Abstract

Plasmonic hybridized transverse magnetic like (TM-like) cavity modes in multi-layered metal-dielectric circular nanoantenna are systematically studied. The main purpose is to explore the symmetry features of the vertical modal profile and its impact on the in-plane interference of gap plasmonic waves that are responsible to the resonant mode. It is found that only vertically in-phase modes are excitable when illuminated by a plane wave under normal incidence and more could be selectively excited using a dipole source, within the wavelength range from 430 nm-1250 nm. More specifically, the excitation of localized cavity modes is shown to be highly sensitive to the dipole position which determines symmetry matching and the degree of field overlap between the dipole source and the cavity mode pattern. Furthermore, we show that the resonance frequencies can be approximately predicted by the dispersion relations of plasmonic wave in the corresponding two-dimensional multilayered structure. Our results would be helpful for the design of photonic nanoantennas with alternative metal and dielectric medium.

© 2015 Optical Society of America

1. Introduction

Surface plasmon polaritons (SPPs) are known as the collective oscillations of conductive electrons at interfaces of metal and dielectric [1]. The fundamental properties of SPs have been widely applied to many areas, such as nanolithography [2], plasmonic modulators [3], plasmonic hyperlens [4, 5], plasmonic optical trapping [6], plasmonic transparency window [7], etc. Photonic elements based on SP offer promising solution to the integration of nanoscale photonic and electronic devices, due to SP’s ability to confine light in subwavelength structures [8]. As one of the most important photonic devices, optical nanoantennas can dramatically manipulate the light-matter interactions, and have attracted numerous attentions in recent years [9–11]. Plasmonic nanoantennas are appealing in optical sensing and detection [12–14]. As a matter of fact, various kinds of photonic nanostructures could be designed as optical antennas, holding great promise for high directivity light emission [15], molecular fluorescence enhancement [16], and high-Q cavity design [17]. For instance, an isolated metallic nanoparticle can be considered as optical nanoantenna for enhancing the spontaneous emission [16] by virtue of the localized surface plasmon (LSP) resonances. However, the quantum efficiency is limited by the narrow bandwidth and the large metal losses around the LSP resonance frequency.

To circumvent these issues, metal-dielectric-metal (MDM) hybrid resonators are designed [18, 19] wherein the resonant field is highly confined inside the dielectric layer and the resonant mode is often regarded as whispering-gallery-like (WG-like) in MDM sandwiched system [20]. In fact, multilayered plasmonic-dielectric film structures [21–23] and subwavelength circular antennas [24] also attracted a lot of interests because one can get a huge Purcell factor which is critically determined by the inhomogeneity of the medium. Recently, Guclu et al. showed that three-dimensional hyperbolic metamaterial nanoantenna (comprising layered metal-dielectric disks) can substantially enhance the radiative emission of a nearby dipole [24]. Such multilayered metal-dielectric nanoantenna achieves high compact field confinement due to the strong SP polariton (SPP) gap mode coupling between multiple metal-dielectric interfaces. These studies are mostly focused on the high quality factor (Q) and small mode volume (Vmode) of the nanoantennas [20]. However, predicting the resonance frequencies to facilitate the design of such finite-sized and multilayered optical nanoantennas is also highly desirable, but remains rarely addressed so far. It appears crucial to understand hybridization across nearby interfaces in terms of the plasmonic gap mode of individual MDM.

In this paper, we examine a multi-layered metal-dielectric nanoantenna and systematically investigate the hybrid modes from the gap SPPs. It is shown that the Neumann boundary conditions can be applied to predict the hybridized mode resonant frequency in these multilayered metal-dielectric resonators. Furthermore, we demonstrate that the cavity modes hybridized from the TM-like MDM gap modes with the same rule follow the same dispersion curve of in-plane SPP wave, and are actually resulted from their interference with the laterally reflected portion. We present explicit examples of selective excitation by an electric dipole source whose radiation properties are strongly modified by the nanoantenna effect.

2. System and results for a plane wave

As shown in Fig. 1, the resonator is designed as a cylindrical rod made of four layers of Ag with thickness d=12.5nmand three layers of SiO2 with the same thickness. The cross radiusis R=54nm. The permittivity of SiO2 is set as εd=2.12 and that of silver,εm, is taken from Ref [25]. We have employed a commercial finite element package (Comsol Multiphysics) to study the resonant characters of the nanoantenna which is assumed freestanding in air (ε0=1). In all the simulations, perfectly matched layers (PML) are set as the boundary conditions and the mesh size along each orthogonal direction is less than 1.6 nm.

 

Fig. 1 Geometry of the multilayered metal-dielectric circular antenna.

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Some of the cavity modes of this nanostructure can be easily excited by an incident plane wave in a configuration that allows the magnetic component crossing the gap horizontally [26]. So we only consider the z-polarized plane wave propagating along the + x [see Fig. 2(a)] axis and x-polarized plane wave and propagating along the + z axis [see Fig. 2(b)] in this section. Figure 2(a) shows the optical spectra where two resonant peaks emerge in the absorption cross section (ACS; black line), scattering cross section (SCS; red line), as well as the extinction cross section (ECS; green line) in the interested band (wavelength from 430 nm to 1250 nm). The wavelengths of the two resonant are λ=463nm and λ=747nm and they are magnetic toroidal moment directed along the z-axis and in-plane magnetic dipole, respectively. It is noted that the slight red-shift between the peaks of ACS (ECS) and SCS can be ascribed to the dissipation in the metal medium [27–29]. Due to the source symmetry with respect to the structure geometry, some resonant modes cannot be excited by plane wave, but remain easily excitable by a nearby dipole source [30]. The seven-layered metal-dielectric resonator can be regarded as a system of three vertically-coupled MDM disks. It should be noted that each MDM disk supports only two types of TM-like modes: symmetrical mode and anti-symmetrical type [9, 19, 31]. Only symmetrical modes survive for small dielectric thickness. The SPP modes supported by our system can be assumed to be hybridization ofthese TM-like modes excited in the three MDM gaps. For the resonances at λ=463 nm and λ=747 nm, the electric field patterns Ez across the xy plane (parallel plane) and the xzplane (vertical plane) are shown in the inserts of Fig. 2(a).

 

Fig. 2 Optical cross sections of the antenna with plane wave excitation. (a) Insets show the resonant electric fields Ez in the xz plane and thexyplane across the top dielectric layer for the two peaks for two different incident plane wave configurations. (b) Inserts show Ex in the xz plane and thexyplane across the top dielectric layer for the resonances.

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In each case we characterize the in-plane resonant mode pattern with radial and azimuthal quantum number (n,m), while the xz pattern with the in-phase or out-of-phase relationship of the field in the three dielectric layers. It is seen that the field profiles of these two modes in the z-direction are the same in view that all the dielectric layers sustain the symmetric MDM gap modes and both of them show in-phase hybridization. This is reasonable because there is no phase retardation effect in the z-direction for the plane wave source. In order to distinguish differently hybridized TM-like modes along the vertical plane, we use the symbol ( + , + , + ) to label the modes according to their patterns in the xz plane [see the insets of Fig. 2(a)]. All the hybridized TM-like modes in the next section are labeled in similar manner for convenience. We stress that cavity modes with higher radial and azimuthal order can be excited in the resonator with appropriate sources, yet only the lower-order modes are studied due to their more compact mode confinement [20]. By this footnoting, in Fig. 2(a) the mode at λ=747nm can be labeled by [( + , + , + ), (1, 1)] and the one at λ=463 nm can be labeled by [( + , + , + ), (1, 0)]. Note that for the same cavity mode, in-planeEzpattern appears the same in the three dielectric layers.

For the other incident plane wave configuration [see the inset of Fig. 2(b)], it is seen in Fig. 2(b) that there are also two resonance peaks appearing in the optical spectra. The hybridized TM-like modes [( + , + , + ), (1, 1)] at λ=747 nm is efficiently excited because there is also magnetic component crossing the dielectric gap horizontally. However, there is an additional resonant mode at λ=530 nm which does not belong to any cavity SPP mode, but can be regarded as parallel combination of in-plane electric dipoles of the four silver disks.

Though the cylindrical multilayer rod is a 3D scatter, approximately we may treat it as a two-dimensional scattering system. Under z-polarization, the Helmholtz equation in cylindrical coordinates reads [32]:

ρ(ρEzρ)+1ρ22Ezϕ2+2Ezz2+k2iEz=0
where ki denotes the wave number in the metal (ki=km) and the dielectric gap (ki=kd). It is known that such axially symmetric structures support radially propagating SPPs termed as Hankel-type SPPs that are described by Hankel functions [33]. The ansatz modal field Ezreads
Ez(ρ,ϕ,z)=a(z)[Hm(1)(kgspρ)+rmHm(2)(kgspρ)]eimϕ
where mis the azimuthal quantum number, Hm(1) (Hm(2)) is the m-th Hankel function of the first (second) kind; kgsp is the gap surface plasmon wave vector in the layered metal-dielectric structure and rm represents the complex reflection coefficient of the Hankel-type SPP from the sidewall boundary (lateral circumference). In Eq. (2), a(z) is the z-direction evanescent modal profile which is correlated with the in-plane propagation constant kgsp [33].

