeam waveguide,” Appl. Phys. Lett. 100(17), 171103 (2012).
[Crossref]

Cicak, K.

R. W. Andrews, R. W. Peterson, T. P. Purdy, K. Cicak, R. W. Simmonds, C. A. Regal, and K. W. Lehnert, “Bidirectional and efficient conversion between microwave and optical light,” Nat. Phys. 10(4), 321–326 (2014).
[Crossref]

Clerk, A. A.

Y. D. Wang and A. A. Clerk, “Using dark modes for high-fidelity optomechanical quantum state transfer,” New J. Phys. 14(10), 105010 (2012).
[Crossref]

Dadgar, A.

Deotare, P. B.

P. B. Deotare, M. W. McCutcheon, I. W. Frank, M. Khan, and M. Lončar, “High quality factor photonic crystal nanobeam cavities,” Appl. Phys. Lett. 94(12), 121106 (2009).
[Crossref]

Deymier, P. A.

J. O. Vasseur, P. A. Deymier, B. Djafari-Rouhani, Y. Pennec, and A. C. Hladky-Hennion, “Absolute forbidden bands and waveguiding in two-dimensional phononic crystal plates,” Phys. Rev. B 77(8), 085415 (2008).
[Crossref]

Distel, M.

D. Razansky, M. Distel, C. Vinegoni, R. Ma, N. Perrimon, R. W. Köster, and V. Ntziachristos, “Multispectral opto-acoustic tomography of deep-seated fluorescent proteins in vivo,” Nat. Photonics 3(7), 412–417 (2009).
[Crossref]

Djafari Rouhani, B.

S. Amoudache, R. Moiseyenko, Y. Pennec, B. Djafari Rouhani, A. Khater, R. Lucklum, and R. Tigrine, “Optical and acoustic sensing using Fano-like resonances in dual phononic and photonic crystal plate,” J. Appl. Phys. 119(11), 114502 (2016).
[Crossref]

S. Amoudache, Y. Pennec, B. Djafari Rouhani, A. Khater, R. Lucklum, and R. Tigrine, “Simultaneous sensing of light and sound velocities of fluids in a two-dimensional phoXonic crystal with defects,” J. Appl. Phys. 115(13), 134503 (2014).
[Crossref]

Y. Pennec, B. Djafari Rouhani, C. Li, J. M. Escalante, A. Martínez, S. Benchabane, V. Laude, and N. Papanikolaou, “Band gaps and cavity modes in dual phononic and photonic strip waveguides,” AIP Adv. 1(4), 041901 (2011).
[Crossref]

Y. Pennec, B. Djafari Rouhani, E. H. El Boudouti, C. Li, Y. El Hassouani, J. O. Vasseur, N. Papanikolaou, S. Benchabane, V. Laude, and A. Martínez, “Simultaneous existence of phononic and photonic band gaps in periodic crystal slabs,” Opt. Express 18(13), 14301–14310 (2010).
[Crossref] [PubMed]

Y. El Hassouani, C. Li, Y. Pennec, E. H. El Boudouti, H. Larabi, A. Akjouj, O. Bou Matar, V. Laude, N. Papanikolaou, A. Martínez, and B. Djafari Rouhani, “Dual phononic and photonic band gaps in a periodic array of pillars deposited on a thin plate,” Phys. Rev. B 82(15), 155405 (2010).
[Crossref]

Djafari-Rouhani, B.

Q. Rolland, S. Dupont, J. Gazalet, J. C. Kastelik, Y. Pennec, B. Djafari-Rouhani, and V. Laude, “Simultaneous bandgaps in LiNbO3 phoxonic crystal slab,” Opt. Express 22(13), 16288–16297 (2014).
[Crossref] [PubMed]

Y. Pennec, V. Laude, N. Papanikolaou, B. Djafari-Rouhani, M. Oudich, S. El-Jallal, J. C. Beugnot, J. M. Escalante, and A. Martínez, “Modeling light-sound interaction in nanoscale cavities and waveguides,” Nanophotonics 3(6), 413–440 (2014).
[Crossref]

M. Oudich, S. El-Jallal, Y. Pennec, B. Djafari-Rouhani, J. Gomis-Bresco, D. Navarro-Urrios, C. M. Sotomayor Torres, A. Martínez, and A. Makhoute, “Optomechanic interaction in a corrugated phoxonic nanobeam cavity,” Phys. Rev. B 89(24), 245122 (2014).
[Crossref]

S. El-Jallal, M. Oudich, Y. Pennec, B. Djafari-Rouhani, A. Makhoute, Q. Rolland, S. Dupont, and J. Gazalet, “Optomechanical interactions in two-dimensional Si and GaAs phoXonic cavities,” J. Phys. Condens. Matter 26(1), 015005 (2014).
[Crossref] [PubMed]

J. Gomis-Bresco, D. Navarro-Urrios, M. Oudich, S. El-Jallal, A. Griol, D. Puerto, E. Chavez, Y. Pennec, B. Djafari-Rouhani, F. Alzina, A. Martínez, and C. M. Torres, “A one-dimensional optomechanical crystal with a complete phononic band gap,” Nat. Commun. 5, 4452 (2014).
[Crossref] [PubMed]

S. El-Jallal, M. Oudich, Y. Pennec, B. Djafari-Rouhani, V. Laude, J. C. Beugnot, A. Martínez, J. M. Escalante, and A. Makhoute, “Analysis of optomechanical coupling in two-dimensional square lattice phoxonic crystal slab cavities,” Phys. Rev. B 88(20), 205410 (2013).
[Crossref]

Q. Rolland, M. Oudich, S. El-Jallal, S. Dupont, Y. Pennec, J. Gazalet, J. C. Kastelik, G. Lévêque, and B. Djafari-Rouhani, “Acousto-optic couplings in two-dimensional phoxonic crystal cavities,” Appl. Phys. Lett. 101(6), 061109 (2012).
[Crossref]

N. Papanikolaou, I. E. Psarobas, N. Stefanou, B. Djafari-Rouhani, B. Bonello, and V. Laude, “Light modulation in phoxonic nanocavities,” Microelectron. Eng. 90, 155–158 (2012).
[Crossref]

D. Bria, M. B. Assouar, M. Oudich, Y. Pennec, J. Vasseur, and B. Djafari-Rouhani, “Opening of simultaneous photonic and phononic band gap in two-dimensional square lattice periodic structure,” J. Appl. Phys. 109(1), 014507 (2011).
[Crossref]

I. E. Psarobas, N. Papanikolaou, N. Stefanou, B. Djafari-Rouhani, B. Bonello, and V. Laude, “Enhanced acousto-optic interactions in a one-dimensional phoxonic cavity,” Phys. Rev. B 82(17), 174303 (2010).
[Crossref]

J. O. Vasseur, P. A. Deymier, B. Djafari-Rouhani, Y. Pennec, and A. C. Hladky-Hennion, “Absolute forbidden bands and waveguiding in two-dimensional phononic crystal plates,” Phys. Rev. B 77(8), 085415 (2008).
[Crossref]

Y. Pennec, B. Djafari-Rouhani, H. Larabi, J. O. Vasseur, and A. C. Hladky-Hennion, “Low-frequency gaps in a phononic crystal constituted of cylindrical dots deposited on a thin homogeneous plate,” Phys. Rev. B 78(10), 104105 (2008).
[Crossref]

Dong, C.

C. Dong, V. Fiore, M. C. Kuzyk, L. Tian, and H. Wang, “Optical wavelength conversion via optomechanical coupling in a silica resonator,” Ann. Phys. 527(1-2), 100–106 (2015).
[Crossref]

Drechsler, U.

Dupont, S.

Q. Rolland, S. Dupont, J. Gazalet, J. C. Kastelik, Y. Pennec, B. Djafari-Rouhani, and V. Laude, “Simultaneous bandgaps in LiNbO3 phoxonic crystal slab,” Opt. Express 22(13), 16288–16297 (2014).
[Crossref] [PubMed]

S. El-Jallal, M. Oudich, Y. Pennec, B. Djafari-Rouhani, A. Makhoute, Q. Rolland, S. Dupont, and J. Gazalet, “Optomechanical interactions in two-dimensional Si and GaAs phoXonic cavities,” J. Phys. Condens. Matter 26(1), 015005 (2014).
[Crossref] [PubMed]

Q. Rolland, M. Oudich, S. El-Jallal, S. Dupont, Y. Pennec, J. Gazalet, J. C. Kastelik, G. Lévêque, and B. Djafari-Rouhani, “Acousto-optic couplings in two-dimensional phoxonic crystal cavities,” Appl. Phys. Lett. 101(6), 061109 (2012).
[Crossref]

Eftekhar, A. A.

Eichenfield, M.

El Boudouti, E. H.

Y. El Hassouani, C. Li, Y. Pennec, E. H. El Boudouti, H. Larabi, A. Akjouj, O. Bou Matar, V. Laude, N. Papanikolaou, A. Martínez, and B. Djafari Rouhani, “Dual phononic and photonic band gaps in a periodic array of pillars deposited on a thin plate,” Phys. Rev. B 82(15), 155405 (2010).
[Crossref]

Y. Pennec, B. Djafari Rouhani, E. H. El Boudouti, C. Li, Y. El Hassouani, J. O. Vasseur, N. Papanikolaou, S. Benchabane, V. Laude, and A. Martínez, “Simultaneous existence of phononic and photonic band gaps in periodic crystal slabs,” Opt. Express 18(13), 14301–14310 (2010).
[Crossref] [PubMed]

El Hassouani, Y.

Y. Pennec, B. Djafari Rouhani, E. H. El Boudouti, C. Li, Y. El Hassouani, J. O. Vasseur, N. Papanikolaou, S. Benchabane, V. Laude, and A. Martínez, “Simultaneous existence of phononic and photonic band gaps in periodic crystal slabs,” Opt. Express 18(13), 14301–14310 (2010).
[Crossref] [PubMed]

Y. El Hassouani, C. Li, Y. Pennec, E. H. El Boudouti, H. Larabi, A. Akjouj, O. Bou Matar, V. Laude, N. Papanikolaou, A. Martínez, and B. Djafari Rouhani, “Dual phononic and photonic band gaps in a periodic array of pillars deposited on a thin plate,” Phys. Rev. B 82(15), 155405 (2010).
[Crossref]

El-Jallal, S.

Y. Pennec, V. Laude, N. Papanikolaou, B. Djafari-Rouhani, M. Oudich, S. El-Jallal, J. C. Beugnot, J. M. Escalante, and A. Martínez, “Modeling light-sound interaction in nanoscale cavities and waveguides,” Nanophotonics 3(6), 413–440 (2014).
[Crossref]

M. Oudich, S. El-Jallal, Y. Pennec, B. Djafari-Rouhani, J. Gomis-Bresco, D. Navarro-Urrios, C. M. Sotomayor Torres, A. Martínez, and A. Makhoute, “Optomechanic interaction in a corrugated phoxonic nanobeam cavity,” Phys. Rev. B 89(24), 245122 (2014).
[Crossref]

S. El-Jallal, M. Oudich, Y. Pennec, B. Djafari-Rouhani, A. Makhoute, Q. Rolland, S. Dupont, and J. Gazalet, “Optomechanical interactions in two-dimensional Si and GaAs phoXonic cavities,” J. Phys. Condens. Matter 26(1), 015005 (2014).
[Crossref] [PubMed]

J. Gomis-Bresco, D. Navarro-Urrios, M. Oudich, S. El-Jallal, A. Griol, D. Puerto, E. Chavez, Y. Pennec, B. Djafari-Rouhani, F. Alzina, A. Martínez, and C. M. Torres, “A one-dimensional optomechanical crystal with a complete phononic band gap,” Nat. Commun. 5, 4452 (2014).
[Crossref] [PubMed]

S. El-Jallal, M. Oudich, Y. Pennec, B. Djafari-Rouhani, V. Laude, J. C. Beugnot, A. Martínez, J. M. Escalante, and A. Makhoute, “Analysis of optomechanical coupling in two-dimensional square lattice phoxonic crystal slab cavities,” Phys. Rev. B 88(20), 205410 (2013).
[Crossref]

Q. Rolland, M. Oudich, S. El-Jallal, S. Dupont, Y. Pennec, J. Gazalet, J. C. Kastelik, G. Lévêque, and B. Djafari-Rouhani, “Acousto-optic couplings in two-dimensional phoxonic crystal cavities,” Appl. Phys. Lett. 101(6), 061109 (2012).
[Crossref]

El-Kady, I.

