Abstract

In continuation of a previous paper [J. Opt. Soc. Am. B 27, 2218 (2010)], by solving a canonical boundary-value problem we found that the planar interface of a metal and a rugate filter can guide surface-plasmon-polariton (SPP) waves with phase speeds greater than the speed of light in free space. These SPP waves can be either p or s polarized, and can have extremely high phase speeds, but are very loosely bound to the metal/rugate-filter interface. In two practically implementable configurations with both partnering materials of finite thickness, both p- and s-polarized SPP waves with high phase speeds can be excited, provided that the thickness of the rugate filter is much larger than needed for SPP waves with low phase speeds.

© 2012 Optical Society of America

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2012

T. G. Mackay and A. Lakhtakia, “Modeling chiral sculptured thin films as platforms for surface-plasmonic-polaritonic optical sensing,” IEEE Sens. J. 12, 273–280 (2012).
[CrossRef]

S. Xiao, E. Stassen, and N. A. Mortensen, “Ultrathin silicon solar cells with enhanced photocurrents assisted by plasmonic nanostructures,” J. Nanophoton. 6, 061503 (2012).
[CrossRef]

2011

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]

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

H. Maab, M. Faryad, and A. Lakhtakia, “Surface electromagnetic waves supported by the interface of two semi-infinite rugate filters with sinusoidal refractive-index profiles,” J. Opt. Soc. Am. B 28, 1204–1212 (2011).
[CrossRef]

2010

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

M. E. Sasin, R. P. Seisyan, M. A. Kaliteevski, S. Brand, R. A. Abram, J. M. Chamberlain, I. V. Iorsh, I. A. Shelykh, A. Yu. Egorov, A. P. Vasil’ev, V. S. Mikhrin, and A. V. Kavokin, “Tamm plasmon-polaritons: first experimental observation,” Superlattices Microstruct. 47, 44–49 (2010).
[CrossRef]

2008

M. Dragoman and D. Dragoman, “Plasmonics: applications to nanoscale terahertz and optical devices,” Prog. Quantum Electron. 32, 1–41 (2008).
[CrossRef]

I. Abdulhalim, M. Zourob, and A. Lakhtakia, “Surface plasmon resonance for biosensing: a mini-review,” Electromagnetics 28, 214–242 (2008).
[CrossRef]

2006

A. P. Vinogradov, A. V. Dorofeenko, S. G. Erokhin, M. Inoue, A. A. Lisyansky, A. M. Merzlikin, and A. B. Granovsky, “Surface state peculiarities in one-dimensional photonic crystal interfaces,” Phys. Rev. B 74, 045128 (2006).
[CrossRef]

2005

A. Kavokin, I. Shelykh, and G. Malpuech, “Lossless interface modes at the boundary between two periodic dielectric structures,” Phys. Rev. B 72, 233102 (2005).
[CrossRef]

A. Kavokin, I. Shelykh, and G. Malpuech, “Optical Tamm states for the fabrication of polariton lasers,” Appl. Phys. Lett. 87, 261105 (2005).
[CrossRef]

1995

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

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. 73, 40–44 (1959).
[CrossRef]

Abdulhalim, I.

I. Abdulhalim, M. Zourob, and A. Lakhtakia, “Surface plasmon resonance for biosensing: a mini-review,” Electromagnetics 28, 214–242 (2008).
[CrossRef]

Abram, R. A.

M. E. Sasin, R. P. Seisyan, M. A. Kaliteevski, S. Brand, R. A. Abram, J. M. Chamberlain, I. V. Iorsh, I. A. Shelykh, A. Yu. Egorov, A. P. Vasil’ev, V. S. Mikhrin, and A. V. Kavokin, “Tamm plasmon-polaritons: first experimental observation,” Superlattices Microstruct. 47, 44–49 (2010).
[CrossRef]

Baumeister, P. W.

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

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]

Born, M.

M. Born and E. Wolf, Principles of Optics, 6th ed. (Pergamon, 1980).

Bovard, B. G.

Brand, S.

M. E. Sasin, R. P. Seisyan, M. A. Kaliteevski, S. Brand, R. A. Abram, J. M. Chamberlain, I. V. Iorsh, I. A. Shelykh, A. Yu. Egorov, A. P. Vasil’ev, V. S. Mikhrin, and A. V. Kavokin, “Tamm plasmon-polaritons: first experimental observation,” Superlattices Microstruct. 47, 44–49 (2010).
[CrossRef]

Chamberlain, J. M.

