OSA's Digital Library

Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 20, Iss. 11 — May. 21, 2012
  • pp: 11615–11624
« Show journal navigation

Cavity modes and their excitations in elliptical plasmonic patch nanoantennas

Ayan Chakrabarty, Feng Wang, Fred Minkowski, Kai Sun, and Qi-Huo Wei  »View Author Affiliations


Optics Express, Vol. 20, Issue 11, pp. 11615-11624 (2012)
http://dx.doi.org/10.1364/OE.20.011615


View Full Text Article

Acrobat PDF (1444 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

We present experimental and theoretical studies of two dimensional periodic arrays of elliptical plasmonic patch nanoantennas. Experimental and simulation results demonstrate that the azimuthal symmetry breaking of the metal patches leads to the occurrence of even and odd resonant cavity modes and the excitation geometries dependent on their modal symmetries. We show that the cavity modes can be described by the product of radial and angular Mathieu functions with excellent agreements with both simulations and experiments. The effects of the patch periodicity on the excitation of the surface plasmon and its coupling with the cavity modes are also discussed.

© 2012 OSA

1. Introduction

Plasmonic nanoantennas have attracted significant attention in recent years due to their ability in coupling free space electromagnetic radiation into sub-diffraction limited volumes and vice versa based on the electrodynamics reciprocity [1

1. L. Novotny and N. van Hulst, “Antennas for light,” Nat. Photonics 5(2), 83–90 (2011). [CrossRef]

, 2

2. J. A. Schuller, E. S. Barnard, W. Cai, Y. C. Jun, J. S. White, and M. L. Brongersma, “Plasmonics for extreme light concentration and manipulation,” Nat. Mater. 9(3), 193–204 (2010). [CrossRef] [PubMed]

]. Resonantly enhanced local fields in these nanoantennas facilitate applications in various fields including surface enhanced fluorescence and Raman spectroscopy [3

3. K. Aslan, I. Gryczynski, J. Malicka, E. Matveeva, J. R. Lakowicz, and C. D. Geddes, “Metal-enhanced fluorescence: an emerging tool in biotechnology,” Curr. Opin. Biotechnol. 16(1), 55–62 (2005). [CrossRef] [PubMed]

6

6. L. Qin, S. Zou, C. Xue, A. Atkinson, G. C. Schatz, and C. A. Mirkin, “Designing, fabricating, and imaging Raman hot spots,” Proc. Natl. Acad. Sci. U.S.A. 103(36), 13300–13303 (2006). [CrossRef] [PubMed]

] and in nonlinear optics [7

7. T. Schumacher, K. Kratzer, D. Molnar, M. Hentschel, H. Giessen, and M. Lippitz, “Nanoantenna-enhanced ultrafast nonlinear spectroscopy of a single gold nanoparticle,” Nat. Commun. 2, 333 (2011). [CrossRef]

,8

8. K. D. Ko, A. Kumar, K. H. Fung, R. Ambekar, G. L. Liu, N. X. Fang, and K. C. Toussaint Jr., “Nonlinear optical response from arrays of Au bowtie nanoantennas,” Nano Lett. 11(1), 61–65 (2011). [CrossRef] [PubMed]

]. For examples, as the optical analogues to their radio frequency counterparts, Hertzian dipole and Yagi-Uda antennas enable not only focusing light into nanometer spots but also emitting light unidirectionally by coupling quantum dots with them [9

9. A. G. Curto, G. Volpe, T. H. Taminiau, M. P. Kreuzer, R. Quidant, and N. F. van Hulst, “Unidirectional emission of a quantum dot coupled to a nanoantenna,” Science 329(5994), 930–933 (2010). [CrossRef] [PubMed]

11

11. D. Dregely, R. Taubert, J. Dorfmüller, R. Vogelgesang, K. Kern, and H. Giessen, “3D optical Yagi-Uda nanoantenna array,” Nat Commun 2, 267 (2011). [CrossRef] [PubMed]

]. Vertical metal-dielectric-metal (MDM) designs of plasmonic nanoantennas and nanocavities have been proposed and demonstrated with the great advantage that the nanogap thickness can be precisely controlled by using the advanced thin film deposition techniques [12

12. H. T. Miyazaki and Y. Kurokawa, “Squeezing visible light waves into a 3-nm-thick and 55-nm-long plasmon cavity,” Phys. Rev. Lett. 96(9), 097401 (2006). [CrossRef] [PubMed]

14

14. B. Joshi, A. Chakrabarty, and Q.-H. Wei, “Numerical studies of metal-dielectric-metal nanoantennas,” IEEE Trans. Nanotechnol. 9(6), 701–707 (2010). [CrossRef]

].