D. Goettler, M. Su, Z. Leseman, Y. Soliman, R. Olsson, and I. El-Kady, “Realizing the frequency quality factor product limit in silicon via compact phononic crystal resonators,” J. Appl. Phys. 108(8), 084505 (2010).
[Crossref]

Escalante, J. M.

Y. Pennec, V. Laude, N. Papanikolaou, B. Djafari-Rouhani, M. Oudich, S. El-Jallal, J. C. Beugnot, J. M. Escalante, and A. Martínez, “Modeling light-sound interaction in nanoscale cavities and waveguides,” Nanophotonics 3(6), 413–440 (2014).
[Crossref]

S. El-Jallal, M. Oudich, Y. Pennec, B. Djafari-Rouhani, V. Laude, J. C. Beugnot, A. Martínez, J. M. Escalante, and A. Makhoute, “Analysis of optomechanical coupling in two-dimensional square lattice phoxonic crystal slab cavities,” Phys. Rev. B 88(20), 205410 (2013).
[Crossref]

Y. Pennec, B. Djafari Rouhani, C. Li, J. M. Escalante, A. Martínez, S. Benchabane, V. Laude, and N. Papanikolaou, “Band gaps and cavity modes in dual phononic and photonic strip waveguides,” AIP Adv. 1(4), 041901 (2011).
[Crossref]

Fauchet, P. M.

Fink, Y.

S. G. Johnson, M. Ibanescu, M. A. Skorobogatiy, O. Weisberg, J. D. Joannopoulos, and Y. Fink, “Perturbation theory for Maxwell’s equations with shifting material boundaries,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 65(6), 066611 (2002).
[Crossref] [PubMed]

Fiore, V.

C. Dong, V. Fiore, M. C. Kuzyk, L. Tian, and H. Wang, “Optical wavelength conversion via optomechanical coupling in a silica resonator,” Ann. Phys. 527(1-2), 100–106 (2015).
[Crossref]

Frank, I. W.

P. B. Deotare, M. W. McCutcheon, I. W. Frank, M. Khan, and M. Lončar, “High quality factor photonic crystal nanobeam cavities,” Appl. Phys. Lett. 94(12), 121106 (2009).
[Crossref]

Fuhrmann, D. A.

D. A. Fuhrmann, S. M. Thon, H. Kim, D. Bouwmeester, P. M. Petroff, A. Wixforth, and H. J. Krenner, “Dynamic modulation of photonic crystal nanocavities using gigahertz acoustic phonons,” Nat. Photonics 5(10), 605–609 (2011).
[Crossref]

Ganot, F.

C. Charles, B. Bonello, and F. Ganot, “Propagation of guided elastic waves in 2D phononic crystals,” Ultrasonics 44(Suppl 1), e1209–e1213 (2006).
[Crossref] [PubMed]

Gantzounis, G.

Gauthier, D. J.

Z. Zhu, D. J. Gauthier, and R. W. Boyd, “Stored light in an optical fiber via stimulated Brillouin scattering,” Science 318(5857), 1748–1750 (2007).
[Crossref] [PubMed]

Gazalet, J.

S. El-Jallal, M. Oudich, Y. Pennec, B. Djafari-Rouhani, A. Makhoute, Q. Rolland, S. Dupont, and J. Gazalet, “Optomechanical interactions in two-dimensional Si and GaAs phoXonic cavities,” J. Phys. Condens. Matter 26(1), 015005 (2014).
[Crossref] [PubMed]

Q. Rolland, S. Dupont, J. Gazalet, J. C. Kastelik, Y. Pennec, B. Djafari-Rouhani, and V. Laude, “Simultaneous bandgaps in LiNbO3 phoxonic crystal slab,” Opt. Express 22(13), 16288–16297 (2014).
[Crossref] [PubMed]

Q. Rolland, M. Oudich, S. El-Jallal, S. Dupont, Y. Pennec, J. Gazalet, J. C. Kastelik, G. Lévêque, and B. Djafari-Rouhani, “Acousto-optic couplings in two-dimensional phoxonic crystal cavities,” Appl. Phys. Lett. 101(6), 061109 (2012).
[Crossref]

Goettler, D.

D. Goettler, M. Su, Z. Leseman, Y. Soliman, R. Olsson, and I. El-Kady, “Realizing the frequency quality factor product limit in silicon via compact phononic crystal resonators,” J. Appl. Phys. 108(8), 084505 (2010).
[Crossref]

Gomis-Bresco, J.

M. Oudich, S. El-Jallal, Y. Pennec, B. Djafari-Rouhani, J. Gomis-Bresco, D. Navarro-Urrios, C. M. Sotomayor Torres, A. Martínez, and A. Makhoute, “Optomechanic interaction in a corrugated phoxonic nanobeam cavity,” Phys. Rev. B 89(24), 245122 (2014).
[Crossref]

J. Gomis-Bresco, D. Navarro-Urrios, M. Oudich, S. El-Jallal, A. Griol, D. Puerto, E. Chavez, Y. Pennec, B. Djafari-Rouhani, F. Alzina, A. Martínez, and C. M. Torres, “A one-dimensional optomechanical crystal with a complete phononic band gap,” Nat. Commun. 5, 4452 (2014).
[Crossref] [PubMed]

Griol, A.

J. Gomis-Bresco, D. Navarro-Urrios, M. Oudich, S. El-Jallal, A. Griol, D. Puerto, E. Chavez, Y. Pennec, B. Djafari-Rouhani, F. Alzina, A. Martínez, and C. M. Torres, “A one-dimensional optomechanical crystal with a complete phononic band gap,” Nat. Commun. 5, 4452 (2014).
[Crossref] [PubMed]

Gröblacher, S.

J. Chan, T. P. Alegre, A. H. Safavi-Naeini, J. T. Hill, A. Krause, S. Gröblacher, M. Aspelmeyer, and O. Painter, “Laser cooling of a nanomechanical oscillator into its quantum ground state,” Nature 478(7367), 89–92 (2011).
[Crossref] [PubMed]

Grudinin, I. S.

I. S. Grudinin, H. Lee, O. Painter, and K. J. Vahala, “Phonon laser action in a tunable two-level system,” Phys. Rev. Lett. 104(8), 083901 (2010).
[Crossref] [PubMed]

Guldner, F.

Gurudev Dutt, M. V.

P. Rabl, P. Cappellaro, M. V. Gurudev Dutt, L. Jiang, J. R. Maze, and M. D. Lukin, “Strong magnetic coupling between an electronic spin qubit and a mechanical resonator,” Phys. Rev. B 79(4), 041302 (2009).
[Crossref]

Hill, J. T.

J. T. Hill, A. H. Safavi-Naeini, J. Chan, and O. Painter, “Coherent optical wavelength conversion via cavity optomechanics,” Nat. Commun. 3, 1196 (2012).
[Crossref] [PubMed]

J. Chan, T. P. Alegre, A. H. Safavi-Naeini, J. T. Hill, A. Krause, S. Gröblacher, M. Aspelmeyer, and O. Painter, “Laser cooling of a nanomechanical oscillator into its quantum ground state,” Nature 478(7367), 89–92 (2011).
[Crossref] [PubMed]

Hladky-Hennion, A. C.

J. O. Vasseur, P. A. Deymier, B. Djafari-Rouhani, Y. Pennec, and A. C. Hladky-Hennion, “Absolute forbidden bands and waveguiding in two-dimensional phononic crystal plates,” Phys. Rev. B 77(8), 085415 (2008).
[Crossref]

Y. Pennec, B. Djafari-Rouhani, H. Larabi, J. O. Vasseur, and A. C. Hladky-Hennion, “Low-frequency gaps in a phononic crystal constituted of cylindrical dots deposited on a thin homogeneous plate,” Phys. Rev. B 78(10), 104105 (2008).
[Crossref]

Ho, W. D.

Hofrichter, J.

Hsiao, F. L.

F. L. Hsiao, C. Y. Hsieh, H. Y. Hsieh, and C. C. Chiu, “High-efficiency acousto-optical interaction in phoxonic nanobeam waveguide,” Appl. Phys. Lett. 100(17), 171103 (2012).
[Crossref]

Hsiao, Y. H.

Hsieh, C. Y.

F. L. Hsiao, C. Y. Hsieh, H. Y. Hsieh, and C. C. Chiu, “High-efficiency acousto-optical interaction in phoxonic nanobeam waveguide,” Appl. Phys. Lett. 100(17), 171103 (2012).
[Crossref]

Hsieh, H. Y.

F. L. Hsiao, C. Y. Hsieh, H. Y. Hsieh, and C. C. Chiu, “High-efficiency acousto-optical interaction in phoxonic nanobeam waveguide,” Appl. Phys. Lett. 100(17), 171103 (2012).
[Crossref]

Hsu, J. C.

T. R. Lin, C. H. Lin, and J. C. Hsu, “Enhanced acousto-optic interaction in two-dimensional phoxonic crystals with a line defect,” J. Appl. Phys. 113(5), 053508 (2013).
[Crossref]

J. C. Hsu and T. T. Wu, “Efficient formulation for band-structure calculations of two-dimensional phononic- crystal plates,” Phys. Rev. B 74(14), 144303 (2006).
[Crossref]

Hu, Q.

B. S. Williams, H. Callebaut, S. Kumar, Q. Hu, and J. L. Reno, “3.4-THz quantum cascade laser based on longitudinal-optical-phonon scattering for depopulation,” Appl. Phys. Lett. 82(7), 1015–1017 (2003).
[Crossref]

Huang, Z. G.

T. T. Wu, Z. G. Huang, T. C. Tsai, and T. C. Wu, “Evidence of complete band gap and resonances in a plate with periodic stubbed surface,” Appl. Phys. Lett. 93(11), 111902 (2008).
[Crossref]

Ibanescu, M.

S. G. Johnson, M. Ibanescu, M. A. Skorobogatiy, O. Weisberg, J. D. Joannopoulos, and Y. Fink, “Perturbation theory for Maxwell’s equations with shifting material boundaries,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 65(6), 066611 (2002).
[Crossref] [PubMed]

Ishizaki, K.

K. Ishizaki and S. Noda, “Manipulation of photons at the surface of three-dimensional photonic crystals,” Nature 460(7253), 367–370 (2009).
[Crossref] [PubMed]

Jiang, L.

P. Rabl, P. Cappellaro, M. V. Gurudev Dutt, L. Jiang, J. R. Maze, and M. D. Lukin, “Strong magnetic coupling between an electronic spin qubit and a mechanical resonator,” Phys. Rev. B 79(4), 041302 (2009).
[Crossref]

Joannopoulos, J. D.

S. G. Johnson, M. Ibanescu, M. A. Skorobogatiy, O. Weisberg, J. D. Joannopoulos, and Y. Fink, “Perturbation theory for Maxwell’s equations with shifting material boundaries,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 65(6), 066611 (2002).
[Crossref] [PubMed]

Johnson, S. G.

S. G. Johnson, M. Ibanescu, M. A. Skorobogatiy, O. Weisberg, J. D. Joannopoulos, and Y. Fink, “Perturbation theory for Maxwell’s equations with shifting material boundaries,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 65(6), 066611 (2002).
[Crossref] [PubMed]

Kastelik, J. C.

Q. Rolland, S. Dupont, J. Gazalet, J. C. Kastelik, Y. Pennec, B. Djafari-Rouhani, and V. Laude, “Simultaneous bandgaps in LiNbO3 phoxonic crystal slab,” Opt. Express 22(13), 16288–16297 (2014).
[Crossref] [PubMed]

Q. Rolland, M. Oudich, S. El-Jallal, S. Dupont, Y. Pennec, J. Gazalet, J. C. Kastelik, G. Lévêque, and B. Djafari-Rouhani, “Acousto-optic couplings in two-dimensional phoxonic crystal cavities,” Appl. Phys. Lett. 101(6), 061109 (2012).
[Crossref]

Khan, M.