M. E. Sasin, R. P. Seisyan, M. A. Kaliteevski, S. Brand, R. A. Abram, J. M. Chamberlain, I. V. Iorsh, I. A. Shelykh, A. Yu. Egorov, A. P. Vasil’ev, V. S. Mikhrin, and A. V. Kavokin, “Tamm plasmon-polaritons: first experimental observation,” Superlattices Microstruct. 47, 44–49 (2010).
[CrossRef]

Dorofeenko, A. V.

A. P. Vinogradov, A. V. Dorofeenko, S. G. Erokhin, M. Inoue, A. A. Lisyansky, A. M. Merzlikin, and A. B. Granovsky, “Surface state peculiarities in one-dimensional photonic crystal interfaces,” Phys. Rev. B 74, 045128 (2006).
[CrossRef]

Dragoman, D.

M. Dragoman and D. Dragoman, “Plasmonics: applications to nanoscale terahertz and optical devices,” Prog. Quantum Electron. 32, 1–41 (2008).
[CrossRef]

Dragoman, M.

M. Dragoman and D. Dragoman, “Plasmonics: applications to nanoscale terahertz and optical devices,” Prog. Quantum Electron. 32, 1–41 (2008).
[CrossRef]

Egorov, A. Yu.

M. E. Sasin, R. P. Seisyan, M. A. Kaliteevski, S. Brand, R. A. Abram, J. M. Chamberlain, I. V. Iorsh, I. A. Shelykh, A. Yu. Egorov, A. P. Vasil’ev, V. S. Mikhrin, and A. V. Kavokin, “Tamm plasmon-polaritons: first experimental observation,” Superlattices Microstruct. 47, 44–49 (2010).
[CrossRef]

Erokhin, S. G.

A. P. Vinogradov, A. V. Dorofeenko, S. G. Erokhin, M. Inoue, A. A. Lisyansky, A. M. Merzlikin, and A. B. Granovsky, “Surface state peculiarities in one-dimensional photonic crystal interfaces,” Phys. Rev. B 74, 045128 (2006).
[CrossRef]

Faryad, M.

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

H. Maab, M. Faryad, and A. Lakhtakia, “Surface electromagnetic waves supported by the interface of two semi-infinite rugate filters with sinusoidal refractive-index profiles,” J. Opt. Soc. Am. B 28, 1204–1212 (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]

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

Gaylord, T. K.

Granovsky, A. B.

A. P. Vinogradov, A. V. Dorofeenko, S. G. Erokhin, M. Inoue, A. A. Lisyansky, A. M. Merzlikin, and A. B. Granovsky, “Surface state peculiarities in one-dimensional photonic crystal interfaces,” Phys. Rev. B 74, 045128 (2006).
[CrossRef]

Heine, C.

Inoue, M.

A. P. Vinogradov, A. V. Dorofeenko, S. G. Erokhin, M. Inoue, A. A. Lisyansky, A. M. Merzlikin, and A. B. Granovsky, “Surface state peculiarities in one-dimensional photonic crystal interfaces,” Phys. Rev. B 74, 045128 (2006).
[CrossRef]

Iorsh, I. V.

M. E. Sasin, R. P. Seisyan, M. A. Kaliteevski, S. Brand, R. A. Abram, J. M. Chamberlain, I. V. Iorsh, I. A. Shelykh, A. Yu. Egorov, A. P. Vasil’ev, V. S. Mikhrin, and A. V. Kavokin, “Tamm plasmon-polaritons: first experimental observation,” Superlattices Microstruct. 47, 44–49 (2010).
[CrossRef]

Jaluria, Y.

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

Kaliteevski, M. A.

M. E. Sasin, R. P. Seisyan, M. A. Kaliteevski, S. Brand, R. A. Abram, J. M. Chamberlain, I. V. Iorsh, I. A. Shelykh, A. Yu. Egorov, A. P. Vasil’ev, V. S. Mikhrin, and A. V. Kavokin, “Tamm plasmon-polaritons: first experimental observation,” Superlattices Microstruct. 47, 44–49 (2010).
[CrossRef]

Kavokin, A.

A. Kavokin, I. Shelykh, and G. Malpuech, “Lossless interface modes at the boundary between two periodic dielectric structures,” Phys. Rev. B 72, 233102 (2005).
[CrossRef]

A. Kavokin, I. Shelykh, and G. Malpuech, “Optical Tamm states for the fabrication of polariton lasers,” Appl. Phys. Lett. 87, 261105 (2005).
[CrossRef]

Kavokin, A. V.