2. Sample fabrication

To fabricate the plasmonic patch nanoantennas [Fig. 1(a)
Fig. 1 (a) Schematic elliptical plasmonic patch nanoantennas. The sky blue layers represent Ag, and the dark blue represents Al2O3. Grey is the silicon substrate. (b) An SEM image of a 2D array of plasmonic patch nanoantennas with a period of 500nm and two major axis radii a = 72nm, b = 52nm. The long axis of the patches is tilted about 22° from vertical direction.
], a 10 nm NiCr adhesion layer and a 100 nm Ag film were sequentially deposited on a Si wafer using electron beam evaporation, and then a 15 nm Al2O3 dielectric layer was deposited using atomic layer deposition (ALD). The 45 nm thick top elliptical Ag patches were fabricated using the standard electron beam lithography and lift-off processes. The reason that we used Ag instead of Au is to design the resonant wavelengths of the first few cavity modes below 950nm (the limit of our imaging spectrograph system). The advantages of using ALD process include the conformal and uniform film coverage and sub-nm accuracy in thickness control. An exemplary SEM picture of the fabricated patch nanoantennas is shown in Fig. 1(b). To measure the reflection spectra, a collimated white light beam was focused onto the samples using a 40 × (0.6NA) objective, and the reflected light was collected using the same objective for spectral measurements. The reflection spectra are normalized by the spectra measured from the areas without the patches.

The major axial radii of the elliptical patches are varied from 40 nm to 96 nm. Two patch periods, 300 nm and 500 nm, are used for the patch antenna samples. As will be discussed later, these patch periods are small enough to ensure minimal effect of surface plasmons excitation outside the cavity on the cavity modes, and large enough to ensure no overlapping of the fringe fields between neighboring patches.

3. Excitation of the cavity modes: experiments and simulations

The measured reflection spectra for two representative patch sizes are presented in Fig. 2(a)
Fig. 2 The measured and simulated reflection spectra for two representative patch sizes: a = 93nm, b = 74nm (blue) and a = 72nm, and b = 52nm (red). The polarization of the incident light is parallel to the long (a, b) and short axes (c, d) of the patches respectively. The dotted curves in b and d are the local field enhancement spectra calculated at the cavity edges. The cavity modes are indicated with the mode indices. The e02 cavity mode is hard to locate for the smaller patch antennas (red curves) and thus not labeled.
and 2(c), where several dips with different absorption depths can be observed. The resonant wavelengths of these dips shift to blue when the incident polarization is changed from the direction parallel to the long axis to the direction parallel to the short axis of the elliptical patches.

4. Discussion

The cavity modes observed in the elliptical patch nanoantennas are due to constructive interferences of gap surface plasmons generated and reflected at the patch boundaries propagating parallel to the interface. To understand these cavity modes, we consider the electromagnetic waves propagating in the metal-dielectric-metal (MDM) waveguide structure. The electrical field E can be described by the Helmholtz Eq. 2E+ki2E=0 where ki2=εiω2/c2are the total wave vectors with the subscript i = m, d referring to metal and dielectric regions, ω and c are the radial frequency and speed of light in vacuum. Since the gap surface plasmons need to be evanescent in the direction (z) perpendicular to the MDM plane, the propagation constant along z should be imaginary, denoted as ikzi. Therefore, the total wave vector ki is the summation of the propagation constant ikzi, and the propagation constant along the MDM plane or the gap plasmon wave vector kgsp, ki2=kgsp2kzi2.

There exist two gap surface plasmon modes with one symmetric and one anti-symmetric profile of field distribution [29

29. J. A. Dionne, L. A. Sweatlock, H. A. Atwater, and A. Polman, “Plasmon slot waveguides: towards chip-scale propagation with subwavelength-scale localization,” Phys. Rev. B 73(3), 035407 (2006). [CrossRef]

]. For small dielectric thicknesses, the symmetric mode exists at high frequencies and can be ignored in our case. For the top metal layer of the MDM structure with a finite thickness tm, the dispersion relation for the anti-symmetric mode can be expressed as [30

30. E. N. Economou, “Surface plasmons in thin films,” Phys. Rev. 182(2), 539–554 (1969). [CrossRef]

]:
kzmεdkzdεm=1+r1+r2+r1r21+r1+r2+r1r2,
(1)
where kzm=kgsp2εmω2/c2,kzd=kgsp2εdω2/c2,r1=exp(2kzmtm),r2=exp(2kzdtd), and td is the thicknesses of the dielectric layer.

Given the elliptical shape of the nanocavities, it is convenient to consider the Helmholtz Eqs. in the elliptical cylindrical coordinates (ξ, η, z). The transformation from the Cartesian coordinates (x, y, z) to the elliptical coordinates is:x=fcoshξcosη, y=fsinhξsinη, z = z where f is the focal length of the ellipse, f=(a2b2)1/2 . Since our primary interest is in the electrical field distributions inside the dielectric layer, we focus only on the dominant component of the electrical field Ezd (ξ, η, z). After the transformation, the Helmholtz Eq. for Ezd (ξ,η,z) can be written as [28

28. P. Billaud, J. R. Huntzinger, E. Cottancin, J. Lermé, M. Pellarin, L. Arnaud, M. Broyer, N. Del Fatti, and F. Vallée, “Optical extinction spectroscopy of single silver nanoparticles,” Eur. Phys. J. D 43(1-3), 271–274 (2007). [CrossRef]

