Vol. 82

Latest Volume
All Volumes
All Issues
2018-09-27

Extraordinary Transmission through Subwavelength Hole Arrays for General Oblique Incidence - Mechanism as Related to Surface Wave Dispersion and Floquet Lattice Diagrams

By Malcolm Ng Mou Kehn
Progress In Electromagnetics Research B, Vol. 82, 49-71, 2018
doi:10.2528/PIERB18070504

Abstract

An array of rectangular holes pierced through a conducting screen is treated herein by a rigorous full-wave modal analysis using the moment method entailing Green's functions for rectangular cavities and planar multilayer structures in the spectral domain. Unexpectedly strong diffusions of incident plane waves are observed even at frequencies where the size of each hole is considerably less than the wavelength, posing a transmission efficiency that exceeds unity and thus leading to extraordinary transmission since this defies classical aperture diffraction theory. This paper fortifies the present understanding of the role surface plasmon polaritons (SPP) play in explaining this phenomenon, by using surface-wave dispersion and Floquet lattice diagrams to link up with the peaks in the transmission spectra. The incidence angle and polarization of the irradiation are taken into account in this work.

Citation


Malcolm Ng Mou Kehn, "Extraordinary Transmission through Subwavelength Hole Arrays for General Oblique Incidence - Mechanism as Related to Surface Wave Dispersion and Floquet Lattice Diagrams," Progress In Electromagnetics Research B, Vol. 82, 49-71, 2018.
doi:10.2528/PIERB18070504
http://test.jpier.org/PIERB/pier.php?paper=18070504

References


    1. Renk, K. F. and L. Genzel, "Interference filters and Fabry-Perot interferometers for the far infrared," Appl. Opt., Vol. 1, No. 5, 643-648, Sep. 1962.
    doi:10.1364/AO.1.000643

    2. Ulrich, R., "Far-infrared properties of metallic mesh and its complementary structure," Infrared Phys., Vol. 7, No. 1, 37-55, Mar. 1967.
    doi:10.1016/0020-0891(67)90028-0

    3. Ressler, G. M. and K. D. Moller, "Far infrared bandpass filters and measurements on a reciprocal grid," Appl. Opt., Vol. 6, No. 5, 893-896, May 1967.
    doi:10.1364/AO.6.000893

    4. Mitsuishi, A., Y. Otsuka, S. Fujita, and H. Yoshinaga, "Metal mesh filters in the far infrared region," Jpn. J. Appl. Phys., Vol. 2, No. 9, 574-577, Sep. 1963.
    doi:10.1143/JJAP.2.574

    5. Chen, C. C., "Diffraction of electromagnetic waves by a conducting screen perforated periodically with circular holes," IEEE Trans. Microw. Theory Tech., Vol. 19, No. 5, 475-481, May 1971.
    doi:10.1109/TMTT.1971.1127548

    6. Chen, C. C., "Transmission through a conducting screen perforated periodically with apertures," IEEE Trans. Microw. Theory Tech., Vol. 18, No. 9, 627-632, Sep. 1970.
    doi:10.1109/TMTT.1970.1127298

    7. Lee, S. W., G. Zarrillo, and C. L. Law, "Simple formulas for transmission through periodic metal grids or plates," IEEE Trans. Antennas Propag., Vol. 30, No. 5, 904-909, Sep. 1982.
    doi:10.1109/TAP.1982.1142923

    8. 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, London, Feb. 1998.

    9. Bethe, H. A., "Theory of diffraction by small holes," Phys. Rev., Vol. 66, No. 7 & 8, 163-182, Oct. 1944.

    10. Sambles, J. R., "More than transparent," Nature, Vol. 391, No. 6668, 641-642, London, Feb. 1998.
    doi:10.1038/35509

    11. Thio, T., H. J. Lezec, and T. W. Ebbesen, "Strongly enhanced optical transmission through subwavelength holes in metal films," Physica B, Vol. 279, 90-93, Amsterdam, 2000.
    doi:10.1016/S0921-4526(99)00677-8

    12. Gordon, R., A. G. Brolo, D. Sinton, and K. L. Kavanagh, "Resonant optical transmission through hole-arrays in metal films: physics and applications," Laser & Photon. Rev., Vol. 4, No. 2, 311-335, Feb. 2010.
    doi:10.1002/lpor.200810079

    13. Genet, C. and T. W. Ebbesen, "Light in tiny holes," Nature, Vol. 445, 39-46, Jan. 2007.
    doi:10.1038/nature05350

    14. Coe, J. V., J. M. Heer, S. Teeters-Kennedy, H. Tian, and K. R. Rodriguez, "Extraordinary transmission of metal films with arrays of subwavelength holes," Ann. Rev. Phys. Chem., Vol. 59, 179-202, 2008.
    doi:10.1146/annurev.physchem.59.032607.093703

    15. Stewart, M. E., C. R. Anderton, L. B. Thompson, J. Maria, S. K. Gray, J. A. Rogers, and R. G. Nuzzo, "Nanostructured plasmonic sensors," Chem. Rev., Vol. 108, 494-521, Jan. 2008.
    doi:10.1021/cr068126n

    16. Gordon, R., D. Sinton, K. L. Kavanagh, and A. G. Brolo, "A new generation of sensors based on extraordinary optical transmission," Acc. Chem. Res., Vol. 41, No. 8, 1049-1057, Jul. 2008.
    doi:10.1021/ar800074d

    17. Raether, H., Surface Plasmons on Smooth and Rough Surfaces and on Gratings, Springer-Verlag, Berlin, 1988.
    doi:10.1007/BFb0048317

    18. Ghaemi, H. F., T. Thio, D. E. Grupp, T. W. Ebbesen, and H. J. Lezec, "Surface plasmons enhance optical transmission through subwavelength holes," Phy. Rev. B, Vol. 58, 6779-6782, Sep. 1998.
    doi:10.1103/PhysRevB.58.6779

    19. Grupp, D. E., H. J. Lezec, T. W. Ebbesen, K. M. Pellerin, and T. Thio, "Crucial role of metal surface in enhanced transmission through subwavelength apertures," Appl. Phys. Lett., Vol. 77, 1569-1571, 2000.
    doi:10.1063/1.1308530

    20. Schroter, U. and D. Heitmann, "Surface-plasmon-enhanced transmission through metallic gratings," Phys. Rev. B, Vol. 58, No. v, 419-421, Dec. 1998.

    21. Treacy, M. M. J., "Dynamical diffraction in metallic optical gratings," Appl. Phys. Lett., Vol. 75, No. 5, 606-608, Aug. 1999.
    doi:10.1063/1.124455

    22. Porto, J. A., F. J. Garcia-Vidal, and J. B. Pendry, "Transmission resonances on metallic gratings with very narrow slits," Phys. Rev. Lett., Vol. 83, No. 14, 2845-2848, Oct. 1999.
    doi:10.1103/PhysRevLett.83.2845

    23. Popov, E., M. Neviere, S. Enoch, and R. Reinisch, "Theory of light transmission through subwavelength periodic hole arrays," Phys. Rev. B, Vol. 62, No. 23, 16100-16108, Dec. 2000.
    doi:10.1103/PhysRevB.62.16100

    24. Enoch, S., E. Popov, M. Neviere, and R. Reinisch, "Enhanced light transmission by hole arrays," J. Opt. A, Vol. 4, No. 5, S83-S87, Aug. 2002.
    doi:10.1088/1464-4258/4/5/351

    25. Krishan, A., T. Thio, T. J. Kim, H. J. Lezec, T. W. Ebbesen, P. A. Wolff, J. B. Pendry, L. Martin-Moreno, and F. J. Garcia-Vidal, "Evanescently coupled resonance in surface plasmon enhanced transmission," Opt. Commun., Vol. 200, No. 1-6, 1-7, Dec. 2001.
    doi:10.1016/S0030-4018(01)01558-9

    26. 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, Feb. 2001.
    doi:10.1103/PhysRevLett.86.1114

    27. Darmanyan, S. A. and A. V. Zayats, "Light tunneling via resonant surface plasmon polariton states and the enhanced transmission of periodically nanostructured metal films: an analytical study," Phys. Rev. B, Vol. 67, 035424, 1-7, Jan. 2003.

    28. Popov, E., M. Neviere, P. Boyer, and N. Bonod, "Light transmission through a subwavelength hole," Optics Commun., Vol. 255, 338-348, Jun. 2005.
    doi:10.1016/j.optcom.2005.06.010

    29. Sobnack, M. B., W. C. Tan, N. P. Wanstall, T. W. Preist, and J. R. Sambles, "Stationary surface plasmons on a zero-order metal grating," Phys. Rev. Lett., Vol. 80, No. 25, 5667-5670, Jun. 1998.
    doi:10.1103/PhysRevLett.80.5667

    30. Astilean, S., P. Lalanne, and M. Palamaru, "Light transmission through metallic channels much smaller than the wavelength," Opt. Commun., Vol. 175, 265-273, Mar. 2000.
    doi:10.1016/S0030-4018(00)00462-4

    31. Takakura, Y., "Optical resonance in a narrow slit in a thick metallic screen," Phys. Rev. Lett., Vol. 86, No. 24, 5601-5603, Jun. 2001.
    doi:10.1103/PhysRevLett.86.5601

    32. Krishnan, A., T. Thio, T. J. Kim, H. J. Lezec, T. W. Ebbesen, P. A. Wolff, J. Pendry, L. Martin-Moreno, and F. J. Garcia-Vidal, "Evanescently coupled resonance in surface plasmon enhanced transmission," Optics Commun., Vol. 200, 1-7, Dec. 2001.
    doi:10.1016/S0030-4018(01)01558-9

    33. Medina, F., F. Mesa, and R. Marques, "Extraordinary transmission through arrays of electrically small holes from a circuit theory perspective," IEEE Trans. Microw. Theory Techn., Vol. 56, No. 2, 3108-3120, Dec. 2008.
    doi:10.1109/TMTT.2008.2007343

    33. Medina, F., F. Mesa, and R. Marque, "Extraordinary transmission through arrays of electrically small holes from a circuit theory perspective,", Vol. 56, No. 2, 3108-3120, Dec. 2008.
    doi:10.1109/TMTT.2008.2007343

    34. Medina, F., F. Mesa, and D. C. Skigin, "Extraordinary transmission through arrays of slits: a circuit theory model," IEEE Trans. Microw. Theory Techn., Vol. 58, No. 1, 105-115, Jan. 2010.
    doi:10.1109/TMTT.2009.2036341

    35. Beruete, M., M. Navarro-Cia, and M. S. Ayza, "Understanding anomalous extraordinary transmission from equivalent circuit and grounded slab concepts," IEEE Trans. Microw. Theory Techn., Vol. 59, No. 9, 2180-2188, Sep. 2011.
    doi:10.1109/TMTT.2011.2160076

    36. Beruete, M., I. Campillo, M. Navarro-Ca, F. Falcone, and M. Sorolla, "Molding left- or right-handed metamaterials by stacked cutoff metallic hole arrays," IEEE Trans. Antennas Propag., Vol. 55, No. 6, 1514-1521, Jun. 2007.
    doi:10.1109/TAP.2007.897324

    37. Delgado, V., R. Marques, and L. Jelinek, "Coupled-wave surface-impedance analysis of extraordinary transmission through single and stacked metallic screens," IEEE Trans. Antennas Propag., Vol. 61, No. 3, 1342-1351, Mar. 2013.
    doi:10.1109/TAP.2012.2227657

    38. Beruete, M., M. Sorolla, I. Campillo, and J. S. Dolado, "Increase of the transmission in cut-off metallic hole arrays," IEEE Microw. Wireless Comp. Lett., Vol. 15, No. 2, 116-118, Feb. 2005.
    doi:10.1109/LMWC.2004.842852

    39. Lomakin, V. and E. Michielssen, "Enhanced transmission through metallic plates perforated by arrays of subwavelength holes and sandwiched between dielectric slabs," Phys. Rev. B, Vol. 71, No. 23, 235117, Jun. 2005.
    doi:10.1103/PhysRevB.71.235117

    40. Lomakin, V. and E. Michielssen, "Transmission of transient plane waves through perfect electrically conducting plates perforated by periodic arrays of subwavelength holes," IEEE Trans. Antennas Propag., Vol. 54, No. 3, 970-984, Mar. 2006.
    doi:10.1109/TAP.2006.869896

