Mode conversion based on forward stimulated Brillouin scattering in a hybrid phononic-photonic waveguide

Guodong Chen; Ruiwen Zhang; Junqiang Sun; Heng Xie; Ya Gao; Danqi Feng; Huang Xiong

doi:10.1364/OE.22.032060

1. Introduction

Mode-division multiplexing (MDM) is a promising space-division multiplexing technique in which multiple optical modes are used as independent data channels to transmit optical data [1]. Although most of the efforts in MDM systems are focused on optical fiber communication systems, realizing integrated multimode systems is also a highly valued field [2]. Several basic building blocks for MDM in integrated optics, such as the mode add/drop multiplexer [3] and the mode generator [4], have been proposed. Mode converter is another important building block for MDM systems. The major ways to realize mode conversion are based on phase plates [4–6], fiber grating [7] and on-chip optical devices [8–10]. Compared to the other mode converters, silicon-based on-chip optical mode converters offer solid stability and broad bandwidth, and can be conveniently integrated. In on-chip optical devices, adiabatic coupling [9] and resonant coupling [10] are the primary tools for mode conversion. The mode converter based on adiabatic coupling is influenced by the input optical wavelength, which limits the device bandwidth. By designing the coupling region of a resonant mode converter with half of the beat length, one can convert light from one mode to the other [10]. Despite the fact that resonant mode converter can be made very short, the exact beat length is a very rigour challenge due to the device parameter variations arising from fabrication. Recently, based on interaction between acoustic wave and optical wave, the optical mode conversion has been reported in order to relax the fabrication tolerance by external acoustic wave injection [11]. As a special acousto-optical effect, the forward stimulated Brillouin scattering (FSBS) can be utilized in the mode conversion [12, 13]. In schemes of FSBS, due to the lack of consideration of the acoustic properties in optical waveguides, two extra pumps for producing a continual acoustic field for mode conversion are required. This makes the structure complicated and increases the cost of production. In addition, recent work has demonstrated that the electrostrictive force and radiation pressure can enhance the FSBS gain by 1,000 times in the nanoscale waveguide systems [14–17], which will be very useful for mode conversion on-chip.

In this paper, we propose an approach for on-chip all optical mode conversion employing the FSBS in a hybrid phononic-photonic waveguide, and present a theoretical model to analyze the property of mode converter under considering the electrostriction force and the radiation pressure. The hybrid waveguide is designed to guide both optical and acoustic waves, and to independently control the photonic and phononic waveguide dispersions to satisfy the phase-matched condition. Through the numerical simulation, we exhibit that the mode conversion efficiency can reach upto 88% under considering the optical and acoustic absorption losses by adjusting the input optical power. And we also show that the conversion bandwidth can be dramatically extended over 12.5 THz, which covers the 1550 nm band of the optical communication systems.

2. Principle and theory

Figure 1(a) shows our designed hybrid photonic-phononic waveguide for performing mode conversion based on the FSBS. This hybrid waveguide is suspended in air over the silica substrate. In the hybrid waveguide, the z-direction rectangular silicon (Si) waveguide is embedded in silicon nitride (Si₃N₄) slab perforated by a honeycomb lattice of circular holes, and designed for guiding the fundamental TE-like mode $E_{11}^{x}$ and the higher-order TE-like mode $E_{21}^{x}$ . The Si waveguide also serves as a linear defect in the Si₃N₄ honeycomb phononic crystal to form a phononic crystal waveguide (PCW), which will confine the acoustic wave in the hybrid waveguide. A honeycomb-lattice of circular in the Si₃N₄ slab gives rise to phononic bandgaps for guided modes by properly choosing the configuration parameters [18]. It is expected that the absence of radiative modes in the gap region will inhibit the strong acoustic propagation loss in the hybrid waveguide.

Fig. 1 (a) Schematic diagram of the mode conversion based on the FSBS. (b) Energy conservation diagram of FSBS process. (c) Phase matching diagram during the FSBS.