,29

29. J. A. Dionne, L. A. Sweatlock, H. A. Atwater, and A. Polman, “Plasmon slot waveguides: towards chip-scale propagation with subwavelength-scale localization,” Phys. Rev. B 73(3), 035407 (2006). [CrossRef]

]:

1f2(sinh2ξ+sin2η)[d2Ezddξ2+d2Ezddη2]+d2Ezddz2+kd2Ezd=0,
(2)

Assuming Ezd(ξ,η,z) = R(ξ)Φ(η)Z(z), Z(z)=Aekzdz+Bekzdz, separation of variables decomposes Eq. (2) into the radial and angular Mathieu Eqs [25

25. H. Liu, J. Ng, S. B. Wang, Z. F. Lin, Z. H. Hang, C. T. Chan, and S. N. Zhu, “Strong light-induced negative optical pressure arising from kinetic energy of conduction electrons in plasmon-type cavities,” Phys. Rev. Lett. 106(8), 087401 (2011). [CrossRef] [PubMed]

,30

30. E. N. Economou, “Surface plasmons in thin films,” Phys. Rev. 182(2), 539–554 (1969). [CrossRef]

]:
d2Rdξ2(c2qcosh2ξ)R=0,d2Φdη2+(c2qcos2η)Φ=0,
(3)
where c is the separation constant and q=f2kgsp2/4. The fact that Φ should be a periodic function of η with either a π or 2π period determines the possible eigen values of c [31

31. G. Blanch, “Mathieu Functions,” in Handbook of mathematical functions, M. Abramowitz, I. A. Stegun, ed. (Dover, New York, 1953).

,32

32. J. C. Gutierrez-Vega, R. M. Rodriguez-Dagnino, M. A. Meneses-Nava, and S. Chavez-Cerda, “Mathieu functions, a visual approach,” Am. J. Phys. 71(3), 233–242 (2003). [CrossRef]

]. The allowed solutions for Φ are two independent families of even (e) and odd (o) angular Mathieu functions: Cem(η,q) for m0 and Som(η,q) for m1 respectively. The radial function R should be a non-periodic, decreasing oscillatory function of ξ in 0≤ξ<∞ with non-singularity at the origin; the standing wave solutions for R are the even and odd radial Mathieu functions of the first kind: Jem(ξ,q) for m0 and Jom(ξ,q)form1. For fixed z, Ezd(ξ,η,z) is proportional to the product of the angular and radial Mathieu function:
EzdmJem(ξ,q)Cem(η,q),m0(even)Jom(ξ,q)Sem(η,q),m1(odd),
(4)
where the superscript m stands for the m-th order. Since the nanocavities have an open edge, the electrical field Ezd(ξ,η,z) is approximately at its local maximum at the boundary. As a result, the cavity resonances are determined by the Neumann boundary condition:
(even):Jem(ξ,q)Cem(η,q)(odd):Jom(ξ,q)Sem(η,q)=0,
(5)
whereξ0=arcsinh(b/f) defines the cavity boundary. For a given order m, there exists an infinite number of q values satisfying Eq. (5). We use qmne,o to denote the nth zero of J'em(ξ0,q) orJom(ξ0,q), and use emn and omn to denote the even and odd cavity modes.

For one givenqmne,o, the gap surface plasmons forming the standing waves should satisfy:

kgsp=(4qmne,o/f2)1/2,
(6)

To validate this resonant condition, we calculated the kgsp for these cavity modes by using Eqs. (5-6) based on their resonant wavelengths and patch sizes observed in the experiments, and compare it with the kgsp calculated using the dispersion relation (Eq. (1). The results for different patch sizes in Fig. 5(a)
Fig. 5 Data points represent the measured cavity resonant frequencies versus the gap plasmon wave vector calculated using Eq. (6) for real patch sizes (a) and for the effective patch sizes a´ = a + h, b´ = b + h (b). The blue solid curves represent the dispersion curve for the gap plasmons calculated using Eq. (1).
show reasonable agreements between the resonant condition and the gap plasmon dispersion curve. To note here, we only included the data for e11/o11, e12/o12 and e31/o31 modes in Fig. 5 because their features can be easily identified in the measured reflection spectra.

It is also discernible that the resonant frequencies obtained using Eq. (6) are systematically lower than the dispersion curve for the gap surface plasmons obtained using Eq. (1). This systematic discrepancy can be ascribed to the fringing fields, i.e. the electrical fields do not go to zero beyond the cavity edge. In another word, the antinodes of the cavity modes are not exactly located at the cavity boundary, and there exists effectively a phase shift upon excitation/reflection of the gap surface plasmons at the boundary [12

12. H. T. Miyazaki and Y. Kurokawa, “Squeezing visible light waves into a 3-nm-thick and 55-nm-long plasmon cavity,” Phys. Rev. Lett. 96(9), 097401 (2006). [CrossRef] [PubMed]

,33

33. R. Gordon, “Light in a subwavelength slit in a metal: propagation and reflection,” Phys. Rev. B 73(15), 153405 (2006). [CrossRef]

]. This fringing field effect can also be considered as a result of the capacitance between the patch edges and the bottom metal film [34