Recently, Minkowski et al. [32] and Zhang et al. [26] studied the radial and azimuthal distribution functions (e.g., determined by [Hm(1)(kgspρ)+rmHm(2)(kgspρ)]eimϕ in Eq. (2)) of Ez in three-layer MDM disks. However, only the symmetrical gap SPP modes are considered and the anti-symmetrical ones are ignored, particularly due to the high resonant frequency for small dielectric thicknesses. Furthermore, the role of a(z)in Eq. (2) is not reflected in theirsituations. Unlike in a five-layered resonator consisting two gap layers [20], where primary even and odd hybridization dominate, the vertical modal profile a(z) in our proposed multi-layered MDM antenna can be very rich and the scope of resonant frequency is larger, enabling deeper exploration on the impact of a(z). Nevertheless, Fig. 2 shows that only modes with a(z)of ( + , + , + ) type can be excited in the plane wave configuration. Modes of other types of a(z), which characterizes different hybridization fashion of the MDM gap modes, remain completely “dark”. In order to examine these literally “dark” modes, we consider using near-field excitation source (e.g., an active electric dipole) since “dark” modes can strongly interact with their immediate environment via their optical near field [30].

3. Cases for an active dipole source excitation

The electric fields of the TM-like modes inside the gaps are preliminarily directed parallel to the z-axis, a dipole longitudinally polarized (oscillating out-of-plane) can strongly couple to these modes. We firstly consider the case of the longitudinal polarization. Figure 3 shows the nonradiative decay rate γnrof an active electric dipole placed at different positions P1, P2,P3, and P4near the resonator (see right column of Fig. 3). For the case of P1 and P2, the dipole source is above the top surface with h=30 nm and P1 is on the z-axis, whileP2 is deviated off it by R/2. The cases of P3 and P4 correspond to P1 and P2 by moving the source to the middle SiO2 layer (P3 denoting the central position and P4 the R/2 off-center position, respectively). The γnr spectrum is defined as γnr=Pnr/P0 [29], where Pnris thenonradiative power and P0 denotes the radiative power by the dipole source absence of the structure, i.e., for P1 and P2 cases, P0 is the radiative power in the vacuum; while for P3 and P4 cases, P0is the radiative power in homogeneous SiO2 medium. Peaks in the spectrum are then used to identify the resonant mode.

 

Fig. 3 Non-radiative decay rate spectra for electric dipole atP1,P2,P3, and P4.

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Figure 3(a) shows that when the dipole source is atP1, there are three obvious peaks, respectively atλ=605nm,λ=538nm, and λ=463nm. The corresponding Ez field for the three modes are shown in Fig. 4 (see the “P1” row). It is observed that these modes have the same in-plane mode index (1, 0) but have different vertical profile a(z) that are marked by ( + , -, + ), ( + , o, -), and ( + , + , + ), respectively. This labeling actually reflects the relative phase of Ez in the three dielectric layers. Note that “o” represents field amplitude nearly close to zero. When the excitation position is shifted from the P1 to P2, plasmon resonant peaks are visible at λ=1150nm,λ=977nm,λ=747nm, and λ=661 nm (see Fig. 3(b)), the corresponding cavity modes are indexed by [( + , -, + ), (1, 1)], [( + , o, -), (1, 1)], [( + , + , + ), (1, 1)], and [( + , o, -), (1, 2)], respectively (see the “P2” row in Fig. 4). Comparing these two cases, we see that only modes of P1 pattern with a doughnut-like symmetry (i.e., zero azimuthal number m=0) can be excited by the dipole at positionP1. This cavity excitation rule is set by the symmetry matching between the dipole source and the cavity modes. If one excites a cylindrically symmetric structure at its symmetry axis with a z-polarized dipole, a decomposition of the emitted radiation into radial and azimuthal contributions must lead to zero azimuthal component (e.g., for the P1 case). Any nonzero azimuthal component would require a broken symmetry between the dipole and structure (e.g., for the P2 case). Consequently, in order to effectively excite the in-plane zero azimuthal cavity modes, we shall locate the dipole source in the symmetry axis of the disk. The resonant excitation by the dipole source at P3 are similar as the case of P1. However, comparing the γnr spectra for P1 and P3 (see Figs. 3(a) and 3(b)), it is found that the resonant peak of mode [( + , o, -), (1, 0)] at λ=538nm is absent in the later case. This is because when the z-polarized dipole source is located in the center of the middle dielectric layer, only modes of symmetrical a(z) could be matched. Based on the above reasoning, it is easily to predict that all cavity modes can be excited except for those with m=0and a(z)~( + , o, -) when the dipole source is atP4. Indeed, the “P4” row in Fig. 4 confirms this. The situation, however, is more complicated: there is an unexpected peak at λ=605nm, corresponding to the cavity mode [( + , -, + ), (1, 0)] (see Fig. 3(d)). This can be ascribed to fact that the distance between the dipole and the metal layer is too small (R/2=6.25nm) and the phase retardation effect becomes strong along the x-axis.

 

Fig. 4 Selective mode excitation by a dipole source. Shown in the table are xz plane and xyplane electric field when dipole source is positioned at P1, P2, P3, and P4. The resonant wavelength and mode labeling are shown for each column.

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For the case for a horizontally-polarized dipole, the TM-like modes are essentially excitable by its magnetic component across each gap layer. By virtue of symmetry, only modes of a(z)(+,0,) are expected to be excitable for P3 and P4, while only odd modes are excitable for P1 and P3. These are indeed observed in the numerical calculations [figures not shown]. Notice that the spontaneous emission rate can be quite high (~102 and ~103 times the vacuum emission rate for horizontal and vertical polarizations, respectively) when the active dipole is located inside the dielectric layer. This is ascribed to the fact that the gap mode local fields are highly confined near the multiple metal-dielectric interfaces and enhanced dramatically in the gap layers. Furthermore, the decay rate enhancement is weaker for horizontal polarization than that of vertical polarization simply because of the TM-like characteristics. These features may enable directional lasing and enhanced spectroscopy of our structure.

4. Resonant condition and modal analysis

We are now in a position to have an intuitive perspective of these modes. Since the resonator’s total thickness is far less than the working wavelength, we can regard the resonance caused by interfering cylindrical Hankel-type SPP waves of in-plane wave vector kgsp in all layers. According to Neumann boundary condition, the resonant condition for these cavity modes is given by [26, 32, 33]:

kgspReff=χ'nm
where χ'nmis the nth root of the first derivative of the mth Bessel function, and Reff=R+dis the effective radius of this resonator. Since there is a phase shift of the gap surface plasmons upon reflection at the lateral edges, we must consider the the fringe field effect. To take this fringing field into account, one simple while effective empirical approach is to use the sum of the actual disk radius (R) and the dielectric layer thickness (d) as the effective radius [19, 26, 32].

According to Eq. (3), the plasmon resonant frequency and the radius of the multilayer metal-dielectric resonator is correlated bykgsp. In an attempt to find the resonant conditions, we invoke the transfer matrix method [34, 35] which is a powerful tool in the analysis of light propagation through layered media to obtain the dispersion relation of hybridized gap SPPs. The process is as following: we firstly extend the radius to infinite (i.e.,R) and treat the system as a 9-layer film system with air on the top and at the bottom, alternatively consisting of four layered homogeneous metal and three layered homogeneous dielectric. For the TM polarization, the transfer matrix that relates electric fields of the interface from layer i to jcan be obtained as:

Dij=12[1+ηij1ηij1ηij1+ηij]
where ηij is given byηij=kz,jεi/kz,iεj, here εi is the permittivity in the material i, kz,iis the z-component of the wave vector in material i, and can be written as kz,i=k20εikx2, where k0 and kx are the free space wave vector and the propagation constant, respectively. And the field at z+Δz can relate to this at position z in the material j by the matrix ϕj:
ϕj=[eikz,jΔz00eikz,jΔz]
Then the total transfer matrix to describe the 9-layer structure can be written as M=D12ϕ2D23ϕ3D34ϕ4D45ϕ5D56ϕ6D67ϕ7D78ϕ8D89, and the reflection coefficient rc=M2,1/M1,1. Where the reflection coefficient rc is undefined (i.e.,M1,1=0) correspond to eigenmodes of the structure and then the gap plasmon dispersion relation of this nanostructure can be obtained. By the analysis of transfer matrix method in two-dimensional multilayers, it is shown that there is a one-to-one correspondence between a(z) and kgsp, namely, a(z)describes the vertical hybridization style/symmetry of gap plasmon modes and yields unique in-plane wave vector kgsp.

Figure 5 shows the numerically calculated cavity resonant frequencies versus χ'mn/(R+d)for different radius of our system. Here, the (n,m)pairs are marked by different symbols and a(z) patterns are distinguished by different colors. It is found that almost all the resonant frequencies fall on the dispersion relation (solid curves in Fig. 5) obtained by the transfer matrix method. More interesting, it is shown that the cavity modes with the same type of a(z) fall on the same dispersion curve, justifying the validity of the 2D analysis. For example, the red symbols correspond to mode with a(z)~( + , -, + ), the green and blue symbols belongs to a(z)~( + , o, -) and ( + , + , + ), respectively. We note that the dispersion curve in higher frequency is not considered here because the peaks of these modes are too weak to identify. Further note that metal loss does not play a critical role here. Calculations without loss basically yielded similar resonant positions (not shown).

 

Fig. 5 Cavity resonant frequencies (symbols) versus χ'nm/(R+d) for different radius of the nanoantenna. The 2D theoretically calculated dispersion (black lines) of hybridized SPP are also shown.