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The operation principle for realizing mode conversion via the FSBS process is described as follows. The $E_{11}^{x}$ mode pump light with frequency at $ω_{1}$ is injected into the Si waveguide and generates a spatially dependent optical force distribution which is the tendency of materials to become denser in regions of high optical intensity. The density variation induced by optical force drives the excitation of Brillouin active phonons with frequency at $Ω$ [15, 19]. The interaction between the pump light and acoustic wave produces a $E_{21}^{x}$ mode Stokes light with frequency at $ω_{2}$ , and thus the mode conversion occurs between the generated Stokes wave and launched pump light [11, 13]. Moreover, the optical forces that dominate the FSBS process include the well-known electrostriction force [17, 20], and the radiation pressure whose contribution is only recently recognized [16, 17]. It has proved that the electrostrictive force and radiation pressure enhance the FSBS gain by 1,000 times in the nanoscale waveguide systems [14, 21] and leads to the enhancement of FSBS-based mode conversion.

In the mode conversion, energy and momentum conservations require that $Ω = ω_{1} - ω_{2}$ and $q (Ω) = β_{1} (ω_{1}) - β_{2} (ω_{2})$ , respectively. Here $β (ω)$ and $q (Ω)$ are the optical and acoustic dispersion relationships, respectively. The strong photon-phonon coupling is mediated by a set of phonons, whose dispersion relationships satisfy the phase-matched condition $Δ β = β_{1} (ω_{1}) - β_{2} (ω_{1} - Ω) = q (Ω)$ . Vector representation of this phase-matched condition is shown in Fig. 1(c).

There are two optical modes involved in the FSBS process, the each electric field $E_{m}$ can be expressed as

E_{m} (z, t) = \frac{1}{2} e_{m} (x, y) A_{m} (z, t) e^{i (β_{m} z - w_{m} t)} + c . c

for m = 1, 2. Here

e_{m} (x, y)

represents the electric field of the

m^{t h}

mode with frequency

ω_{m}

and propagation constant

β_{m}

,

A_{m} (z, t)

is an envelope function, which is assumed to be slowly varying in the z-direction. For the following analysis, we normalize each optical mode such that

{\iint_{S} | e_{k} (x, y) |}^{2} d x d y = 1

, where the integral extends over the waveguide cross-section S.

During the FSBS process, the phonons are produced by optical forces which are originated from the electrostriction force and the radiation pressure. The electrostriction force is derived from the electrostriction tensor with an instantaneous electrostriction tensor given by [15]

σ_{i j} = - \frac{1}{2} ε_{0} n^{4} p_{i j k l} E_{k} E_{l}

where

n

is the material refractive index, and

p_{i j k l}

is the photoelastic tensor [22]. The radiation pressure contribution to the optical forces is derived from Maxwell stress tensor (MST). Since the magnetic fields are continuous at the boundary, it can be assumed that only the electric part of MST contributes to radiation pressure which is written to be [15, 23–25]

T_{i j}^{r p} = ε_{0} ε (x, y) [E_{i} E_{j} - \frac{1}{2} δ_{i j} E^{2}]

where

ε_{0}

is the electric permittivity of free space,

ε (x, y)

is the relative electric permittivity. Considering

E_{y} = 0

for TE-like modes and the common impact from the electrostriction force and the radiation pressure, the total optical pressures