34. H. E. Kamchouchi and A. A. Zaky, “A direct method for the calculation of the edge capacitance of thick electrodes,” J. Phys. D Appl. Phys. 8(12), 1365–1371 (1975). [CrossRef]

,35

35. S. Zhang, Y. S. Park, Y. M. Liu, T. Zentgraf, and X. Zhang, “Far-field measurement of ultra-small plasmonic mode volume,” Opt. Express 18(6), 6048–6055 (2010). [CrossRef] [PubMed]

]. To take this fringing field into account, one simple while effective empirical approach suggested in microwave frequencies is to use the sum of the actual patch radius and the dielectric layer thickness as the effective radius [36

36. P. Mythili and A. Das, “Simple approach to determine resonant frequencies of microstrip antennas,” IEE Proc., Microw. Antennas Propag. 145(2), 159–162 (1998). [CrossRef]

]. By following this empirical correction, we recalculated the resonant frequencies using a´ = a + h and b´ = b + h as the two main axial radii in Eq. (6). The results show excellent agreements with the dispersion for gap surface plasmons [Fig. 5(b)].

One interesting observation is that the resonant frequencies for even mode and odd modes are noticeably different except for the e31 and o31 modes. This is fortuitous and because the resonant conditions for these two modes are almost the same. For example, the value of q31e and q31o are 1.9159 and 1.963 for the same patch size with a = 93nm, b = 74nm respectively.

The effects of array periods on the resonant wavelengths are very interesting while quite complicated. We speculate that there exist three regions: (1) For small periods where the fringe fields between neighboring patches overlap, the cavity modes are coupled with each other (in analog to the systems of atoms with overlapping wave functions), and form a 2D photonic crystal system. In this case, it can be expected that the gap plasmons will be delocalized at certain frequency bands, while be prohibited to propagate forming band gaps at the other frequencies. (2) For large periods, the surface plasmons at the Ag/Al2O3 interface outside the cavities are often excited, causing the complex interactions between cavity modes and surface plasmon modes. (3) For the intermediate periods like those in our experiments, the cavity fringe fields are not overlapping, and the surface plasmon modes are not crowded. In the following, we show numerical studies for the last two situations as a proof that the cavity modes and resonant conditions in our case are not affected by these array effects.

The 2D periodicity of the metal patches provides a reciprocal vector to compensate for the momentum mismatch between the incident light and the surface plasmon waves at the Ag-Al2O3 interface; a natural question is therefore how the surface plasmon excitation outside the cavity affects the cavity resonances. Although the incident angles vary in a range determined by the objective N.A., the excitation condition for the surface plasmons propagating at the direction perpendicular to the incident plane remains unchanged. For example, for 500 nm array period, the dips at about 540 nm in the reflection spectra are due to the excitation of the surface plasmons. This can be verified by looking at the local field distributions at this resonant wavelength, where the interference patterns of surface plasmons outside the cavities can clearly be seen. For a small thickness (15nm) of the Al2O3 film, the dispersion for the surface plasmon waves at the Ag-Al2O3 interface can be approximated as ksp=ksp0+Δkwhere ksp0=ωcεm/(εm+1) is the wave vector for the excited surface plasmons at the Ag-air interface, Δk=ωcεd1εd(εm1εm)2εdεm1εm1|εm|2πλ, εm'is the real part of the permittivity for Ag, and εdis the permittivity for Al2O3 [37

37. H. Raether, “Surface plasmons on smooth and rough surfaces and on gratings,” Springer Tracts Mod. Phys. 111, 1–133 (1988).

]. Simple calculations show that for the incident light at 540 nm wavelength, kgsp = 0.0125 nm−1 matches with the reciprocal vector of the patch arrays.

The coupling effects between surface plasmons and cavity resonances usually induce Fano type resonances. For a fixed patch period, the excited surface plasmon may couple with different cavity modes for different patch sizes. As it can be seen in Fig. 6
Fig. 6 Snapshots of the z-component Ezd of the electric field calculated at the middle plane through the dielectric layer at the resonant wavelength 540 nm for two different patch radii: 72nm × 52nm (a) and 93nm × 74nm (b). The illumination is normal to the plane.
, for 500 nm array period, the surface plasmon excited by 540 nm wavelength light can couple with either e11 mode or e31 mode depending on different patch sizes. It is also interesting to note that for the e11 mode not at resonance, the surface plasmon waves outside and inside the nanocavities are in opposite phase [Fig. 6(a)]. While for the e31 mode which is at resonance, the electrical fields due to the surface plasmons outside and inside the nanocavities are in phase [Fig. 6(b)]. It is important to note that the small patch periods (300 nm and 500 nm) are used in the experiments to minimize the excitations of surface plasmons outside the cavities and their effects on the cavity resonances. This can be seen from the simulated reflection spectra for different patch periodicities (Fig. 7
Fig. 7 Calculated reflection spectra for different periods with the elliptical patch size: a = 70 nm; b = 50 nm. a) and c): periods vary between 300nm to 500nm; b) and d): periods vary between 600nm to 900nm. a) and b): Incident polarization is along the long axis of elliptical patches for; c) and d): Incident polarization is along the short axis of elliptical patches.
). For the patch period below 500nm, the narrow dips due to the excitation of surface plasmons shift to red with the period increase, while the reflection dips due to the cavity modes remain unchanged as long as they are not overlapping with the surface plasmon excitation [Fig. 7(a)]. When the patch period is larger than 600 nm, the resonant wavelengths of these cavity modes start to vary with the changes in the patch period due to the excitation of multiple surface plasmon modes [Fig. 7(b)].