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It is visually noticed that the blue symbols deviate slightly from the dispersion curve of the hybridized mode with a(z)~( + , + , + ) (see Fig. 5). As a matter of fact, in our study the size of the multilayer metal-dielectric nanoantenna is finite, representing a 3D object which shall only support TM-like modes instead of pure TM mode. Namely, magnetic field would have out-of-plane component. In the transfer matrix analysis, we treat its radius as infinite in order to obtain the dispersion curve. To further understand this point, we show in Fig. 6 the in-plane field ratio|E///Etot|2, as a function of z for excitations at three resonant wavelengths (corresponding to three kinds of the hybridized TM-like modes) when the dipole source is at P1. The amplitude of |E///Etot|2 can be regarded as a measure of how the mode approach to a pure TM one, namely, to what degree can the system be regarded as 2D. For example, E//=0 corresponds to a pure TM mode. For the modes of a(z)~( + , -, + ) (red line) and a(z)~( + , o, -) (green line), |E///Etot|2 is much smaller and these modes very much resemble a TM mode, consequently the cavity resonant frequencies perfectly match the dispersion curve of the gap SPPs (see Fig. 5). However, for the hybridized modes of a(z)~( + , + , + ), the in-plane field ratio is about three order of magnitudes larger (see inset of Fig. 6), which leads to visible deviation from the theoretical kgsp(ω) curve in Fig. 5.

 

Fig. 6 In-plane field ratio |E///Etot|2 measured along the z axis for the three different resonance modes excited by a dipole source at P1. The symbols “M” and “D” represent the metal and dielectric layer, respectively.

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Finally, we stress that Fig. 5 is the main contribution of this work. Previous studies have reported that the cavity modes of MDM disk can all fall on the symmetric gap SPP mode dispersion curve where there is only one kind of TM-like modes considered [19, 26, 32, 33] and the impact of a(z) pattern is not reflected.

5. Conclusion

In summary, we theoretically and numerically investigated the resonance properties of cavity modes in multi-layered metal-dielectric nanoantenna. We verify that the resonant conditions based on the Neumann boundary conditions apply to the hybridized modes in multilayered metal-dielectric disk. Furthermore, it is demonstrated that the cavity modes hybridized from TM-like MDM modes with the same rule (same a(z) symmetry) approximately follow the same resonant conditions by the in-plane SPP wave interference. In view that such multilayer structures are readily fabricated in experiments, these results can be used to engineer the resonances of layered metal-dielectric nanoantennas in the design for practical applications and experiments.

Acknowledgments

This work was financially supported by NSFC (Nos. 11274083 and 11004043), and the Shenzhen Municipal Science and Technology Plan (Grant Nos. KQCX20120801093710373, JCYJ20120613114137248, and 2011PTZZ048). JJX is also supported by the Natural Scientific Research Innovation Foundation in Harbin Institute of Technology (No. HIT.NSFIR.2010131). We acknowledge assistance from the Key Lab of Terminals of IoT and the National Supercomputer Shenzhen Center.

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35. M. A. Kats, D. Woolf, R. Blanchard, N. Yu, and F. Capasso, “Spoof plasmon analogue of metal-insulator-metal waveguides,” Opt. Express 19(16), 14860–14870 (2011). [CrossRef]   [PubMed]  

References

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  5. D. Aronovich and G. Bartal, “Nonlinear hyperlens,” Opt. Lett. 38(4), 413–415 (2013).
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    [Crossref] [PubMed]
  18. M. Frederiksen, V. E. Bochenkov, R. Ogaki, and D. S. Sutherland, “Onset of bonding plasmon hybridization preceded by gap modes in dielectric splitting of metal disks,” Nano Lett. 13(12), 6033–6039 (2013).
    [Crossref] [PubMed]
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    [Crossref]
  24. C. Guclu, T. S. Luk, G. T. Wang, and F. Capolino, “Radiative emission enhancement using nano-antennas made of hyperbolic metamaterial resonators,” Appl. Phys. Lett. 105(12), 123101 (2014).
    [Crossref]
  25. A. D. Rakić, A. B. Djurišić, J. M. Elazar, and M. L. Majewski, “Optical properties of metallic films for vertical-cavity optoelectronic devices,” Appl. Opt. 37(22), 5271–5283 (1998).
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  26. Q. Zhang, J. J. Xiao, X. M. Zhang, D. Z. Han, and L. Gao, “Core-shell-structured dielectric−metal circular nanodisk antenna: gap plasmon assisted magnetic toroid-like cavity modes,” ACS Photonics 2(1), 60–65 (2015).
    [Crossref]
  27. B. M. Ross and L. P. Lee, “Comparison of near- and far-field measures for plasmon resonance of metallic nanoparticles,” Opt. Lett. 34(7), 896–898 (2009).
    [Crossref] [PubMed]
  28. J. Zuloaga and P. Nordlander, “On the energy shift between near-field and far-field peak intensities in localized plasmon systems,” Nano Lett. 11(3), 1280–1283 (2011).
    [Crossref] [PubMed]
  29. X. M. Zhang, J. J. Xiao, and Q. Zhang, “Interaction between single nano-emitter and plasmonic disk–ring nanostructure with multiple Fano resonances,” J. Opt. Soc. Am. B 31(9), 2193–2200 (2014).
    [Crossref]
  30. M. Liu, T. W. Lee, S. K. Gray, P. Guyot-Sionnest, and M. Pelton, “Excitation of dark plasmons in metal nanoparticles by a localized emitter,” Phys. Rev. Lett. 102(10), 107401 (2009).
    [Crossref] [PubMed]
  31. Y. C. Chang, S. M. Wang, H. C. Chung, C. B. Tseng, and S. H. Chang, “Observation of absorption-dominated bonding dark plasmon mode from metal-insulator-metal nanodisk arrays fabricated by nanospherical-lens lithography,” ACS Nano 6(4), 3390–3396 (2012).
    [Crossref] [PubMed]
  32. F. Minkowski, F. Wang, A. Chakrabarty, and Q. H. Wei, “Resonant cavity modes of circular plasmonic patch nanoantennas,” Appl. Phys. Lett. 104(2), 021111 (2014).
    [Crossref]
  33. R. Filter, J. Qi, C. Rockstuhl, and F. Lederer, “Circular optical nanoantennas: an analytical theory,” Phys. Rev. B 85(12), 125429 (2012).
    [Crossref]
  34. T. Zhan, X. Shi, Y. Dai, X. Liu, and J. Zi, “Transfer matrix method for optics in graphene layers,” J. Phys. Condens. Matter 25(21), 215301 (2013).
    [Crossref] [PubMed]
  35. M. A. Kats, D. Woolf, R. Blanchard, N. Yu, and F. Capasso, “Spoof plasmon analogue of metal-insulator-metal waveguides,” Opt. Express 19(16), 14860–14870 (2011).
    [Crossref] [PubMed]

2015 (1)

Q. Zhang, J. J. Xiao, X. M. Zhang, D. Z. Han, and L. Gao, “Core-shell-structured dielectric−metal circular nanodisk antenna: gap plasmon assisted magnetic toroid-like cavity modes,” ACS Photonics 2(1), 60–65 (2015).
[Crossref]

2014 (10)

F. Lou, M. Yan, L. Thylen, M. Qiu, and L. Wosinski, “Whispering gallery mode nanodisk resonator based on layered metal-dielectric waveguide,” Opt. Express 22(7), 8490–8502 (2014).
[Crossref] [PubMed]

H. L. Ning, N. A. Krueger, X. Sheng, H. Keum, C. Zhang, K. D. Choquette, X. L. Li, S. Kim, J. A. Rogers, and P. Braun, “Transfer-printing of tunable porous silicon microcavities with embedded emitters,” ACS Photonics 1(11), 1144–1150 (2014).
[Crossref]

C. Guclu, T. S. Luk, G. T. Wang, and F. Capolino, “Radiative emission enhancement using nano-antennas made of hyperbolic metamaterial resonators,” Appl. Phys. Lett. 105(12), 123101 (2014).
[Crossref]

X. M. Zhang, J. J. Xiao, and Q. Zhang, “Interaction between single nano-emitter and plasmonic disk–ring nanostructure with multiple Fano resonances,” J. Opt. Soc. Am. B 31(9), 2193–2200 (2014).
[Crossref]

F. Minkowski, F. Wang, A. Chakrabarty, and Q. H. Wei, “Resonant cavity modes of circular plasmonic patch nanoantennas,” Appl. Phys. Lett. 104(2), 021111 (2014).
[Crossref]

A. Mohtashami, T. Coenen, A. Antoncecchi, A. Polman, and A. F. Koenderink, “Nanoscale execitation mapping of plasmonic patch antennas,” ACS Photonics 1(11), 1134–1143 (2014).
[Crossref]

S. R. K. Rodriguez, F. Bernal Arango, T. P. Steinbusch, M. A. Verschuuren, A. F. Koenderink, and J. Gómez Rivas, “Breaking the symmetry of forward-backward light emission with localized and collective magnetoelectric resonances in arrays of pyramid-shaped aluminum nanoparticles,” Phys. Rev. Lett. 113(24), 247401 (2014).
[Crossref] [PubMed]

