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. 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, “?³/1000 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).

ACS Nano

• 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]

Am. J. Phys.

• 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]

Appl. Phys. Lett.

• 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]

Curr. Opin. Biotechnol.

• 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]

Eur. Phys. J. D

• 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]

IEE Proc., Microw. Antennas Propag.

• 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]

IEEE Trans. Antenn. Propag.

• 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]

IEEE Trans. Nanotechnol.

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

J. Chem. Phys.

• 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]

J. Phys. D Appl. Phys.

• 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]

Nano Lett.

• A. Cattoni, P. Ghenuche, A. M. Haghiri-Gosnet, D. Decanini, J. Chen, J. L. Pelouard, and S. Collin, “?³/1000 plasmonic nanocavities for biosensing fabricated by soft UV nanoimprint lithography,” Nano Lett. 11(9), 3557–3563 (2011). [CrossRef] [PubMed]
• 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]
• 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]
• T. Pakizeh and M. Käll, “Unidirectional ultracompact optical nanoantennas,” Nano Lett. 9(6), 2343–2349 (2009). [CrossRef] [PubMed]
• 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]

Nat Commun

• 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]

Nat. Commun.

• 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]

Nat. Mater.

• 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]

Nat. Photonics

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

Opt. Express

• 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]
• 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]
• 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]
• 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]

Opt. Lett.

• 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]

Phys. Rev.

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

Phys. Rev. B

• R. Gordon, “Light in a subwavelength slit in a metal: propagation and reflection,” Phys. Rev. B 73(15), 153405 (2006). [CrossRef]
• 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]
• P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6(12), 4370–4379 (1972). [CrossRef]

Phys. Rev. Lett.

• 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]
• 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]
• 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]

Proc. Natl. Acad. Sci. U.S.A.

• 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]

Science

• 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]

Springer Tracts Mod. Phys.

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

Other

• G. Blanch, “Mathieu Functions,” in Handbook of mathematical functions, M. Abramowitz, I. A. Stegun, ed. (Dover, New York, 1953).
• D. W. Lynch and W. R. Hunter, in Handbook of Optical Constants of Solids, E. D. Palik, ed. (Academic Press: New York, 1985).

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