Abstract

We have investigated extraordinary optical transmission (EOT) with enhanced Faraday effect in one-dimensional metallic-magnetic slit arrays under polar magnetization using the rigorous coupled-wave analysis performed by the Airy-like internal reflection series. The roles of surface plasmon polaritons and quasi-guided waves are studied in which the latter plays a key role. Based on the mechanism of EOT with an enhanced Faraday effect, both enhanced transmittance and enhanced Faraday effect are optimized by adjusting the geometric parameters of slit arrays evaluated by the figure of merit.

© 2008 Optical Society of America

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2008 (5)

H. Liu and P. Lalanne, "Microscopic theory of the extraordinary optical transmission," Nature 452, 728-731 (2008).
[CrossRef] [PubMed]

D. Crouse, A. P. Hibbins, and M. J. Lockyear, "Tuning the polarization state of enhanced transmission in gratings," Appl. Phys. Lett. 92, 191105 (2008).
[CrossRef]

Y. H. Lu, M. H. Cho, Y. P. Lee, and J. Y. Rhee, "Polarization-independent extraordinary optical transmission in one-dimensional metallic gratings with broad slits," Appl. Phys. Lett. 93, 061102 (2008).
[CrossRef]

P. Vasa, R. Pomraenke, S. Schwieger, Y. I. Mazur, V. Kunets, P. Srinivasan, E. Johnson, J. E. Kihm, D. S. Kim, E. Runge, G. Salamo, and C. Lienau, "Coherent exciton-surface-plasmon-polariton interaction in hybrid metalsemiconductor nanostructures," Phys. Rev. Lett. 101, 116801(2008).
[CrossRef] [PubMed]

Y. H. Lu, M. H. Cho, J. B. Kim, G. J. Lee, Y. P. Lee, and J. Y. Rhee, "Magneto-optical enhancement through gyrotropic gratings," Opt. Express 16, 5378-5384 (2008).
[CrossRef] [PubMed]

2007 (4)

A. B. Khanikaev, A. V. Baryshev, A. A. Fedyanin, A. B. Granovsky, and M. Inoue, "Anomalous Faraday effect of a system with extraordinary optical transmittance," Opt. Express 15, 6612-6622 (2007).
[CrossRef] [PubMed]

X. Fang, Z. Li, Y. Long, H. Wei, R. Liu, J. Ma, M. Kamran, H. Zhao, X. Han, B. Zhao, and X. Qiu, "Surfaceplasmon-polariton assisted diffraction in periodic subwavelength holes of metal films with reduced interplane coupling," Phys. Rev. Lett. 99, 066805 (2007).
[CrossRef] [PubMed]

V. I. Belotelov, L. L. Doskolovich, and A. K. Zvezdin, "Extraordinary magneto-optical effects and transmission through metal-dielectric plasmonic systems," Phys. Rev. Lett. 98, 077401 (2007).
[CrossRef] [PubMed]

V. I. Belotelov, L. L. Doskolovich, V. A. Kotov, E. A. Bezus, D. A. Bykov, and A. K. Zvezdin, "Magnetooptical effects in the metal-dielectric gratings," Opt. Coummun. 278, 104-109 (2007).
[CrossRef]

2006 (5)

M. Inoue, R. Fujikawa, A. Baryshev, A. Khanikaev, P. B. Lim, H. Uchida, O. Aktsipetrov, A. Fedyanin, T. Murzina, and A. Granovsky, "Magnetophotonic crystals," J. Phys. D: Appl. Phys. 39, R151-R161 (2006).
[CrossRef]

Z. Ruan and M. Qiu, "Enhanced transmission through periodic arrays of subwavelength holes: The role of localized waveguide resonances," Phys. Rev. Lett. 96, 233901 (2006).
[CrossRef] [PubMed]

E. Moreno, L. Martín-Moreno, and F. J. García-Vidal, "Extraordinary optical transmission without plasmons: the s-polarization case," J. Opt. A: Pure Appl. Opt. 8, S94-S97 (2006).
[CrossRef]

R. Antos, J. Postora, J. Mistrik, T. Yamaguchi, S. Yamaguchi, M. Horie, S. Visnovsky, and Y. Otani, "Convergence properties of critical dimension measurements by spectroscopic ellipsometry on gratings made of various materials," J. Appl. Phys. 100, 054906 (2006).
[CrossRef]

B. Sepulveda, L. M. Lechuga, and G. Armelles, "Magnetooptic effects in surface-plasmon-polaritons slab waveguides," J. Lightwave Technol. 24, 945-955 (2006).
[CrossRef]

2005 (2)

C. Ropers, D. J. Park, G. Stibenz, G. Steinmeyer, J. Kim, D. S. Kim, and C. Lienau, "Femtosecond light transmission and subradiant damping in plasmonic crystals," Phys. Rev. Lett. 94, 113901(2005).
[CrossRef] [PubMed]

V. Lomakin and E. Michielssen, "Enhanced transmission through metallic plates perforated by arrays of subwavelength holes and sandwiched between dielectric slabs," Phys. Rev. B 71, 235117 (2005).
[CrossRef]

2004 (1)

W. L. Barnes, W. A. Murray, J. Dintinger, E. Devaux, and T. W. Ebbesen, "Surface plasmon polaritons and their role in the enhanced transmission of light through periodic arrays of subwavelength holes in a metal film," Phys. Rev. Lett. 92, 107401 (2004).
[CrossRef] [PubMed]

2003 (1)

W. L. Barnes, A. Dereux, and T. W. Ebbesen, "Surface plasmon subwavelength optics," Nature 424, 824-830 (2003).
[CrossRef] [PubMed]

2002 (2)

F. J. García-Vidal and L. Martín-Moreno, "Transmission and focusing of light in one-dimensional periodically nanostructured metals," Phys. Rev. B 66, 155412 (2002).
[CrossRef]

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]

2001 (1)

C. Hermann, V. A. Kosobukin, G. Lampel, J. Peretti, V. Safarov, and P. Bertrand, "Surface-enhanced magnetooptics in metallic multilayer films," Phys. Rev. B 64, 235422 (2001).
[CrossRef]

2000 (2)

P. Lalanne, J. P. Hugonin, S. Astilean, M. Palamaru, and K. D. Möller, "One-mode model and Airy-like formulae for one-dimensional metallic gratings," J. Opt. A: Pure Appl. Opt. 2, 48-51 (2000).
[CrossRef]

M. J. Steel, M. Levy, and R. M. Osgood, "Large magnetooptical Kerr rotation with high reflectivity from photonic bandgap structures with defects," J. Lightwave Technol. 18, 1289-1296 (2000).
[CrossRef]

1999 (1)

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]

1998 (1)

T. W. Ebbesen, H. J. Lezec, H. G. Ghaemi, T. Thio, and R. A. Wolff, "Extraordinary optical transmission through sub-wavelength hole arrays," Nature 391, 667-669 (1998).
[CrossRef]

Aktsipetrov, O.

M. Inoue, R. Fujikawa, A. Baryshev, A. Khanikaev, P. B. Lim, H. Uchida, O. Aktsipetrov, A. Fedyanin, T. Murzina, and A. Granovsky, "Magnetophotonic crystals," J. Phys. D: Appl. Phys. 39, R151-R161 (2006).
[CrossRef]

Antos, R.

R. Antos, J. Postora, J. Mistrik, T. Yamaguchi, S. Yamaguchi, M. Horie, S. Visnovsky, and Y. Otani, "Convergence properties of critical dimension measurements by spectroscopic ellipsometry on gratings made of various materials," J. Appl. Phys. 100, 054906 (2006).
[CrossRef]

Armelles, G.

Astilean, S.

P. Lalanne, J. P. Hugonin, S. Astilean, M. Palamaru, and K. D. Möller, "One-mode model and Airy-like formulae for one-dimensional metallic gratings," J. Opt. A: Pure Appl. Opt. 2, 48-51 (2000).
[CrossRef]

Barnes, W. L.

W. L. Barnes, W. A. Murray, J. Dintinger, E. Devaux, and T. W. Ebbesen, "Surface plasmon polaritons and their role in the enhanced transmission of light through periodic arrays of subwavelength holes in a metal film," Phys. Rev. Lett. 92, 107401 (2004).
[CrossRef] [PubMed]

W. L. Barnes, A. Dereux, and T. W. Ebbesen, "Surface plasmon subwavelength optics," Nature 424, 824-830 (2003).
[CrossRef] [PubMed]

Baryshev, A.

M. Inoue, R. Fujikawa, A. Baryshev, A. Khanikaev, P. B. Lim, H. Uchida, O. Aktsipetrov, A. Fedyanin, T. Murzina, and A. Granovsky, "Magnetophotonic crystals," J. Phys. D: Appl. Phys. 39, R151-R161 (2006).
[CrossRef]

Baryshev, A. V.

Belotelov, V. I.

V. I. Belotelov, L. L. Doskolovich, and A. K. Zvezdin, "Extraordinary magneto-optical effects and transmission through metal-dielectric plasmonic systems," Phys. Rev. Lett. 98, 077401 (2007).
[CrossRef] [PubMed]

V. I. Belotelov, L. L. Doskolovich, V. A. Kotov, E. A. Bezus, D. A. Bykov, and A. K. Zvezdin, "Magnetooptical effects in the metal-dielectric gratings," Opt. Coummun. 278, 104-109 (2007).
[CrossRef]

Bertrand, P.

C. Hermann, V. A. Kosobukin, G. Lampel, J. Peretti, V. Safarov, and P. Bertrand, "Surface-enhanced magnetooptics in metallic multilayer films," Phys. Rev. B 64, 235422 (2001).
[CrossRef]

Bezus, E. A.

V. I. Belotelov, L. L. Doskolovich, V. A. Kotov, E. A. Bezus, D. A. Bykov, and A. K. Zvezdin, "Magnetooptical effects in the metal-dielectric gratings," Opt. Coummun. 278, 104-109 (2007).
[CrossRef]

Bykov, D. A.

V. I. Belotelov, L. L. Doskolovich, V. A. Kotov, E. A. Bezus, D. A. Bykov, and A. K. Zvezdin, "Magnetooptical effects in the metal-dielectric gratings," Opt. Coummun. 278, 104-109 (2007).
[CrossRef]

Cao, Q.

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]

Cho, M. H.

Y. H. Lu, M. H. Cho, J. B. Kim, G. J. Lee, Y. P. Lee, and J. Y. Rhee, "Magneto-optical enhancement through gyrotropic gratings," Opt. Express 16, 5378-5384 (2008).
[CrossRef] [PubMed]

Y. H. Lu, M. H. Cho, Y. P. Lee, and J. Y. Rhee, "Polarization-independent extraordinary optical transmission in one-dimensional metallic gratings with broad slits," Appl. Phys. Lett. 93, 061102 (2008).
[CrossRef]

Crouse, D.

D. Crouse, A. P. Hibbins, and M. J. Lockyear, "Tuning the polarization state of enhanced transmission in gratings," Appl. Phys. Lett. 92, 191105 (2008).
[CrossRef]

Dereux, A.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, "Surface plasmon subwavelength optics," Nature 424, 824-830 (2003).
[CrossRef] [PubMed]

Devaux, E.

W. L. Barnes, W. A. Murray, J. Dintinger, E. Devaux, and T. W. Ebbesen, "Surface plasmon polaritons and their role in the enhanced transmission of light through periodic arrays of subwavelength holes in a metal film," Phys. Rev. Lett. 92, 107401 (2004).
[CrossRef] [PubMed]

Dintinger, J.

W. L. Barnes, W. A. Murray, J. Dintinger, E. Devaux, and T. W. Ebbesen, "Surface plasmon polaritons and their role in the enhanced transmission of light through periodic arrays of subwavelength holes in a metal film," Phys. Rev. Lett. 92, 107401 (2004).
[CrossRef] [PubMed]

Doskolovich, L. L.

V. I. Belotelov, L. L. Doskolovich, and A. K. Zvezdin, "Extraordinary magneto-optical effects and transmission through metal-dielectric plasmonic systems," Phys. Rev. Lett. 98, 077401 (2007).
[CrossRef] [PubMed]

V. I. Belotelov, L. L. Doskolovich, V. A. Kotov, E. A. Bezus, D. A. Bykov, and A. K. Zvezdin, "Magnetooptical effects in the metal-dielectric gratings," Opt. Coummun. 278, 104-109 (2007).
[CrossRef]

Ebbesen, T. W.

W. L. Barnes, W. A. Murray, J. Dintinger, E. Devaux, and T. W. Ebbesen, "Surface plasmon polaritons and their role in the enhanced transmission of light through periodic arrays of subwavelength holes in a metal film," Phys. Rev. Lett. 92, 107401 (2004).
[CrossRef] [PubMed]

W. L. Barnes, A. Dereux, and T. W. Ebbesen, "Surface plasmon subwavelength optics," Nature 424, 824-830 (2003).
[CrossRef] [PubMed]

T. W. Ebbesen, H. J. Lezec, H. G. Ghaemi, T. Thio, and R. A. Wolff, "Extraordinary optical transmission through sub-wavelength hole arrays," Nature 391, 667-669 (1998).
[CrossRef]

Fang, X.

X. Fang, Z. Li, Y. Long, H. Wei, R. Liu, J. Ma, M. Kamran, H. Zhao, X. Han, B. Zhao, and X. Qiu, "Surfaceplasmon-polariton assisted diffraction in periodic subwavelength holes of metal films with reduced interplane coupling," Phys. Rev. Lett. 99, 066805 (2007).
[CrossRef] [PubMed]

Fedyanin, A.

M. Inoue, R. Fujikawa, A. Baryshev, A. Khanikaev, P. B. Lim, H. Uchida, O. Aktsipetrov, A. Fedyanin, T. Murzina, and A. Granovsky, "Magnetophotonic crystals," J. Phys. D: Appl. Phys. 39, R151-R161 (2006).
[CrossRef]

Fedyanin, A. A.

Fujikawa, R.

M. Inoue, R. Fujikawa, A. Baryshev, A. Khanikaev, P. B. Lim, H. Uchida, O. Aktsipetrov, A. Fedyanin, T. Murzina, and A. Granovsky, "Magnetophotonic crystals," J. Phys. D: Appl. Phys. 39, R151-R161 (2006).
[CrossRef]

García-Vidal, F. J.

E. Moreno, L. Martín-Moreno, and F. J. García-Vidal, "Extraordinary optical transmission without plasmons: the s-polarization case," J. Opt. A: Pure Appl. Opt. 8, S94-S97 (2006).
[CrossRef]

F. J. García-Vidal and L. Martín-Moreno, "Transmission and focusing of light in one-dimensional periodically nanostructured metals," Phys. Rev. B 66, 155412 (2002).
[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]

Ghaemi, H. G.

T. W. Ebbesen, H. J. Lezec, H. G. Ghaemi, T. Thio, and R. A. Wolff, "Extraordinary optical transmission through sub-wavelength hole arrays," Nature 391, 667-669 (1998).
[CrossRef]

Granovsky, A.

M. Inoue, R. Fujikawa, A. Baryshev, A. Khanikaev, P. B. Lim, H. Uchida, O. Aktsipetrov, A. Fedyanin, T. Murzina, and A. Granovsky, "Magnetophotonic crystals," J. Phys. D: Appl. Phys. 39, R151-R161 (2006).
[CrossRef]

Granovsky, A. B.

Han, X.

X. Fang, Z. Li, Y. Long, H. Wei, R. Liu, J. Ma, M. Kamran, H. Zhao, X. Han, B. Zhao, and X. Qiu, "Surfaceplasmon-polariton assisted diffraction in periodic subwavelength holes of metal films with reduced interplane coupling," Phys. Rev. Lett. 99, 066805 (2007).
[CrossRef] [PubMed]

Hermann, C.

C. Hermann, V. A. Kosobukin, G. Lampel, J. Peretti, V. Safarov, and P. Bertrand, "Surface-enhanced magnetooptics in metallic multilayer films," Phys. Rev. B 64, 235422 (2001).
[CrossRef]

Hibbins, A. P.

D. Crouse, A. P. Hibbins, and M. J. Lockyear, "Tuning the polarization state of enhanced transmission in gratings," Appl. Phys. Lett. 92, 191105 (2008).
[CrossRef]

Horie, M.

R. Antos, J. Postora, J. Mistrik, T. Yamaguchi, S. Yamaguchi, M. Horie, S. Visnovsky, and Y. Otani, "Convergence properties of critical dimension measurements by spectroscopic ellipsometry on gratings made of various materials," J. Appl. Phys. 100, 054906 (2006).
[CrossRef]

Hugonin, J. P.

P. Lalanne, J. P. Hugonin, S. Astilean, M. Palamaru, and K. D. Möller, "One-mode model and Airy-like formulae for one-dimensional metallic gratings," J. Opt. A: Pure Appl. Opt. 2, 48-51 (2000).
[CrossRef]

Inoue, M.

A. B. Khanikaev, A. V. Baryshev, A. A. Fedyanin, A. B. Granovsky, and M. Inoue, "Anomalous Faraday effect of a system with extraordinary optical transmittance," Opt. Express 15, 6612-6622 (2007).
[CrossRef] [PubMed]

M. Inoue, R. Fujikawa, A. Baryshev, A. Khanikaev, P. B. Lim, H. Uchida, O. Aktsipetrov, A. Fedyanin, T. Murzina, and A. Granovsky, "Magnetophotonic crystals," J. Phys. D: Appl. Phys. 39, R151-R161 (2006).
[CrossRef]

Johnson, E.

P. Vasa, R. Pomraenke, S. Schwieger, Y. I. Mazur, V. Kunets, P. Srinivasan, E. Johnson, J. E. Kihm, D. S. Kim, E. Runge, G. Salamo, and C. Lienau, "Coherent exciton-surface-plasmon-polariton interaction in hybrid metalsemiconductor nanostructures," Phys. Rev. Lett. 101, 116801(2008).
[CrossRef] [PubMed]

Kamran, M.

X. Fang, Z. Li, Y. Long, H. Wei, R. Liu, J. Ma, M. Kamran, H. Zhao, X. Han, B. Zhao, and X. Qiu, "Surfaceplasmon-polariton assisted diffraction in periodic subwavelength holes of metal films with reduced interplane coupling," Phys. Rev. Lett. 99, 066805 (2007).
[CrossRef] [PubMed]

Khanikaev, A.

M. Inoue, R. Fujikawa, A. Baryshev, A. Khanikaev, P. B. Lim, H. Uchida, O. Aktsipetrov, A. Fedyanin, T. Murzina, and A. Granovsky, "Magnetophotonic crystals," J. Phys. D: Appl. Phys. 39, R151-R161 (2006).
[CrossRef]

Khanikaev, A. B.

Kihm, J. E.

P. Vasa, R. Pomraenke, S. Schwieger, Y. I. Mazur, V. Kunets, P. Srinivasan, E. Johnson, J. E. Kihm, D. S. Kim, E. Runge, G. Salamo, and C. Lienau, "Coherent exciton-surface-plasmon-polariton interaction in hybrid metalsemiconductor nanostructures," Phys. Rev. Lett. 101, 116801(2008).
[CrossRef] [PubMed]

Kim, D. S.

P. Vasa, R. Pomraenke, S. Schwieger, Y. I. Mazur, V. Kunets, P. Srinivasan, E. Johnson, J. E. Kihm, D. S. Kim, E. Runge, G. Salamo, and C. Lienau, "Coherent exciton-surface-plasmon-polariton interaction in hybrid metalsemiconductor nanostructures," Phys. Rev. Lett. 101, 116801(2008).
[CrossRef] [PubMed]

C. Ropers, D. J. Park, G. Stibenz, G. Steinmeyer, J. Kim, D. S. Kim, and C. Lienau, "Femtosecond light transmission and subradiant damping in plasmonic crystals," Phys. Rev. Lett. 94, 113901(2005).
[CrossRef] [PubMed]

Kim, J.

C. Ropers, D. J. Park, G. Stibenz, G. Steinmeyer, J. Kim, D. S. Kim, and C. Lienau, "Femtosecond light transmission and subradiant damping in plasmonic crystals," Phys. Rev. Lett. 94, 113901(2005).
[CrossRef] [PubMed]

Kim, J. B.

Kosobukin, V. A.

C. Hermann, V. A. Kosobukin, G. Lampel, J. Peretti, V. Safarov, and P. Bertrand, "Surface-enhanced magnetooptics in metallic multilayer films," Phys. Rev. B 64, 235422 (2001).
[CrossRef]

Kotov, V. A.

V. I. Belotelov, L. L. Doskolovich, V. A. Kotov, E. A. Bezus, D. A. Bykov, and A. K. Zvezdin, "Magnetooptical effects in the metal-dielectric gratings," Opt. Coummun. 278, 104-109 (2007).
[CrossRef]

Kunets, V.

P. Vasa, R. Pomraenke, S. Schwieger, Y. I. Mazur, V. Kunets, P. Srinivasan, E. Johnson, J. E. Kihm, D. S. Kim, E. Runge, G. Salamo, and C. Lienau, "Coherent exciton-surface-plasmon-polariton interaction in hybrid metalsemiconductor nanostructures," Phys. Rev. Lett. 101, 116801(2008).
[CrossRef] [PubMed]

Lalanne, P.

H. Liu and P. Lalanne, "Microscopic theory of the extraordinary optical transmission," Nature 452, 728-731 (2008).
[CrossRef] [PubMed]

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]

P. Lalanne, J. P. Hugonin, S. Astilean, M. Palamaru, and K. D. Möller, "One-mode model and Airy-like formulae for one-dimensional metallic gratings," J. Opt. A: Pure Appl. Opt. 2, 48-51 (2000).
[CrossRef]

Lampel, G.

C. Hermann, V. A. Kosobukin, G. Lampel, J. Peretti, V. Safarov, and P. Bertrand, "Surface-enhanced magnetooptics in metallic multilayer films," Phys. Rev. B 64, 235422 (2001).
[CrossRef]

Lechuga, L. M.

Lee, G. J.

Lee, Y. P.

Y. H. Lu, M. H. Cho, J. B. Kim, G. J. Lee, Y. P. Lee, and J. Y. Rhee, "Magneto-optical enhancement through gyrotropic gratings," Opt. Express 16, 5378-5384 (2008).
[CrossRef] [PubMed]

Y. H. Lu, M. H. Cho, Y. P. Lee, and J. Y. Rhee, "Polarization-independent extraordinary optical transmission in one-dimensional metallic gratings with broad slits," Appl. Phys. Lett. 93, 061102 (2008).
[CrossRef]

Levy, M.

Lezec, H. J.

T. W. Ebbesen, H. J. Lezec, H. G. Ghaemi, T. Thio, and R. A. Wolff, "Extraordinary optical transmission through sub-wavelength hole arrays," Nature 391, 667-669 (1998).
[CrossRef]

Li, Z.

X. Fang, Z. Li, Y. Long, H. Wei, R. Liu, J. Ma, M. Kamran, H. Zhao, X. Han, B. Zhao, and X. Qiu, "Surfaceplasmon-polariton assisted diffraction in periodic subwavelength holes of metal films with reduced interplane coupling," Phys. Rev. Lett. 99, 066805 (2007).
[CrossRef] [PubMed]

Lienau, C.

P. Vasa, R. Pomraenke, S. Schwieger, Y. I. Mazur, V. Kunets, P. Srinivasan, E. Johnson, J. E. Kihm, D. S. Kim, E. Runge, G. Salamo, and C. Lienau, "Coherent exciton-surface-plasmon-polariton interaction in hybrid metalsemiconductor nanostructures," Phys. Rev. Lett. 101, 116801(2008).
[CrossRef] [PubMed]

C. Ropers, D. J. Park, G. Stibenz, G. Steinmeyer, J. Kim, D. S. Kim, and C. Lienau, "Femtosecond light transmission and subradiant damping in plasmonic crystals," Phys. Rev. Lett. 94, 113901(2005).
[CrossRef] [PubMed]

Lim, P. B.

M. Inoue, R. Fujikawa, A. Baryshev, A. Khanikaev, P. B. Lim, H. Uchida, O. Aktsipetrov, A. Fedyanin, T. Murzina, and A. Granovsky, "Magnetophotonic crystals," J. Phys. D: Appl. Phys. 39, R151-R161 (2006).
[CrossRef]

Liu, H.