N. Zhang, Y. J. Liu, J. Yang, X. Su, J. Deng, C. C. Chum, M. Hong, and J. Teng, “High sensitivity molecule detection by plasmonic nanoantennas with selective binding at electromagnetic hotspots,” Nanoscale 6(3), 1416–1422 (2014).
[Crossref] [PubMed]

T. Coenen, F. Bernal Arango, A. Femius Koenderink, and A. Polman, “Directional emission from a single plasmonic scatterer,” Nat. Commun. 5, 3250 (2014).
[Crossref] [PubMed]

H. Zhang, H. V. Demir, and A. O. Govorov, “Plasmonic metamaterials and nanocomposites with the narrow transparency window effect in broad extinction spectra,” ACS Photonics 1(9), 822–832 (2014).
[Crossref]

2013 (6)

M. Frederiksen, V. E. Bochenkov, R. Ogaki, and D. S. Sutherland, “Onset of bonding plasmon hybridization preceded by gap modes in dielectric splitting of metal disks,” Nano Lett. 13(12), 6033–6039 (2013).
[Crossref] [PubMed]

G. Lu, J. Liu, T. Zhang, H. Shen, P. Perriat, M. Martini, O. Tillement, Y. Gu, Y. He, Y. Wang, and Q. Gong, “Enhancing molecule fluorescence with asymmetrical plasmonic antennas,” Nanoscale 5(14), 6545–6551 (2013).
[Crossref] [PubMed]

X. Ren, W. E. I. Sha, and W. C. H. Choy, “Tuning optical responses of metallic dipole nanoantenna using graphene,” Opt. Express 21(26), 31824–31829 (2013).
[Crossref] [PubMed]

D. Aronovich and G. Bartal, “Nonlinear hyperlens,” Opt. Lett. 38(4), 413–415 (2013).
[Crossref] [PubMed]

T. Zhan, X. Shi, Y. Dai, X. Liu, and J. Zi, “Transfer matrix method for optics in graphene layers,” J. Phys. Condens. Matter 25(21), 215301 (2013).
[Crossref] [PubMed]

W. D. Newman, C. L. Cortes, and Z. Jacob, “Enhanced and directional single-photon emission in hyperbolic metamaterials,” J. Opt. Soc. Am. B 30(4), 766–775 (2013).

2012 (3)

Y. C. Chang, S. M. Wang, H. C. Chung, C. B. Tseng, and S. H. Chang, “Observation of absorption-dominated bonding dark plasmon mode from metal-insulator-metal nanodisk arrays fabricated by nanospherical-lens lithography,” ACS Nano 6(4), 3390–3396 (2012).
[Crossref] [PubMed]

R. Filter, J. Qi, C. Rockstuhl, and F. Lederer, “Circular optical nanoantennas: an analytical theory,” Phys. Rev. B 85(12), 125429 (2012).
[Crossref]

A. Chakrabarty, F. Wang, F. Minkowski, K. Sun, and Q. H. Wei, “Cavity modes and their excitations in elliptical plasmonic patch nanoantennas,” Opt. Express 20(11), 11615–11624 (2012).
[PubMed]

2011 (4)

N. Liu, M. L. Tang, M. Hentschel, H. Giessen, and A. P. Alivisatos, “Nanoantenna-enhanced gas sensing in a single tailored nanofocus,” Nat. Mater. 10(8), 631–636 (2011).
[Crossref] [PubMed]

M. A. Kats, D. Woolf, R. Blanchard, N. Yu, and F. Capasso, “Spoof plasmon analogue of metal-insulator-metal waveguides,” Opt. Express 19(16), 14860–14870 (2011).
[Crossref] [PubMed]

O. Kidwai, S. V. Zhukovsky, and J. E. Sipe, “Dipole radiation near hyperbolic metamaterials: applicability of effective-medium approximation,” Opt. Lett. 36(13), 2530–2532 (2011).
[Crossref] [PubMed]

J. Zuloaga and P. Nordlander, “On the energy shift between near-field and far-field peak intensities in localized plasmon systems,” Nano Lett. 11(3), 1280–1283 (2011).
[Crossref] [PubMed]

2010 (1)

2009 (4)

Z. Y. Fang, F. Lin, S. Huang, W. T. Song, and X. Zhu, “Focusing surface plasmon polariton trapping of colloidal particles,” Appl. Phys. Lett. 94(6), 063306 (2009).
[Crossref]

B. Min, E. Ostby, V. Sorger, E. Ulin-Avila, L. Yang, X. Zhang, and K. Vahala, “High-Q surface-plasmon-polariton whispering-gallery microcavity,” Nature 457(7228), 455–458 (2009).
[Crossref] [PubMed]

B. M. Ross and L. P. Lee, “Comparison of near- and far-field measures for plasmon resonance of metallic nanoparticles,” Opt. Lett. 34(7), 896–898 (2009).
[Crossref] [PubMed]

M. Liu, T. W. Lee, S. K. Gray, P. Guyot-Sionnest, and M. Pelton, “Excitation of dark plasmons in metal nanoparticles by a localized emitter,” Phys. Rev. Lett. 102(10), 107401 (2009).
[Crossref] [PubMed]

2008 (1)

F. Neubrech, A. Pucci, T. W. Cornelius, S. Karim, A. García-Etxarri, and J. Aizpurua, “Resonant plasmonic and vibrational coupling in a tailored nanoantenna for infrared detection,” Phys. Rev. Lett. 101(15), 157403 (2008).
[Crossref] [PubMed]

2007 (2)

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, “Far-field optical hyperlens magnifying sub-diffraction-limited objects,” Science 315(5819), 1686 (2007).
[Crossref] [PubMed]

X. Wei, X. Luo, X. Dong, and C. Du, “Localized surface plasmon nanolithography with ultrahigh resolution,” Opt. Express 15(21), 14177–14183 (2007).
[Crossref] [PubMed]

2006 (1)

E. Ozbay, “Plasmonics: merging photonics and electronics at nanoscale dimensions,” Science 311(5758), 189–193 (2006).
[Crossref] [PubMed]

1998 (1)

Aizpurua, J.

F. Neubrech, A. Pucci, T. W. Cornelius, S. Karim, A. García-Etxarri, and J. Aizpurua, “Resonant plasmonic and vibrational coupling in a tailored nanoantenna for infrared detection,” Phys. Rev. Lett. 101(15), 157403 (2008).
[Crossref] [PubMed]

Alivisatos, A. P.

N. Liu, M. L. Tang, M. Hentschel, H. Giessen, and A. P. Alivisatos, “Nanoantenna-enhanced gas sensing in a single tailored nanofocus,” Nat. Mater. 10(8), 631–636 (2011).
[Crossref] [PubMed]

Andersen, D. R.

Antoncecchi, A.

A. Mohtashami, T. Coenen, A. Antoncecchi, A. Polman, and A. F. Koenderink, “Nanoscale execitation mapping of plasmonic patch antennas,” ACS Photonics 1(11), 1134–1143 (2014).
[Crossref]

Aronovich, D.

Bartal, G.

Bernal Arango, F.

S. R. K. Rodriguez, F. Bernal Arango, T. P. Steinbusch, M. A. Verschuuren, A. F. Koenderink, and J. Gómez Rivas, “Breaking the symmetry of forward-backward light emission with localized and collective magnetoelectric resonances in arrays of pyramid-shaped aluminum nanoparticles,” Phys. Rev. Lett. 113(24), 247401 (2014).
[Crossref] [PubMed]

T. Coenen, F. Bernal Arango, A. Femius Koenderink, and A. Polman, “Directional emission from a single plasmonic scatterer,” Nat. Commun. 5, 3250 (2014).
[Crossref] [PubMed]

Blanchard, R.

Bochenkov, V. E.

M. Frederiksen, V. E. Bochenkov, R. Ogaki, and D. S. Sutherland, “Onset of bonding plasmon hybridization preceded by gap modes in dielectric splitting of metal disks,” Nano Lett. 13(12), 6033–6039 (2013).
[Crossref] [PubMed]

Braun, P.

H. L. Ning, N. A. Krueger, X. Sheng, H. Keum, C. Zhang, K. D. Choquette, X. L. Li, S. Kim, J. A. Rogers, and P. Braun, “Transfer-printing of tunable porous silicon microcavities with embedded emitters,” ACS Photonics 1(11), 1144–1150 (2014).
[Crossref]

Capasso, F.

Capolino, F.

C. Guclu, T. S. Luk, G. T. Wang, and F. Capolino, “Radiative emission enhancement using nano-antennas made of hyperbolic metamaterial resonators,” Appl. Phys. Lett. 105(12), 123101 (2014).
[Crossref]

Chakrabarty, A.

F. Minkowski, F. Wang, A. Chakrabarty, and Q. H. Wei, “Resonant cavity modes of circular plasmonic patch nanoantennas,” Appl. Phys. Lett. 104(2), 021111 (2014).
[Crossref]

A. Chakrabarty, F. Wang, F. Minkowski, K. Sun, and Q. H. Wei, “Cavity modes and their excitations in elliptical plasmonic patch nanoantennas,” Opt. Express 20(11), 11615–11624 (2012).
[PubMed]

Chang, S. H.

Y. C. Chang, S. M. Wang, H. C. Chung, C. B. Tseng, and S. H. Chang, “Observation of absorption-dominated bonding dark plasmon mode from metal-insulator-metal nanodisk arrays fabricated by nanospherical-lens lithography,” ACS Nano 6(4), 3390–3396 (2012).
[Crossref] [PubMed]

Chang, Y. C.

