Vol. 78

Front:[PDF file] Back:[PDF file]
Latest Volume
All Volumes
All Issues

The Role of Hybrid Modes in Extraordinary Optical Transmission through a Plasmonic Nanohole Array

By Christopher Trampel
Progress In Electromagnetics Research C, Vol. 78, 145-158, 2017


A mode-matching solution to plane wave scattering by a plasmonic nanohole array consisting of a silver film perforated by an infinite square array of circular holes is presented. A complete orthonormal basis set consisting of waveguide modes satisfying an impedance boundary condition on the hole wall is derived. Impedance boundary conditions are satisfied on the upper and lower horizontal surfaces of the film and on the walls of the hole. Extraordinary optical transmission (EOT) is studied over optical wavelengths. Theory predicts a peak transmission value that is in better agreement with experiment than previous modal studies. The effect of film thickness on coupling between modes bound to the upper and lower surfaces is studied. The transmission profile for thinner films evinces two peaks at different wavelengths resulting from strong coupling between surface waves bound to the upper and lower surfaces. For thicker films, the surface waves decouple and a single peak is observed. The effect of hole radius on EOT is considered. It is demonstrated that transmission peaks occur for holes of a roughly constant electrical size. A relationship between the lattice constant and the transmission-to-area efficiency is quantified.


Christopher Trampel, "The Role of Hybrid Modes in Extraordinary Optical Transmission through a Plasmonic Nanohole Array," Progress In Electromagnetics Research C, Vol. 78, 145-158, 2017.


    1. Pendry, J. B., "Playing tricks with light," Science, Vol. 285, 1687, 1999.

    2. Politano, A., "Influence of structural and electronic properties on the collective excitations of Ag/Cu(111)," Plasmonics, Vol. 7, No. 1, 131-136, 2012.

    3. Politano, A., "Low-energy collective electronic mode at a noble metal interface," Plasmonics, Vol. 8, No. 2, 357-360, 2013.

    4. Politano, A., V. Formoso, and G. Chiarello, "Dispersion and damping of gold surface plasmon," Plasmonics, Vol. 3, No. 4, 165, 2008.

    5. Politano, A., V. Formoso, and G. Chiarello, "Collective electronic excitations in thin Ag films on Ni(111)," Plasmonics, Vol. 8, No. 4, 1683-1690, 2013.

    6. King, M. D., S. Khadka, G. A. Craig, and M. D. Mason, "Effect of local heating on the SERS efficiency of optically trapped prismatic nanoparticles," The Journal of Physical Chemistry C, Vol. 112, No. 31, 11751-11757, 2008.

    7. Politano, A. and G. Chiarello, "The influence of electron confinement, quantum size effects, and film morphology on the dispersion and the damping of plasmonic modes in Ag and Au thin films," Prog. Surf. Sci., Vol. 90, No. 2, 144-193, 2015.

    8. Haynes, C. L., A. D. McFarland, and R. P. Van Duyne, "Surface-enhanced raman spectroscopy," Anal. Chem., Vol. 77, No. 17, 338A-346A, 2005.

    9. Politano, A., A. Cupolillo, G. Di Profio, H. A. Arafat, G. Chiarello, and E. Curcio, "When plasmonics meets membrane technology," Journal of Physics: Condensed Matter, Vol. 28, No. 36, 363003, 2016.

    10. Politano, A., P. Argurio, G. Di Profio, V. Sanna, A. Cupolillo, S. Chakraborty, H. A. Arafat, and E. Curcio, "Photothermal membrane distillation for seawater desalination," Advanced Materials, Vol. 29, No. 2, 1603504, 2017.

    11. Harmsen, S., R. Huang, M. A. Wall, H. Karabeber, J. M. Samii, M. Spaliviero, J. R. White, S. Monette, R. O’Connor, K. L. Pitter, S. A. Sastra, M. Saborowski, E. C. Holland, S. Singer, K. P. Olive, S. W. Lowe, R. G. Blasberg, and M. F. Kircher, "Surface-enhanced resonance Raman scattering nanostars for high-precision cancer imaging," Science Translational Medicine, Vol. 7, No. 271, 271ra7-271ra7, 2015.

    12. Krenn, J. R., A. Dereux, J. C. Weeber, E. Bourillot, Y. Lacroute, J. P. Goudonnet, G. Schider, W. Gotschy, A. Leitner, F. R. Aussenegg, and C. Girard, "Squeezing the optical near-field zone by plasmon coupling of metallic nanoparticles," Phys. Rev. Lett., Vol. 82, 2590, 1999.

    13. Krenn, J. R., B. Lamprecht, H. Ditlbacher, G. Schider, M. Salerno, A. Leitner, and F. R. Aussenegg, "Non-diffraction limited light transport by gold nanowires," Europhys. Lett., Vol. 60, No. 5, 663-669, 2001.