M. E. Sasin, R. P. Seisyan, M. A. Kaliteevski, S. Brand, R. A. Abram, J. M. Chamberlain, I. V. Iorsh, I. A. Shelykh, A. Yu. Egorov, A. P. Vasil’ev, V. S. Mikhrin, and A. V. Kavokin, “Tamm plasmon-polaritons: first experimental observation,” Superlattices Microstruct. 47, 44–49 (2010).
[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.

T. G. Mackay and A. Lakhtakia, “Modeling chiral sculptured thin films as platforms for surface-plasmonic-polaritonic optical sensing,” IEEE Sens. J. 12, 273–280 (2012).
[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]

H. Maab, M. Faryad, and A. Lakhtakia, “Surface electromagnetic waves supported by the interface of two semi-infinite rugate filters with sinusoidal refractive-index profiles,” J. Opt. Soc. Am. B 28, 1204–1212 (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, “On surface plasmon-polariton waves guided by the interface of a metal and a rugate filter with a sinusoidal refractive-index profile,” J. Opt. Soc. Am. B 27, 2218–2223 (2010).
[CrossRef]

I. Abdulhalim, M. Zourob, and A. Lakhtakia, “Surface plasmon resonance for biosensing: a mini-review,” Electromagnetics 28, 214–242 (2008).
[CrossRef]

Li, L.

Lisyansky, A. A.

A. P. Vinogradov, A. V. Dorofeenko, S. G. Erokhin, M. Inoue, A. A. Lisyansky, A. M. Merzlikin, and A. B. Granovsky, “Surface state peculiarities in one-dimensional photonic crystal interfaces,” Phys. Rev. B 74, 045128 (2006).
[CrossRef]

Maab, H.

Mackay, T. G.

T. G. Mackay and A. Lakhtakia, “Modeling chiral sculptured thin films as platforms for surface-plasmonic-polaritonic optical sensing,” IEEE Sens. J. 12, 273–280 (2012).
[CrossRef]

Maier, S. A.

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

Malpuech, G.

A. Kavokin, I. Shelykh, and G. Malpuech, “Lossless interface modes at the boundary between two periodic dielectric structures,” Phys. Rev. B 72, 233102 (2005).
[CrossRef]

A. Kavokin, I. Shelykh, and G. Malpuech, “Optical Tamm states for the fabrication of polariton lasers,” Appl. Phys. Lett. 87, 261105 (2005).
[CrossRef]

Merzlikin, A. M.

A. P. Vinogradov, A. V. Dorofeenko, S. G. Erokhin, M. Inoue, A. A. Lisyansky, A. M. Merzlikin, and A. B. Granovsky, “Surface state peculiarities in one-dimensional photonic crystal interfaces,” Phys. Rev. B 74, 045128 (2006).
[CrossRef]

Mikhrin, V. S.

M. E. Sasin, R. P. Seisyan, M. A. Kaliteevski, S. Brand, R. A. Abram, J. M. Chamberlain, I. V. Iorsh, I. A. Shelykh, A. Yu. Egorov, A. P. Vasil’ev, V. S. Mikhrin, and A. V. Kavokin, “Tamm plasmon-polaritons: first experimental observation,” Superlattices Microstruct. 47, 44–49 (2010).
[CrossRef]

Moharam, M. G.

Morf, R. H.

Mortensen, N. A.

S. Xiao, E. Stassen, and N. A. Mortensen, “Ultrathin silicon solar cells with enhanced photocurrents assisted by plasmonic nanostructures,” J. Nanophoton. 6, 061503 (2012).
[CrossRef]

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]

Raether, H.

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

Sasin, M. E.

M. E. Sasin, R. P. Seisyan, M. A. Kaliteevski, S. Brand, R. A. Abram, J. M. Chamberlain, I. V. Iorsh, I. A. Shelykh, A. Yu. Egorov, A. P. Vasil’ev, V. S. Mikhrin, and A. V. Kavokin, “Tamm plasmon-polaritons: first experimental observation,” Superlattices Microstruct. 47, 44–49 (2010).
[CrossRef]

Seisyan, R. P.

M. E. Sasin, R. P. Seisyan, M. A. Kaliteevski, S. Brand, R. A. Abram, J. M. Chamberlain, I. V. Iorsh, I. A. Shelykh, A. Yu. Egorov, A. P. Vasil’ev, V. S. Mikhrin, and A. V. Kavokin, “Tamm plasmon-polaritons: first experimental observation,” Superlattices Microstruct. 47, 44–49 (2010).
[CrossRef]

Shelykh, I.