5. Conclusion

Acknowledgments

We acknowledge valuable discussions with Jonathan Selinger and the help from Cheng Sun during the early stage of this work. This work is supported by NSF CAREER award ECCS-0954976 and NSF IIP-1010368, and used used the Lurie Nanofabrication Facility at the University of Michigan, a member of the National Nanotechnology Infrastructure Network (NNIN) supported by NSF.

References and links

1.

L. Novotny and N. van Hulst, “Antennas for light,” Nat. Photonics 5(2), 83–90 (2011). [CrossRef]

2.

J. A. Schuller, E. S. Barnard, W. Cai, Y. C. Jun, J. S. White, and M. L. Brongersma, “Plasmonics for extreme light concentration and manipulation,” Nat. Mater. 9(3), 193–204 (2010). [CrossRef] [PubMed]

3.

K. Aslan, I. Gryczynski, J. Malicka, E. Matveeva, J. R. Lakowicz, and C. D. Geddes, “Metal-enhanced fluorescence: an emerging tool in biotechnology,” Curr. Opin. Biotechnol. 16(1), 55–62 (2005). [CrossRef] [PubMed]

4.

A. Kinkhabwala, Z. F. Yu, S. H. Fan, Y. Avlasevich, K. Mullen, and W. E. Moerner, “Large single-molecule fluorescence enhancements produced by a bowtie nanoantenna,” Nat. Photonics 3(11), 654–657 (2009). [CrossRef]

5.

D. P. Fromm, A. Sundaramurthy, A. Kinkhabwala, P. J. Schuck, G. S. Kino, and W. E. Moerner, “Exploring the chemical enhancement for surface-enhanced Raman scattering with Au bowtie nanoantennas,” J. Chem. Phys. 124(6), 061101 (2006). [CrossRef] [PubMed]

6.

L. Qin, S. Zou, C. Xue, A. Atkinson, G. C. Schatz, and C. A. Mirkin, “Designing, fabricating, and imaging Raman hot spots,” Proc. Natl. Acad. Sci. U.S.A. 103(36), 13300–13303 (2006). [CrossRef] [PubMed]

7.

T. Schumacher, K. Kratzer, D. Molnar, M. Hentschel, H. Giessen, and M. Lippitz, “Nanoantenna-enhanced ultrafast nonlinear spectroscopy of a single gold nanoparticle,” Nat. Commun. 2, 333 (2011). [CrossRef]

8.

K. D. Ko, A. Kumar, K. H. Fung, R. Ambekar, G. L. Liu, N. X. Fang, and K. C. Toussaint Jr., “Nonlinear optical response from arrays of Au bowtie nanoantennas,” Nano Lett. 11(1), 61–65 (2011). [CrossRef] [PubMed]

9.

A. G. Curto, G. Volpe, T. H. Taminiau, M. P. Kreuzer, R. Quidant, and N. F. van Hulst, “Unidirectional emission of a quantum dot coupled to a nanoantenna,” Science 329(5994), 930–933 (2010). [CrossRef] [PubMed]

10.

T. Pakizeh and M. Käll, “Unidirectional ultracompact optical nanoantennas,” Nano Lett. 9(6), 2343–2349 (2009). [CrossRef] [PubMed]

11.

D. Dregely, R. Taubert, J. Dorfmüller, R. Vogelgesang, K. Kern, and H. Giessen, “3D optical Yagi-Uda nanoantenna array,” Nat Commun 2, 267 (2011). [CrossRef] [PubMed]

12.

H. T. Miyazaki and Y. Kurokawa, “Squeezing visible light waves into a 3-nm-thick and 55-nm-long plasmon cavity,” Phys. Rev. Lett. 96(9), 097401 (2006). [CrossRef] [PubMed]

13.

M. Kuttge, F. J. García de Abajo, and A. Polman, “Ultrasmall mode volume plasmonic nanodisk resonators,” Nano Lett. 10(5), 1537–1541 (2010). [CrossRef] [PubMed]

14.

B. Joshi, A. Chakrabarty, and Q.-H. Wei, “Numerical studies of metal-dielectric-metal nanoantennas,” IEEE Trans. Nanotechnol. 9(6), 701–707 (2010). [CrossRef]

15.

Y. Chu, M. G. Banaee, and K. B. Crozier, “Double-resonance plasmon substrates for surface-enhanced Raman scattering with enhancement at excitation and stokes frequencies,” ACS Nano 4(5), 2804–2810 (2010). [CrossRef] [PubMed]

16.