P. B. Deotare, M. W. McCutcheon, I. W. Frank, M. Khan, and M. Lončar, “High quality factor photonic crystal nanobeam cavities,” Appl. Phys. Lett. 94(12), 121106 (2009).
[Crossref]

Khater, A.

S. Amoudache, R. Moiseyenko, Y. Pennec, B. Djafari Rouhani, A. Khater, R. Lucklum, and R. Tigrine, “Optical and acoustic sensing using Fano-like resonances in dual phononic and photonic crystal plate,” J. Appl. Phys. 119(11), 114502 (2016).
[Crossref]

S. Amoudache, Y. Pennec, B. Djafari Rouhani, A. Khater, R. Lucklum, and R. Tigrine, “Simultaneous sensing of light and sound velocities of fluids in a two-dimensional phoXonic crystal with defects,” J. Appl. Phys. 115(13), 134503 (2014).
[Crossref]

Khelif, A.

S. Mohammadi, A. A. Eftekhar, A. Khelif, and A. Adibi, “Simultaneous two-dimensional phononic and photonic band gaps in opto-mechanical crystal slabs,” Opt. Express 18(9), 9164–9172 (2010).
[Crossref] [PubMed]

A. Khelif, B. Aoubiza, S. Mohammadi, A. Adibi, and V. Laude, “Complete band gaps in two-dimensional phononic crystal slabs,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 74(4), 046610 (2006).
[Crossref] [PubMed]

Kim, H.

D. A. Fuhrmann, S. M. Thon, H. Kim, D. Bouwmeester, P. M. Petroff, A. Wixforth, and H. J. Krenner, “Dynamic modulation of photonic crystal nanocavities using gigahertz acoustic phonons,” Nat. Photonics 5(10), 605–609 (2011).
[Crossref]

Kipfstuhl, L.

Köster, R. W.

D. Razansky, M. Distel, C. Vinegoni, R. Ma, N. Perrimon, R. W. Köster, and V. Ntziachristos, “Multispectral opto-acoustic tomography of deep-seated fluorescent proteins in vivo,” Nat. Photonics 3(7), 412–417 (2009).
[Crossref]

Krause, A.

J. Chan, T. P. Alegre, A. H. Safavi-Naeini, J. T. Hill, A. Krause, S. Gröblacher, M. Aspelmeyer, and O. Painter, “Laser cooling of a nanomechanical oscillator into its quantum ground state,” Nature 478(7367), 89–92 (2011).
[Crossref] [PubMed]

Krenner, H. J.

D. A. Fuhrmann, S. M. Thon, H. Kim, D. Bouwmeester, P. M. Petroff, A. Wixforth, and H. J. Krenner, “Dynamic modulation of photonic crystal nanocavities using gigahertz acoustic phonons,” Nat. Photonics 5(10), 605–609 (2011).
[Crossref]

Kumar, S.

B. S. Williams, H. Callebaut, S. Kumar, Q. Hu, and J. L. Reno, “3.4-THz quantum cascade laser based on longitudinal-optical-phonon scattering for depopulation,” Appl. Phys. Lett. 82(7), 1015–1017 (2003).
[Crossref]

Kuzyk, M. C.

C. Dong, V. Fiore, M. C. Kuzyk, L. Tian, and H. Wang, “Optical wavelength conversion via optomechanical coupling in a silica resonator,” Ann. Phys. 527(1-2), 100–106 (2015).
[Crossref]

Larabi, H.

Y. El Hassouani, C. Li, Y. Pennec, E. H. El Boudouti, H. Larabi, A. Akjouj, O. Bou Matar, V. Laude, N. Papanikolaou, A. Martínez, and B. Djafari Rouhani, “Dual phononic and photonic band gaps in a periodic array of pillars deposited on a thin plate,” Phys. Rev. B 82(15), 155405 (2010).
[Crossref]

Y. Pennec, B. Djafari-Rouhani, H. Larabi, J. O. Vasseur, and A. C. Hladky-Hennion, “Low-frequency gaps in a phononic crystal constituted of cylindrical dots deposited on a thin homogeneous plate,” Phys. Rev. B 78(10), 104105 (2008).
[Crossref]

Laude, V.

Q. Rolland, S. Dupont, J. Gazalet, J. C. Kastelik, Y. Pennec, B. Djafari-Rouhani, and V. Laude, “Simultaneous bandgaps in LiNbO3 phoxonic crystal slab,” Opt. Express 22(13), 16288–16297 (2014).
[Crossref] [PubMed]

Y. Pennec, V. Laude, N. Papanikolaou, B. Djafari-Rouhani, M. Oudich, S. El-Jallal, J. C. Beugnot, J. M. Escalante, and A. Martínez, “Modeling light-sound interaction in nanoscale cavities and waveguides,” Nanophotonics 3(6), 413–440 (2014).
[Crossref]

S. El-Jallal, M. Oudich, Y. Pennec, B. Djafari-Rouhani, V. Laude, J. C. Beugnot, A. Martínez, J. M. Escalante, and A. Makhoute, “Analysis of optomechanical coupling in two-dimensional square lattice phoxonic crystal slab cavities,” Phys. Rev. B 88(20), 205410 (2013).
[Crossref]

N. Papanikolaou, I. E. Psarobas, N. Stefanou, B. Djafari-Rouhani, B. Bonello, and V. Laude, “Light modulation in phoxonic nanocavities,” Microelectron. Eng. 90, 155–158 (2012).
[Crossref]

Y. Pennec, B. Djafari Rouhani, C. Li, J. M. Escalante, A. Martínez, S. Benchabane, V. Laude, and N. Papanikolaou, “Band gaps and cavity modes in dual phononic and photonic strip waveguides,” AIP Adv. 1(4), 041901 (2011).
[Crossref]

Y. Pennec, B. Djafari Rouhani, E. H. El Boudouti, C. Li, Y. El Hassouani, J. O. Vasseur, N. Papanikolaou, S. Benchabane, V. Laude, and A. Martínez, “Simultaneous existence of phononic and photonic band gaps in periodic crystal slabs,” Opt. Express 18(13), 14301–14310 (2010).
[Crossref] [PubMed]

I. E. Psarobas, N. Papanikolaou, N. Stefanou, B. Djafari-Rouhani, B. Bonello, and V. Laude, “Enhanced acousto-optic interactions in a one-dimensional phoxonic cavity,” Phys. Rev. B 82(17), 174303 (2010).
[Crossref]

Y. El Hassouani, C. Li, Y. Pennec, E. H. El Boudouti, H. Larabi, A. Akjouj, O. Bou Matar, V. Laude, N. Papanikolaou, A. Martínez, and B. Djafari Rouhani, “Dual phononic and photonic band gaps in a periodic array of pillars deposited on a thin plate,” Phys. Rev. B 82(15), 155405 (2010).
[Crossref]

S. Sadat-Saleh, S. Benchabane, F. I. Baida, M. P. Bernal, and V. Laude, “Tailoring simultaneous photonic and phononic band gaps,” J. Appl. Phys. 106(7), 074912 (2009).
[Crossref]

A. Khelif, B. Aoubiza, S. Mohammadi, A. Adibi, and V. Laude, “Complete band gaps in two-dimensional phononic crystal slabs,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 74(4), 046610 (2006).
[Crossref] [PubMed]

Lee, H.

I. S. Grudinin, H. Lee, O. Painter, and K. J. Vahala, “Phonon laser action in a tunable two-level system,” Phys. Rev. Lett. 104(8), 083901 (2010).
[Crossref] [PubMed]

Lee, P. T.

Lehnert, K. W.

R. W. Andrews, R. W. Peterson, T. P. Purdy, K. Cicak, R. W. Simmonds, C. A. Regal, and K. W. Lehnert, “Bidirectional and efficient conversion between microwave and optical light,” Nat. Phys. 10(4), 321–326 (2014).
[Crossref]

Leseman, Z.

D. Goettler, M. Su, Z. Leseman, Y. Soliman, R. Olsson, and I. El-Kady, “Realizing the frequency quality factor product limit in silicon via compact phononic crystal resonators,” J. Appl. Phys. 108(8), 084505 (2010).
[Crossref]

Lévêque, G.

Q. Rolland, M. Oudich, S. El-Jallal, S. Dupont, Y. Pennec, J. Gazalet, J. C. Kastelik, G. Lévêque, and B. Djafari-Rouhani, “Acousto-optic couplings in two-dimensional phoxonic crystal cavities,” Appl. Phys. Lett. 101(6), 061109 (2012).
[Crossref]

Li, C.

Y. Pennec, B. Djafari Rouhani, C. Li, J. M. Escalante, A. Martínez, S. Benchabane, V. Laude, and N. Papanikolaou, “Band gaps and cavity modes in dual phononic and photonic strip waveguides,” AIP Adv. 1(4), 041901 (2011).
[Crossref]

Y. Pennec, B. Djafari Rouhani, E. H. El Boudouti, C. Li, Y. El Hassouani, J. O. Vasseur, N. Papanikolaou, S. Benchabane, V. Laude, and A. Martínez, “Simultaneous existence of phononic and photonic band gaps in periodic crystal slabs,” Opt. Express 18(13), 14301–14310 (2010).
[Crossref] [PubMed]

Y. El Hassouani, C. Li, Y. Pennec, E. H. El Boudouti, H. Larabi, A. Akjouj, O. Bou Matar, V. Laude, N. Papanikolaou, A. Martínez, and B. Djafari Rouhani, “Dual phononic and photonic band gaps in a periodic array of pillars deposited on a thin plate,” Phys. Rev. B 82(15), 155405 (2010).
[Crossref]

Li, Y.

Liao, Q.

Lin, C. H.

T. R. Lin, C. H. Lin, and J. C. Hsu, “Enhanced acousto-optic interaction in two-dimensional phoxonic crystals with a line defect,” J. Appl. Phys. 113(5), 053508 (2013).
[Crossref]

Lin, T. R.

T. R. Lin, C. H. Lin, and J. C. Hsu, “Enhanced acousto-optic interaction in two-dimensional phoxonic crystals with a line defect,” J. Appl. Phys. 113(5), 053508 (2013).
[Crossref]

Lister, K.

Liu, N.

Liu, W.

Loncar, M.

P. B. Deotare, M. W. McCutcheon, I. W. Frank, M. Khan, and M. Lončar, “High quality factor photonic crystal nanobeam cavities,” Appl. Phys. Lett. 94(12), 121106 (2009).
[Crossref]

Lu, T. W.

Lucklum, R.

S. Amoudache, R. Moiseyenko, Y. Pennec, B. Djafari Rouhani, A. Khater, R. Lucklum, and R. Tigrine, “Optical and acoustic sensing using Fano-like resonances in dual phononic and photonic crystal plate,” J. Appl. Phys. 119(11), 114502 (2016).
[Crossref]

S. Amoudache, Y. Pennec, B. Djafari Rouhani, A. Khater, R. Lucklum, and R. Tigrine, “Simultaneous sensing of light and sound velocities of fluids in a two-dimensional phoXonic crystal with defects,” J. Appl. Phys. 115(13), 134503 (2014).
[Crossref]

R. Lucklum, M. Zubtsov, and A. Oseev, “Phoxonic crystals--a new platform for chemical and biochemical sensors,” Anal. Bioanal. Chem. 405(20), 6497–6509 (2013).
[Crossref] [PubMed]

Lukin, M. D.

K. Stannigel, P. Rabl, A. S. Sørensen, P. Zoller, and M. D. Lukin, “Optomechanical transducers for long-distance quantum communication,” Phys. Rev. Lett. 105(22), 220501 (2010).
[Crossref] [PubMed]

P. Rabl, P. Cappellaro, M. V. Gurudev Dutt, L. Jiang, J. R. Maze, and M. D. Lukin, “Strong magnetic coupling between an electronic spin qubit and a mechanical resonator,” Phys. Rev. B 79(4), 041302 (2009).
[Crossref]

Ma, R.