Y. C. Chang, S. M. Wang, H. C. Chung, C. B. Tseng, and S. H. Chang, “Observation of absorption-dominated bonding dark plasmon mode from metal-insulator-metal nanodisk arrays fabricated by nanospherical-lens lithography,” ACS Nano 6(4), 3390–3396 (2012).
[Crossref] [PubMed]

Choquette, K. D.

H. L. Ning, N. A. Krueger, X. Sheng, H. Keum, C. Zhang, K. D. Choquette, X. L. Li, S. Kim, J. A. Rogers, and P. Braun, “Transfer-printing of tunable porous silicon microcavities with embedded emitters,” ACS Photonics 1(11), 1144–1150 (2014).
[Crossref]

Choy, W. C. H.

Chum, C. C.

N. Zhang, Y. J. Liu, J. Yang, X. Su, J. Deng, C. C. Chum, M. Hong, and J. Teng, “High sensitivity molecule detection by plasmonic nanoantennas with selective binding at electromagnetic hotspots,” Nanoscale 6(3), 1416–1422 (2014).
[Crossref] [PubMed]

Chung, H. C.

Y. C. Chang, S. M. Wang, H. C. Chung, C. B. Tseng, and S. H. Chang, “Observation of absorption-dominated bonding dark plasmon mode from metal-insulator-metal nanodisk arrays fabricated by nanospherical-lens lithography,” ACS Nano 6(4), 3390–3396 (2012).
[Crossref] [PubMed]

Coenen, T.

T. Coenen, F. Bernal Arango, A. Femius Koenderink, and A. Polman, “Directional emission from a single plasmonic scatterer,” Nat. Commun. 5, 3250 (2014).
[Crossref] [PubMed]

A. Mohtashami, T. Coenen, A. Antoncecchi, A. Polman, and A. F. Koenderink, “Nanoscale execitation mapping of plasmonic patch antennas,” ACS Photonics 1(11), 1134–1143 (2014).
[Crossref]

Cornelius, T. W.

F. Neubrech, A. Pucci, T. W. Cornelius, S. Karim, A. García-Etxarri, and J. Aizpurua, “Resonant plasmonic and vibrational coupling in a tailored nanoantenna for infrared detection,” Phys. Rev. Lett. 101(15), 157403 (2008).
[Crossref] [PubMed]

Cortes, C. L.

Dai, Y.

T. Zhan, X. Shi, Y. Dai, X. Liu, and J. Zi, “Transfer matrix method for optics in graphene layers,” J. Phys. Condens. Matter 25(21), 215301 (2013).
[Crossref] [PubMed]

Demir, H. V.

H. Zhang, H. V. Demir, and A. O. Govorov, “Plasmonic metamaterials and nanocomposites with the narrow transparency window effect in broad extinction spectra,” ACS Photonics 1(9), 822–832 (2014).
[Crossref]

Deng, J.

N. Zhang, Y. J. Liu, J. Yang, X. Su, J. Deng, C. C. Chum, M. Hong, and J. Teng, “High sensitivity molecule detection by plasmonic nanoantennas with selective binding at electromagnetic hotspots,” Nanoscale 6(3), 1416–1422 (2014).
[Crossref] [PubMed]

Djurišic, A. B.

Dong, X.

Du, C.

Elazar, J. M.

Fang, Z. Y.

Z. Y. Fang, F. Lin, S. Huang, W. T. Song, and X. Zhu, “Focusing surface plasmon polariton trapping of colloidal particles,” Appl. Phys. Lett. 94(6), 063306 (2009).
[Crossref]

Femius Koenderink, A.

T. Coenen, F. Bernal Arango, A. Femius Koenderink, and A. Polman, “Directional emission from a single plasmonic scatterer,” Nat. Commun. 5, 3250 (2014).
[Crossref] [PubMed]

Filter, R.

R. Filter, J. Qi, C. Rockstuhl, and F. Lederer, “Circular optical nanoantennas: an analytical theory,” Phys. Rev. B 85(12), 125429 (2012).
[Crossref]

Frederiksen, M.

M. Frederiksen, V. E. Bochenkov, R. Ogaki, and D. S. Sutherland, “Onset of bonding plasmon hybridization preceded by gap modes in dielectric splitting of metal disks,” Nano Lett. 13(12), 6033–6039 (2013).
[Crossref] [PubMed]

Gao, L.

Q. Zhang, J. J. Xiao, X. M. Zhang, D. Z. Han, and L. Gao, “Core-shell-structured dielectric−metal circular nanodisk antenna: gap plasmon assisted magnetic toroid-like cavity modes,” ACS Photonics 2(1), 60–65 (2015).
[Crossref]

García-Etxarri, A.

F. Neubrech, A. Pucci, T. W. Cornelius, S. Karim, A. García-Etxarri, and J. Aizpurua, “Resonant plasmonic and vibrational coupling in a tailored nanoantenna for infrared detection,” Phys. Rev. Lett. 101(15), 157403 (2008).
[Crossref] [PubMed]

Giessen, H.

N. Liu, M. L. Tang, M. Hentschel, H. Giessen, and A. P. Alivisatos, “Nanoantenna-enhanced gas sensing in a single tailored nanofocus,” Nat. Mater. 10(8), 631–636 (2011).
[Crossref] [PubMed]

Gómez Rivas, J.

S. R. K. Rodriguez, F. Bernal Arango, T. P. Steinbusch, M. A. Verschuuren, A. F. Koenderink, and J. Gómez Rivas, “Breaking the symmetry of forward-backward light emission with localized and collective magnetoelectric resonances in arrays of pyramid-shaped aluminum nanoparticles,” Phys. Rev. Lett. 113(24), 247401 (2014).
[Crossref] [PubMed]

Gong, Q.

G. Lu, J. Liu, T. Zhang, H. Shen, P. Perriat, M. Martini, O. Tillement, Y. Gu, Y. He, Y. Wang, and Q. Gong, “Enhancing molecule fluorescence with asymmetrical plasmonic antennas,” Nanoscale 5(14), 6545–6551 (2013).
[Crossref] [PubMed]

Govorov, A. O.

H. Zhang, H. V. Demir, and A. O. Govorov, “Plasmonic metamaterials and nanocomposites with the narrow transparency window effect in broad extinction spectra,” ACS Photonics 1(9), 822–832 (2014).
[Crossref]

Gray, S. K.

M. Liu, T. W. Lee, S. K. Gray, P. Guyot-Sionnest, and M. Pelton, “Excitation of dark plasmons in metal nanoparticles by a localized emitter,” Phys. Rev. Lett. 102(10), 107401 (2009).
[Crossref] [PubMed]

Gu, Y.

G. Lu, J. Liu, T. Zhang, H. Shen, P. Perriat, M. Martini, O. Tillement, Y. Gu, Y. He, Y. Wang, and Q. Gong, “Enhancing molecule fluorescence with asymmetrical plasmonic antennas,” Nanoscale 5(14), 6545–6551 (2013).
[Crossref] [PubMed]

Guclu, C.

C. Guclu, T. S. Luk, G. T. Wang, and F. Capolino, “Radiative emission enhancement using nano-antennas made of hyperbolic metamaterial resonators,” Appl. Phys. Lett. 105(12), 123101 (2014).
[Crossref]

Guyot-Sionnest, P.

M. Liu, T. W. Lee, S. K. Gray, P. Guyot-Sionnest, and M. Pelton, “Excitation of dark plasmons in metal nanoparticles by a localized emitter,” Phys. Rev. Lett. 102(10), 107401 (2009).
[Crossref] [PubMed]

Han, D. Z.

Q. Zhang, J. J. Xiao, X. M. Zhang, D. Z. Han, and L. Gao, “Core-shell-structured dielectric−metal circular nanodisk antenna: gap plasmon assisted magnetic toroid-like cavity modes,” ACS Photonics 2(1), 60–65 (2015).
[Crossref]

He, Y.

G. Lu, J. Liu, T. Zhang, H. Shen, P. Perriat, M. Martini, O. Tillement, Y. Gu, Y. He, Y. Wang, and Q. Gong, “Enhancing molecule fluorescence with asymmetrical plasmonic antennas,” Nanoscale 5(14), 6545–6551 (2013).
[Crossref] [PubMed]

Hentschel, M.

N. Liu, M. L. Tang, M. Hentschel, H. Giessen, and A. P. Alivisatos, “Nanoantenna-enhanced gas sensing in a single tailored nanofocus,” Nat. Mater. 10(8), 631–636 (2011).
[Crossref] [PubMed]

Hong, M.

N. Zhang, Y. J. Liu, J. Yang, X. Su, J. Deng, C. C. Chum, M. Hong, and J. Teng, “High sensitivity molecule detection by plasmonic nanoantennas with selective binding at electromagnetic hotspots,” Nanoscale 6(3), 1416–1422 (2014).
[Crossref] [PubMed]

Huang, S.

Z. Y. Fang, F. Lin, S. Huang, W. T. Song, and X. Zhu, “Focusing surface plasmon polariton trapping of colloidal particles,” Appl. Phys. Lett. 94(6), 063306 (2009).
[Crossref]

Jacob, Z.

Karim, S.