A. Kavokin, I. Shelykh, and G. Malpuech, “Lossless interface modes at the boundary between two periodic dielectric structures,” Phys. Rev. B 72, 233102 (2005).
[CrossRef]

A. Kavokin, I. Shelykh, and G. Malpuech, “Optical Tamm states for the fabrication of polariton lasers,” Appl. Phys. Lett. 87, 261105 (2005).
[CrossRef]

Shelykh, I. A.

M. E. Sasin, R. P. Seisyan, M. A. Kaliteevski, S. Brand, R. A. Abram, J. M. Chamberlain, I. V. Iorsh, I. A. Shelykh, A. Yu. Egorov, A. P. Vasil’ev, V. S. Mikhrin, and A. V. Kavokin, “Tamm plasmon-polaritons: first experimental observation,” Superlattices Microstruct. 47, 44–49 (2010).
[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]

Starzhinskii, V. M.

V. A. Yakubovich and V. M. Starzhinskii, Linear Differential Equations with Periodic Coefficients (Wiley, 1975).

Stassen, E.

S. Xiao, E. Stassen, and N. A. Mortensen, “Ultrathin silicon solar cells with enhanced photocurrents assisted by plasmonic nanostructures,” J. Nanophoton. 6, 061503 (2012).
[CrossRef]

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]

Turbadar, T.

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

Vasil’ev, A. P.

M. E. Sasin, R. P. Seisyan, M. A. Kaliteevski, S. Brand, R. A. Abram, J. M. Chamberlain, I. V. Iorsh, I. A. Shelykh, A. Yu. Egorov, A. P. Vasil’ev, V. S. Mikhrin, and A. V. Kavokin, “Tamm plasmon-polaritons: first experimental observation,” Superlattices Microstruct. 47, 44–49 (2010).
[CrossRef]

Vinogradov, A. P.

A. P. Vinogradov, A. V. Dorofeenko, S. G. Erokhin, M. Inoue, A. A. Lisyansky, A. M. Merzlikin, and A. B. Granovsky, “Surface state peculiarities in one-dimensional photonic crystal interfaces,” Phys. Rev. B 74, 045128 (2006).
[CrossRef]

Wolf, E.

M. Born and E. Wolf, Principles of Optics, 6th ed. (Pergamon, 1980).

Xiao, S.

S. Xiao, E. Stassen, and N. A. Mortensen, “Ultrathin silicon solar cells with enhanced photocurrents assisted by plasmonic nanostructures,” J. Nanophoton. 6, 061503 (2012).
[CrossRef]

Yakubovich, V. A.

V. A. Yakubovich and V. M. Starzhinskii, Linear Differential Equations with Periodic Coefficients (Wiley, 1975).

Zourob, M.

I. Abdulhalim, M. Zourob, and A. Lakhtakia, “Surface plasmon resonance for biosensing: a mini-review,” Electromagnetics 28, 214–242 (2008).
[CrossRef]

Appl. Opt.

Appl. Phys. Lett.

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]

A. Kavokin, I. Shelykh, and G. Malpuech, “Optical Tamm states for the fabrication of polariton lasers,” Appl. Phys. Lett. 87, 261105 (2005).
[CrossRef]

Electromagnetics

I. Abdulhalim, M. Zourob, and A. Lakhtakia, “Surface plasmon resonance for biosensing: a mini-review,” Electromagnetics 28, 214–242 (2008).
[CrossRef]

IEEE Sens. J.

T. G. Mackay and A. Lakhtakia, “Modeling chiral sculptured thin films as platforms for surface-plasmonic-polaritonic optical sensing,” IEEE Sens. J. 12, 273–280 (2012).
[CrossRef]

J. Nanophoton.

S. Xiao, E. Stassen, and N. A. Mortensen, “Ultrathin silicon solar cells with enhanced photocurrents assisted by plasmonic nanostructures,” J. Nanophoton. 6, 061503 (2012).
[CrossRef]

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

J. Opt. Soc. Am. B

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]

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

A. Kavokin, I. Shelykh, and G. Malpuech, “Lossless interface modes at the boundary between two periodic dielectric structures,” Phys. Rev. B 72, 233102 (2005).
[CrossRef]

A. P. Vinogradov, A. V. Dorofeenko, S. G. Erokhin, M. Inoue, A. A. Lisyansky, A. M. Merzlikin, and A. B. Granovsky, “Surface state peculiarities in one-dimensional photonic crystal interfaces,” Phys. Rev. B 74, 045128 (2006).
[CrossRef]

Proc. Phys. Soc.