p r_{i j} = σ_{i j}^{e s} + T_{i j}^{r p}

can be written as

\begin{array}{l} p r_{x x} = - \frac{1}{4} ε_{0} γ E_{1 x} E_{2 x}^{*} - \frac{1}{4} ε_{0} n^{4} p_{12} E_{1 z} E_{2 z}^{*} + \frac{1}{4} ε_{0} ε (x, y) [E_{1 x} E_{2 x}^{*} - E_{1} E_{2}^{*}] \\ p r_{y y} = - \frac{1}{4} ε_{0} n^{4} p_{12} E_{1 x} E_{2 x}^{*} - \frac{1}{4} ε_{0} n^{4} p_{12} E_{1 z} E_{2 z}^{*} - \frac{1}{4} ε_{0} ε (x, y) E_{1} E_{2}^{*} \\ p r_{z z} = - \frac{1}{4} ε_{0} n^{4} p_{12} E_{1 x} E_{2 x}^{*} - \frac{1}{4} ε_{0} γ E_{1 z} E_{2 z}^{*} + \frac{1}{4} ε_{0} ε (x, y) [E_{1 z} E_{2 z}^{*} - E_{1} E_{2}^{*}] \end{array}

Here, we introduce an optical pressure constant

γ = n^{4} p_{11} - ε (x, y)

. The total optical forces are given by [17, 22]

F_{j} = - \partial_{i} p r_{i j}

The optical forces are simultaneously frequency-matched and phase-matched to an elastic mode, leading to strong elastic-wave excitations in the waveguide, and efficient coupling between pump and Stokes-wave photons. Now, we analyze how the optical forces result in acoustic wave excitation. The material vibrations, represented by the material density variation from equilibrium $ρ$ , obey the acoustic wave equation [19]

\frac{\partial^{2} ρ}{\partial t^{2}} - Γ^{'} \nabla^{2} \frac{\partial ρ}{\partial t} - v^{2} \nabla^{2} ρ = \nabla • F

where

v

is the bulk longitudinal velocity of sound, and the parameter

Γ^{'}

is a damping parameter, which can be used to define the Brillouin linewidth

Γ_{B} = Ω_{}^{2} Γ^{'}

. Here, the acoustic field can be written as

ρ (z, t) = \frac{1}{2 i} C (z, t) U (x, y) \exp [i (q z - Ω t)] + c . c

where

U (x, y)

denotes the mode profile of the material density variation and

C (z, t)

is the longitudinal acoustic amplitude. In a manner analogous to the optical modes, we normalize

U (x, y)

such that

{\iint_{S} | U |}^{2} d x d y = 1

.

Assuming that the acoustic amplitude varies slowly, inserting Eq. (7) into Eq. (6), and applying the overlap integral on both sides, the acoustic field propagation equation of C in steady-state conditions can be gotten as

\frac{\partial C (z, t)}{\partial z} = - \frac{(Ω^{2} - Ω_{a}^{2} + i Ω Γ_{B})}{2 i q v^{2}} C (z, t) - \frac{\iint \nabla • F * U^{*} (x, y) \exp [- i (Ω t - q z)] d x d y}{q v^{2}}

Then we analyze how the acoustic wave affects the amplitude of the optical waves. The spatial evolution of the optical fields is described by the wave equation.

\nabla^{2} E - \frac{1}{c^{2}} ε \frac{\partial^{2} E}{\partial t^{2}} - \frac{α n}{c} \frac{\partial E}{\partial t} = \frac{1}{c^{2} ε_{0}} \frac{\partial^{2} P^{N L}}{\partial t^{2}}

where c is the light velocity of free space,

α

is the optical absorption coefficient and

P^{N L}

is the nonlinear polarization generated by total optical field E = E₁ + E₂ [25]

P^{N L} = ε_{0} ρ_{0}^{- 1} γ ρ E

where

ρ_{0}

denotes the mean density of the medium. Inserting Eq. (1), Eq. (7), and Eq. (10) into Eq. (9), applying the overlap integral on both sides and using the normalization condition yield the following coupled equations for

A_{1}

and

A_{2}

\frac{d A_{1} (z)}{d z} = \frac{γ ω_{1}^{2}}{4 c^{2} β_{1} ρ_{0}} \iint U^{*} (x, y) e_{2} (x, y) e_{1}^{*} (x, y) d x d y A_{2} (z) C (z) - \frac{α n}{2 n_{e f f 1}} A_{1} (z)

\frac{d A_{2} (z)}{d z} = - \frac{γ ω_{2}^{2}}{4 c^{2} β_{2} ρ_{0}} \iint U^{*} (x, y) e_{1} (x, y) e_{2}^{*} (x, y) d x d y A_{1} (z) C (z) - \frac{α n}{2 n_{e f f 2}} A_{2} (z)

where

n_{e f f}_{m}

(m = 1,2) is the effective index of

m^{t h}

optical mode.