F. Neubrech, A. Pucci, T. W. Cornelius, S. Karim, A. García-Etxarri, and J. Aizpurua, “Resonant plasmonic and vibrational coupling in a tailored nanoantenna for infrared detection,” Phys. Rev. Lett. 101(15), 157403 (2008).
[Crossref] [PubMed]

Kats, M. A.

Keum, H.

H. L. Ning, N. A. Krueger, X. Sheng, H. Keum, C. Zhang, K. D. Choquette, X. L. Li, S. Kim, J. A. Rogers, and P. Braun, “Transfer-printing of tunable porous silicon microcavities with embedded emitters,” ACS Photonics 1(11), 1144–1150 (2014).
[Crossref]

Kidwai, O.

Kim, S.

H. L. Ning, N. A. Krueger, X. Sheng, H. Keum, C. Zhang, K. D. Choquette, X. L. Li, S. Kim, J. A. Rogers, and P. Braun, “Transfer-printing of tunable porous silicon microcavities with embedded emitters,” ACS Photonics 1(11), 1144–1150 (2014).
[Crossref]

Koenderink, A. F.

A. Mohtashami, T. Coenen, A. Antoncecchi, A. Polman, and A. F. Koenderink, “Nanoscale execitation mapping of plasmonic patch antennas,” ACS Photonics 1(11), 1134–1143 (2014).
[Crossref]

S. R. K. Rodriguez, F. Bernal Arango, T. P. Steinbusch, M. A. Verschuuren, A. F. Koenderink, and J. Gómez Rivas, “Breaking the symmetry of forward-backward light emission with localized and collective magnetoelectric resonances in arrays of pyramid-shaped aluminum nanoparticles,” Phys. Rev. Lett. 113(24), 247401 (2014).
[Crossref] [PubMed]

Krueger, N. A.

H. L. Ning, N. A. Krueger, X. Sheng, H. Keum, C. Zhang, K. D. Choquette, X. L. Li, S. Kim, J. A. Rogers, and P. Braun, “Transfer-printing of tunable porous silicon microcavities with embedded emitters,” ACS Photonics 1(11), 1144–1150 (2014).
[Crossref]

Lederer, F.

R. Filter, J. Qi, C. Rockstuhl, and F. Lederer, “Circular optical nanoantennas: an analytical theory,” Phys. Rev. B 85(12), 125429 (2012).
[Crossref]

Lee, H.

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, “Far-field optical hyperlens magnifying sub-diffraction-limited objects,” Science 315(5819), 1686 (2007).
[Crossref] [PubMed]

Lee, L. P.

Lee, T. W.

M. Liu, T. W. Lee, S. K. Gray, P. Guyot-Sionnest, and M. Pelton, “Excitation of dark plasmons in metal nanoparticles by a localized emitter,” Phys. Rev. Lett. 102(10), 107401 (2009).
[Crossref] [PubMed]

Li, X. L.

H. L. Ning, N. A. Krueger, X. Sheng, H. Keum, C. Zhang, K. D. Choquette, X. L. Li, S. Kim, J. A. Rogers, and P. Braun, “Transfer-printing of tunable porous silicon microcavities with embedded emitters,” ACS Photonics 1(11), 1144–1150 (2014).
[Crossref]

Lin, F.

Z. Y. Fang, F. Lin, S. Huang, W. T. Song, and X. Zhu, “Focusing surface plasmon polariton trapping of colloidal particles,” Appl. Phys. Lett. 94(6), 063306 (2009).
[Crossref]

Liu, J.

G. Lu, J. Liu, T. Zhang, H. Shen, P. Perriat, M. Martini, O. Tillement, Y. Gu, Y. He, Y. Wang, and Q. Gong, “Enhancing molecule fluorescence with asymmetrical plasmonic antennas,” Nanoscale 5(14), 6545–6551 (2013).
[Crossref] [PubMed]

Liu, M.

M. Liu, T. W. Lee, S. K. Gray, P. Guyot-Sionnest, and M. Pelton, “Excitation of dark plasmons in metal nanoparticles by a localized emitter,” Phys. Rev. Lett. 102(10), 107401 (2009).
[Crossref] [PubMed]

Liu, N.

N. Liu, M. L. Tang, M. Hentschel, H. Giessen, and A. P. Alivisatos, “Nanoantenna-enhanced gas sensing in a single tailored nanofocus,” Nat. Mater. 10(8), 631–636 (2011).
[Crossref] [PubMed]

Liu, X.

T. Zhan, X. Shi, Y. Dai, X. Liu, and J. Zi, “Transfer matrix method for optics in graphene layers,” J. Phys. Condens. Matter 25(21), 215301 (2013).
[Crossref] [PubMed]

Liu, Y. J.

N. Zhang, Y. J. Liu, J. Yang, X. Su, J. Deng, C. C. Chum, M. Hong, and J. Teng, “High sensitivity molecule detection by plasmonic nanoantennas with selective binding at electromagnetic hotspots,” Nanoscale 6(3), 1416–1422 (2014).
[Crossref] [PubMed]

Liu, Z.

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, “Far-field optical hyperlens magnifying sub-diffraction-limited objects,” Science 315(5819), 1686 (2007).
[Crossref] [PubMed]

Lou, F.

Lu, G.

G. Lu, J. Liu, T. Zhang, H. Shen, P. Perriat, M. Martini, O. Tillement, Y. Gu, Y. He, Y. Wang, and Q. Gong, “Enhancing molecule fluorescence with asymmetrical plasmonic antennas,” Nanoscale 5(14), 6545–6551 (2013).
[Crossref] [PubMed]

Luk, T. S.

C. Guclu, T. S. Luk, G. T. Wang, and F. Capolino, “Radiative emission enhancement using nano-antennas made of hyperbolic metamaterial resonators,” Appl. Phys. Lett. 105(12), 123101 (2014).
[Crossref]

Luo, X.

Majewski, M. L.

Martini, M.

G. Lu, J. Liu, T. Zhang, H. Shen, P. Perriat, M. Martini, O. Tillement, Y. Gu, Y. He, Y. Wang, and Q. Gong, “Enhancing molecule fluorescence with asymmetrical plasmonic antennas,” Nanoscale 5(14), 6545–6551 (2013).
[Crossref] [PubMed]

Min, B.

B. Min, E. Ostby, V. Sorger, E. Ulin-Avila, L. Yang, X. Zhang, and K. Vahala, “High-Q surface-plasmon-polariton whispering-gallery microcavity,” Nature 457(7228), 455–458 (2009).
[Crossref] [PubMed]

Minkowski, F.

F. Minkowski, F. Wang, A. Chakrabarty, and Q. H. Wei, “Resonant cavity modes of circular plasmonic patch nanoantennas,” Appl. Phys. Lett. 104(2), 021111 (2014).
[Crossref]

A. Chakrabarty, F. Wang, F. Minkowski, K. Sun, and Q. H. Wei, “Cavity modes and their excitations in elliptical plasmonic patch nanoantennas,” Opt. Express 20(11), 11615–11624 (2012).
[PubMed]

Mohtashami, A.

A. Mohtashami, T. Coenen, A. Antoncecchi, A. Polman, and A. F. Koenderink, “Nanoscale execitation mapping of plasmonic patch antennas,” ACS Photonics 1(11), 1134–1143 (2014).
[Crossref]

Neubrech, F.

F. Neubrech, A. Pucci, T. W. Cornelius, S. Karim, A. García-Etxarri, and J. Aizpurua, “Resonant plasmonic and vibrational coupling in a tailored nanoantenna for infrared detection,” Phys. Rev. Lett. 101(15), 157403 (2008).
[Crossref] [PubMed]

Newman, W. D.

Ning, H. L.

H. L. Ning, N. A. Krueger, X. Sheng, H. Keum, C. Zhang, K. D. Choquette, X. L. Li, S. Kim, J. A. Rogers, and P. Braun, “Transfer-printing of tunable porous silicon microcavities with embedded emitters,” ACS Photonics 1(11), 1144–1150 (2014).
[Crossref]

Nordlander, P.

J. Zuloaga and P. Nordlander, “On the energy shift between near-field and far-field peak intensities in localized plasmon systems,” Nano Lett. 11(3), 1280–1283 (2011).
[Crossref] [PubMed]

Ogaki, R.

M. Frederiksen, V. E. Bochenkov, R. Ogaki, and D. S. Sutherland, “Onset of bonding plasmon hybridization preceded by gap modes in dielectric splitting of metal disks,” Nano Lett. 13(12), 6033–6039 (2013).
[Crossref] [PubMed]

Ostby, E.

B. Min, E. Ostby, V. Sorger, E. Ulin-Avila, L. Yang, X. Zhang, and K. Vahala, “High-Q surface-plasmon-polariton whispering-gallery microcavity,” Nature 457(7228), 455–458 (2009).
[Crossref] [PubMed]

Ozbay, E.

E. Ozbay, “Plasmonics: merging photonics and electronics at nanoscale dimensions,” Science 311(5758), 189–193 (2006).
[Crossref] [PubMed]

Pelton, M.

M. Liu, T. W. Lee, S. K. Gray, P. Guyot-Sionnest, and M. Pelton, “Excitation of dark plasmons in metal nanoparticles by a localized emitter,” Phys. Rev. Lett. 102(10), 107401 (2009).
[Crossref] [PubMed]

Perriat, P.

G. Lu, J. Liu, T. Zhang, H. Shen, P. Perriat, M. Martini, O. Tillement, Y. Gu, Y. He, Y. Wang, and Q. Gong, “Enhancing molecule fluorescence with asymmetrical plasmonic antennas,” Nanoscale 5(14), 6545–6551 (2013).
[Crossref] [PubMed]

Polman, A.

T. Coenen, F. Bernal Arango, A. Femius Koenderink, and A. Polman, “Directional emission from a single plasmonic scatterer,” Nat. Commun. 5, 3250 (2014).
[Crossref] [PubMed]

A. Mohtashami, T. Coenen, A. Antoncecchi, A. Polman, and A. F. Koenderink, “Nanoscale execitation mapping of plasmonic patch antennas,” ACS Photonics 1(11), 1134–1143 (2014).
[Crossref]

Pucci, A.

F. Neubrech, A. Pucci, T. W. Cornelius, S. Karim, A. García-Etxarri, and J. Aizpurua, “Resonant plasmonic and vibrational coupling in a tailored nanoantenna for infrared detection,” Phys. Rev. Lett. 101(15), 157403 (2008).
[Crossref] [PubMed]

Qi, J.

R. Filter, J. Qi, C. Rockstuhl, and F. Lederer, “Circular optical nanoantennas: an analytical theory,” Phys. Rev. B 85(12), 125429 (2012).
[Crossref]

Qiu, M.

Rakic, A. D.

Ren, X.

Rockstuhl, C.

R. Filter, J. Qi, C. Rockstuhl, and F. Lederer, “Circular optical nanoantennas: an analytical theory,” Phys. Rev. B 85(12), 125429 (2012).
[Crossref]

Rodriguez, S. R. K.

S. R. K. Rodriguez, F. Bernal Arango, T. P. Steinbusch, M. A. Verschuuren, A. F. Koenderink, and J. Gómez Rivas, “Breaking the symmetry of forward-backward light emission with localized and collective magnetoelectric resonances in arrays of pyramid-shaped aluminum nanoparticles,” Phys. Rev. Lett. 113(24), 247401 (2014).
[Crossref] [PubMed]

Rogers, J. A.

H. L. Ning, N. A. Krueger, X. Sheng, H. Keum, C. Zhang, K. D. Choquette, X. L. Li, S. Kim, J. A. Rogers, and P. Braun, “Transfer-printing of tunable porous silicon microcavities with embedded emitters,” ACS Photonics 1(11), 1144–1150 (2014).
[Crossref]

Ross, B. M.

Sha, W. E. I.

Shen, H.

G. Lu, J. Liu, T. Zhang, H. Shen, P. Perriat, M. Martini, O. Tillement, Y. Gu, Y. He, Y. Wang, and Q. Gong, “Enhancing molecule fluorescence with asymmetrical plasmonic antennas,” Nanoscale 5(14), 6545–6551 (2013).
[Crossref] [PubMed]

Sheng, X.

H. L. Ning, N. A. Krueger, X. Sheng, H. Keum, C. Zhang, K. D. Choquette, X. L. Li, S. Kim, J. A. Rogers, and P. Braun, “Transfer-printing of tunable porous silicon microcavities with embedded emitters,” ACS Photonics 1(11), 1144–1150 (2014).
[Crossref]

Shi, X.

T. Zhan, X. Shi, Y. Dai, X. Liu, and J. Zi, “Transfer matrix method for optics in graphene layers,” J. Phys. Condens. Matter 25(21), 215301 (2013).
[Crossref] [PubMed]

Sipe, J. E.

Song, W. T.

Z. Y. Fang, F. Lin, S. Huang, W. T. Song, and X. Zhu, “Focusing surface plasmon polariton trapping of colloidal particles,” Appl. Phys. Lett. 94(6), 063306 (2009).
[Crossref]

Sorger, V.

B. Min, E. Ostby, V. Sorger, E. Ulin-Avila, L. Yang, X. Zhang, and K. Vahala, “High-Q surface-plasmon-polariton whispering-gallery microcavity,” Nature 457(7228), 455–458 (2009).
[Crossref] [PubMed]

Steinbusch, T. P.

S. R. K. Rodriguez, F. Bernal Arango, T. P. Steinbusch, M. A. Verschuuren, A. F. Koenderink, and J. Gómez Rivas, “Breaking the symmetry of forward-backward light emission with localized and collective magnetoelectric resonances in arrays of pyramid-shaped aluminum nanoparticles,” Phys. Rev. Lett. 113(24), 247401 (2014).
[Crossref] [PubMed]

Su, X.

N. Zhang, Y. J. Liu, J. Yang, X. Su, J. Deng, C. C. Chum, M. Hong, and J. Teng, “High sensitivity molecule detection by plasmonic nanoantennas with selective binding at electromagnetic hotspots,” Nanoscale 6(3), 1416–1422 (2014).
[Crossref] [PubMed]

Sun, C.

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, “Far-field optical hyperlens magnifying sub-diffraction-limited objects,” Science 315(5819), 1686 (2007).
[Crossref] [PubMed]

Sun, K.

Sutherland, D. S.

M. Frederiksen, V. E. Bochenkov, R. Ogaki, and D. S. Sutherland, “Onset of bonding plasmon hybridization preceded by gap modes in dielectric splitting of metal disks,” Nano Lett. 13(12), 6033–6039 (2013).
[Crossref] [PubMed]

Tang, M. L.

N. Liu, M. L. Tang, M. Hentschel, H. Giessen, and A. P. Alivisatos, “Nanoantenna-enhanced gas sensing in a single tailored nanofocus,” Nat. Mater. 10(8), 631–636 (2011).
[Crossref] [PubMed]

Teng, J.

N. Zhang, Y. J. Liu, J. Yang, X. Su, J. Deng, C. C. Chum, M. Hong, and J. Teng, “High sensitivity molecule detection by plasmonic nanoantennas with selective binding at electromagnetic hotspots,” Nanoscale 6(3), 1416–1422 (2014).
[Crossref] [PubMed]

Thylen, L.

Tillement, O.

G. Lu, J. Liu, T. Zhang, H. Shen, P. Perriat, M. Martini, O. Tillement, Y. Gu, Y. He, Y. Wang, and Q. Gong, “Enhancing molecule fluorescence with asymmetrical plasmonic antennas,” Nanoscale 5(14), 6545–6551 (2013).
[Crossref] [PubMed]

Tseng, C. B.

Y. C. Chang, S. M. Wang, H. C. Chung, C. B. Tseng, and S. H. Chang, “Observation of absorption-dominated bonding dark plasmon mode from metal-insulator-metal nanodisk arrays fabricated by nanospherical-lens lithography,” ACS Nano 6(4), 3390–3396 (2012).
[Crossref] [PubMed]

Ulin-Avila, E.

B. Min, E. Ostby, V. Sorger, E. Ulin-Avila, L. Yang, X. Zhang, and K. Vahala, “High-Q surface-plasmon-polariton whispering-gallery microcavity,” Nature 457(7228), 455–458 (2009).
[Crossref] [PubMed]

Vahala, K.

B. Min, E. Ostby, V. Sorger, E. Ulin-Avila, L. Yang, X. Zhang, and K. Vahala, “High-Q surface-plasmon-polariton whispering-gallery microcavity,” Nature 457(7228), 455–458 (2009).
[Crossref] [PubMed]

Verschuuren, M. A.

S. R. K. Rodriguez, F. Bernal Arango, T. P. Steinbusch, M. A. Verschuuren, A. F. Koenderink, and J. Gómez Rivas, “Breaking the symmetry of forward-backward light emission with localized and collective magnetoelectric resonances in arrays of pyramid-shaped aluminum nanoparticles,” Phys. Rev. Lett. 113(24), 247401 (2014).
[Crossref] [PubMed]

Wang, F.

F. Minkowski, F. Wang, A. Chakrabarty, and Q. H. Wei, “Resonant cavity modes of circular plasmonic patch nanoantennas,” Appl. Phys. Lett. 104(2), 021111 (2014).
[Crossref]

A. Chakrabarty, F. Wang, F. Minkowski, K. Sun, and Q. H. Wei, “Cavity modes and their excitations in elliptical plasmonic patch nanoantennas,” Opt. Express 20(11), 11615–11624 (2012).
[PubMed]

Wang, G. T.

C. Guclu, T. S. Luk, G. T. Wang, and F. Capolino, “Radiative emission enhancement using nano-antennas made of hyperbolic metamaterial resonators,” Appl. Phys. Lett. 105(12), 123101 (2014).
[Crossref]

Wang, S. M.

Y. C. Chang, S. M. Wang, H. C. Chung, C. B. Tseng, and S. H. Chang, “Observation of absorption-dominated bonding dark plasmon mode from metal-insulator-metal nanodisk arrays fabricated by nanospherical-lens lithography,” ACS Nano 6(4), 3390–3396 (2012).
[Crossref] [PubMed]

Wang, Y.

G. Lu, J. Liu, T. Zhang, H. Shen, P. Perriat, M. Martini, O. Tillement, Y. Gu, Y. He, Y. Wang, and Q. Gong, “Enhancing molecule fluorescence with asymmetrical plasmonic antennas,” Nanoscale 5(14), 6545–6551 (2013).
[Crossref] [PubMed]

Wei, Q. H.