Y. Chu, D. Wang, W. Zhu, and K. B. Crozier, “Double resonance surface enhanced Raman scattering substrates: an intuitive coupled oscillator model,” Opt. Express 19(16), 14919–14928 (2011). [CrossRef] [PubMed]

17.

Y. Chu, W. Zhu, D. Wang, and K. B. Crozier, “Beamed Raman: directional excitation and emission enhancement in a plasmonic crystal double resonance SERS substrate,” Opt. Express 19(21), 20054–20068 (2011). [CrossRef] [PubMed]

18.

J. Hao, J. Wang, X. Liu, W. J. Padilla, L. Zhou, and M. Qiu, “High performance optical absorber based on a plasmonic metamaterials,” Appl. Phys. Lett. 96(25), 251104 (2010). [CrossRef]

19.

N. Liu, M. Mesch, T. Weiss, M. Hentschel, and H. Giessen, “Infrared perfect absorber and its application as plasmonic sensor,” Nano Lett. 10(7), 2342–2348 (2010). [CrossRef] [PubMed]

20.

B. Zhang, Y. Zhao, Q. Hao, B. Kiraly, I. C. Khoo, S. Chen, and T. J. Huang, “Polarization-independent dual-band infrared perfect absorber based on a metal-dielectric-metal elliptical nanodisk array,” Opt. Express 19(16), 15221–15228 (2011). [CrossRef] [PubMed]

21.

J. Hendrickson, J. Guo, B. Zhang, W. Buchwald, and R. Soref, “Wideband perfect light absorber at midwave infrared using multiplexed metal structures,” Opt. Lett. 37(3), 371–373 (2012). [CrossRef] [PubMed]

22.

R. Esteban, T. V. Teperik, and J. J. Greffet, “Optical patch antennas for single photon emission using surface plasmon resonances,” Phys. Rev. Lett. 104(2), 026802 (2010). [CrossRef] [PubMed]

23.

P. Chen and A. Alu, “Sub-wavelength elliptical patch antenna loaded with µ-negative metamaterials,” IEEE Trans. Antenn. Propag. 58(9), 2909–2919 (2010). [CrossRef]

24.

A. Cattoni, P. Ghenuche, A. M. Haghiri-Gosnet, D. Decanini, J. Chen, J. L. Pelouard, and S. Collin, “λ³/1000 plasmonic nanocavities for biosensing fabricated by soft UV nanoimprint lithography,” Nano Lett. 11(9), 3557–3563 (2011). [CrossRef] [PubMed]

25.

H. Liu, J. Ng, S. B. Wang, Z. F. Lin, Z. H. Hang, C. T. Chan, and S. N. Zhu, “Strong light-induced negative optical pressure arising from kinetic energy of conduction electrons in plasmon-type cavities,” Phys. Rev. Lett. 106(8), 087401 (2011). [CrossRef] [PubMed]

26.

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6(12), 4370–4379 (1972). [CrossRef]

27.

D. W. Lynch and W. R. Hunter, in Handbook of Optical Constants of Solids, E. D. Palik, ed. (Academic Press: New York, 1985).

28.

P. Billaud, J. R. Huntzinger, E. Cottancin, J. Lermé, M. Pellarin, L. Arnaud, M. Broyer, N. Del Fatti, and F. Vallée, “Optical extinction spectroscopy of single silver nanoparticles,” Eur. Phys. J. D 43(1-3), 271–274 (2007). [CrossRef]

29.

J. A. Dionne, L. A. Sweatlock, H. A. Atwater, and A. Polman, “Plasmon slot waveguides: towards chip-scale propagation with subwavelength-scale localization,” Phys. Rev. B 73(3), 035407 (2006). [CrossRef]

30.

E. N. Economou, “Surface plasmons in thin films,” Phys. Rev. 182(2), 539–554 (1969). [CrossRef]

31.

G. Blanch, “Mathieu Functions,” in Handbook of mathematical functions, M. Abramowitz, I. A. Stegun, ed. (Dover, New York, 1953).

32.

J. C. Gutierrez-Vega, R. M. Rodriguez-Dagnino, M. A. Meneses-Nava, and S. Chavez-Cerda, “Mathieu functions, a visual approach,” Am. J. Phys. 71(3), 233–242 (2003). [CrossRef]

33.

R. Gordon, “Light in a subwavelength slit in a metal: propagation and reflection,” Phys. Rev. B 73(15), 153405 (2006). [CrossRef]

34.

H. E. Kamchouchi and A. A. Zaky, “A direct method for the calculation of the edge capacitance of thick electrodes,” J. Phys. D Appl. Phys. 8(12), 1365–1371 (1975). [CrossRef]

35.

S. Zhang, Y. S. Park, Y. M. Liu, T. Zentgraf, and X. Zhang, “Far-field measurement of ultra-small plasmonic mode volume,” Opt. Express 18(6), 6048–6055 (2010). [CrossRef] [PubMed]

36.

P. Mythili and A. Das, “Simple approach to determine resonant frequencies of microstrip antennas,” IEE Proc., Microw. Antennas Propag. 145(2), 159–162 (1998). [CrossRef]

37.