The coupled-mode equations Eq. (8) and Eqs. (11)-(12) provide a general method to analyze the mode conversion based on the FSBS with arbitrary waveguide structure. In the following simulation, the optical and acoustic field distributions in the waveguide are obtained by utilizing the finite element package COMSOL. We calculate the optical forces generated by optical waves using Eqs. (2)-(5), which play an important role in the mode conversion. Finally, by solving the coupled-mode equations, the characteristics of the mode conversion based on the FSBS can be numerically simulated.

3. Anatomy of optical forces within rectangular silicon waveguides in the FSBS

To best understand the behavior of the on-chip mode conversion, the optical field distributions and the configuration of optical forces should be correctly drawn. Figure 2(a) describes the waveguide cross-section, and Fig. 2(b) and Fig. 2(c) show the computed $E_{11}^{x}$ and $E_{21}^{x}$ mode profiles corresponding the optical wavelength at 1550 nm. The optical waveguide consists of a nanoscale Si waveguide with width w = 770 nm and height h = 280 nm embedded in a silicon nitride (Si₃N₄) phononic crystal slab with height h = 280 nm. Total internal reflection between Si (n = 3.45) and Si₃N₄ (n = 2.05) tightly confines the optical modes to the Si waveguide core.

Fig. 2 (a) The optical waveguide cross-section. (b, c) The $E_{11}^{x}$ and $E_{21}^{x}$ field profiles. (d, e) The x and y components of the electrostriction force generated by $E_{11}^{x}$ mode, respectively. (f, g) The x and y components of radiation pressure-induced boundary force, respectively, produced by $E_{11}^{x}$ mode. (h, i) The x and y components of the electrostriction force generated by $E_{21}^{x}$ mode, respectively. (j, k) The x and y components of radiation pressure-induced boundary force, respectively, produced by $E_{21}^{x}$ mode.

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Using the Eqs. (2)-(3) and Eq. (5), the normalized electrostriction force distributions $F^{e s}$ and radiation pressure-induced force distributions $F^{r p}$ generated by the $E_{11}^{x}$ mode are sketched in Figs. 3(d)-3(e) and Figs. 3(f)-3(g), respectively. The electrostriction force distribution is not uniform, but is instead more localized within the center of the waveguide. Radiation-pressure-induced optical forces result from the scattering of light at boundaries, producing forces exactly localized to the discontinuous dielectric boundary of the step-index waveguide. It is shown that the electrostrictive force and the radiation pressure add constructively, effectively bringing on a larger total outward optical force on the lateral boundaries of the waveguide (x-direction). In contrast, the electrostrictive force is opposite in sign to the radiation pressure, which will cause the decrease of the total force on the vertical boundary (y-direction). Moreover, the electrostriction force is largely in the x direction, because $E^{x}$ is the dominant component in electric field and photoelastic tensor $| p_{11} |$ is about five times larger than $| p_{12} |$ in Si waveguide [15]. So the optical forces in x-direction are far larger than that in y-direction, which will drive the acoustic field propagation and vibration in x-z plane. Similarly, the optical forces generated by $E_{21}^{x}$ mode can be obtained by using the similar method, the results are shown in Fig. 2 (h)-2(k).

Fig. 3 (a) The x-z plan view of the waveguide. (b) Displacement field pattern of the phononic mode. (c) Phononic band structure for phononic crystal slab (purple dots indicate the phononic dispersion relationship without defect). (d) Phononic dispersion relationship and group velocity for the guided phononic mode.

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4. Acoustic eigenmodes in waveguide

Driving by the optical forces, the acoustic eigenmodes in the hybrid waveguide are excited, which depend on the waveguide structure. During the calculation, we choose the honeycomb PCW with the following parameters, h = 0.4a (slab thickness), r = 0.25a (radius of the holes) and $d = a / \sqrt{3}$ , where a = 700 nm is the lattice period. The x-z plan view of the PCW is shown in Fig. 3(a). The local velocities for longitudinal sound wave are chosen to be $v_{S i} = 8433 m / s$ and $v_{S i_{3} N_{4}} = 10612 m / s$ , with material densities $ρ_{S i} = 2329 k g / m^{3}$ , $ρ_{S i_{3} N_{4}} = 3440 k g / m^{3}$ [26]. To obtain the dispersion characteristics of the phononic crystal waveguide, the finite element package COMSOL together with the appropriate boundary conditions is utilized in our calculation. The dimensions of the super-cell have been properly chosen to avoid the interaction between neighboring waveguides when the defect is introduced.

Figure 3(b) illustrates the displacement field of the guided phononic mode. Figure 3(c) displays the dispersion characteristics of the Brillouin-active phonon mode guided by the PCW. It can be noted that there is a phononic guided mode (red dots) appearing inside the bandgap (blue region), and we find that the frequency of the acoustic guided mode (eigenmode) is close to 6.7 GHz. Interestingly, the dispersion curve of the guided phononic mode is very flat, which is a signature of guided modes with the slow group velocity. The group velocity of the guided phononic mode normalized with respect to longitudinal sound velocity in PCW is plotted (red curve) in Fig. 3(d), which is reduced by at least two orders of magnitude comparing with the velocity in thin silicon rods.

There are two important advantages of the proposed PCW. Firstly, the phononic mode inside the bandgap displays a very slow group velocity. It will induce stronger strain in the core of the photonic waveguide than slab modes do [27]. The reason is that the confinement of the slow group velocity phononic mode is stronger than that of the slab modes in the waveguide core. There is more energy confined in the waveguide core for the slow group velocity phononic mode. Moreover, the energy of the acoustic is a quadratic function of the strain [28]. Hence, we can deduce that the slow group velocity phononic mode will enhance the mode conversion thanks to the energy of the acoustic field concentrated in the waveguide core. Secondly, the phonon mode with the good confinement in the Si waveguide through good overlap between the elastic displacement field and the optical mode distributions manifest a strong Brillouin coupling.

5. Phase-matched coupling via FSBS

We note that the frequency of the acoustic eigenmode is far less than optical frequency. Consequently, it can be assumed that the optical frequency difference is 6.7 GHz between the different optical modes which involve in the mode conversion, when the optical and acoustic waves satisfy the phase-matched condition. In Fig. 4(a), the blue and green curves display the dispersion properties of the $E_{11}^{x}$ and $E_{21}^{x}$ modes in the hybrid waveguide, respectively. The optical wave vector mismatch, $Δ β$ with $ω_{1} - ω_{2} = 6.7 GHz$ , is plotted (red curve) atop the optical dispersion curves, as shown in Fig. 4(a). It is shown that the values of $Δ β$ cover the region from 1.965 to 2.18 μm⁻¹ with the pump light frequency changing from 187.5 to 200 THz, which falls within the range of the guided acoustic wave propagation constant q. For conveniently searching the frequency of the phase-matched acoustic wave ( $q (Ω) = Δ β (ω)$ ), the optical wave vector mismatch curve (blue) and the acoustic dispersion curve (red) are plotted on the same figure, as shown in Fig. 4(b). The green area stands for the phase-matched range (1.965 μm⁻¹< $Δ β = q$ < 2.18 μm⁻¹). Corresponding to the phase-matched range, the acoustic frequency ranges from 6.662 to 6.735 GHz, as shown in Fig. 4(b) with the purple area. So when the input pump light frequency is in the range of 187.5 to 200 THz, we can always find an acoustic wave with a suitable frequency in the range from 6.662 to 6.735 GHz for realizing a high efficient mode conversion.

Fig. 4 (a) The optical dispersion relationship and the propagation constant difference (red curve) among the guided optical modes with frequency difference at 6.7 GHz. (b) The optical wave vector mismatch curve (blue) and the acoustic dispersion curve (red).

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Because the phase-matched acoustic eigenmode generated as a result of optical forces stimulates further FSBS, the FSBS in turn enhances the energy exchange between the pump and the Stokes waves and reinforces the acoustic wave. Finally, the different optical modes produce resonant coupling to implement the mode conversion through the FSBS in the large bandwidth of 12.5 THz.

6. Numerical Results of the mode conversion

After we obtain the optical and acoustic eigenmode distributions and the phase-matched condition in the hybrid waveguide, the mode conversion from the $E_{11}^{x}$ mode to $E_{21}^{x}$ mode based on the FSBS can be numerically simulated by solving the coupled-mode equations. In our simulation, we take into account the optical and acoustic field absorption losses. It is assumed that the optical loss $α = 2 dB/cm$ [29] and the mechanical quality factor of Q = 1000 [30] which decides the acoustic loss. And the $E_{11}^{x}$ mode with frequency $ω_{1} = 192 THz$ and power $P_{1} (0) = 150 mW$ is chosen as the input pump light.

The variations of optical powers P_m(z) and acoustic power P_a(z) along the propagation direction z can be obtained by the calculation of Eq. (8) and Eqs. (11)-(12), as shown in Fig. 5. The obtained results show that the variations of the powers are the damped oscillation processes. At the beginning, a $E_{11}^{x}$ mode pump photon translates into a $E_{21}^{x}$ mode Stokes photon and a phase-matched phonon resulting from the FSBS. Due to the confinement of the PCW, the generated phonons propagate and accumulate along the hybrid waveguide. Therefore, the acoustic power will rapidly grow with the increase of the Stokes light power until the pump photons are consumed completely. Immediately, the accumulated phonons will continue to propagate in the hybrid waveguide and drive the reverse mode conversion until the acoustic power decreases to zero. Owing to that acoustic absorption loss is larger than optical loss in the hybrid waveguide, the acoustic power cannot drive all of the Stokes light to be inversely converted to pump light in this process. The above oscillation process will continue until there is no phase-matched phonon accumulation in the hybrid waveguide.

Fig. 5 The optical and acoustic powers vary with the hybrid waveguide length: (a) by considering the electrostriction force only; (b) by considering the radiation pressure only; (c) by considering both the electrostriction force and the radiation pressure.

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Closer examination of the photon-phonon coupling within this system reveals that both the radiation pressure and the electrostriction force play an important role in the FSBS process for realizing the mode conversion at nanoscales. The graphs demonstrate individual contributions of the electrostriction force (shown in Fig. 5(a)) and the radiation pressure (shown in Fig. 5(b)) to the mode conversion, along with their combined effect (shown in Fig. 5(c)) due to the coherent combination of the radiation pressure and the electrostriction force. It is found that the radiation pressure behaves as the dominant function during the mode conversion process.

To explain the influence of the hybrid waveguide length on the performance of the mode conversion, we introduce an efficient length (L_eff) in the mode conversion process, which is defined as the hybrid waveguide length when the Stokes light power first reaches to the maximum value. Notably, the coherent addition of the radiation pressure and the electrostriction force dramatically enhance FSBS to make the L_eff be shortened to 4.78 mm, which is nearly half of the L_eff by considering the electrostriction force only and a quarter of the L_eff by considering the radiation pressure only.

Figure 6(a) show the relationship between the L_eff and the input pump power with different optical losses in the hybrid waveguide. When the input pump power is lower than 70 mW, the L_eff decreases exponentially with the increase of pump power. It is shown that the small optical loss will effectively reduce the L_eff under the same input pump power. If the pump power continues to increase, the rate of deceleration of L_eff will be weak and the influence of the optical loss can also be ignored. This implies that there is a proper waveguide length under the suitable pump power.

Fig. 6 (a) Efficient length as a function of the input pump light power for hybrid waveguide under different optical absorption losses. (b) Mode conversion efficiency varies with waveguide width under the given length and pump power. (c) Mode conversion efficiency varies with input pump power under different hybrid waveguide lengths.

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The optical force and overlap between the optical and acoustic waves are highly depended on the Si waveguide height and width in the hybrid waveguide. Therefore, the waveguide height and width will finally affect the mode conversion efficiency under the given waveguide length and pump power. Since the practical waveguide fabrication is based on SOI, the waveguide height is usually a fixed value. Based on this, the relationship between the waveguide width and the mode conversion efficiency is given by Fig. 6(b) with the waveguide length of 5 mm and pump power of 150 mW.

Nonetheless, in the practical waveguide fabrication, the waveguide structure is usually a fixed value after the waveguide is made. Based on this evidence, Fig. 6(c) shows the mode conversion efficiency as a function of the input pump power under different waveguide lengths. Taking the waveguide length with 5 mm as an example to analyze the influence of pump power, the conversion efficiency grows rapidly with the pump power increasing, after the pump power exceeds 80mW. As the pump power reaches to optimal value with 131.2 mW, the conversion efficiency get to the maximum value, meaning that all the pump power at that point is converted to the Stokes light and acoustic wave. Due to the existence of the optical and acoustic absorption losses, the optimal conversion efficiency can reach upto 88%. If we continue to increase the pump power, the conversion efficiency will reduce because of the reverse mode conversion. Therefore, the oscillation processes of the mode conversion occur in the waveguide, which induces the peak to appear periodically in Fig. 6(c) with the pump power increasing. In addition, it is shown that the curves have the same variation regular pattern with different waveguide lengths, and the optimal pump power will decrease with the increase of waveguide length. Therefore, although it is difficult to fabricate the hybrid waveguide with the optimal length, we can still achieve the optimal mode conversion efficiency by adjusting the input pump power, which is significant for the hybrid waveguide fabrication and integration.

7. Conclusion

We propose a hybrid photonic-phononic waveguide to realize the all optical mode conversion based on the FSBS. The theoretical model and simulation of FSBS are presented to illustrate the mode conversion in the hybrid waveguide. This proposed hybrid waveguide enables independent control of optical and acoustic wave to yield Brillouin coupling over the bandwidth of 12.5 THz. By analyzing the optical forces, we point out that transverse forces of the radiation pressure dominate FSBS process in the mode conversion. The high mode conversion efficiency can be achieved by adjusting the input pump light power in a fixed-length waveguide and is mainly limited by the waveguide loss. These waveguides can also be tuned post-design so as to achieve various optical mode conversions. A chip-based mode converter scheme that is capable of linear operation over a range of wavelengths will be a powerful and useful addition in modern integrated photonics.

Acknowledgments

This work is supported by the National Natural Science Foundation of China under Grant No. 61377074

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Mode conversion based on forward stimulated Brillouin scattering in a hybrid phononic-photonic waveguide

Abstract

1. Introduction

2. Principle and theory

3. Anatomy of optical forces within rectangular silicon waveguides in the FSBS

4. Acoustic eigenmodes in waveguide

5. Phase-matched coupling via FSBS

6. Numerical Results of the mode conversion

7. Conclusion

Acknowledgments

References and links

Cited By

Figures (6)

Equations (12)

Optics Express