    41. Bravo-Abad, J., I. Martin-Moreno, and F. J. Garcia-Vidal, "Resonant transmission of light through subwavelength holes in thick metal films," IEEE J. Selec. Topics Quan. Electron., Vol. 12, No. 6, 1221-1227, Nov./Dec. 2006.
    doi:10.1109/JSTQE.2006.881640

    42. Mary, A., S. Rodrigo, L. Martin-Moreno, and F. Garcia-Vidal, "Theory of light transmission through an array of rectangular holes," Phys. Rev. B, Vol. 76, No. 19, 195414, Nov. 2007.
    doi:10.1103/PhysRevB.76.195414

    43. Chen, Y., Y.Wang, Y. Zhang, and S. Liu, "Numerical investigation of the transmission enhancement through subwavelength hole array," Optics Commun., Vol. 274, 236-240, Feb. 2007.
    doi:10.1016/j.optcom.2007.02.001

    44. Schuchinsky, A. G., D. E. Zelenchuk, and A. M. Lerer, "Enhanced transmission in microwave arrays of periodic sub-wavelength apertures," J. Opt. A: Pure Appl. Opt., Vol. 7, S102-S109, Jan. 2005.
    doi:10.1088/1464-4258/7/2/014

    45. Schuchinsky, A. G., D. E. Zelenchuk, A. M. Lerer, and R. Dickie, "Full-wave analysis of layered aperture arrays," IEEE Trans. Antennas Propag., Vol. 54, No. 2, 490-502, Feb. 2006.
    doi:10.1109/TAP.2005.863086

    46. Monni, S., G. Gerini, A. Neto, and A. G. Tijhuis, "Multi-mode equivalent networks for the design and analysis of frequency selective surfaces," IEEE Trans. Antennas Propag., Vol. 55, No. 10, 2824-2835, Oct. 2007.
    doi:10.1109/TAP.2007.905846

    47. Beruete, M., M. Sorolla, I. Campillo, J. S. Dolado, L. Martin-Moreno, J. Bravo-Abad, and F. J. Garcia-Vidal, "Enhanced millimeter-wave transmission through subwavelength hole arrays," Opt. Lett., Vol. 29, No. 21, 2500-2502, Nov. 2004.
    doi:10.1364/OL.29.002500

    48. Beruete, M., M. Sorolla, I. Campillo, J. S. Dolado, L. Martin-Moreno, J. Bravo-Abad, and F. J. Garcia-Vidal, "Enhanced millimeter wave transmission through quasioptical subwavelength perforated plates," IEEE Trans. Antennas Propag., Vol. 53, No. 6, 1897-1903, Jun. 2005.
    doi:10.1109/TAP.2005.848689

    49. Hu, D. and Y. Zhang, "Localized surface plasmons-based transmission enhancement of terahertz radiation through metal aperture arrays," Optik, Vol. 121, 1423-1426, Feb. 2009.

    50. Shirmanesh, G. K., A. Khavasi, and K. Mehrany, "Accurate effective medium theory for arrays of metallic nanowires," Journal of Optics, Vol. 17, 025104, 2015.
    doi:10.1088/2040-8978/17/2/025104

    51. Yarmoghaddam, E., G. K. Shirmanesh, A. Khavasi, and K. Mehrany, "Circuit model for periodic array of slits with multiple propagating diffracted orders," IEEE Trans. Antennas Propag., Vol. 62, No. 8, 4041-4048, Aug. 2018.
    doi:10.1109/TAP.2014.2322884

    52. Ng Mou Kehn, M., "Modal analysis of substrate integrated waveguides with rectangular via-holes using cavity and multilayer Green's functions," IEEE Trans. Microw. Theory Techn., Vol. 62, No. 10, 2214-2231, Oct. 2014.
    doi:10.1109/TMTT.2014.2344626

    53. Lord Rayleigh, "On the dynamical theory of gratings," Proc. R. Soc. London, Ser. A, Vol. 79, 399, 1907.

    54. Lord Rayleigh, "Note on the remarkable case of diffraction spectra described by Prof. Wood," Philos. Mag., Vol. 14, 60, 1907.
    doi:10.1080/14786440709463661

    55. Balanis, C. A., Antenna Theory, Analysis and Design, 2nd Ed., John Wiley & Sons, Inc., 1997.