H. Raether, “Surface plasmons on smooth and rough surfaces and on gratings,” Springer Tracts Mod. Phys. 111, 1–133 (1988).

OCIS Codes
(130.2790) Integrated optics : Guided waves
(160.3918) Materials : Metamaterials
(250.5403) Optoelectronics : Plasmonics
(050.6624) Diffraction and gratings : Subwavelength structures

ToC Category:
Optics at Surfaces

History
Original Manuscript: February 16, 2012
Revised Manuscript: April 28, 2012
Manuscript Accepted: April 30, 2012
Published: May 7, 2012

Citation
Ayan Chakrabarty, Feng Wang, Fred Minkowski, Kai Sun, and Qi-Huo Wei, "Cavity modes and their excitations in elliptical plasmonic patch nanoantennas," Opt. Express 20, 11615-11624 (2012)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-11-11615


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. L. Novotny and N. van Hulst, “Antennas for light,” Nat. Photonics 5(2), 83–90 (2011). [CrossRef]
  2. J. A. Schuller, E. S. Barnard, W. Cai, Y. C. Jun, J. S. White, and M. L. Brongersma, “Plasmonics for extreme light concentration and manipulation,” Nat. Mater. 9(3), 193–204 (2010). [CrossRef] [PubMed]
  3. K. Aslan, I. Gryczynski, J. Malicka, E. Matveeva, J. R. Lakowicz, and C. D. Geddes, “Metal-enhanced fluorescence: an emerging tool in biotechnology,” Curr. Opin. Biotechnol. 16(1), 55–62 (2005). [CrossRef] [PubMed]
  4. A. Kinkhabwala, Z. F. Yu, S. H. Fan, Y. Avlasevich, K. Mullen, and W. E. Moerner, “Large single-molecule fluorescence enhancements produced by a bowtie nanoantenna,” Nat. Photonics 3(11), 654–657 (2009). [CrossRef]
  5. D. P. Fromm, A. Sundaramurthy, A. Kinkhabwala, P. J. Schuck, G. S. Kino, and W. E. Moerner, “Exploring the chemical enhancement for surface-enhanced Raman scattering with Au bowtie nanoantennas,” J. Chem. Phys. 124(6), 061101 (2006). [CrossRef] [PubMed]
  6. L. Qin, S. Zou, C. Xue, A. Atkinson, G. C. Schatz, and C. A. Mirkin, “Designing, fabricating, and imaging Raman hot spots,” Proc. Natl. Acad. Sci. U.S.A. 103(36), 13300–13303 (2006). [CrossRef] [PubMed]
  7. T. Schumacher, K. Kratzer, D. Molnar, M. Hentschel, H. Giessen, and M. Lippitz, “Nanoantenna-enhanced ultrafast nonlinear spectroscopy of a single gold nanoparticle,” Nat. Commun. 2, 333 (2011). [CrossRef]
  8. K. D. Ko, A. Kumar, K. H. Fung, R. Ambekar, G. L. Liu, N. X. Fang, and K. C. Toussaint., “Nonlinear optical response from arrays of Au bowtie nanoantennas,” Nano Lett. 11(1), 61–65 (2011). [CrossRef] [PubMed]
  9. A. G. Curto, G. Volpe, T. H. Taminiau, M. P. Kreuzer, R. Quidant, and N. F. van Hulst, “Unidirectional emission of a quantum dot coupled to a nanoantenna,” Science 329(5994), 930–933 (2010). [CrossRef] [PubMed]
  10. T. Pakizeh and M. Käll, “Unidirectional ultracompact optical nanoantennas,” Nano Lett. 9(6), 2343–2349 (2009). [CrossRef] [PubMed]
  11. D. Dregely, R. Taubert, J. Dorfmüller, R. Vogelgesang, K. Kern, and H. Giessen, “3D optical Yagi-Uda nanoantenna array,” Nat Commun 2, 267 (2011). [CrossRef] [PubMed]
  12. H. T. Miyazaki and Y. Kurokawa, “Squeezing visible light waves into a 3-nm-thick and 55-nm-long plasmon cavity,” Phys. Rev. Lett. 96(9), 097401 (2006). [CrossRef] [PubMed]
  13. M. Kuttge, F. J. García de Abajo, and A. Polman, “Ultrasmall mode volume plasmonic nanodisk resonators,” Nano Lett. 10(5), 1537–1541 (2010). [CrossRef] [PubMed]
  14. B. Joshi, A. Chakrabarty, and Q.-H. Wei, “Numerical studies of metal-dielectric-metal nanoantennas,” IEEE Trans. Nanotechnol. 9(6), 701–707 (2010). [CrossRef]
  15. Y. Chu, M. G. Banaee, and K. B. Crozier, “Double-resonance plasmon substrates for surface-enhanced Raman scattering with enhancement at excitation and stokes frequencies,” ACS Nano 4(5), 2804–2810 (2010). [CrossRef] [PubMed]
  16. Y. Chu, D. Wang, W. Zhu, and K. B. Crozier, “Double resonance surface enhanced Raman scattering substrates: an intuitive coupled oscillator model,” Opt. Express 19(16), 14919–14928 (2011). [CrossRef] [PubMed]
