Semi-analytical method for light
interaction with 1D-periodic
nanoplasmonic structures

doi:10.1364/OE.16.008938

Semi-analytical method for light interaction with 1D-periodic nanoplasmonic structures

Andrey Kobyakov, Aramais R. Zakharian, Arash Mafi, and Sergey A. Darmanyan »View Author Affiliations

Optics Express, Vol. 16, Issue 12, pp. 8938-8957 (2008)
http://dx.doi.org/10.1364/OE.16.008938

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Abstract

We present a detailed description of a computationally efficient, semi-analytical method (SAM) to calculate the electomagnetic field distribution in a 1D-periodic, subwavelength-structured metal film placed between dielectric substrates. The method is roughly three orders of magnitude faster than the finite-element method (FEM). SAM is used to study the resonant transmission of light through nanoplasmonic structures, and to analyze the role of fundamental and higher-order Bloch surface plasmons in transmission enhancement. The method is also suitable for solving the eigenvalue problem and finding modes of the structure. Results obtained with SAM, FEM, and the finite-difference time-domain method show very good agreement for various parameters of the structure.

OCIS Codes
(240.0310) Optics at surfaces : Thin films
(240.6680) Optics at surfaces : Surface plasmons
(050.1755) Diffraction and gratings : Computational electromagnetic methods
(310.6628) Thin films : Subwavelength structures, nanostructures

ToC Category:
Optics at Surfaces

History
Original Manuscript: March 7, 2008
Revised Manuscript: May 21, 2008
Manuscript Accepted: May 29, 2008
Published: June 3, 2008

Citation
Andrey Kobyakov, Aramais R. Zakharian, Arash Mafi, and Sergey A. Darmanyan, "Semi-analytical method for light interaction with 1D-periodic nanoplasmonic structures," Opt. Express 16, 8938-8957 (2008)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-12-8938

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References

V. M. Agranovich and D. L. Mills, eds., Surface Polaritons (North Holland, Amsterdam, 1982).
A. D. Boardman, ed., Electromagnetic Surface Modes (Wiley, 1982).
J. Homola, ed., Surface Plasmon Resonance Based Sensors (Springer, 2006). [CrossRef]
S. A. Maier, Plasmonics: Fundamentals and Applications (Springer, 2007).
S. Kawata and H. Masuhara, eds., Nanoplasmonics. From Fundamentals to Applications (Elsevier, 2006).
A. V. Zayats, I. I. Smolyaninov, and A. A. Maradudin, "Nano-optics of surface plasmon polaritons," Phys. Rep. 408, 131-314 (2005). [CrossRef]
J. A. Porto, F. J. García-Vidal, and J. B. Pendry, "Transmission resonances on metallic gratings with very narrow slits," Phys. Rev. Lett. 83, 2845-2848 (1999). [CrossRef]
A. Krishnan, T. Thio, T. J. Kim, H. 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," Opt. Commun. 200, 1-7 (2001). [CrossRef]
S. A. Darmanyan 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 67, 035424 (2003). [CrossRef]
A. M. Dykhne, A. K. Sarychev, and V. M. Shalaev, "Resonant transmission through metal films with fabricated and light-induced modulation," Phys. Rev. B 67, 195402 (2003). [CrossRef]
N. Bonod, S. Enoch, L. Li, E. Popov, and M. Nevière, "Resonant optical transmission through thin metallic films with and without holes," Opt. Express 11, 482-490 (2003). [CrossRef] [PubMed]
D. Gérard, L. Salomon, F. de Fornel, and A. V. Zayats, "Ridge-enhanced optical transmission through a continuous metal film," Phys. Rev. B 69, 113405 (2004). [CrossRef]
Y. Xie, A. R. Zakharian, J. V. Moloney, and M. Mansuripur, "Transmission of light through a periodic array of slits in a thick metallic film," Opt. Express 13, 4485-4491 (2005). [CrossRef] [PubMed]
N. Garcia and M. Nieto-Vesperinas, "Theory of electromagnetic wave transmission through metallic gratings of subwavelength slits," J. Opt. A: Pure Appl. Opt. 9, 490-495 (2007). [CrossRef]
K. Busch, G. von Freymann, S. Linden, S. F. Mingaleev, L. Tkeshelashvili, and M. Wegener, "Periodic nanostructures for photonics," Phys. Rep. 444, 101-202 (2007). [CrossRef]
A. Kobyakov, A. Mafi, A. R. Zakharian, and S. A. Darmanyan, "Fundamental and higher-order Bloch surface plasmons in planar bimetallic gratings on silicon and glass substrates," J. Opt. Soc. Am. B (submitted).
J. L. Volakis, A. Chatterjee, and J. L. Kempel, Finite Element Method for Electromagnetics (IEEE Press, New York, 1998). [CrossRef]
K. S. Yee, "Numerical solution of initial boundary value problems involving Maxwell???s equations in isotropic media," IEEE Trans. Antennas and Prop. 14, 302-307 (1966). [CrossRef]
M. G. Moharam, E. B. Grann, D. A. Pommet, and T. K. Gaylord, "Formulation for stable and efficient implementation of the rigorous coupled-wave analysis of binary gratings," J. Opt. Soc. Am. A 12, 1068-1076 (1995). [CrossRef]
P. Lalanne and G. M. Morris, "Highly improved convergence of the coupled-wave method for TM polarization," J. Opt. Soc. Am. A 13, 779-784 (1996). [CrossRef]
L. Li, "Use of Fourier series in the analysis of discontinuous periodic structures," J. Opt. Soc. Am. A 13, 1870-1876 (1996). [CrossRef]
G. Granet and B. Guizal, "Efficient implementation of the coupled-wave method for metallic lamellar gratings in TM polarization," J. Opt. Soc. Am. A 13, 1019-1023 (1996). [CrossRef]
E. Popov and M. Nevière, "Grating theory: new equations in Fourier space leading to fast converging results for TM polarization," J. Opt. Soc. Am. A 17, 1773-1784 (2000). [CrossRef]
S. A. Darmanyan, M. Nevière, and A. V. Zayats, "Analytical theory of optical transmission through periodically structured metal films via tunnel-coupled surface polariton modes," Phys. Rev. B 70, 075103 (2004). [CrossRef]
A. Benabbas, V. Halté, and J.-Y. Bigot, "Analytical model of the optical response of periodically structured metallic films," Opt. Express 13, 8730-8745 (2005). [CrossRef] [PubMed]
E. Popov and M. Nevière, "Analytical model of the optical response of periodically structured metallic films: Comment," Opt. Express 14, 6583-6587 (2006). [CrossRef] [PubMed]
W. Cai, D. A. Genov, and V. M. Shalaev, "Superlens based metal-dielectric composites," Phys. Rev. B 72, 193101 (2005). [CrossRef]
M. I. Markovic and A. D. Rakic, "Determination of the reflection coefficients of laser light of wavelengths ? (0.22 ?m, 200 ?m) from the surface of aluminium using the Lorentz-Drude model," Appl. Opt. 29, 3479-3483 (1990). [CrossRef] [PubMed]
P. G. Etchegoin, E. C. L. Ru, and M. Meyer, "An analytic model for the optical properties of gold," J. Chem. Phys. 125, 164705 (2006). [CrossRef] [PubMed]
E. Palik and G. Ghosh, eds., The Electronic Handbook of Optical Constants of Solids (Academic, New York, 1999).
F. Tisseur and K. Meerbergen, "The quadratic eigenvalue problem," SIAM Rev. 43, 235-286 (2001). [CrossRef]
http://www.mathworks.com.
http://comsol.com.
Q. Cao and P. Lalanne, "Negative role of surface plasmons in the transmission of metallic gratings with very narrow slits," Phys. Rev. Lett. 88, 057403 (2002). [CrossRef] [PubMed]
M. Nevière and E. Popov, Light Propagation in Periodic Media: Differential Theory and Design (Marcel Dekker, 2003).
N. M. Lyndin, O. Parriaux, and A. V. Tishchenko, "Modal analysis and suppression of the Fourier modal method instabilities in highly conductive gratings," J. Opt. Soc. Am. A 24, 3781-3788 (2007). [CrossRef]

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[1] V. M. Agranovich and D. L. Mills, eds., Surface Polaritons (North Holland, Amsterdam, 1982).

[2] A. D. Boardman, ed., Electromagnetic Surface Modes (Wiley, 1982).

[3] J. Homola, ed., Surface Plasmon Resonance Based Sensors (Springer, 2006). [CrossRef]

[4] S. A. Maier, Plasmonics: Fundamentals and Applications (Springer, 2007).

[5] S. Kawata and H. Masuhara, eds., Nanoplasmonics. From Fundamentals to Applications (Elsevier, 2006).

[6] A. V. Zayats, I. I. Smolyaninov, and A. A. Maradudin, "Nano-optics of surface plasmon polaritons," Phys. Rep. 408, 131-314 (2005). [CrossRef]

[7] J. A. Porto, F. J. García-Vidal, and J. B. Pendry, "Transmission resonances on metallic gratings with very narrow slits," Phys. Rev. Lett. 83, 2845-2848 (1999). [CrossRef]

[8] A. Krishnan, T. Thio, T. J. Kim, H. 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," Opt. Commun. 200, 1-7 (2001). [CrossRef]

[9] S. A. Darmanyan 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 67, 035424 (2003). [CrossRef]

[10] A. M. Dykhne, A. K. Sarychev, and V. M. Shalaev, "Resonant transmission through metal films with fabricated and light-induced modulation," Phys. Rev. B 67, 195402 (2003). [CrossRef]

[11] N. Bonod, S. Enoch, L. Li, E. Popov, and M. Nevière, "Resonant optical transmission through thin metallic films with and without holes," Opt. Express 11, 482-490 (2003). [CrossRef] [PubMed]

[12] D. Gérard, L. Salomon, F. de Fornel, and A. V. Zayats, "Ridge-enhanced optical transmission through a continuous metal film," Phys. Rev. B 69, 113405 (2004). [CrossRef]

[13] Y. Xie, A. R. Zakharian, J. V. Moloney, and M. Mansuripur, "Transmission of light through a periodic array of slits in a thick metallic film," Opt. Express 13, 4485-4491 (2005). [CrossRef] [PubMed]

[14] N. Garcia and M. Nieto-Vesperinas, "Theory of electromagnetic wave transmission through metallic gratings of subwavelength slits," J. Opt. A: Pure Appl. Opt. 9, 490-495 (2007). [CrossRef]

[15] K. Busch, G. von Freymann, S. Linden, S. F. Mingaleev, L. Tkeshelashvili, and M. Wegener, "Periodic nanostructures for photonics," Phys. Rep. 444, 101-202 (2007). [CrossRef]

[16] A. Kobyakov, A. Mafi, A. R. Zakharian, and S. A. Darmanyan, "Fundamental and higher-order Bloch surface plasmons in planar bimetallic gratings on silicon and glass substrates," J. Opt. Soc. Am. B (submitted).

[17] J. L. Volakis, A. Chatterjee, and J. L. Kempel, Finite Element Method for Electromagnetics (IEEE Press, New York, 1998). [CrossRef]

[18] K. S. Yee, "Numerical solution of initial boundary value problems involving Maxwell???s equations in isotropic media," IEEE Trans. Antennas and Prop. 14, 302-307 (1966). [CrossRef]

[19] M. G. Moharam, E. B. Grann, D. A. Pommet, and T. K. Gaylord, "Formulation for stable and efficient implementation of the rigorous coupled-wave analysis of binary gratings," J. Opt. Soc. Am. A 12, 1068-1076 (1995). [CrossRef]

[20] P. Lalanne and G. M. Morris, "Highly improved convergence of the coupled-wave method for TM polarization," J. Opt. Soc. Am. A 13, 779-784 (1996). [CrossRef]

[21] L. Li, "Use of Fourier series in the analysis of discontinuous periodic structures," J. Opt. Soc. Am. A 13, 1870-1876 (1996). [CrossRef]

[22] G. Granet and B. Guizal, "Efficient implementation of the coupled-wave method for metallic lamellar gratings in TM polarization," J. Opt. Soc. Am. A 13, 1019-1023 (1996). [CrossRef]

[23] E. Popov and M. Nevière, "Grating theory: new equations in Fourier space leading to fast converging results for TM polarization," J. Opt. Soc. Am. A 17, 1773-1784 (2000). [CrossRef]

[24] S. A. Darmanyan, M. Nevière, and A. V. Zayats, "Analytical theory of optical transmission through periodically structured metal films via tunnel-coupled surface polariton modes," Phys. Rev. B 70, 075103 (2004). [CrossRef]

[25] A. Benabbas, V. Halté, and J.-Y. Bigot, "Analytical model of the optical response of periodically structured metallic films," Opt. Express 13, 8730-8745 (2005). [CrossRef] [PubMed]

[26] E. Popov and M. Nevière, "Analytical model of the optical response of periodically structured metallic films: Comment," Opt. Express 14, 6583-6587 (2006). [CrossRef] [PubMed]

[27] W. Cai, D. A. Genov, and V. M. Shalaev, "Superlens based metal-dielectric composites," Phys. Rev. B 72, 193101 (2005). [CrossRef]

[28] M. I. Markovic and A. D. Rakic, "Determination of the reflection coefficients of laser light of wavelengths ? (0.22 ?m, 200 ?m) from the surface of aluminium using the Lorentz-Drude model," Appl. Opt. 29, 3479-3483 (1990). [CrossRef] [PubMed]

[29] P. G. Etchegoin, E. C. L. Ru, and M. Meyer, "An analytic model for the optical properties of gold," J. Chem. Phys. 125, 164705 (2006). [CrossRef] [PubMed]

[30] E. Palik and G. Ghosh, eds., The Electronic Handbook of Optical Constants of Solids (Academic, New York, 1999).

[31] F. Tisseur and K. Meerbergen, "The quadratic eigenvalue problem," SIAM Rev. 43, 235-286 (2001). [CrossRef]

[32] http://www.mathworks.com.

[33] http://comsol.com.

[34] Q. Cao and P. Lalanne, "Negative role of surface plasmons in the transmission of metallic gratings with very narrow slits," Phys. Rev. Lett. 88, 057403 (2002). [CrossRef] [PubMed]

[35] M. Nevière and E. Popov, Light Propagation in Periodic Media: Differential Theory and Design (Marcel Dekker, 2003).

[36] N. M. Lyndin, O. Parriaux, and A. V. Tishchenko, "Modal analysis and suppression of the Fourier modal method instabilities in highly conductive gratings," J. Opt. Soc. Am. A 24, 3781-3788 (2007). [CrossRef]

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Semi-analytical method for light interaction with 1D-periodic nanoplasmonic structures