    14. Lamprecht, B., J. R. Krenn, G. Schider, H. Ditlbacher, M. Salerno, N. Felidj, A. Leitner, F. R. Aussenegg, and J. C. Weeber, "Surface plasmon propagation in microscale metal stripes," Appl. Phys. Lett., Vol. 79, No. 1, 513, 2001.

    15. Maier, S. A., P. G. Kik, H. A. Atwater, S.Meltzer, E.Harel, B. E. Koel, and A. A. Requicha, "Local detection of electromagnetic energy transport below the diffraction limit in metal nanoparticle plasmon waveguides," Nature Materials, Vol. 2, 229-232, 2003.

    16. Zia, R., M. D. Selker, P. B. Catrysse, and M. L. Brongersma, "Geometries and materials for subwavelength surface plasmon modes," J. Opt. Soc. Am. A, Vol. 21, No. 12, 2442, 2005.

    17. De Menezes, J. W., A. Thesing, C. Valsecchi, L. E. G. Armas, and A. G. Brolo, "Improving the performance of gold nanohole array biosensors by controlling the optical collimation conditions," Appl. Opt., Vol. 54, No. 21, 6502-6507, 2015.

    18. Li, X., M. Soler, C. I. Ozdemir, A. Belushkin, F. Yesilkoy, and H. Altug, "Plasmonic nanohole array biosensor for label-free and real-time analysis of live cell secretion," Lab Chip, Vol. 17, No. 13, 2017.

    19. Cetin, A. E., D. Etezadi, B. C. Galarreta, M. P. Busson, Y. Eksioglu, and H. Altug, "Plasmonic nanohole arrays on a robust hybrid substrate for highly sensitive label-free biosensing," ACS Photonics, Vol. 2, No. 8, 1167-1174, 2015.

    20. Ebbesen, T. W., H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, "Extraordinary optical transmission through sub-wavelength hole arrays," Nature, Vol. 391, 667-669, 1998.

    21. Bethe, H. A., "Theory of diffraction by small holes," Phys. Rev.,, Vol. 66, 163, 1944.

    22. Baida, F. I. and D. Van Labeke, "Three-dimensional structures for enhanced transmission through a metallic film: Annular aperture arrays," Phys. Rev. B, Vol. 67, 155314, 2003.

    23. Li, Z. and L. Lin, "Photonic band structures solved by a plane-wave-based transfer-matrix method," Phys. Rev. E, Vol. 67, 046607, 2003.

    24. Biswas, R., C. G. Ding, I. Puscasu, M. Pralle, M. McNeal, J. Daly, A. Greenwald, and E. Johnson, "Theory of subwavelength hole arrays coupled with photonic crystals for extraordinary thermal emission," Phys. Rev. B, Vol. 74, 045106, 2006.

    25. Martin-Moreno, L. and F. J. Garcia-Vidal, "Minimal model for optical transmission through holey metal films," J. Phys.: Condens. Matter, Vol. 20, 304214, 2008.

    26. De Leon-Perez, F., G. Brucoli, F. J. Garcia-Vidal, and L. Martin-Moreno, "Theory on the scattering of light and surface plasmon polaritons by arrays of holes and dimples in a metal film," New Journal of Physics, Vol. 10, 105017, 2008.

    27. Zhang, M., C. Huang, G. Huang, and Y. Zhu, "Theory of extraordinary light transmission through sub-wavelength circular hole arrays," Journal of Optics, Vol. 12, 015004, 2010.

    28. Huang, C., Q. Wang, and Y. Zhu, "Dual effect of surface plasmons in light transmission through perforated metal films," Physical Review B, Vol. 75, 245421, 2007.

    29. Martin-Moreno, L. and F. J. Garcia-Vidal, "Optical transmission through circular hole arrays in optically thick metal films," Optics Express, Vol. 12, 3619, 2004.

    30. Rothwell, E. J. and M. J. Cloud, Electromagnetics, CRC Press LLC, Boca Raton, FL, 2001.

    31. Tretyakov, S., Analytical Modeling in Applied Electromagnetics, Artech House, Inc., Norwood,MA, 2003.

    32. Hunter, J. K. and B. Nachtergaele, Applied Analysis, World Scientific, Hackensack, NJ, 2001.

    33. Drude, P., "Zur Elektronentheorie der Metalle," Ann. Phys., Vol. 306, 566-613, 1900.

    34. Martin-Moreno, L., F. J. Garcia-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T.W. Ebbesen, "Theory of extraordinary optical transmission through subwavelength hole arrays," Phys. Rev. Lett., Vol. 86, 1114-1117, 2001.

    35. Martin-Moreno, L., F. J. Garcia-Vidal, H. J. Lezec, A. Degiron, and T. W. Ebbesen, "Theory of highly directional emission from a single subwavelength aperture surrounded by surface corrugations," Phys. Rev. Lett., Vol. 90, 167401, 2003.