  17. Y. Chu, W. Zhu, D. Wang, and K. B. Crozier, “Beamed Raman: directional excitation and emission enhancement in a plasmonic crystal double resonance SERS substrate,” Opt. Express 19(21), 20054–20068 (2011). [CrossRef] [PubMed]
  18. J. Hao, J. Wang, X. Liu, W. J. Padilla, L. Zhou, and M. Qiu, “High performance optical absorber based on a plasmonic metamaterials,” Appl. Phys. Lett. 96(25), 251104 (2010). [CrossRef]
  19. N. Liu, M. Mesch, T. Weiss, M. Hentschel, and H. Giessen, “Infrared perfect absorber and its application as plasmonic sensor,” Nano Lett. 10(7), 2342–2348 (2010). [CrossRef] [PubMed]
  20. B. Zhang, Y. Zhao, Q. Hao, B. Kiraly, I. C. Khoo, S. Chen, and T. J. Huang, “Polarization-independent dual-band infrared perfect absorber based on a metal-dielectric-metal elliptical nanodisk array,” Opt. Express 19(16), 15221–15228 (2011). [CrossRef] [PubMed]
  21. J. Hendrickson, J. Guo, B. Zhang, W. Buchwald, and R. Soref, “Wideband perfect light absorber at midwave infrared using multiplexed metal structures,” Opt. Lett. 37(3), 371–373 (2012). [CrossRef] [PubMed]
  22. R. Esteban, T. V. Teperik, and J. J. Greffet, “Optical patch antennas for single photon emission using surface plasmon resonances,” Phys. Rev. Lett. 104(2), 026802 (2010). [CrossRef] [PubMed]
  23. P. Chen and A. Alu, “Sub-wavelength elliptical patch antenna loaded with µ-negative metamaterials,” IEEE Trans. Antenn. Propag. 58(9), 2909–2919 (2010). [CrossRef]
  24. A. Cattoni, P. Ghenuche, A. M. Haghiri-Gosnet, D. Decanini, J. Chen, J. L. Pelouard, and S. Collin, “λ³/1000 plasmonic nanocavities for biosensing fabricated by soft UV nanoimprint lithography,” Nano Lett. 11(9), 3557–3563 (2011). [CrossRef] [PubMed]
  25. H. Liu, J. Ng, S. B. Wang, Z. F. Lin, Z. H. Hang, C. T. Chan, and S. N. Zhu, “Strong light-induced negative optical pressure arising from kinetic energy of conduction electrons in plasmon-type cavities,” Phys. Rev. Lett. 106(8), 087401 (2011). [CrossRef] [PubMed]
  26. P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6(12), 4370–4379 (1972). [CrossRef]
  27. D. W. Lynch and W. R. Hunter, in Handbook of Optical Constants of Solids, E. D. Palik, ed. (Academic Press: New York, 1985).
  28. P. Billaud, J. R. Huntzinger, E. Cottancin, J. Lermé, M. Pellarin, L. Arnaud, M. Broyer, N. Del Fatti, and F. Vallée, “Optical extinction spectroscopy of single silver nanoparticles,” Eur. Phys. J. D 43(1-3), 271–274 (2007). [CrossRef]
  29. J. A. Dionne, L. A. Sweatlock, H. A. Atwater, and A. Polman, “Plasmon slot waveguides: towards chip-scale propagation with subwavelength-scale localization,” Phys. Rev. B 73(3), 035407 (2006). [CrossRef]
  30. E. N. Economou, “Surface plasmons in thin films,” Phys. Rev. 182(2), 539–554 (1969). [CrossRef]
  31. G. Blanch, “Mathieu Functions,” in Handbook of mathematical functions, M. Abramowitz, I. A. Stegun, ed. (Dover, New York, 1953).
  32. J. C. Gutierrez-Vega, R. M. Rodriguez-Dagnino, M. A. Meneses-Nava, and S. Chavez-Cerda, “Mathieu functions, a visual approach,” Am. J. Phys. 71(3), 233–242 (2003). [CrossRef]
  33. R. Gordon, “Light in a subwavelength slit in a metal: propagation and reflection,” Phys. Rev. B 73(15), 153405 (2006). [CrossRef]
  34. H. E. Kamchouchi and A. A. Zaky, “A direct method for the calculation of the edge capacitance of thick electrodes,” J. Phys. D Appl. Phys. 8(12), 1365–1371 (1975). [CrossRef]
  35. S. Zhang, Y. S. Park, Y. M. Liu, T. Zentgraf, and X. Zhang, “Far-field measurement of ultra-small plasmonic mode volume,” Opt. Express 18(6), 6048–6055 (2010). [CrossRef] [PubMed]
  36. P. Mythili and A. Das, “Simple approach to determine resonant frequencies of microstrip antennas,” IEE Proc., Microw. Antennas Propag. 145(2), 159–162 (1998). [CrossRef]
  37. H. Raether, “Surface plasmons on smooth and rough surfaces and on gratings,” Springer Tracts Mod. Phys. 111, 1–133 (1988).

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.


« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited