Abstract

The excitation of multiple surface-plasmon-polariton (SPP) waves guided by the periodically corrugated interface of a homogeneous metal and a periodic multilayered isotropic dielectric (PMLID) material was studied theoretically. The solution of the underlying canonical boundary-value problem (with a planar interface) indicates that multiple SPP waves of different polarization states, phase speeds, and attenuation rates can be guided by the periodically corrugated interface. Accordingly, the boundary-value problem was formulated using rigorous coupled-wave analysis and solved using a numerically stable algorithm. A linearly polarized plane wave was considered obliquely incident on a PMLID material of finite thickness and backed by a metallic surface-relief grating. The total reflectance, total transmittance, and the absorptance were calculated as functions of the incidence angle for different numbers of unit cells in the PMLID material of fixed period. The excitation of SPP waves was indicated by those peaks in the absorptance curves that were independent of the number of unit cells, and these peaks were also correlated with the solutions of a dispersion equation obtained from the canonical boundary-value problem.

© 2012 Optical Society of America

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    [CrossRef]
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2011

M. Faryad and A. Lakhtakia, “On multiple surface-plasmon-polariton waves guided by the interface of a metal film and a rugate filter in the Kretschmann configuration,” Opt. Commun. 284, 5678–5687 (2011).
[CrossRef]

Y. Lu, J. F. Sell, M. D. Johnson, K. Reinhardt, and R. J. Knize, “Adding a thin metallic plasmonic layer to silicon thin film solar cells,” Phys. Status Solidi C 8, 843–845 (2011).
[CrossRef]

M. Faryad and A. Lakhtakia, “Grating-coupled excitation of multiple surface plasmon-polariton waves,” Phys. Rev. A 84, 033852 (2011).
[CrossRef]

M. Faryad and A. Lakhtakia, “Enhanced absorption of light due to multiple surface-plasmon-polariton waves,” Proc. SPIE 8110, 81100F (2011).
[CrossRef]

M. Faryad and A. Lakhtakia, “Multiple trains of same-color surface plasmon-polaritons guided by the planar interface of a metal and a sculptured nematic thin film. Part V: Grating-coupled excitation,” J. Nanophoton. 5, 053527 (2011).
[CrossRef]

A. Lakhtakia, “Reflection from a semi-infinite rugate filter,” J. Mod. Opt. 58, 562–565 (2011).
[CrossRef]

2010

2006

V. N. Konopsky and E. V. Alieva, “Long-range propagation of plasmon polaritons in a thin metal film on a one-dimensional photonic crystal surface,” Phys. Rev. Lett. 97, 253904 (2006).
[CrossRef]

2004

F. Wang, M. W. Horn, and A. Lakhtakia, “Rigorous electromagnetic modeling of near-field phase-shifting contact lithography,” Microelectron. Eng. 71, 34–53 (2004).
[CrossRef]

2003

2001

Z. Salamon and G. Tollin, “Optical anisotropy in lipid bilayer membrane: coupled plasmon-waveguide resonance measurements of molecular orientation, polarizability, and shape,” Biophys. J. 80, 1557–1567 (2001).
[CrossRef]

P. T. Worthing and W. L. Barnes, “Efficient coupling of surface plasmon polaritons to radiation using a bi-grating,” Appl. Phys. Lett. 79, 3035–3037 (2001).
[CrossRef]

1999

W. M. Robertson and M. S. May, “Surface electromagnetic wave excitation on one-dimensional photonic band-gap arrays,” Appl. Phys. Lett. 74, 1800–1802 (1999).
[CrossRef]

1997

Z. Salamon, H. A. Macleod, and G. Tollin, “Coupled plasmon-waveguide resonators: a new spectroscopic tool for probing proteolipid film structure and properties,” Biophys. J. 73, 2791–2797 (1997).
[CrossRef]

1995

1994

1993

1983

P. Sheng, A. N. Bloch, and R. S. Stepleman, “Wavelength-selective absorption enhancement in thin-film solar cells,” Appl. Phys. Lett. 43, 579–581 (1983).
[CrossRef]

1982

J. Moreland, A. Adams, and P. K. Hansma, “Efficiency of light emission from surface plasmons,” Phys. Rev. B 25, 2297–2300 (1982).
[CrossRef]

M. G. Moharam and T. K. Gaylord, “Diffraction analysis of dielectric surface-relief gratings,” J. Opt. Soc. Am. 72, 1385–1392 (1982).
[CrossRef]

1977

1968

A. Otto, “Excitation of nonradiative surface plasma waves in silver by the method of frustrated total reflection,” Z. Phys. 216, 398–410 (1968).
[CrossRef]

E. Kretschmann and H. Raether, “Radiative decay of non-radiative surface plasmons excited by light,” Z. Naturforsch. A 23, 2135–2136 (1968).

1959

T. Turbadar, “Complete absorption of light by thin metal films,” Proc. Phys. Soc. London 73, 40–44 (1959).
[CrossRef]

Adams, A.

J. Moreland, A. Adams, and P. K. Hansma, “Efficiency of light emission from surface plasmons,” Phys. Rev. B 25, 2297–2300 (1982).
[CrossRef]

Alieva, E. V.

V. N. Konopsky and E. V. Alieva, “Long-range propagation of plasmon polaritons in a thin metal film on a one-dimensional photonic crystal surface,” Phys. Rev. Lett. 97, 253904 (2006).
[CrossRef]

Atwater, H. A.

Barnes, W. L.

P. T. Worthing and W. L. Barnes, “Efficient coupling of surface plasmon polaritons to radiation using a bi-grating,” Appl. Phys. Lett. 79, 3035–3037 (2001).
[CrossRef]

Baumeister, P. W.

P. W. Baumeister, Optical Coating Technology (SPIE, 2004), Sec. 5.3.3.2.

Bloch, A. N.

P. Sheng, A. N. Bloch, and R. S. Stepleman, “Wavelength-selective absorption enhancement in thin-film solar cells,” Appl. Phys. Lett. 43, 579–581 (1983).
[CrossRef]

Bovard, B. G.

Burke, J. J.

N. S. Kapany and J. J. Burke, Optical Waveguides (Academic, 1972).

Chateau, N.

Faryad, M.

M. Faryad and A. Lakhtakia, “On multiple surface-plasmon-polariton waves guided by the interface of a metal film and a rugate filter in the Kretschmann configuration,” Opt. Commun. 284, 5678–5687 (2011).
[CrossRef]

M. Faryad and A. Lakhtakia, “Grating-coupled excitation of multiple surface plasmon-polariton waves,” Phys. Rev. A 84, 033852 (2011).
[CrossRef]

M. Faryad and A. Lakhtakia, “Enhanced absorption of light due to multiple surface-plasmon-polariton waves,” Proc. SPIE 8110, 81100F (2011).
[CrossRef]

M. Faryad and A. Lakhtakia, “Multiple trains of same-color surface plasmon-polaritons guided by the planar interface of a metal and a sculptured nematic thin film. Part V: Grating-coupled excitation,” J. Nanophoton. 5, 053527 (2011).
[CrossRef]

M. Faryad and A. Lakhtakia, “On surface plasmon-polariton waves guided by the interface of a metal and a rugate filter with sinusoidal refractive-index profile,” J. Opt. Soc. Am. B 27, 2218–2223 (2010).
[CrossRef]

Ferry, V. E.

Fujiwara, H.

H. Fujiwara, Spectroscopic Ellipsometry, Principles and Applications (Wiley, 2007), pp. 82 and 190.

Gaspar-Armenta, J. A.

Gaylord, T. K.

Grann, E. B.

Hansma, P. K.

J. Moreland, A. Adams, and P. K. Hansma, “Efficiency of light emission from surface plasmons,” Phys. Rev. B 25, 2297–2300 (1982).
[CrossRef]

Heine, C.

Hong, C.-S.

Horn, M. W.

F. Wang, M. W. Horn, and A. Lakhtakia, “Rigorous electromagnetic modeling of near-field phase-shifting contact lithography,” Microelectron. Eng. 71, 34–53 (2004).
[CrossRef]

Hugonin, J.-P.

Jaluria, Y.

Y. Jaluria, Computer Methods for Engineering (Taylor & Francis, 1996).

Johnson, M. D.

Y. Lu, J. F. Sell, M. D. Johnson, K. Reinhardt, and R. J. Knize, “Adding a thin metallic plasmonic layer to silicon thin film solar cells,” Phys. Status Solidi C 8, 843–845 (2011).
[CrossRef]

Kapany, N. S.

N. S. Kapany and J. J. Burke, Optical Waveguides (Academic, 1972).

Khaleque, T.

T. Khaleque, J. Yoon, W. Wu, M. Shokooh-Saremi, and R. Magnusson, “Guided-mode-resonance enabled absorption in amorphous silicon for thin-film solar cell applications,” in Integrated Photonics Research, Silicon and Nanophotonics, OSA Technical Digest (CD) (Optical Society of America, 2011), paper ITuD3.

Knize, R. J.

Y. Lu, J. F. Sell, M. D. Johnson, K. Reinhardt, and R. J. Knize, “Adding a thin metallic plasmonic layer to silicon thin film solar cells,” Phys. Status Solidi C 8, 843–845 (2011).
[CrossRef]

Konopsky, V. N.

V. N. Konopsky and E. V. Alieva, “Long-range propagation of plasmon polaritons in a thin metal film on a one-dimensional photonic crystal surface,” Phys. Rev. Lett. 97, 253904 (2006).
[CrossRef]

Kretschmann, E.

E. Kretschmann and H. Raether, “Radiative decay of non-radiative surface plasmons excited by light,” Z. Naturforsch. A 23, 2135–2136 (1968).

Lakhtakia, A.

M. Faryad and A. Lakhtakia, “Grating-coupled excitation of multiple surface plasmon-polariton waves,” Phys. Rev. A 84, 033852 (2011).
[CrossRef]

M. Faryad and A. Lakhtakia, “Enhanced absorption of light due to multiple surface-plasmon-polariton waves,” Proc. SPIE 8110, 81100F (2011).
[CrossRef]

M. Faryad and A. Lakhtakia, “On multiple surface-plasmon-polariton waves guided by the interface of a metal film and a rugate filter in the Kretschmann configuration,” Opt. Commun. 284, 5678–5687 (2011).
[CrossRef]

A. Lakhtakia, “Reflection from a semi-infinite rugate filter,” J. Mod. Opt. 58, 562–565 (2011).
[CrossRef]

M. Faryad and A. Lakhtakia, “Multiple trains of same-color surface plasmon-polaritons guided by the planar interface of a metal and a sculptured nematic thin film. Part V: Grating-coupled excitation,” J. Nanophoton. 5, 053527 (2011).
[CrossRef]

M. Faryad and A. Lakhtakia, “On surface plasmon-polariton waves guided by the interface of a metal and a rugate filter with sinusoidal refractive-index profile,” J. Opt. Soc. Am. B 27, 2218–2223 (2010).
[CrossRef]

F. Wang, M. W. Horn, and A. Lakhtakia, “Rigorous electromagnetic modeling of near-field phase-shifting contact lithography,” Microelectron. Eng. 71, 34–53 (2004).
[CrossRef]

Li, H. B. T.

Li, L.

Lu, Y.

Y. Lu, J. F. Sell, M. D. Johnson, K. Reinhardt, and R. J. Knize, “Adding a thin metallic plasmonic layer to silicon thin film solar cells,” Phys. Status Solidi C 8, 843–845 (2011).
[CrossRef]

Macleod, H. A.

Z. Salamon, H. A. Macleod, and G. Tollin, “Coupled plasmon-waveguide resonators: a new spectroscopic tool for probing proteolipid film structure and properties,” Biophys. J. 73, 2791–2797 (1997).
[CrossRef]

Magnusson, R.

T. Khaleque, J. Yoon, W. Wu, M. Shokooh-Saremi, and R. Magnusson, “Guided-mode-resonance enabled absorption in amorphous silicon for thin-film solar cell applications,” in Integrated Photonics Research, Silicon and Nanophotonics, OSA Technical Digest (CD) (Optical Society of America, 2011), paper ITuD3.

Maier, S. A.

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

Marcuse, D.

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

May, M. S.

W. M. Robertson and M. S. May, “Surface electromagnetic wave excitation on one-dimensional photonic band-gap arrays,” Appl. Phys. Lett. 74, 1800–1802 (1999).
[CrossRef]

Moharam, M. G.

Moreland, J.

J. Moreland, A. Adams, and P. K. Hansma, “Efficiency of light emission from surface plasmons,” Phys. Rev. B 25, 2297–2300 (1982).
[CrossRef]

Morf, R. H.

Otto, A.

A. Otto, “Excitation of nonradiative surface plasma waves in silver by the method of frustrated total reflection,” Z. Phys. 216, 398–410 (1968).
[CrossRef]

Polson, A.

Pommet, D. A.

Raether, H.

E. Kretschmann and H. Raether, “Radiative decay of non-radiative surface plasmons excited by light,” Z. Naturforsch. A 23, 2135–2136 (1968).

Reinhardt, K.

Y. Lu, J. F. Sell, M. D. Johnson, K. Reinhardt, and R. J. Knize, “Adding a thin metallic plasmonic layer to silicon thin film solar cells,” Phys. Status Solidi C 8, 843–845 (2011).
[CrossRef]

Robertson, W. M.

W. M. Robertson and M. S. May, “Surface electromagnetic wave excitation on one-dimensional photonic band-gap arrays,” Appl. Phys. Lett. 74, 1800–1802 (1999).
[CrossRef]

Salamon, Z.

Z. Salamon and G. Tollin, “Optical anisotropy in lipid bilayer membrane: coupled plasmon-waveguide resonance measurements of molecular orientation, polarizability, and shape,” Biophys. J. 80, 1557–1567 (2001).
[CrossRef]

Z. Salamon, H. A. Macleod, and G. Tollin, “Coupled plasmon-waveguide resonators: a new spectroscopic tool for probing proteolipid film structure and properties,” Biophys. J. 73, 2791–2797 (1997).
[CrossRef]

Schropp, R. E. I.

Sell, J. F.

Y. Lu, J. F. Sell, M. D. Johnson, K. Reinhardt, and R. J. Knize, “Adding a thin metallic plasmonic layer to silicon thin film solar cells,” Phys. Status Solidi C 8, 843–845 (2011).
[CrossRef]

Sheng, P.

P. Sheng, A. N. Bloch, and R. S. Stepleman, “Wavelength-selective absorption enhancement in thin-film solar cells,” Appl. Phys. Lett. 43, 579–581 (1983).
[CrossRef]

Shokooh-Saremi, M.

T. Khaleque, J. Yoon, W. Wu, M. Shokooh-Saremi, and R. Magnusson, “Guided-mode-resonance enabled absorption in amorphous silicon for thin-film solar cell applications,” in Integrated Photonics Research, Silicon and Nanophotonics, OSA Technical Digest (CD) (Optical Society of America, 2011), paper ITuD3.

Stepleman, R. S.

P. Sheng, A. N. Bloch, and R. S. Stepleman, “Wavelength-selective absorption enhancement in thin-film solar cells,” Appl. Phys. Lett. 43, 579–581 (1983).
[CrossRef]

Tollin, G.

Z. Salamon and G. Tollin, “Optical anisotropy in lipid bilayer membrane: coupled plasmon-waveguide resonance measurements of molecular orientation, polarizability, and shape,” Biophys. J. 80, 1557–1567 (2001).
[CrossRef]

Z. Salamon, H. A. Macleod, and G. Tollin, “Coupled plasmon-waveguide resonators: a new spectroscopic tool for probing proteolipid film structure and properties,” Biophys. J. 73, 2791–2797 (1997).
[CrossRef]

Turbadar, T.

T. Turbadar, “Complete absorption of light by thin metal films,” Proc. Phys. Soc. London 73, 40–44 (1959).
[CrossRef]

Verhagen, E.

Verschuuren, M. A.

Villa, F.

Walters, R. J.

Wang, F.

F. Wang, M. W. Horn, and A. Lakhtakia, “Rigorous electromagnetic modeling of near-field phase-shifting contact lithography,” Microelectron. Eng. 71, 34–53 (2004).
[CrossRef]

Worthing, P. T.

P. T. Worthing and W. L. Barnes, “Efficient coupling of surface plasmon polaritons to radiation using a bi-grating,” Appl. Phys. Lett. 79, 3035–3037 (2001).
[CrossRef]

Wu, W.

T. Khaleque, J. Yoon, W. Wu, M. Shokooh-Saremi, and R. Magnusson, “Guided-mode-resonance enabled absorption in amorphous silicon for thin-film solar cell applications,” in Integrated Photonics Research, Silicon and Nanophotonics, OSA Technical Digest (CD) (Optical Society of America, 2011), paper ITuD3.

Yariv, A.

Yeh, P.

Yoon, J.

T. Khaleque, J. Yoon, W. Wu, M. Shokooh-Saremi, and R. Magnusson, “Guided-mode-resonance enabled absorption in amorphous silicon for thin-film solar cell applications,” in Integrated Photonics Research, Silicon and Nanophotonics, OSA Technical Digest (CD) (Optical Society of America, 2011), paper ITuD3.

Appl. Opt.

Appl. Phys. Lett.

P. T. Worthing and W. L. Barnes, “Efficient coupling of surface plasmon polaritons to radiation using a bi-grating,” Appl. Phys. Lett. 79, 3035–3037 (2001).
[CrossRef]

W. M. Robertson and M. S. May, “Surface electromagnetic wave excitation on one-dimensional photonic band-gap arrays,” Appl. Phys. Lett. 74, 1800–1802 (1999).
[CrossRef]

P. Sheng, A. N. Bloch, and R. S. Stepleman, “Wavelength-selective absorption enhancement in thin-film solar cells,” Appl. Phys. Lett. 43, 579–581 (1983).
[CrossRef]

Biophys. J.

Z. Salamon, H. A. Macleod, and G. Tollin, “Coupled plasmon-waveguide resonators: a new spectroscopic tool for probing proteolipid film structure and properties,” Biophys. J. 73, 2791–2797 (1997).
[CrossRef]

Z. Salamon and G. Tollin, “Optical anisotropy in lipid bilayer membrane: coupled plasmon-waveguide resonance measurements of molecular orientation, polarizability, and shape,” Biophys. J. 80, 1557–1567 (2001).
[CrossRef]

J. Mod. Opt.

A. Lakhtakia, “Reflection from a semi-infinite rugate filter,” J. Mod. Opt. 58, 562–565 (2011).
[CrossRef]

J. Nanophoton.

M. Faryad and A. Lakhtakia, “Multiple trains of same-color surface plasmon-polaritons guided by the planar interface of a metal and a sculptured nematic thin film. Part V: Grating-coupled excitation,” J. Nanophoton. 5, 053527 (2011).
[CrossRef]

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

J. Opt. Soc. Am. B

Microelectron. Eng.

F. Wang, M. W. Horn, and A. Lakhtakia, “Rigorous electromagnetic modeling of near-field phase-shifting contact lithography,” Microelectron. Eng. 71, 34–53 (2004).
[CrossRef]

Opt. Commun.

M. Faryad and A. Lakhtakia, “On multiple surface-plasmon-polariton waves guided by the interface of a metal film and a rugate filter in the Kretschmann configuration,” Opt. Commun. 284, 5678–5687 (2011).
[CrossRef]

Opt. Express

Phys. Rev. A

M. Faryad and A. Lakhtakia, “Grating-coupled excitation of multiple surface plasmon-polariton waves,” Phys. Rev. A 84, 033852 (2011).
[CrossRef]

Phys. Rev. B

J. Moreland, A. Adams, and P. K. Hansma, “Efficiency of light emission from surface plasmons,” Phys. Rev. B 25, 2297–2300 (1982).
[CrossRef]

Phys. Rev. Lett.

V. N. Konopsky and E. V. Alieva, “Long-range propagation of plasmon polaritons in a thin metal film on a one-dimensional photonic crystal surface,” Phys. Rev. Lett. 97, 253904 (2006).
[CrossRef]

Phys. Status Solidi C

Y. Lu, J. F. Sell, M. D. Johnson, K. Reinhardt, and R. J. Knize, “Adding a thin metallic plasmonic layer to silicon thin film solar cells,” Phys. Status Solidi C 8, 843–845 (2011).
[CrossRef]

Proc. Phys. Soc. London

T. Turbadar, “Complete absorption of light by thin metal films,” Proc. Phys. Soc. London 73, 40–44 (1959).
[CrossRef]

Proc. SPIE

M. Faryad and A. Lakhtakia, “Enhanced absorption of light due to multiple surface-plasmon-polariton waves,” Proc. SPIE 8110, 81100F (2011).
[CrossRef]

Z. Naturforsch. A

E. Kretschmann and H. Raether, “Radiative decay of non-radiative surface plasmons excited by light,” Z. Naturforsch. A 23, 2135–2136 (1968).

Z. Phys.

A. Otto, “Excitation of nonradiative surface plasma waves in silver by the method of frustrated total reflection,” Z. Phys. 216, 398–410 (1968).
[CrossRef]

Other

Turbadar in 1959 [13] had anticipated the 1968 papers of both Otto [14] and Kretschmann and Raether [15], but had not used the word plasmon.

H. Fujiwara, Spectroscopic Ellipsometry, Principles and Applications (Wiley, 2007), pp. 82 and 190.

Y. Jaluria, Computer Methods for Engineering (Taylor & Francis, 1996).

J. Homola, ed., Surface Plasmon Resonance Based Sensors (Springer, 2006).

N. S. Kapany and J. J. Burke, Optical Waveguides (Academic, 1972).

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

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

T. Khaleque, J. Yoon, W. Wu, M. Shokooh-Saremi, and R. Magnusson, “Guided-mode-resonance enabled absorption in amorphous silicon for thin-film solar cell applications,” in Integrated Photonics Research, Silicon and Nanophotonics, OSA Technical Digest (CD) (Optical Society of America, 2011), paper ITuD3.

P. W. Baumeister, Optical Coating Technology (SPIE, 2004), Sec. 5.3.3.2.

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Figures (12)

Fig. 1.
Fig. 1.

Schematic of the canonical boundary-value problem involving a planar interface between a homogeneous and isotropic metal and a periodic multilayered isotropic dielectric material.

Fig. 2.
Fig. 2.

Schematic of the boundary-value problem involving a periodically corrugated interface between a homogeneous and isotropic metal and a periodic multilayered isotropic dielectric material.

Fig. 3.
Fig. 3.

Measured values of the real and imaginary parts of the relative permittivity ϵm of evaporated silver with respect to the free-space wavelength λ0. These data were used for the numerical results presented in Subsections 3.B and 3.C.

Fig. 4.
Fig. 4.

Measured values of the real parts of relative permittivity ϵrj of nine dielectric materials (used to make the PMLID material) with respect to the free-space wavelength λ0. The imaginary parts are all less than 104 and were therefore ignored. These data were used for the numerical results presented in Subsections 3.B and 3.C. The composition and the Cauchy coefficients of the dielectric layers are given in Table 1.

Fig. 5.
Fig. 5.

Left, relative phase speed vp/c and, right, e-folding distance Δx of possible SPP waves guided by the planar metal/PMLID interface. The relative wavenumbers κ/k0 were obtained by the solution of the canonical boundary-value problem described in Subsection 2.A, except for the black solid curve (labeled p0) that was obtained by the solution of Eq. (19).

Fig. 6.
Fig. 6.

Total reflectances (a) Rp and (c) Rs, and absorptances (b) Ap and (d) As versus the angle of incidence θ when λ0=500nm, L=400nm, L1=0.5L, Lg=35nm, Lm=30nm, and Ld=2ΩNp. The vertical arrows identify the reflectance dips or absorptance peaks that represent the excitation of SPP waves.

Fig. 7.
Fig. 7.

Variation of the x-component Px(x,z) of the time-averaged Poynting vector P(x,z) along the z axis in the regions (left) 0<z<Ld and (right) Ld<z<Ld+Lg+Lm, when λ0=500nm, x=0.75L, Np=3, Lg=35nm, Lm=30nm, and L=400nm. The incident plane wave is p polarized with ap(0)=1Vm1, and the angles of incidence are those of the peaks identified by vertical arrows in Fig. 6(b).

Fig. 8.
Fig. 8.

Same as Fig. 7, except that the incident plane wave is s polarized with as(0)=1Vm1, and the angles of incidence are those of the peaks identified by vertical arrows in Fig. 6(d).

Fig. 9.
Fig. 9.

Same as Fig. 6, except for λ0=700nm.

Fig. 10.
Fig. 10.

Same as Fig. 7, except that λ0=700nm and the angles of incidence are those of the peaks identified by vertical arrows in Fig. 9(b).

Fig. 11.
Fig. 11.

Same as Fig. 8, except that λ0=700nm and the angles of incidence are those of the peaks identified by vertical arrows in Fig. 9(d).

Fig. 12.
Fig. 12.

Same as Fig. 8, except that λ0=700nm and the angles of incidence are of the two chosen peaks in Fig. 9(d) that represent the excitation of waveguide modes.

Tables (5)

Tables Icon

Table 1. Composition and Cauchy Coefficients for Nine Dielectric Layers in the PMLID Materiala

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Table 2. Relative Wavenumbers κ/k0 of Possible SPP Waves for λ0=500nm Obtained by the Solution of the Canonical Boundary-Value Problem Described in Subsection 2.A, Except for the Italicized Entry that was Obtained by the Solution of Eq. (19)a

Tables Icon

Table 3. Relative Wavenumbers kx(n)/k0 of Floquet Harmonics at the θ-Values of the Peaks Identified by Vertical Arrows in Fig. 6 when λ0=500nm, Np=3, and L=400nma

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Table 4. Same as Table 2, Except for λ0=700nm

Tables Icon

Table 5. Relative Wavenumbers kx(n)/k0 of Floquet Harmonics at the θ-Values of the Peaks Identified in Fig. 9 when λ0=700nm, Np=3, and L=400nma

Equations (20)

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kmet=κu^xαmetu^z,
E(r)=[ap(αmetk0u^x+κk0u^z)+asu^y]exp(ikmet·r),z0,
ddz[f(z)]=i[P̲̲j]·[f(z)],j[1,),
[P̲̲j]=[000ωμ0κ2ωϵ0ϵrj00ωμ000ωϵ0ϵrj+κ2ωμ000ωϵ0ϵrj000],j[1,).
[Q̲̲]=exp(i[P̲̲N]dN)·exp(i[P̲̲N1]dN1)··exp(i[P̲̲2]d2)·exp(i[P̲̲1]d1)
[f(0+)]=b1[t](1)+b2[t](2)
ϵg(x,z)={ϵm,x[0,L1]ϵr1,x[L1,L],
Einc(r)=nZ(u^yas(n)+p+nap(n))exp[i(kx(n)x+kz(n)z)],z0,
Eref(r)=nZ(u^yrs(n)+pnrp(n))exp[i(kx(n)xkz(n)z)],z0,
Etr(r)=nZ(u^yts(n)+p+ntp(n))exp{i[kx(n)x+kz(n)(zLt)]},zLt,
pn±=kz(n)k0u^x+kx(n)k0u^z,
kz(n)={+k02(kx(n))2,k02>(kx(n))2+i(kx(n))2k02,k02<(kx(n))2.
ϵ(x,z)=nZϵ(n)(z)exp(inκxx),z[0,Lt],
ϵ(0)(z)={ϵd(z),z[0,Ld]1L0Lϵg(x,z)dx,z(Ld,Ld+Lg]ϵm,z[Ld+Lg,Lt],
ϵ(n)(z)={1L0Lϵg(x,z)exp(inκxx)dx,z[Ld,Ld+Lg]0,otherwise;n0.
Rp=n=NtNtRp(n),Tp=n=NtNtTp(n),Ap=1RpTp,
Rs=n=NtNtRs(n),Ts=n=NtNtTs(n),As=1RsTs,
Re(ϵrj)=(Aj+Bjλ02+Cjλ04)2,j[1,9].
κp0=k0ϵmϵr1ϵm+ϵr1.
P(x,z)=12Re[E(x,z)×H*(x,z)],

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