F. Minkowski, F. Wang, A. Chakrabarty, and Q. H. Wei, “Resonant cavity modes of circular plasmonic patch nanoantennas,” Appl. Phys. Lett. 104(2), 021111 (2014).
[Crossref]

A. Chakrabarty, F. Wang, F. Minkowski, K. Sun, and Q. H. Wei, “Cavity modes and their excitations in elliptical plasmonic patch nanoantennas,” Opt. Express 20(11), 11615–11624 (2012).
[PubMed]

Wei, X.

Woolf, D.

Wosinski, L.

Xiao, J. J.

Q. Zhang, J. J. Xiao, X. M. Zhang, D. Z. Han, and L. Gao, “Core-shell-structured dielectric−metal circular nanodisk antenna: gap plasmon assisted magnetic toroid-like cavity modes,” ACS Photonics 2(1), 60–65 (2015).
[Crossref]

X. M. Zhang, J. J. Xiao, and Q. Zhang, “Interaction between single nano-emitter and plasmonic disk–ring nanostructure with multiple Fano resonances,” J. Opt. Soc. Am. B 31(9), 2193–2200 (2014).
[Crossref]

Xiong, Y.

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, “Far-field optical hyperlens magnifying sub-diffraction-limited objects,” Science 315(5819), 1686 (2007).
[Crossref] [PubMed]

Yan, M.

Yang, J.

N. Zhang, Y. J. Liu, J. Yang, X. Su, J. Deng, C. C. Chum, M. Hong, and J. Teng, “High sensitivity molecule detection by plasmonic nanoantennas with selective binding at electromagnetic hotspots,” Nanoscale 6(3), 1416–1422 (2014).
[Crossref] [PubMed]

Yang, L.

B. Min, E. Ostby, V. Sorger, E. Ulin-Avila, L. Yang, X. Zhang, and K. Vahala, “High-Q surface-plasmon-polariton whispering-gallery microcavity,” Nature 457(7228), 455–458 (2009).
[Crossref] [PubMed]

Yu, N.

Zhan, T.

T. Zhan, X. Shi, Y. Dai, X. Liu, and J. Zi, “Transfer matrix method for optics in graphene layers,” J. Phys. Condens. Matter 25(21), 215301 (2013).
[Crossref] [PubMed]

Zhang, C.

H. L. Ning, N. A. Krueger, X. Sheng, H. Keum, C. Zhang, K. D. Choquette, X. L. Li, S. Kim, J. A. Rogers, and P. Braun, “Transfer-printing of tunable porous silicon microcavities with embedded emitters,” ACS Photonics 1(11), 1144–1150 (2014).
[Crossref]

Zhang, H.

H. Zhang, H. V. Demir, and A. O. Govorov, “Plasmonic metamaterials and nanocomposites with the narrow transparency window effect in broad extinction spectra,” ACS Photonics 1(9), 822–832 (2014).
[Crossref]

Zhang, N.

N. Zhang, Y. J. Liu, J. Yang, X. Su, J. Deng, C. C. Chum, M. Hong, and J. Teng, “High sensitivity molecule detection by plasmonic nanoantennas with selective binding at electromagnetic hotspots,” Nanoscale 6(3), 1416–1422 (2014).
[Crossref] [PubMed]

Zhang, Q.

Q. Zhang, J. J. Xiao, X. M. Zhang, D. Z. Han, and L. Gao, “Core-shell-structured dielectric−metal circular nanodisk antenna: gap plasmon assisted magnetic toroid-like cavity modes,” ACS Photonics 2(1), 60–65 (2015).
[Crossref]

X. M. Zhang, J. J. Xiao, and Q. Zhang, “Interaction between single nano-emitter and plasmonic disk–ring nanostructure with multiple Fano resonances,” J. Opt. Soc. Am. B 31(9), 2193–2200 (2014).
[Crossref]

Zhang, T.

G. Lu, J. Liu, T. Zhang, H. Shen, P. Perriat, M. Martini, O. Tillement, Y. Gu, Y. He, Y. Wang, and Q. Gong, “Enhancing molecule fluorescence with asymmetrical plasmonic antennas,” Nanoscale 5(14), 6545–6551 (2013).
[Crossref] [PubMed]

Zhang, X.

B. Min, E. Ostby, V. Sorger, E. Ulin-Avila, L. Yang, X. Zhang, and K. Vahala, “High-Q surface-plasmon-polariton whispering-gallery microcavity,” Nature 457(7228), 455–458 (2009).
[Crossref] [PubMed]

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, “Far-field optical hyperlens magnifying sub-diffraction-limited objects,” Science 315(5819), 1686 (2007).
[Crossref] [PubMed]

Zhang, X. M.

Q. Zhang, J. J. Xiao, X. M. Zhang, D. Z. Han, and L. Gao, “Core-shell-structured dielectric−metal circular nanodisk antenna: gap plasmon assisted magnetic toroid-like cavity modes,” ACS Photonics 2(1), 60–65 (2015).
[Crossref]

X. M. Zhang, J. J. Xiao, and Q. Zhang, “Interaction between single nano-emitter and plasmonic disk–ring nanostructure with multiple Fano resonances,” J. Opt. Soc. Am. B 31(9), 2193–2200 (2014).
[Crossref]

Zhu, X.

Z. Y. Fang, F. Lin, S. Huang, W. T. Song, and X. Zhu, “Focusing surface plasmon polariton trapping of colloidal particles,” Appl. Phys. Lett. 94(6), 063306 (2009).
[Crossref]

Zhukovsky, S. V.

Zi, J.

T. Zhan, X. Shi, Y. Dai, X. Liu, and J. Zi, “Transfer matrix method for optics in graphene layers,” J. Phys. Condens. Matter 25(21), 215301 (2013).
[Crossref] [PubMed]

Zuloaga, J.

J. Zuloaga and P. Nordlander, “On the energy shift between near-field and far-field peak intensities in localized plasmon systems,” Nano Lett. 11(3), 1280–1283 (2011).
[Crossref] [PubMed]

ACS Nano (1)

Y. C. Chang, S. M. Wang, H. C. Chung, C. B. Tseng, and S. H. Chang, “Observation of absorption-dominated bonding dark plasmon mode from metal-insulator-metal nanodisk arrays fabricated by nanospherical-lens lithography,” ACS Nano 6(4), 3390–3396 (2012).
[Crossref] [PubMed]

ACS Photonics (4)

Q. Zhang, J. J. Xiao, X. M. Zhang, D. Z. Han, and L. Gao, “Core-shell-structured dielectric−metal circular nanodisk antenna: gap plasmon assisted magnetic toroid-like cavity modes,” ACS Photonics 2(1), 60–65 (2015).
[Crossref]

H. L. Ning, N. A. Krueger, X. Sheng, H. Keum, C. Zhang, K. D. Choquette, X. L. Li, S. Kim, J. A. Rogers, and P. Braun, “Transfer-printing of tunable porous silicon microcavities with embedded emitters,” ACS Photonics 1(11), 1144–1150 (2014).
[Crossref]

H. Zhang, H. V. Demir, and A. O. Govorov, “Plasmonic metamaterials and nanocomposites with the narrow transparency window effect in broad extinction spectra,” ACS Photonics 1(9), 822–832 (2014).
[Crossref]

A. Mohtashami, T. Coenen, A. Antoncecchi, A. Polman, and A. F. Koenderink, “Nanoscale execitation mapping of plasmonic patch antennas,” ACS Photonics 1(11), 1134–1143 (2014).
[Crossref]

Appl. Opt. (1)

Appl. Phys. Lett. (3)

C. Guclu, T. S. Luk, G. T. Wang, and F. Capolino, “Radiative emission enhancement using nano-antennas made of hyperbolic metamaterial resonators,” Appl. Phys. Lett. 105(12), 123101 (2014).
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Figures (6)

Fig. 1
Fig. 1 Geometry of the multilayered metal-dielectric circular antenna.
Fig. 2
Fig. 2 Optical cross sections of the antenna with plane wave excitation. (a) Insets show the resonant electric fields E z in the xz plane and the xy plane across the top dielectric layer for the two peaks for two different incident plane wave configurations. (b) Inserts show E x in the xz plane and the xy plane across the top dielectric layer for the resonances.
Fig. 3
Fig. 3 Non-radiative decay rate spectra for electric dipole at P 1 , P 2 , P 3 , and P 4 .
Fig. 4
Fig. 4 Selective mode excitation by a dipole source. Shown in the table are xz plane and xy plane electric field when dipole source is positioned at P 1 , P 2 , P 3 , and P 4 . The resonant wavelength and mode labeling are shown for each column.
Fig. 5
Fig. 5 Cavity resonant frequencies (symbols) versus χ ' nm /(R+d) for different radius of the nanoantenna. The 2D theoretically calculated dispersion (black lines) of hybridized SPP are also shown.
Fig. 6
Fig. 6 In-plane field ratio | E // / E tot | 2 measured along the z axis for the three different resonance modes excited by a dipole source at P 1 . The symbols “M” and “D” represent the metal and dielectric layer, respectively.

Equations (5)

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ρ (ρ E z ρ )+ 1 ρ 2 2 E z ϕ 2 + 2 E z z 2 + k 2 i E z =0
E z (ρ,ϕ,z)=a(z)[ H m (1) ( k gsp ρ)+ r m H m (2) ( k gsp ρ)] e imϕ
k gsp R eff =χ ' nm
D ij = 1 2 [ 1+ η ij 1 η i j 1 η i j 1+ η ij ]
ϕ j =[ e i k z,j Δz 0 0 e i k z,j Δz ]

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