D. Razansky, M. Distel, C. Vinegoni, R. Ma, N. Perrimon, R. W. Köster, and V. Ntziachristos, “Multispectral opto-acoustic tomography of deep-seated fluorescent proteins in vivo,” Nat. Photonics 3(7), 412–417 (2009).
[Crossref]

Ma, T. X.

T. X. Ma, Y. S. Wang, C. Zhang, and X. X. Su, “Theoretical research on a two-dimensional phoxonic crystal liquid sensor by utilizing surface optical and acoustic waves,” Sens. Actuators A Phys. 242, 123–131 (2016).
[Crossref]

T. X. Ma, Y. S. Wang, and C. Zhang, “Investigation of dual photonic and phononic bandgaps in two- dimensional phoxonic crystals with veins,” Opt. Commun. 312, 68–72 (2014).
[Crossref]

T. X. Ma, Y. S. Wang, Y. F. Wang, and X. X. Su, “Three-dimensional dielectric phoxonic crystals with network topology,” Opt. Express 21(3), 2727–2732 (2013).
[Crossref] [PubMed]

Makhoute, A.

M. Oudich, S. El-Jallal, Y. Pennec, B. Djafari-Rouhani, J. Gomis-Bresco, D. Navarro-Urrios, C. M. Sotomayor Torres, A. Martínez, and A. Makhoute, “Optomechanic interaction in a corrugated phoxonic nanobeam cavity,” Phys. Rev. B 89(24), 245122 (2014).
[Crossref]

S. El-Jallal, M. Oudich, Y. Pennec, B. Djafari-Rouhani, A. Makhoute, Q. Rolland, S. Dupont, and J. Gazalet, “Optomechanical interactions in two-dimensional Si and GaAs phoXonic cavities,” J. Phys. Condens. Matter 26(1), 015005 (2014).
[Crossref] [PubMed]

S. El-Jallal, M. Oudich, Y. Pennec, B. Djafari-Rouhani, V. Laude, J. C. Beugnot, A. Martínez, J. M. Escalante, and A. Makhoute, “Analysis of optomechanical coupling in two-dimensional square lattice phoxonic crystal slab cavities,” Phys. Rev. B 88(20), 205410 (2013).
[Crossref]

Maldovan, M.

M. Maldovan and E. L. Thomas, “Simultaneous localization of photons and phonons in two-dimensional periodic structures,” Appl. Phys. Lett. 88(25), 251907 (2006).
[Crossref]

Manzanares-Martinez, B.

J. Manzanares-Martinez, D. Moctezuma-Enriquez, Y. J. Rodriguez-Viveros, B. Manzanares-Martinez, and P. Castro-Garay, “Non-perpendicular hypersonic and optical stop-bands in porous silicon multilayers,” Appl. Phys. Lett. 101(26), 261902 (2012).
[Crossref]

Manzanares-Martinez, J.

J. Manzanares-Martinez, D. Moctezuma-Enriquez, Y. J. Rodriguez-Viveros, B. Manzanares-Martinez, and P. Castro-Garay, “Non-perpendicular hypersonic and optical stop-bands in porous silicon multilayers,” Appl. Phys. Lett. 101(26), 261902 (2012).
[Crossref]

Martínez, A.

J. Gomis-Bresco, D. Navarro-Urrios, M. Oudich, S. El-Jallal, A. Griol, D. Puerto, E. Chavez, Y. Pennec, B. Djafari-Rouhani, F. Alzina, A. Martínez, and C. M. Torres, “A one-dimensional optomechanical crystal with a complete phononic band gap,” Nat. Commun. 5, 4452 (2014).
[Crossref] [PubMed]

Y. Pennec, V. Laude, N. Papanikolaou, B. Djafari-Rouhani, M. Oudich, S. El-Jallal, J. C. Beugnot, J. M. Escalante, and A. Martínez, “Modeling light-sound interaction in nanoscale cavities and waveguides,” Nanophotonics 3(6), 413–440 (2014).
[Crossref]

M. Oudich, S. El-Jallal, Y. Pennec, B. Djafari-Rouhani, J. Gomis-Bresco, D. Navarro-Urrios, C. M. Sotomayor Torres, A. Martínez, and A. Makhoute, “Optomechanic interaction in a corrugated phoxonic nanobeam cavity,” Phys. Rev. B 89(24), 245122 (2014).
[Crossref]

S. El-Jallal, M. Oudich, Y. Pennec, B. Djafari-Rouhani, V. Laude, J. C. Beugnot, A. Martínez, J. M. Escalante, and A. Makhoute, “Analysis of optomechanical coupling in two-dimensional square lattice phoxonic crystal slab cavities,” Phys. Rev. B 88(20), 205410 (2013).
[Crossref]

Y. Pennec, B. Djafari Rouhani, C. Li, J. M. Escalante, A. Martínez, S. Benchabane, V. Laude, and N. Papanikolaou, “Band gaps and cavity modes in dual phononic and photonic strip waveguides,” AIP Adv. 1(4), 041901 (2011).
[Crossref]

Y. Pennec, B. Djafari Rouhani, E. H. El Boudouti, C. Li, Y. El Hassouani, J. O. Vasseur, N. Papanikolaou, S. Benchabane, V. Laude, and A. Martínez, “Simultaneous existence of phononic and photonic band gaps in periodic crystal slabs,” Opt. Express 18(13), 14301–14310 (2010).
[Crossref] [PubMed]

Y. El Hassouani, C. Li, Y. Pennec, E. H. El Boudouti, H. Larabi, A. Akjouj, O. Bou Matar, V. Laude, N. Papanikolaou, A. Martínez, and B. Djafari Rouhani, “Dual phononic and photonic band gaps in a periodic array of pillars deposited on a thin plate,” Phys. Rev. B 82(15), 155405 (2010).
[Crossref]

Maze, J. R.

P. Rabl, P. Cappellaro, M. V. Gurudev Dutt, L. Jiang, J. R. Maze, and M. D. Lukin, “Strong magnetic coupling between an electronic spin qubit and a mechanical resonator,” Phys. Rev. B 79(4), 041302 (2009).
[Crossref]

McCutcheon, M. W.

P. B. Deotare, M. W. McCutcheon, I. W. Frank, M. Khan, and M. Lončar, “High quality factor photonic crystal nanobeam cavities,” Appl. Phys. Lett. 94(12), 121106 (2009).
[Crossref]

Moctezuma-Enriquez, D.

J. Manzanares-Martinez, D. Moctezuma-Enriquez, Y. J. Rodriguez-Viveros, B. Manzanares-Martinez, and P. Castro-Garay, “Non-perpendicular hypersonic and optical stop-bands in porous silicon multilayers,” Appl. Phys. Lett. 101(26), 261902 (2012).
[Crossref]

Mohammadi, S.

S. Mohammadi, A. A. Eftekhar, A. Khelif, and A. Adibi, “Simultaneous two-dimensional phononic and photonic band gaps in opto-mechanical crystal slabs,” Opt. Express 18(9), 9164–9172 (2010).
[Crossref] [PubMed]

A. Khelif, B. Aoubiza, S. Mohammadi, A. Adibi, and V. Laude, “Complete band gaps in two-dimensional phononic crystal slabs,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 74(4), 046610 (2006).
[Crossref] [PubMed]

Moiseyenko, R.

S. Amoudache, R. Moiseyenko, Y. Pennec, B. Djafari Rouhani, A. Khater, R. Lucklum, and R. Tigrine, “Optical and acoustic sensing using Fano-like resonances in dual phononic and photonic crystal plate,” J. Appl. Phys. 119(11), 114502 (2016).
[Crossref]

Navarro-Urrios, D.

J. Gomis-Bresco, D. Navarro-Urrios, M. Oudich, S. El-Jallal, A. Griol, D. Puerto, E. Chavez, Y. Pennec, B. Djafari-Rouhani, F. Alzina, A. Martínez, and C. M. Torres, “A one-dimensional optomechanical crystal with a complete phononic band gap,” Nat. Commun. 5, 4452 (2014).
[Crossref] [PubMed]

M. Oudich, S. El-Jallal, Y. Pennec, B. Djafari-Rouhani, J. Gomis-Bresco, D. Navarro-Urrios, C. M. Sotomayor Torres, A. Martínez, and A. Makhoute, “Optomechanic interaction in a corrugated phoxonic nanobeam cavity,” Phys. Rev. B 89(24), 245122 (2014).
[Crossref]

Noda, S.

K. Ishizaki and S. Noda, “Manipulation of photons at the surface of three-dimensional photonic crystals,” Nature 460(7253), 367–370 (2009).
[Crossref] [PubMed]

Ntziachristos, V.

D. Razansky, M. Distel, C. Vinegoni, R. Ma, N. Perrimon, R. W. Köster, and V. Ntziachristos, “Multispectral opto-acoustic tomography of deep-seated fluorescent proteins in vivo,” Nat. Photonics 3(7), 412–417 (2009).
[Crossref]

Olsson, R.

D. Goettler, M. Su, Z. Leseman, Y. Soliman, R. Olsson, and I. El-Kady, “Realizing the frequency quality factor product limit in silicon via compact phononic crystal resonators,” J. Appl. Phys. 108(8), 084505 (2010).
[Crossref]

Oseev, A.

R. Lucklum, M. Zubtsov, and A. Oseev, “Phoxonic crystals--a new platform for chemical and biochemical sensors,” Anal. Bioanal. Chem. 405(20), 6497–6509 (2013).
[Crossref] [PubMed]

Oudich, M.

J. Gomis-Bresco, D. Navarro-Urrios, M. Oudich, S. El-Jallal, A. Griol, D. Puerto, E. Chavez, Y. Pennec, B. Djafari-Rouhani, F. Alzina, A. Martínez, and C. M. Torres, “A one-dimensional optomechanical crystal with a complete phononic band gap,” Nat. Commun. 5, 4452 (2014).
[Crossref] [PubMed]

M. Oudich, S. El-Jallal, Y. Pennec, B. Djafari-Rouhani, J. Gomis-Bresco, D. Navarro-Urrios, C. M. Sotomayor Torres, A. Martínez, and A. Makhoute, “Optomechanic interaction in a corrugated phoxonic nanobeam cavity,” Phys. Rev. B 89(24), 245122 (2014).
[Crossref]

S. El-Jallal, M. Oudich, Y. Pennec, B. Djafari-Rouhani, A. Makhoute, Q. Rolland, S. Dupont, and J. Gazalet, “Optomechanical interactions in two-dimensional Si and GaAs phoXonic cavities,” J. Phys. Condens. Matter 26(1), 015005 (2014).
[Crossref] [PubMed]

Y. Pennec, V. Laude, N. Papanikolaou, B. Djafari-Rouhani, M. Oudich, S. El-Jallal, J. C. Beugnot, J. M. Escalante, and A. Martínez, “Modeling light-sound interaction in nanoscale cavities and waveguides,” Nanophotonics 3(6), 413–440 (2014).
[Crossref]

S. El-Jallal, M. Oudich, Y. Pennec, B. Djafari-Rouhani, V. Laude, J. C. Beugnot, A. Martínez, J. M. Escalante, and A. Makhoute, “Analysis of optomechanical coupling in two-dimensional square lattice phoxonic crystal slab cavities,” Phys. Rev. B 88(20), 205410 (2013).
[Crossref]

Q. Rolland, M. Oudich, S. El-Jallal, S. Dupont, Y. Pennec, J. Gazalet, J. C. Kastelik, G. Lévêque, and B. Djafari-Rouhani, “Acousto-optic couplings in two-dimensional phoxonic crystal cavities,” Appl. Phys. Lett. 101(6), 061109 (2012).
[Crossref]

D. Bria, M. B. Assouar, M. Oudich, Y. Pennec, J. Vasseur, and B. Djafari-Rouhani, “Opening of simultaneous photonic and phononic band gap in two-dimensional square lattice periodic structure,” J. Appl. Phys. 109(1), 014507 (2011).
[Crossref]

Painter, O.

J. T. Hill, A. H. Safavi-Naeini, J. Chan, and O. Painter, “Coherent optical wavelength conversion via cavity optomechanics,” Nat. Commun. 3, 1196 (2012).
[Crossref] [PubMed]

J. Chan, T. P. Alegre, A. H. Safavi-Naeini, J. T. Hill, A. Krause, S. Gröblacher, M. Aspelmeyer, and O. Painter, “Laser cooling of a nanomechanical oscillator into its quantum ground state,” Nature 478(7367), 89–92 (2011).
[Crossref] [PubMed]

I. S. Grudinin, H. Lee, O. Painter, and K. J. Vahala, “Phonon laser action in a tunable two-level system,” Phys. Rev. Lett. 104(8), 083901 (2010).
[Crossref] [PubMed]

A. H. Safavi-Naeini and O. Painter, “Design of optomechanical cavities and waveguides on a simultaneous bandgap phononic-photonic crystal slab,” Opt. Express 18(14), 14926–14943 (2010).
[Crossref] [PubMed]

M. Eichenfield, J. Chan, R. M. Camacho, K. J. Vahala, and O. Painter, “Optomechanical crystals,” Nature 462(7269), 78–82 (2009).
[Crossref] [PubMed]

M. Eichenfield, J. Chan, A. H. Safavi-Naeini, K. J. Vahala, and O. Painter, “Modeling dispersive coupling and losses of localized optical and mechanical modes in optomechanical crystals,” Opt. Express 17(22), 20078–20098 (2009).
[Crossref] [PubMed]

Papanikolaou, N.

Y. Pennec, V. Laude, N. Papanikolaou, B. Djafari-Rouhani, M. Oudich, S. El-Jallal, J. C. Beugnot, J. M. Escalante, and A. Martínez, “Modeling light-sound interaction in nanoscale cavities and waveguides,” Nanophotonics 3(6), 413–440 (2014).
[Crossref]

N. Papanikolaou, I. E. Psarobas, N. Stefanou, B. Djafari-Rouhani, B. Bonello, and V. Laude, “Light modulation in phoxonic nanocavities,” Microelectron. Eng. 90, 155–158 (2012).
[Crossref]

E. Almpanis, N. Papanikolaou, G. Gantzounis, and N. Stefanou, “Tuning the spontaneous light emission in phoxonic cavities,” J. Opt. Soc. Am. B 29(9), 2567–2574 (2012).
[Crossref]

Y. Pennec, B. Djafari Rouhani, C. Li, J. M. Escalante, A. Martínez, S. Benchabane, V. Laude, and N. Papanikolaou, “Band gaps and cavity modes in dual phononic and photonic strip waveguides,” AIP Adv. 1(4), 041901 (2011).
[Crossref]

Y. Pennec, B. Djafari Rouhani, E. H. El Boudouti, C. Li, Y. El Hassouani, J. O. Vasseur, N. Papanikolaou, S. Benchabane, V. Laude, and A. Martínez, “Simultaneous existence of phononic and photonic band gaps in periodic crystal slabs,” Opt. Express 18(13), 14301–14310 (2010).
[Crossref] [PubMed]

Y. El Hassouani, C. Li, Y. Pennec, E. H. El Boudouti, H. Larabi, A. Akjouj, O. Bou Matar, V. Laude, N. Papanikolaou, A. Martínez, and B. Djafari Rouhani, “Dual phononic and photonic band gaps in a periodic array of pillars deposited on a thin plate,” Phys. Rev. B 82(15), 155405 (2010).
[Crossref]

I. E. Psarobas, N. Papanikolaou, N. Stefanou, B. Djafari-Rouhani, B. Bonello, and V. Laude, “Enhanced acousto-optic interactions in a one-dimensional phoxonic cavity,” Phys. Rev. B 82(17), 174303 (2010).
[Crossref]

Pennec, Y.

S. Amoudache, R. Moiseyenko, Y. Pennec, B. Djafari Rouhani, A. Khater, R. Lucklum, and R. Tigrine, “Optical and acoustic sensing using Fano-like resonances in dual phononic and photonic crystal plate,” J. Appl. Phys. 119(11), 114502 (2016).
[Crossref]

S. Amoudache, Y. Pennec, B. Djafari Rouhani, A. Khater, R. Lucklum, and R. Tigrine, “Simultaneous sensing of light and sound velocities of fluids in a two-dimensional phoXonic crystal with defects,” J. Appl. Phys. 115(13), 134503 (2014).
[Crossref]

J. Gomis-Bresco, D. Navarro-Urrios, M. Oudich, S. El-Jallal, A. Griol, D. Puerto, E. Chavez, Y. Pennec, B. Djafari-Rouhani, F. Alzina, A. Martínez, and C. M. Torres, “A one-dimensional optomechanical crystal with a complete phononic band gap,” Nat. Commun. 5, 4452 (2014).
[Crossref] [PubMed]

Q. Rolland, S. Dupont, J. Gazalet, J. C. Kastelik, Y. Pennec, B. Djafari-Rouhani, and V. Laude, “Simultaneous bandgaps in LiNbO3 phoxonic crystal slab,” Opt. Express 22(13), 16288–16297 (2014).
[Crossref] [PubMed]

Y. Pennec, V. Laude, N. Papanikolaou, B. Djafari-Rouhani, M. Oudich, S. El-Jallal, J. C. Beugnot, J. M. Escalante, and A. Martínez, “Modeling light-sound interaction in nanoscale cavities and waveguides,” Nanophotonics 3(6), 413–440 (2014).
[Crossref]

M. Oudich, S. El-Jallal, Y. Pennec, B. Djafari-Rouhani, J. Gomis-Bresco, D. Navarro-Urrios, C. M. Sotomayor Torres, A. Martínez, and A. Makhoute, “Optomechanic interaction in a corrugated phoxonic nanobeam cavity,” Phys. Rev. B 89(24), 245122 (2014).
[Crossref]

S. El-Jallal, M. Oudich, Y. Pennec, B. Djafari-Rouhani, A. Makhoute, Q. Rolland, S. Dupont, and J. Gazalet, “Optomechanical interactions in two-dimensional Si and GaAs phoXonic cavities,” J. Phys. Condens. Matter 26(1), 015005 (2014).
[Crossref] [PubMed]

S. El-Jallal, M. Oudich, Y. Pennec, B. Djafari-Rouhani, V. Laude, J. C. Beugnot, A. Martínez, J. M. Escalante, and A. Makhoute, “Analysis of optomechanical coupling in two-dimensional square lattice phoxonic crystal slab cavities,” Phys. Rev. B 88(20), 205410 (2013).
[Crossref]

Q. Rolland, M. Oudich, S. El-Jallal, S. Dupont, Y. Pennec, J. Gazalet, J. C. Kastelik, G. Lévêque, and B. Djafari-Rouhani, “Acousto-optic couplings in two-dimensional phoxonic crystal cavities,” Appl. Phys. Lett. 101(6), 061109 (2012).
[Crossref]

Y. Pennec, B. Djafari Rouhani, C. Li, J. M. Escalante, A. Martínez, S. Benchabane, V. Laude, and N. Papanikolaou, “Band gaps and cavity modes in dual phononic and photonic strip waveguides,” AIP Adv. 1(4), 041901 (2011).
[Crossref]

D. Bria, M. B. Assouar, M. Oudich, Y. Pennec, J. Vasseur, and B. Djafari-Rouhani, “Opening of simultaneous photonic and phononic band gap in two-dimensional square lattice periodic structure,” J. Appl. Phys. 109(1), 014507 (2011).
[Crossref]

Y. Pennec, B. Djafari Rouhani, E. H. El Boudouti, C. Li, Y. El Hassouani, J. O. Vasseur, N. Papanikolaou, S. Benchabane, V. Laude, and A. Martínez, “Simultaneous existence of phononic and photonic band gaps in periodic crystal slabs,” Opt. Express 18(13), 14301–14310 (2010).
[Crossref] [PubMed]

Y. El Hassouani, C. Li, Y. Pennec, E. H. El Boudouti, H. Larabi, A. Akjouj, O. Bou Matar, V. Laude, N. Papanikolaou, A. Martínez, and B. Djafari Rouhani, “Dual phononic and photonic band gaps in a periodic array of pillars deposited on a thin plate,” Phys. Rev. B 82(15), 155405 (2010).
[Crossref]

Y. Pennec, B. Djafari-Rouhani, H. Larabi, J. O. Vasseur, and A. C. Hladky-Hennion, “Low-frequency gaps in a phononic crystal constituted of cylindrical dots deposited on a thin homogeneous plate,” Phys. Rev. B 78(10), 104105 (2008).
[Crossref]

J. O. Vasseur, P. A. Deymier, B. Djafari-Rouhani, Y. Pennec, and A. C. Hladky-Hennion, “Absolute forbidden bands and waveguiding in two-dimensional phononic crystal plates,” Phys. Rev. B 77(8), 085415 (2008).
[Crossref]

Pernice, W. H. P.

Perrimon, N.

D. Razansky, M. Distel, C. Vinegoni, R. Ma, N. Perrimon, R. W. Köster, and V. Ntziachristos, “Multispectral opto-acoustic tomography of deep-seated fluorescent proteins in vivo,” Nat. Photonics 3(7), 412–417 (2009).
[Crossref]

Peterson, R. W.

R. W. Andrews, R. W. Peterson, T. P. Purdy, K. Cicak, R. W. Simmonds, C. A. Regal, and K. W. Lehnert, “Bidirectional and efficient conversion between microwave and optical light,” Nat. Phys. 10(4), 321–326 (2014).
[Crossref]

Petroff, P. M.

D. A. Fuhrmann, S. M. Thon, H. Kim, D. Bouwmeester, P. M. Petroff, A. Wixforth, and H. J. Krenner, “Dynamic modulation of photonic crystal nanocavities using gigahertz acoustic phonons,” Nat. Photonics 5(10), 605–609 (2011).
[Crossref]

Poot, M.

Psarobas, I. E.

N. Papanikolaou, I. E. Psarobas, N. Stefanou, B. Djafari-Rouhani, B. Bonello, and V. Laude, “Light modulation in phoxonic nanocavities,” Microelectron. Eng. 90, 155–158 (2012).
[Crossref]

I. E. Psarobas, N. Papanikolaou, N. Stefanou, B. Djafari-Rouhani, B. Bonello, and V. Laude, “Enhanced acousto-optic interactions in a one-dimensional phoxonic cavity,” Phys. Rev. B 82(17), 174303 (2010).
[Crossref]

Puerto, D.

J. Gomis-Bresco, D. Navarro-Urrios, M. Oudich, S. El-Jallal, A. Griol, D. Puerto, E. Chavez, Y. Pennec, B. Djafari-Rouhani, F. Alzina, A. Martínez, and C. M. Torres, “A one-dimensional optomechanical crystal with a complete phononic band gap,” Nat. Commun. 5, 4452 (2014).
[Crossref] [PubMed]

Purdy, T. P.

R. W. Andrews, R. W. Peterson, T. P. Purdy, K. Cicak, R. W. Simmonds, C. A. Regal, and K. W. Lehnert, “Bidirectional and efficient conversion between microwave and optical light,” Nat. Phys. 10(4), 321–326 (2014).
[Crossref]

Rabl, P.

K. Stannigel, P. Rabl, A. S. Sørensen, P. Zoller, and M. D. Lukin, “Optomechanical transducers for long-distance quantum communication,” Phys. Rev. Lett. 105(22), 220501 (2010).
[Crossref] [PubMed]

P. Rabl, P. Cappellaro, M. V. Gurudev Dutt, L. Jiang, J. R. Maze, and M. D. Lukin, “Strong magnetic coupling between an electronic spin qubit and a mechanical resonator,” Phys. Rev. B 79(4), 041302 (2009).
[Crossref]

Rahachou, A. I.

Razansky, D.

D. Razansky, M. Distel, C. Vinegoni, R. Ma, N. Perrimon, R. W. Köster, and V. Ntziachristos, “Multispectral opto-acoustic tomography of deep-seated fluorescent proteins in vivo,” Nat. Photonics 3(7), 412–417 (2009).
[Crossref]

Regal, C. A.

R. W. Andrews, R. W. Peterson, T. P. Purdy, K. Cicak, R. W. Simmonds, C. A. Regal, and K. W. Lehnert, “Bidirectional and efficient conversion between microwave and optical light,” Nat. Phys. 10(4), 321–326 (2014).
[Crossref]

Reno, J. L.

B. S. Williams, H. Callebaut, S. Kumar, Q. Hu, and J. L. Reno, “3.4-THz quantum cascade laser based on longitudinal-optical-phonon scattering for depopulation,” Appl. Phys. Lett. 82(7), 1015–1017 (2003).
[Crossref]

Riedrich-Möller, J.

Rodriguez-Viveros, Y. J.

J. Manzanares-Martinez, D. Moctezuma-Enriquez, Y. J. Rodriguez-Viveros, B. Manzanares-Martinez, and P. Castro-Garay, “Non-perpendicular hypersonic and optical stop-bands in porous silicon multilayers,” Appl. Phys. Lett. 101(26), 261902 (2012).
[Crossref]

Rolland, Q.

S. El-Jallal, M. Oudich, Y. Pennec, B. Djafari-Rouhani, A. Makhoute, Q. Rolland, S. Dupont, and J. Gazalet, “Optomechanical interactions in two-dimensional Si and GaAs phoXonic cavities,” J. Phys. Condens. Matter 26(1), 015005 (2014).
[Crossref] [PubMed]

Q. Rolland, S. Dupont, J. Gazalet, J. C. Kastelik, Y. Pennec, B. Djafari-Rouhani, and V. Laude, “Simultaneous bandgaps in LiNbO3 phoxonic crystal slab,” Opt. Express 22(13), 16288–16297 (2014).
[Crossref] [PubMed]

Q. Rolland, M. Oudich, S. El-Jallal, S. Dupont, Y. Pennec, J. Gazalet, J. C. Kastelik, G. Lévêque, and B. Djafari-Rouhani, “Acousto-optic couplings in two-dimensional phoxonic crystal cavities,” Appl. Phys. Lett. 101(6), 061109 (2012).
[Crossref]

Sadat-Saleh, S.

S. Sadat-Saleh, S. Benchabane, F. I. Baida, M. P. Bernal, and V. Laude, “Tailoring simultaneous photonic and phononic band gaps,” J. Appl. Phys. 106(7), 074912 (2009).
[Crossref]

Safavi-Naeini, A. H.

J. T. Hill, A. H. Safavi-Naeini, J. Chan, and O. Painter, “Coherent optical wavelength conversion via cavity optomechanics,” Nat. Commun. 3, 1196 (2012).
[Crossref] [PubMed]

J. Chan, T. P. Alegre, A. H. Safavi-Naeini, J. T. Hill, A. Krause, S. Gröblacher, M. Aspelmeyer, and O. Painter, “Laser cooling of a nanomechanical oscillator into its quantum ground state,” Nature 478(7367), 89–92 (2011).
[Crossref] [PubMed]

A. H. Safavi-Naeini and O. Painter, “Design of optomechanical cavities and waveguides on a simultaneous bandgap phononic-photonic crystal slab,” Opt. Express 18(14), 14926–14943 (2010).
[Crossref] [PubMed]

M. Eichenfield, J. Chan, A. H. Safavi-Naeini, K. J. Vahala, and O. Painter, “Modeling dispersive coupling and losses of localized optical and mechanical modes in optomechanical crystals,” Opt. Express 17(22), 20078–20098 (2009).
[Crossref] [PubMed]

Seidler, P.

Shi, N. N.

Simmonds, R. W.

R. W. Andrews, R. W. Peterson, T. P. Purdy, K. Cicak, R. W. Simmonds, C. A. Regal, and K. W. Lehnert, “Bidirectional and efficient conversion between microwave and optical light,” Nat. Phys. 10(4), 321–326 (2014).
[Crossref]

Skorobogatiy, M. A.

S. G. Johnson, M. Ibanescu, M. A. Skorobogatiy, O. Weisberg, J. D. Joannopoulos, and Y. Fink, “Perturbation theory for Maxwell’s equations with shifting material boundaries,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 65(6), 066611 (2002).
[Crossref] [PubMed]

Soliman, Y.

D. Goettler, M. Su, Z. Leseman, Y. Soliman, R. Olsson, and I. El-Kady, “Realizing the frequency quality factor product limit in silicon via compact phononic crystal resonators,” J. Appl. Phys. 108(8), 084505 (2010).
[Crossref]

Sørensen, A. S.

K. Stannigel, P. Rabl, A. S. Sørensen, P. Zoller, and M. D. Lukin, “Optomechanical transducers for long-distance quantum communication,” Phys. Rev. Lett. 105(22), 220501 (2010).
[Crossref] [PubMed]

Sotomayor Torres, C. M.

M. Oudich, S. El-Jallal, Y. Pennec, B. Djafari-Rouhani, J. Gomis-Bresco, D. Navarro-Urrios, C. M. Sotomayor Torres, A. Martínez, and A. Makhoute, “Optomechanic interaction in a corrugated phoxonic nanobeam cavity,” Phys. Rev. B 89(24), 245122 (2014).
[Crossref]

Stannigel, K.

K. Stannigel, P. Rabl, A. S. Sørensen, P. Zoller, and M. D. Lukin, “Optomechanical transducers for long-distance quantum communication,” Phys. Rev. Lett. 105(22), 220501 (2010).
[Crossref] [PubMed]

Stefanou, N.

E. Almpanis, N. Papanikolaou, G. Gantzounis, and N. Stefanou, “Tuning the spontaneous light emission in phoxonic cavities,” J. Opt. Soc. Am. B 29(9), 2567–2574 (2012).
[Crossref]

N. Papanikolaou, I. E. Psarobas, N. Stefanou, B. Djafari-Rouhani, B. Bonello, and V. Laude, “Light modulation in phoxonic nanocavities,” Microelectron. Eng. 90, 155–158 (2012).
[Crossref]

I. E. Psarobas, N. Papanikolaou, N. Stefanou, B. Djafari-Rouhani, B. Bonello, and V. Laude, “Enhanced acousto-optic interactions in a one-dimensional phoxonic cavity,” Phys. Rev. B 82(17), 174303 (2010).
[Crossref]

Stöferle, T.

Su, M.

D. Goettler, M. Su, Z. Leseman, Y. Soliman, R. Olsson, and I. El-Kady, “Realizing the frequency quality factor product limit in silicon via compact phononic crystal resonators,” J. Appl. Phys. 108(8), 084505 (2010).
[Crossref]

Su, S. Y.

Su, X. X.

T. X. Ma, Y. S. Wang, C. Zhang, and X. X. Su, “Theoretical research on a two-dimensional phoxonic crystal liquid sensor by utilizing surface optical and acoustic waves,” Sens. Actuators A Phys. 242, 123–131 (2016).
[Crossref]

T. X. Ma, Y. S. Wang, Y. F. Wang, and X. X. Su, “Three-dimensional dielectric phoxonic crystals with network topology,” Opt. Express 21(3), 2727–2732 (2013).
[Crossref] [PubMed]

Sun, X.

Tang, H. X.

Tang, L.

Thomas, E. L.

M. Maldovan and E. L. Thomas, “Simultaneous localization of photons and phonons in two-dimensional periodic structures,” Appl. Phys. Lett. 88(25), 251907 (2006).
[Crossref]

Thon, S. M.

D. A. Fuhrmann, S. M. Thon, H. Kim, D. Bouwmeester, P. M. Petroff, A. Wixforth, and H. J. Krenner, “Dynamic modulation of photonic crystal nanocavities using gigahertz acoustic phonons,” Nat. Photonics 5(10), 605–609 (2011).
[Crossref]

Tian, L.

C. Dong, V. Fiore, M. C. Kuzyk, L. Tian, and H. Wang, “Optical wavelength conversion via optomechanical coupling in a silica resonator,” Ann. Phys. 527(1-2), 100–106 (2015).
[Crossref]

Tigrine, R.

S. Amoudache, R. Moiseyenko, Y. Pennec, B. Djafari Rouhani, A. Khater, R. Lucklum, and R. Tigrine, “Optical and acoustic sensing using Fano-like resonances in dual phononic and photonic crystal plate,” J. Appl. Phys. 119(11), 114502 (2016).
[Crossref]

S. Amoudache, Y. Pennec, B. Djafari Rouhani, A. Khater, R. Lucklum, and R. Tigrine, “Simultaneous sensing of light and sound velocities of fluids in a two-dimensional phoXonic crystal with defects,” J. Appl. Phys. 115(13), 134503 (2014).
[Crossref]

Torres, C. M.

J. Gomis-Bresco, D. Navarro-Urrios, M. Oudich, S. El-Jallal, A. Griol, D. Puerto, E. Chavez, Y. Pennec, B. Djafari-Rouhani, F. Alzina, A. Martínez, and C. M. Torres, “A one-dimensional optomechanical crystal with a complete phononic band gap,” Nat. Commun. 5, 4452 (2014).
[Crossref] [PubMed]

Tsai, T. C.

T. T. Wu, Z. G. Huang, T. C. Tsai, and T. C. Wu, “Evidence of complete band gap and resonances in a plate with periodic stubbed surface,” Appl. Phys. Lett. 93(11), 111902 (2008).
[Crossref]

Tsai, W. C.

T. W. Lu, W. C. Tsai, T. Y. Wu, and P. T. Lee, “Laser emissions from one-dimensional photonic crystal rings on silicon-dioxide,” Appl. Phys. Lett. 102(5), 051103 (2013).
[Crossref]

Vahala, K. J.

I. S. Grudinin, H. Lee, O. Painter, and K. J. Vahala, “Phonon laser action in a tunable two-level system,” Phys. Rev. Lett. 104(8), 083901 (2010).
[Crossref] [PubMed]

M. Eichenfield, J. Chan, A. H. Safavi-Naeini, K. J. Vahala, and O. Painter, “Modeling dispersive coupling and losses of localized optical and mechanical modes in optomechanical crystals,” Opt. Express 17(22), 20078–20098 (2009).
[Crossref] [PubMed]

M. Eichenfield, J. Chan, R. M. Camacho, K. J. Vahala, and O. Painter, “Optomechanical crystals,” Nature 462(7269), 78–82 (2009).
[Crossref] [PubMed]

Vasseur, J.

D. Bria, M. B. Assouar, M. Oudich, Y. Pennec, J. Vasseur, and B. Djafari-Rouhani, “Opening of simultaneous photonic and phononic band gap in two-dimensional square lattice periodic structure,” J. Appl. Phys. 109(1), 014507 (2011).
[Crossref]

Vasseur, J. O.

Y. Pennec, B. Djafari Rouhani, E. H. El Boudouti, C. Li, Y. El Hassouani, J. O. Vasseur, N. Papanikolaou, S. Benchabane, V. Laude, and A. Martínez, “Simultaneous existence of phononic and photonic band gaps in periodic crystal slabs,” Opt. Express 18(13), 14301–14310 (2010).
[Crossref] [PubMed]

Y. Pennec, B. Djafari-Rouhani, H. Larabi, J. O. Vasseur, and A. C. Hladky-Hennion, “Low-frequency gaps in a phononic crystal constituted of cylindrical dots deposited on a thin homogeneous plate,” Phys. Rev. B 78(10), 104105 (2008).
[Crossref]

J. O. Vasseur, P. A. Deymier, B. Djafari-Rouhani, Y. Pennec, and A. C. Hladky-Hennion, “Absolute forbidden bands and waveguiding in two-dimensional phononic crystal plates,” Phys. Rev. B 77(8), 085415 (2008).
[Crossref]

Vinegoni, C.

D. Razansky, M. Distel, C. Vinegoni, R. Ma, N. Perrimon, R. W. Köster, and V. Ntziachristos, “Multispectral opto-acoustic tomography of deep-seated fluorescent proteins in vivo,” Nat. Photonics 3(7), 412–417 (2009).
[Crossref]

Wang, H.