H. Liu and P. Lalanne, "Microscopic theory of the extraordinary optical transmission," Nature 452, 728-731 (2008).
[CrossRef] [PubMed]

Liu, R.

X. Fang, Z. Li, Y. Long, H. Wei, R. Liu, J. Ma, M. Kamran, H. Zhao, X. Han, B. Zhao, and X. Qiu, "Surfaceplasmon-polariton assisted diffraction in periodic subwavelength holes of metal films with reduced interplane coupling," Phys. Rev. Lett. 99, 066805 (2007).
[CrossRef] [PubMed]

Lockyear, M. J.

D. Crouse, A. P. Hibbins, and M. J. Lockyear, "Tuning the polarization state of enhanced transmission in gratings," Appl. Phys. Lett. 92, 191105 (2008).
[CrossRef]

Lomakin, V.

V. Lomakin and E. Michielssen, "Enhanced transmission through metallic plates perforated by arrays of subwavelength holes and sandwiched between dielectric slabs," Phys. Rev. B 71, 235117 (2005).
[CrossRef]

Long, Y.

X. Fang, Z. Li, Y. Long, H. Wei, R. Liu, J. Ma, M. Kamran, H. Zhao, X. Han, B. Zhao, and X. Qiu, "Surfaceplasmon-polariton assisted diffraction in periodic subwavelength holes of metal films with reduced interplane coupling," Phys. Rev. Lett. 99, 066805 (2007).
[CrossRef] [PubMed]

Lu, Y. H.

Y. H. Lu, M. H. Cho, Y. P. Lee, and J. Y. Rhee, "Polarization-independent extraordinary optical transmission in one-dimensional metallic gratings with broad slits," Appl. Phys. Lett. 93, 061102 (2008).
[CrossRef]

Y. H. Lu, M. H. Cho, J. B. Kim, G. J. Lee, Y. P. Lee, and J. Y. Rhee, "Magneto-optical enhancement through gyrotropic gratings," Opt. Express 16, 5378-5384 (2008).
[CrossRef] [PubMed]

Ma, J.

X. Fang, Z. Li, Y. Long, H. Wei, R. Liu, J. Ma, M. Kamran, H. Zhao, X. Han, B. Zhao, and X. Qiu, "Surfaceplasmon-polariton assisted diffraction in periodic subwavelength holes of metal films with reduced interplane coupling," Phys. Rev. Lett. 99, 066805 (2007).
[CrossRef] [PubMed]

Martín-Moreno, L.

E. Moreno, L. Martín-Moreno, and F. J. García-Vidal, "Extraordinary optical transmission without plasmons: the s-polarization case," J. Opt. A: Pure Appl. Opt. 8, S94-S97 (2006).
[CrossRef]

F. J. García-Vidal and L. Martín-Moreno, "Transmission and focusing of light in one-dimensional periodically nanostructured metals," Phys. Rev. B 66, 155412 (2002).
[CrossRef]

Mazur, Y. I.

P. Vasa, R. Pomraenke, S. Schwieger, Y. I. Mazur, V. Kunets, P. Srinivasan, E. Johnson, J. E. Kihm, D. S. Kim, E. Runge, G. Salamo, and C. Lienau, "Coherent exciton-surface-plasmon-polariton interaction in hybrid metalsemiconductor nanostructures," Phys. Rev. Lett. 101, 116801(2008).
[CrossRef] [PubMed]

Michielssen, E.

V. Lomakin and E. Michielssen, "Enhanced transmission through metallic plates perforated by arrays of subwavelength holes and sandwiched between dielectric slabs," Phys. Rev. B 71, 235117 (2005).
[CrossRef]

Mistrik, J.

R. Antos, J. Postora, J. Mistrik, T. Yamaguchi, S. Yamaguchi, M. Horie, S. Visnovsky, and Y. Otani, "Convergence properties of critical dimension measurements by spectroscopic ellipsometry on gratings made of various materials," J. Appl. Phys. 100, 054906 (2006).
[CrossRef]

Möller, K. D.

P. Lalanne, J. P. Hugonin, S. Astilean, M. Palamaru, and K. D. Möller, "One-mode model and Airy-like formulae for one-dimensional metallic gratings," J. Opt. A: Pure Appl. Opt. 2, 48-51 (2000).
[CrossRef]

Moreno, E.

E. Moreno, L. Martín-Moreno, and F. J. García-Vidal, "Extraordinary optical transmission without plasmons: the s-polarization case," J. Opt. A: Pure Appl. Opt. 8, S94-S97 (2006).
[CrossRef]

Murray, W. A.

W. L. Barnes, W. A. Murray, J. Dintinger, E. Devaux, and T. W. Ebbesen, "Surface plasmon polaritons and their role in the enhanced transmission of light through periodic arrays of subwavelength holes in a metal film," Phys. Rev. Lett. 92, 107401 (2004).
[CrossRef] [PubMed]

Murzina, T.

M. Inoue, R. Fujikawa, A. Baryshev, A. Khanikaev, P. B. Lim, H. Uchida, O. Aktsipetrov, A. Fedyanin, T. Murzina, and A. Granovsky, "Magnetophotonic crystals," J. Phys. D: Appl. Phys. 39, R151-R161 (2006).
[CrossRef]

Osgood, R. M.

Otani, Y.

R. Antos, J. Postora, J. Mistrik, T. Yamaguchi, S. Yamaguchi, M. Horie, S. Visnovsky, and Y. Otani, "Convergence properties of critical dimension measurements by spectroscopic ellipsometry on gratings made of various materials," J. Appl. Phys. 100, 054906 (2006).
[CrossRef]

Palamaru, M.

P. Lalanne, J. P. Hugonin, S. Astilean, M. Palamaru, and K. D. Möller, "One-mode model and Airy-like formulae for one-dimensional metallic gratings," J. Opt. A: Pure Appl. Opt. 2, 48-51 (2000).
[CrossRef]

Park, D. J.

C. Ropers, D. J. Park, G. Stibenz, G. Steinmeyer, J. Kim, D. S. Kim, and C. Lienau, "Femtosecond light transmission and subradiant damping in plasmonic crystals," Phys. Rev. Lett. 94, 113901(2005).
[CrossRef] [PubMed]

Pendry, J. B.

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]

Peretti, J.

C. Hermann, V. A. Kosobukin, G. Lampel, J. Peretti, V. Safarov, and P. Bertrand, "Surface-enhanced magnetooptics in metallic multilayer films," Phys. Rev. B 64, 235422 (2001).
[CrossRef]

Pomraenke, R.

P. Vasa, R. Pomraenke, S. Schwieger, Y. I. Mazur, V. Kunets, P. Srinivasan, E. Johnson, J. E. Kihm, D. S. Kim, E. Runge, G. Salamo, and C. Lienau, "Coherent exciton-surface-plasmon-polariton interaction in hybrid metalsemiconductor nanostructures," Phys. Rev. Lett. 101, 116801(2008).
[CrossRef] [PubMed]

Porto, J. A.

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]

Postora, J.

R. Antos, J. Postora, J. Mistrik, T. Yamaguchi, S. Yamaguchi, M. Horie, S. Visnovsky, and Y. Otani, "Convergence properties of critical dimension measurements by spectroscopic ellipsometry on gratings made of various materials," J. Appl. Phys. 100, 054906 (2006).
[CrossRef]

Qiu, M.

Z. Ruan and M. Qiu, "Enhanced transmission through periodic arrays of subwavelength holes: The role of localized waveguide resonances," Phys. Rev. Lett. 96, 233901 (2006).
[CrossRef] [PubMed]

Qiu, X.

X. Fang, Z. Li, Y. Long, H. Wei, R. Liu, J. Ma, M. Kamran, H. Zhao, X. Han, B. Zhao, and X. Qiu, "Surfaceplasmon-polariton assisted diffraction in periodic subwavelength holes of metal films with reduced interplane coupling," Phys. Rev. Lett. 99, 066805 (2007).
[CrossRef] [PubMed]

Rhee, J. Y.

Y. H. Lu, M. H. Cho, Y. P. Lee, and J. Y. Rhee, "Polarization-independent extraordinary optical transmission in one-dimensional metallic gratings with broad slits," Appl. Phys. Lett. 93, 061102 (2008).
[CrossRef]

Y. H. Lu, M. H. Cho, J. B. Kim, G. J. Lee, Y. P. Lee, and J. Y. Rhee, "Magneto-optical enhancement through gyrotropic gratings," Opt. Express 16, 5378-5384 (2008).
[CrossRef] [PubMed]

Ropers, C.

C. Ropers, D. J. Park, G. Stibenz, G. Steinmeyer, J. Kim, D. S. Kim, and C. Lienau, "Femtosecond light transmission and subradiant damping in plasmonic crystals," Phys. Rev. Lett. 94, 113901(2005).
[CrossRef] [PubMed]

Ruan, Z.

Z. Ruan and M. Qiu, "Enhanced transmission through periodic arrays of subwavelength holes: The role of localized waveguide resonances," Phys. Rev. Lett. 96, 233901 (2006).
[CrossRef] [PubMed]

Runge, E.

P. Vasa, R. Pomraenke, S. Schwieger, Y. I. Mazur, V. Kunets, P. Srinivasan, E. Johnson, J. E. Kihm, D. S. Kim, E. Runge, G. Salamo, and C. Lienau, "Coherent exciton-surface-plasmon-polariton interaction in hybrid metalsemiconductor nanostructures," Phys. Rev. Lett. 101, 116801(2008).
[CrossRef] [PubMed]

Safarov, V.

C. Hermann, V. A. Kosobukin, G. Lampel, J. Peretti, V. Safarov, and P. Bertrand, "Surface-enhanced magnetooptics in metallic multilayer films," Phys. Rev. B 64, 235422 (2001).
[CrossRef]

Salamo, G.

P. Vasa, R. Pomraenke, S. Schwieger, Y. I. Mazur, V. Kunets, P. Srinivasan, E. Johnson, J. E. Kihm, D. S. Kim, E. Runge, G. Salamo, and C. Lienau, "Coherent exciton-surface-plasmon-polariton interaction in hybrid metalsemiconductor nanostructures," Phys. Rev. Lett. 101, 116801(2008).
[CrossRef] [PubMed]

Schwieger, S.

P. Vasa, R. Pomraenke, S. Schwieger, Y. I. Mazur, V. Kunets, P. Srinivasan, E. Johnson, J. E. Kihm, D. S. Kim, E. Runge, G. Salamo, and C. Lienau, "Coherent exciton-surface-plasmon-polariton interaction in hybrid metalsemiconductor nanostructures," Phys. Rev. Lett. 101, 116801(2008).
[CrossRef] [PubMed]

Sepulveda, B.

Srinivasan, P.

P. Vasa, R. Pomraenke, S. Schwieger, Y. I. Mazur, V. Kunets, P. Srinivasan, E. Johnson, J. E. Kihm, D. S. Kim, E. Runge, G. Salamo, and C. Lienau, "Coherent exciton-surface-plasmon-polariton interaction in hybrid metalsemiconductor nanostructures," Phys. Rev. Lett. 101, 116801(2008).
[CrossRef] [PubMed]

Steel, M. J.

Steinmeyer, G.

C. Ropers, D. J. Park, G. Stibenz, G. Steinmeyer, J. Kim, D. S. Kim, and C. Lienau, "Femtosecond light transmission and subradiant damping in plasmonic crystals," Phys. Rev. Lett. 94, 113901(2005).
[CrossRef] [PubMed]

Stibenz, G.

C. Ropers, D. J. Park, G. Stibenz, G. Steinmeyer, J. Kim, D. S. Kim, and C. Lienau, "Femtosecond light transmission and subradiant damping in plasmonic crystals," Phys. Rev. Lett. 94, 113901(2005).
[CrossRef] [PubMed]

Thio, T.

T. W. Ebbesen, H. J. Lezec, H. G. Ghaemi, T. Thio, and R. A. Wolff, "Extraordinary optical transmission through sub-wavelength hole arrays," Nature 391, 667-669 (1998).
[CrossRef]

Uchida, H.

M. Inoue, R. Fujikawa, A. Baryshev, A. Khanikaev, P. B. Lim, H. Uchida, O. Aktsipetrov, A. Fedyanin, T. Murzina, and A. Granovsky, "Magnetophotonic crystals," J. Phys. D: Appl. Phys. 39, R151-R161 (2006).
[CrossRef]

Vasa, P.

P. Vasa, R. Pomraenke, S. Schwieger, Y. I. Mazur, V. Kunets, P. Srinivasan, E. Johnson, J. E. Kihm, D. S. Kim, E. Runge, G. Salamo, and C. Lienau, "Coherent exciton-surface-plasmon-polariton interaction in hybrid metalsemiconductor nanostructures," Phys. Rev. Lett. 101, 116801(2008).
[CrossRef] [PubMed]

Visnovsky, S.

R. Antos, J. Postora, J. Mistrik, T. Yamaguchi, S. Yamaguchi, M. Horie, S. Visnovsky, and Y. Otani, "Convergence properties of critical dimension measurements by spectroscopic ellipsometry on gratings made of various materials," J. Appl. Phys. 100, 054906 (2006).
[CrossRef]

Wei, H.

X. Fang, Z. Li, Y. Long, H. Wei, R. Liu, J. Ma, M. Kamran, H. Zhao, X. Han, B. Zhao, and X. Qiu, "Surfaceplasmon-polariton assisted diffraction in periodic subwavelength holes of metal films with reduced interplane coupling," Phys. Rev. Lett. 99, 066805 (2007).
[CrossRef] [PubMed]

Wolff, R. A.

T. W. Ebbesen, H. J. Lezec, H. G. Ghaemi, T. Thio, and R. A. Wolff, "Extraordinary optical transmission through sub-wavelength hole arrays," Nature 391, 667-669 (1998).
[CrossRef]

Yamaguchi, S.

R. Antos, J. Postora, J. Mistrik, T. Yamaguchi, S. Yamaguchi, M. Horie, S. Visnovsky, and Y. Otani, "Convergence properties of critical dimension measurements by spectroscopic ellipsometry on gratings made of various materials," J. Appl. Phys. 100, 054906 (2006).
[CrossRef]

Yamaguchi, T.

R. Antos, J. Postora, J. Mistrik, T. Yamaguchi, S. Yamaguchi, M. Horie, S. Visnovsky, and Y. Otani, "Convergence properties of critical dimension measurements by spectroscopic ellipsometry on gratings made of various materials," J. Appl. Phys. 100, 054906 (2006).
[CrossRef]

Zhao, B.

X. Fang, Z. Li, Y. Long, H. Wei, R. Liu, J. Ma, M. Kamran, H. Zhao, X. Han, B. Zhao, and X. Qiu, "Surfaceplasmon-polariton assisted diffraction in periodic subwavelength holes of metal films with reduced interplane coupling," Phys. Rev. Lett. 99, 066805 (2007).
[CrossRef] [PubMed]

Zhao, H.

X. Fang, Z. Li, Y. Long, H. Wei, R. Liu, J. Ma, M. Kamran, H. Zhao, X. Han, B. Zhao, and X. Qiu, "Surfaceplasmon-polariton assisted diffraction in periodic subwavelength holes of metal films with reduced interplane coupling," Phys. Rev. Lett. 99, 066805 (2007).
[CrossRef] [PubMed]

Zvezdin, A. K.

V. I. Belotelov, L. L. Doskolovich, and A. K. Zvezdin, "Extraordinary magneto-optical effects and transmission through metal-dielectric plasmonic systems," Phys. Rev. Lett. 98, 077401 (2007).
[CrossRef] [PubMed]

V. I. Belotelov, L. L. Doskolovich, V. A. Kotov, E. A. Bezus, D. A. Bykov, and A. K. Zvezdin, "Magnetooptical effects in the metal-dielectric gratings," Opt. Coummun. 278, 104-109 (2007).
[CrossRef]

Appl. Phys. Lett. (2)

D. Crouse, A. P. Hibbins, and M. J. Lockyear, "Tuning the polarization state of enhanced transmission in gratings," Appl. Phys. Lett. 92, 191105 (2008).
[CrossRef]

Y. H. Lu, M. H. Cho, Y. P. Lee, and J. Y. Rhee, "Polarization-independent extraordinary optical transmission in one-dimensional metallic gratings with broad slits," Appl. Phys. Lett. 93, 061102 (2008).
[CrossRef]

J. Appl. Phys. (1)

R. Antos, J. Postora, J. Mistrik, T. Yamaguchi, S. Yamaguchi, M. Horie, S. Visnovsky, and Y. Otani, "Convergence properties of critical dimension measurements by spectroscopic ellipsometry on gratings made of various materials," J. Appl. Phys. 100, 054906 (2006).
[CrossRef]

J. Lightwave Technol. (2)

J. Opt. A: Pure Appl. Opt. (2)

P. Lalanne, J. P. Hugonin, S. Astilean, M. Palamaru, and K. D. Möller, "One-mode model and Airy-like formulae for one-dimensional metallic gratings," J. Opt. A: Pure Appl. Opt. 2, 48-51 (2000).
[CrossRef]

E. Moreno, L. Martín-Moreno, and F. J. García-Vidal, "Extraordinary optical transmission without plasmons: the s-polarization case," J. Opt. A: Pure Appl. Opt. 8, S94-S97 (2006).
[CrossRef]

J. Phys. D: Appl. Phys. (1)

M. Inoue, R. Fujikawa, A. Baryshev, A. Khanikaev, P. B. Lim, H. Uchida, O. Aktsipetrov, A. Fedyanin, T. Murzina, and A. Granovsky, "Magnetophotonic crystals," J. Phys. D: Appl. Phys. 39, R151-R161 (2006).
[CrossRef]

Nature (3)

W. L. Barnes, A. Dereux, and T. W. Ebbesen, "Surface plasmon subwavelength optics," Nature 424, 824-830 (2003).
[CrossRef] [PubMed]

H. Liu and P. Lalanne, "Microscopic theory of the extraordinary optical transmission," Nature 452, 728-731 (2008).
[CrossRef] [PubMed]

T. W. Ebbesen, H. J. Lezec, H. G. Ghaemi, T. Thio, and R. A. Wolff, "Extraordinary optical transmission through sub-wavelength hole arrays," Nature 391, 667-669 (1998).
[CrossRef]

Opt. Coummun. (1)

V. I. Belotelov, L. L. Doskolovich, V. A. Kotov, E. A. Bezus, D. A. Bykov, and A. K. Zvezdin, "Magnetooptical effects in the metal-dielectric gratings," Opt. Coummun. 278, 104-109 (2007).
[CrossRef]

Opt. Express (2)

Phys. Rev. B (3)

F. J. García-Vidal and L. Martín-Moreno, "Transmission and focusing of light in one-dimensional periodically nanostructured metals," Phys. Rev. B 66, 155412 (2002).
[CrossRef]

C. Hermann, V. A. Kosobukin, G. Lampel, J. Peretti, V. Safarov, and P. Bertrand, "Surface-enhanced magnetooptics in metallic multilayer films," Phys. Rev. B 64, 235422 (2001).
[CrossRef]

V. Lomakin and E. Michielssen, "Enhanced transmission through metallic plates perforated by arrays of subwavelength holes and sandwiched between dielectric slabs," Phys. Rev. B 71, 235117 (2005).
[CrossRef]

Phys. Rev. Lett. (8)

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]

X. Fang, Z. Li, Y. Long, H. Wei, R. Liu, J. Ma, M. Kamran, H. Zhao, X. Han, B. Zhao, and X. Qiu, "Surfaceplasmon-polariton assisted diffraction in periodic subwavelength holes of metal films with reduced interplane coupling," Phys. Rev. Lett. 99, 066805 (2007).
[CrossRef] [PubMed]

V. I. Belotelov, L. L. Doskolovich, and A. K. Zvezdin, "Extraordinary magneto-optical effects and transmission through metal-dielectric plasmonic systems," Phys. Rev. Lett. 98, 077401 (2007).
[CrossRef] [PubMed]

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]

W. L. Barnes, W. A. Murray, J. Dintinger, E. Devaux, and T. W. Ebbesen, "Surface plasmon polaritons and their role in the enhanced transmission of light through periodic arrays of subwavelength holes in a metal film," Phys. Rev. Lett. 92, 107401 (2004).
[CrossRef] [PubMed]

Z. Ruan and M. Qiu, "Enhanced transmission through periodic arrays of subwavelength holes: The role of localized waveguide resonances," Phys. Rev. Lett. 96, 233901 (2006).
[CrossRef] [PubMed]

P. Vasa, R. Pomraenke, S. Schwieger, Y. I. Mazur, V. Kunets, P. Srinivasan, E. Johnson, J. E. Kihm, D. S. Kim, E. Runge, G. Salamo, and C. Lienau, "Coherent exciton-surface-plasmon-polariton interaction in hybrid metalsemiconductor nanostructures," Phys. Rev. Lett. 101, 116801(2008).
[CrossRef] [PubMed]

C. Ropers, D. J. Park, G. Stibenz, G. Steinmeyer, J. Kim, D. S. Kim, and C. Lienau, "Femtosecond light transmission and subradiant damping in plasmonic crystals," Phys. Rev. Lett. 94, 113901(2005).
[CrossRef] [PubMed]

Other (5)

D. Maystre, in Electromagnetic Surface Modes, edited by A. D. Boardman (Wiley, Belfast, 1982).

A. K. Zvezdin and V. A. Kotov, Modern Magnetooptics and Magnetooptical Materials (Institute of Physics Publishing, Bristol and Philadelphia, 1997).
[CrossRef]

H. Raether, Surface Plasmons on Smooth and Rough Surfaces and on Gratings (Springer-Verlag, Berlin, 1988).

D. Marcuse, Theory of Dielectric Optical Waveguides (Academic Press, Boston, 1991)

R. B. Wehrspohn, H.-S. Kitzerow, and K. Busch, in Nanophotonic Materials: Photonic Crystals, Plasmonics, and Metamaterials, edited by A. D. Boardman (Wiley-VCH, Weinheim, 2008).

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Figures (5)

Fig. 1.
Fig. 1.

(Color online) Schematic representation of the one-dimensional metallic-magnetic grating under polar magnetization.

Fig. 2.
Fig. 2.

(Color online) Transmittance (black lines) and MO Faraday (red lines) spectra at normal incidence with TM polarization. Solid lines : a bilayer system consisting of the gold slits array (d=750 nm, w=675 nm, h 1=75 nm) and the Bi:YIG layer (h 2=547 nm); Dash lines: a combination of the gold film without slits and the Bi:YIG layer; Dot line: single Bi:YIG layer; Dash dot line: the gold slits array. Arrow indicates the wavelength of λSP.

Fig. 3.
Fig. 3.

(Color online) (a):Transmittance (black lines) and MO Faraday (red lines) spectra with the different period d=650 (dot lines), 700 (dash lines), 750 (solid lines), and 800 nm (dash dot lines); (b):Wavelength of resonant peaks of both transmittance and Faraday effect as a function of array period d.

Fig. 4.
Fig. 4.

(Color online) (a): Transmittance (black points) and MO Faraday (red points) vs. the bar width from w=550 to 675 nm at an interval of 25 nm;(b): Figure of merit vs. the bar width from w=550 to 675 nm at an interval of 25 nm; (c): Transmittance (black lines) and MO Faraday (red lines) spectra with the different bar width and thickness of the magnetic layer: w=675 and h 2=547 nm (solid lines); w=600 and h 2=515 nm (dash lines).

Fig. 5.
Fig. 5.

(Color online) (a):Transmittance spectra as a function of both wavelength and thickness of the magnetic layer h 2 with TM-polarized incidence. Here d=750 nm, w=600 nm, and h 1=75 nm;(b):Top view of (a).

Equations (4)

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T 0 , J + 1 = T J , J + 1 ( 1 Q J ) 1 P J T 0 , J ,
λ SP = d m [ Re ( ε 1 ε d ε 1 + ε d ) ± sin θ i ] ,
β = k 0 sin θ i + 2 π d n ,
i tan ( k z 2 h 2 ) = α 2 ( α 1 + α 3 ) α 2 2 α 1 α 3 ,

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