C. Dong, V. Fiore, M. C. Kuzyk, L. Tian, and H. Wang, “Optical wavelength conversion via optomechanical coupling in a silica resonator,” Ann. Phys. 527(1-2), 100–106 (2015).
[Crossref]

Wang, T.

Wang, Y. D.

Y. D. Wang and A. A. Clerk, “Using dark modes for high-fidelity optomechanical quantum state transfer,” New J. Phys. 14(10), 105010 (2012).
[Crossref]

Wang, Y. F.

Wang, Y. S.

T. X. Ma, Y. S. Wang, C. Zhang, and X. X. Su, “Theoretical research on a two-dimensional phoxonic crystal liquid sensor by utilizing surface optical and acoustic waves,” Sens. Actuators A Phys. 242, 123–131 (2016).
[Crossref]

T. X. Ma, Y. S. Wang, and C. Zhang, “Investigation of dual photonic and phononic bandgaps in two- dimensional phoxonic crystals with veins,” Opt. Commun. 312, 68–72 (2014).
[Crossref]

T. X. Ma, Y. S. Wang, Y. F. Wang, and X. X. Su, “Three-dimensional dielectric phoxonic crystals with network topology,” Opt. Express 21(3), 2727–2732 (2013).
[Crossref] [PubMed]

Wang, Z.

Weisberg, O.

S. G. Johnson, M. Ibanescu, M. A. Skorobogatiy, O. Weisberg, J. D. Joannopoulos, and Y. Fink, “Perturbation theory for Maxwell’s equations with shifting material boundaries,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 65(6), 066611 (2002).
[Crossref] [PubMed]

Williams, B. S.

B. S. Williams, H. Callebaut, S. Kumar, Q. Hu, and J. L. Reno, “3.4-THz quantum cascade laser based on longitudinal-optical-phonon scattering for depopulation,” Appl. Phys. Lett. 82(7), 1015–1017 (2003).
[Crossref]

Wixforth, A.

D. A. Fuhrmann, S. M. Thon, H. Kim, D. Bouwmeester, P. M. Petroff, A. Wixforth, and H. J. Krenner, “Dynamic modulation of photonic crystal nanocavities using gigahertz acoustic phonons,” Nat. Photonics 5(10), 605–609 (2011).
[Crossref]

Wong, C. W.

Wu, T. C.

T. T. Wu, Z. G. Huang, T. C. Tsai, and T. C. Wu, “Evidence of complete band gap and resonances in a plate with periodic stubbed surface,” Appl. Phys. Lett. 93(11), 111902 (2008).
[Crossref]

Wu, T. T.

T. T. Wu, Z. G. Huang, T. C. Tsai, and T. C. Wu, “Evidence of complete band gap and resonances in a plate with periodic stubbed surface,” Appl. Phys. Lett. 93(11), 111902 (2008).
[Crossref]

J. C. Hsu and T. T. Wu, “Efficient formulation for band-structure calculations of two-dimensional phononic- crystal plates,” Phys. Rev. B 74(14), 144303 (2006).
[Crossref]

Wu, T. Y.

T. W. Lu, W. C. Tsai, T. Y. Wu, and P. T. Lee, “Laser emissions from one-dimensional photonic crystal rings on silicon-dioxide,” Appl. Phys. Lett. 102(5), 051103 (2013).
[Crossref]

Yoshie, T.

Yu, T.

Zhang, C.

T. X. Ma, Y. S. Wang, C. Zhang, and X. X. Su, “Theoretical research on a two-dimensional phoxonic crystal liquid sensor by utilizing surface optical and acoustic waves,” Sens. Actuators A Phys. 242, 123–131 (2016).
[Crossref]

T. X. Ma, Y. S. Wang, and C. Zhang, “Investigation of dual photonic and phononic bandgaps in two- dimensional phoxonic crystals with veins,” Opt. Commun. 312, 68–72 (2014).
[Crossref]

Zheng, J.

Zhu, Z.

Z. Zhu, D. J. Gauthier, and R. W. Boyd, “Stored light in an optical fiber via stimulated Brillouin scattering,” Science 318(5857), 1748–1750 (2007).
[Crossref] [PubMed]

Zoller, P.

K. Stannigel, P. Rabl, A. S. Sørensen, P. Zoller, and M. D. Lukin, “Optomechanical transducers for long-distance quantum communication,” Phys. Rev. Lett. 105(22), 220501 (2010).
[Crossref] [PubMed]

Zozoulenko, I. V.

Zubtsov, M.

R. Lucklum, M. Zubtsov, and A. Oseev, “Phoxonic crystals--a new platform for chemical and biochemical sensors,” Anal. Bioanal. Chem. 405(20), 6497–6509 (2013).
[Crossref] [PubMed]

AIP Adv. (1)

Y. Pennec, B. Djafari Rouhani, C. Li, J. M. Escalante, A. Martínez, S. Benchabane, V. Laude, and N. Papanikolaou, “Band gaps and cavity modes in dual phononic and photonic strip waveguides,” AIP Adv. 1(4), 041901 (2011).
[Crossref]

Anal. Bioanal. Chem. (1)

R. Lucklum, M. Zubtsov, and A. Oseev, “Phoxonic crystals--a new platform for chemical and biochemical sensors,” Anal. Bioanal. Chem. 405(20), 6497–6509 (2013).
[Crossref] [PubMed]

Ann. Phys. (1)

C. Dong, V. Fiore, M. C. Kuzyk, L. Tian, and H. Wang, “Optical wavelength conversion via optomechanical coupling in a silica resonator,” Ann. Phys. 527(1-2), 100–106 (2015).
[Crossref]

Appl. Phys. Lett. (8)

T. T. Wu, Z. G. Huang, T. C. Tsai, and T. C. Wu, “Evidence of complete band gap and resonances in a plate with periodic stubbed surface,” Appl. Phys. Lett. 93(11), 111902 (2008).
[Crossref]

F. L. Hsiao, C. Y. Hsieh, H. Y. Hsieh, and C. C. Chiu, “High-efficiency acousto-optical interaction in phoxonic nanobeam waveguide,” Appl. Phys. Lett. 100(17), 171103 (2012).
[Crossref]

Q. Rolland, M. Oudich, S. El-Jallal, S. Dupont, Y. Pennec, J. Gazalet, J. C. Kastelik, G. Lévêque, and B. Djafari-Rouhani, “Acousto-optic couplings in two-dimensional phoxonic crystal cavities,” Appl. Phys. Lett. 101(6), 061109 (2012).
[Crossref]

B. S. Williams, H. Callebaut, S. Kumar, Q. Hu, and J. L. Reno, “3.4-THz quantum cascade laser based on longitudinal-optical-phonon scattering for depopulation,” Appl. Phys. Lett. 82(7), 1015–1017 (2003).
[Crossref]

J. Manzanares-Martinez, D. Moctezuma-Enriquez, Y. J. Rodriguez-Viveros, B. Manzanares-Martinez, and P. Castro-Garay, “Non-perpendicular hypersonic and optical stop-bands in porous silicon multilayers,” Appl. Phys. Lett. 101(26), 261902 (2012).
[Crossref]

M. Maldovan and E. L. Thomas, “Simultaneous localization of photons and phonons in two-dimensional periodic structures,” Appl. Phys. Lett. 88(25), 251907 (2006).
[Crossref]

P. B. Deotare, M. W. McCutcheon, I. W. Frank, M. Khan, and M. Lončar, “High quality factor photonic crystal nanobeam cavities,” Appl. Phys. Lett. 94(12), 121106 (2009).
[Crossref]

T. W. Lu, W. C. Tsai, T. Y. Wu, and P. T. Lee, “Laser emissions from one-dimensional photonic crystal rings on silicon-dioxide,” Appl. Phys. Lett. 102(5), 051103 (2013).
[Crossref]

J. Appl. Phys. (6)

D. Goettler, M. Su, Z. Leseman, Y. Soliman, R. Olsson, and I. El-Kady, “Realizing the frequency quality factor product limit in silicon via compact phononic crystal resonators,” J. Appl. Phys. 108(8), 084505 (2010).
[Crossref]

D. Bria, M. B. Assouar, M. Oudich, Y. Pennec, J. Vasseur, and B. Djafari-Rouhani, “Opening of simultaneous photonic and phononic band gap in two-dimensional square lattice periodic structure,” J. Appl. Phys. 109(1), 014507 (2011).
[Crossref]

T. R. Lin, C. H. Lin, and J. C. Hsu, “Enhanced acousto-optic interaction in two-dimensional phoxonic crystals with a line defect,” J. Appl. Phys. 113(5), 053508 (2013).
[Crossref]

S. Sadat-Saleh, S. Benchabane, F. I. Baida, M. P. Bernal, and V. Laude, “Tailoring simultaneous photonic and phononic band gaps,” J. Appl. Phys. 106(7), 074912 (2009).
[Crossref]

S. Amoudache, Y. Pennec, B. Djafari Rouhani, A. Khater, R. Lucklum, and R. Tigrine, “Simultaneous sensing of light and sound velocities of fluids in a two-dimensional phoXonic crystal with defects,” J. Appl. Phys. 115(13), 134503 (2014).
[Crossref]

S. Amoudache, R. Moiseyenko, Y. Pennec, B. Djafari Rouhani, A. Khater, R. Lucklum, and R. Tigrine, “Optical and acoustic sensing using Fano-like resonances in dual phononic and photonic crystal plate,” J. Appl. Phys. 119(11), 114502 (2016).
[Crossref]

J. Opt. Soc. Am. B (2)

J. Phys. Condens. Matter (1)

S. El-Jallal, M. Oudich, Y. Pennec, B. Djafari-Rouhani, A. Makhoute, Q. Rolland, S. Dupont, and J. Gazalet, “Optomechanical interactions in two-dimensional Si and GaAs phoXonic cavities,” J. Phys. Condens. Matter 26(1), 015005 (2014).
[Crossref] [PubMed]

Microelectron. Eng. (1)

N. Papanikolaou, I. E. Psarobas, N. Stefanou, B. Djafari-Rouhani, B. Bonello, and V. Laude, “Light modulation in phoxonic nanocavities,” Microelectron. Eng. 90, 155–158 (2012).
[Crossref]

Nanophotonics (1)

Y. Pennec, V. Laude, N. Papanikolaou, B. Djafari-Rouhani, M. Oudich, S. El-Jallal, J. C. Beugnot, J. M. Escalante, and A. Martínez, “Modeling light-sound interaction in nanoscale cavities and waveguides,” Nanophotonics 3(6), 413–440 (2014).
[Crossref]

Nat. Commun. (2)

J. Gomis-Bresco, D. Navarro-Urrios, M. Oudich, S. El-Jallal, A. Griol, D. Puerto, E. Chavez, Y. Pennec, B. Djafari-Rouhani, F. Alzina, A. Martínez, and C. M. Torres, “A one-dimensional optomechanical crystal with a complete phononic band gap,” Nat. Commun. 5, 4452 (2014).
[Crossref] [PubMed]

J. T. Hill, A. H. Safavi-Naeini, J. Chan, and O. Painter, “Coherent optical wavelength conversion via cavity optomechanics,” Nat. Commun. 3, 1196 (2012).
[Crossref] [PubMed]

Nat. Photonics (2)

D. A. Fuhrmann, S. M. Thon, H. Kim, D. Bouwmeester, P. M. Petroff, A. Wixforth, and H. J. Krenner, “Dynamic modulation of photonic crystal nanocavities using gigahertz acoustic phonons,” Nat. Photonics 5(10), 605–609 (2011).
[Crossref]

D. Razansky, M. Distel, C. Vinegoni, R. Ma, N. Perrimon, R. W. Köster, and V. Ntziachristos, “Multispectral opto-acoustic tomography of deep-seated fluorescent proteins in vivo,” Nat. Photonics 3(7), 412–417 (2009).
[Crossref]

Nat. Phys. (1)

R. W. Andrews, R. W. Peterson, T. P. Purdy, K. Cicak, R. W. Simmonds, C. A. Regal, and K. W. Lehnert, “Bidirectional and efficient conversion between microwave and optical light,” Nat. Phys. 10(4), 321–326 (2014).
[Crossref]

Nature (3)

M. Eichenfield, J. Chan, R. M. Camacho, K. J. Vahala, and O. Painter, “Optomechanical crystals,” Nature 462(7269), 78–82 (2009).
[Crossref] [PubMed]

K. Ishizaki and S. Noda, “Manipulation of photons at the surface of three-dimensional photonic crystals,” Nature 460(7253), 367–370 (2009).
[Crossref] [PubMed]

J. Chan, T. P. Alegre, A. H. Safavi-Naeini, J. T. Hill, A. Krause, S. Gröblacher, M. Aspelmeyer, and O. Painter, “Laser cooling of a nanomechanical oscillator into its quantum ground state,” Nature 478(7367), 89–92 (2011).
[Crossref] [PubMed]

New J. Phys. (1)

Y. D. Wang and A. A. Clerk, “Using dark modes for high-fidelity optomechanical quantum state transfer,” New J. Phys. 14(10), 105010 (2012).
[Crossref]

Opt. Commun. (1)

T. X. Ma, Y. S. Wang, and C. Zhang, “Investigation of dual photonic and phononic bandgaps in two- dimensional phoxonic crystals with veins,” Opt. Commun. 312, 68–72 (2014).
[Crossref]

Opt. Express (10)

T. X. Ma, Y. S. Wang, Y. F. Wang, and X. X. Su, “Three-dimensional dielectric phoxonic crystals with network topology,” Opt. Express 21(3), 2727–2732 (2013).
[Crossref] [PubMed]

Q. Rolland, S. Dupont, J. Gazalet, J. C. Kastelik, Y. Pennec, B. Djafari-Rouhani, and V. Laude, “Simultaneous bandgaps in LiNbO3 phoxonic crystal slab,” Opt. Express 22(13), 16288–16297 (2014).
[Crossref] [PubMed]

S. Mohammadi, A. A. Eftekhar, A. Khelif, and A. Adibi, “Simultaneous two-dimensional phononic and photonic band gaps in opto-mechanical crystal slabs,” Opt. Express 18(9), 9164–9172 (2010).
[Crossref] [PubMed]

A. H. Safavi-Naeini and O. Painter, “Design of optomechanical cavities and waveguides on a simultaneous bandgap phononic-photonic crystal slab,” Opt. Express 18(14), 14926–14943 (2010).
[Crossref] [PubMed]

J. Zheng, X. Sun, Y. Li, M. Poot, A. Dadgar, N. N. Shi, W. H. P. Pernice, H. X. Tang, and C. W. Wong, “Femtogram dispersive L3-nanobeam optomechanical cavities: design and experimental comparison,” Opt. Express 20(24), 26486–26498 (2012).
[Crossref] [PubMed]

L. Kipfstuhl, F. Guldner, J. Riedrich-Möller, and C. Becher, “Modeling of optomechanical coupling in a phoxonic crystal cavity in diamond,” Opt. Express 22(10), 12410–12423 (2014).
[Crossref] [PubMed]

P. Seidler, K. Lister, U. Drechsler, J. Hofrichter, and T. Stöferle, “Slotted photonic crystal nanobeam cavity with an ultrahigh quality factor-to-mode volume ratio,” Opt. Express 21(26), 32468–32483 (2013).
[Crossref] [PubMed]

M. Eichenfield, J. Chan, A. H. Safavi-Naeini, K. J. Vahala, and O. Painter, “Modeling dispersive coupling and losses of localized optical and mechanical modes in optomechanical crystals,” Opt. Express 17(22), 20078–20098 (2009).
[Crossref] [PubMed]

T. Yu, Z. Wang, W. Liu, T. Wang, N. Liu, and Q. Liao, “Simultaneous large band gaps and localization of electromagnetic and elastic waves in defect-free quasicrystals,” Opt. Express 24(8), 7951–7959 (2016).
[Crossref] [PubMed]

Y. Pennec, B. Djafari Rouhani, E. H. El Boudouti, C. Li, Y. El Hassouani, J. O. Vasseur, N. Papanikolaou, S. Benchabane, V. Laude, and A. Martínez, “Simultaneous existence of phononic and photonic band gaps in periodic crystal slabs,” Opt. Express 18(13), 14301–14310 (2010).
[Crossref] [PubMed]

Opt. Lett. (4)

Phys. Rev. B (8)

J. C. Hsu and T. T. Wu, “Efficient formulation for band-structure calculations of two-dimensional phononic- crystal plates,” Phys. Rev. B 74(14), 144303 (2006).
[Crossref]

Y. El Hassouani, C. Li, Y. Pennec, E. H. El Boudouti, H. Larabi, A. Akjouj, O. Bou Matar, V. Laude, N. Papanikolaou, A. Martínez, and B. Djafari Rouhani, “Dual phononic and photonic band gaps in a periodic array of pillars deposited on a thin plate,” Phys. Rev. B 82(15), 155405 (2010).
[Crossref]

J. O. Vasseur, P. A. Deymier, B. Djafari-Rouhani, Y. Pennec, and A. C. Hladky-Hennion, “Absolute forbidden bands and waveguiding in two-dimensional phononic crystal plates,” Phys. Rev. B 77(8), 085415 (2008).
[Crossref]

Y. Pennec, B. Djafari-Rouhani, H. Larabi, J. O. Vasseur, and A. C. Hladky-Hennion, “Low-frequency gaps in a phononic crystal constituted of cylindrical dots deposited on a thin homogeneous plate,” Phys. Rev. B 78(10), 104105 (2008).
[Crossref]

I. E. Psarobas, N. Papanikolaou, N. Stefanou, B. Djafari-Rouhani, B. Bonello, and V. Laude, “Enhanced acousto-optic interactions in a one-dimensional phoxonic cavity,” Phys. Rev. B 82(17), 174303 (2010).
[Crossref]

S. El-Jallal, M. Oudich, Y. Pennec, B. Djafari-Rouhani, V. Laude, J. C. Beugnot, A. Martínez, J. M. Escalante, and A. Makhoute, “Analysis of optomechanical coupling in two-dimensional square lattice phoxonic crystal slab cavities,” Phys. Rev. B 88(20), 205410 (2013).
[Crossref]

M. Oudich, S. El-Jallal, Y. Pennec, B. Djafari-Rouhani, J. Gomis-Bresco, D. Navarro-Urrios, C. M. Sotomayor Torres, A. Martínez, and A. Makhoute, “Optomechanic interaction in a corrugated phoxonic nanobeam cavity,” Phys. Rev. B 89(24), 245122 (2014).
[Crossref]

P. Rabl, P. Cappellaro, M. V. Gurudev Dutt, L. Jiang, J. R. Maze, and M. D. Lukin, “Strong magnetic coupling between an electronic spin qubit and a mechanical resonator,” Phys. Rev. B 79(4), 041302 (2009).
[Crossref]

Phys. Rev. E Stat. Nonlin. Soft Matter Phys. (2)

S. G. Johnson, M. Ibanescu, M. A. Skorobogatiy, O. Weisberg, J. D. Joannopoulos, and Y. Fink, “Perturbation theory for Maxwell’s equations with shifting material boundaries,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 65(6), 066611 (2002).
[Crossref] [PubMed]

A. Khelif, B. Aoubiza, S. Mohammadi, A. Adibi, and V. Laude, “Complete band gaps in two-dimensional phononic crystal slabs,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 74(4), 046610 (2006).
[Crossref] [PubMed]

Phys. Rev. Lett. (2)

K. Stannigel, P. Rabl, A. S. Sørensen, P. Zoller, and M. D. Lukin, “Optomechanical transducers for long-distance quantum communication,” Phys. Rev. Lett. 105(22), 220501 (2010).
[Crossref] [PubMed]

I. S. Grudinin, H. Lee, O. Painter, and K. J. Vahala, “Phonon laser action in a tunable two-level system,” Phys. Rev. Lett. 104(8), 083901 (2010).
[Crossref] [PubMed]

Science (1)

Z. Zhu, D. J. Gauthier, and R. W. Boyd, “Stored light in an optical fiber via stimulated Brillouin scattering,” Science 318(5857), 1748–1750 (2007).
[Crossref] [PubMed]

Sens. Actuators A Phys. (1)

T. X. Ma, Y. S. Wang, C. Zhang, and X. X. Su, “Theoretical research on a two-dimensional phoxonic crystal liquid sensor by utilizing surface optical and acoustic waves,” Sens. Actuators A Phys. 242, 123–131 (2016).
[Crossref]

Ultrasonics (1)

C. Charles, B. Bonello, and F. Ganot, “Propagation of guided elastic waves in 2D phononic crystals,” Ultrasonics 44(Suppl 1), e1209–e1213 (2006).
[Crossref] [PubMed]

Other (1)

COMSOL Multiphysics 3.5 (2009).

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Figures (9)

Fig. 1
Fig. 1 Schematic of (a) 1D phoxonic crystal nanobeam cavity, (b) unit cell, (c) even symmetric cavity, and (d) odd symmetric cavity.
Fig. 2
Fig. 2 Simulation results for even symmetric cavity (blue) and a reference with no defective region (red): (a) optical transmission spectra, (b) acoustic transmission spectra, and (c) X-direction component of normalized electric field of optical resonance mode (OR1).
Fig. 3
Fig. 3 Simulation results for odd symmetric cavity (blue) and a reference with no defective region (red): (a) optical and transmission spectra, (b) acoustic transmission spectra, and (c) X-direction component of normalized electric field of optical resonance mode (OR2).
Fig. 4
Fig. 4 Simulation results for odd symmetric cavity (blue) and a reference with no defective region (red): (a) Optical photonic band structures of mirror. Blue dotted lines mark the frequencies of OR1 and OR2. Phononic band structure of mirror with corresponding acoustic resonance peaks (marked by black dotted lines) in (b) even symmetric structure and (c) odd symmetric structure.
Fig. 5
Fig. 5 AO coupling rates in even symmetric cavity between optical resonance mode OR1 mode and all acoustic resonance modes from 6.10 to 7.16 GHz.
Fig. 6
Fig. 6 Displacement fields of acoustic resonance modes ϕ1, κ, α, β, δ, γ, ϕ2, and η: black dashed lines mark the defect centers, and Γ and Φ indicate the reference planes of symmetry.
Fig. 7
Fig. 7 AO coupling rates in the odd symmetric cavity between optical resonance mode OR2 mode and all acoustic resonance modes from 6.10 to 7.16 GHz.
Fig. 8
Fig. 8 Displacement fields of acoustic resonance modes A, F, B, C, D, G, and E. Black dashed lines indicate defect centers. Γ and Φ indicate reference planes of symmetry.
Fig. 9
Fig. 9 Θacoustic, Θoptical, and g density plots on the odd symmetrical cavity surface, with individual unit cell contributions to the total g density, for acoustic resonance modes (a) A, (b) B, (c) E, (d) G, (e) C, and (f) F.

Tables (4)

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Table 1 Total AO coupling rates (in MHz) between optical resonance mode OR1 and phononic resonance modes in even symmetric cavity when both PE and MB effects are considered.

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Table 2 Total AO coupling rates (in MHz) between optical resonance mode OR2 and acoustic resonance modes in odd symmetric cavity when both PE and MB effects are considered.

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Table 3 AO interactions and Qacoustic for five phononic modes (α, β, γ, δ, and η) in even symmetric cavity phoxonic crystal nanobeams with different cavity designs.

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Table 4 AO interactions and Qacoustic for six phononic modes in odd symmetric cavity phoxonic crystal nanobeams with different cavity designs.

Equations (6)

Equations on this page are rendered with MathJax. Learn more.

g PE = ω 0 2 E| ε α |E EDdV 2 m eff Ω m
g MB = ω 0 2 ( Q n ^ )( Δε E || 2 Δ ε 1 D 2 ) dS EDdV 2 m eff Ω m
g= g MB + g PE
gdensity= 1 4 ( Q n ^ )[ Δε | E || | 2 Δ( ε 1 ) ( D ) 2 ]
Θ acoustic =Q n ^
Θ optical =Δε | E || | 2 Δ( ε 1 ) | D | 2

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