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

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Figures (11)

Fig. 1.
Fig. 1.

Schematic of the canonical boundary-value problem.

Fig. 2.
Fig. 2.

Schematic of the grating-coupled configuration. Specular components of the reflected and transmitted light are of order 0, whereas nonspecular components are of nonzero orders.

Fig. 3.
Fig. 3.

(Left) Real and (right) imaginary parts of κ/k0 as functions of Ω/λ0 for SPP wave propagation guided by the planar interface of aluminum and a rugate filter with na=1.45 and nb=2.32, in the canonical boundary-value problem.

Fig. 4.
Fig. 4.

Normalized decay parameter Im(α)/k0 versus Ω/λ0 corresponding to the solutions presented in Fig. 3 in the canonical boundary-value problem.

Fig. 5.
Fig. 5.

Variations of the Cartesian components of P(0,0,z) with z in the canonical boundary-value problem. The components parallel to u^x, u^y, and u^z are represented by red solid, blue dashed, and black chain-dashed lines, respectively. The data for the plots on the left were computed for the solutions (top) κ/k0=0.9455+0.0020i, (middle) 0.8444+0.0032i, and (bottom) 0.7144+0.0047i on branch p11 with Ω/λ0=0.31, 0.3, and 0.29, respectively. The data for the plots on the right were computed for the solutions (top) κ/k0=0.9026+0.0053i, (middle) 0.8044+0.0058i, and (bottom) 0.6795+0.0066i on branch s2 with Ω/λ0=0.31, 0.3, and 0.29, respectively. The magnitude of the electric field was fixed at 1Vm1 on the plane z=0—for all six SPP waves.

Fig. 6.
Fig. 6.

Absorptance Ap as a function of the incidence angle θ for d1{40Ω,65Ω,80Ω,100Ω}, when λ0=633nm, Ω=0.31λ0, L=2λ0, L1=0.5L, d2d1=50nm, d3d2=30nm, ϵmet=56+21i, na=1.45, and nb=2.32. A vertical arrow identifies an SPP wave.

Fig. 7.
Fig. 7.

Variation of the x-component of the time-averaged Poynting vector P(0.75L,0,z) along the z axis in the regions (left) 0<z<d1 and (right) d1<z<d3 for p-polarized incidence, when θ=25.69°, λ0=633nm, Ω=0.31λ0, L=2λ0, L1=0.5L, d2d1=50nm, d3d2=30nm, d1=80Ω, ϵmet=56+21i, na=1.45, and nb=2.32.

Fig. 8.
Fig. 8.

Same as Fig. 6 except that As is plotted instead of Ap and d1{15Ω,17.5Ω,22.5Ω,40Ω}.

Fig. 9.
Fig. 9.

Same as Fig. 7 except that θ=21.88°, d1=17.5Ω, and the incident plane wave is s polarized.

Fig. 10.
Fig. 10.

Same as Fig. 6 except that d2d1=0.

Fig. 11.
Fig. 11.

Same as Fig. 8 except that d2d1=0.

Tables (1)

Tables Icon

Table 1. Relative Wavenumbers κ/k0 of Possible SPP Waves Obtained by the Solution of the Canonical Boundary-Value Problem [1] for Ω/λ0=0.31

Equations (15)

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ϵr(z)=[(nb+na2)+(nbna2)sin(πzΩ)]2,z>0,
ϵg(x,z)={ϵmet[ϵmetϵr(d2z)]U[d2zg(x)),x[0,L1]ϵr(d2z),x(L1,L),
Einc(r)=nZ(as(n)u^y+ap(n)pn+)exp[i(kx(n)x+kz(n)z)],z0,
Eref(r)=nZ(rs(n)u^y+rp(n)pn)exp[i(kx(n)xkz(n)z)],z0,
Etr(r)=nZ(ts(n)u^y+rp(n)pn+)exp{i[kx(n)x+kz(n)(zd3)]},z0,
kx(n)=k0sinθ+2πn/L
kz(n)=+k02(kx(n))2
pn±=kz(n)k0u^x+kx(n)k0u^z.
ϵ(x,z)=nZϵ(n)(z)exp(i2πnx/L),z[0,d3],
E(r)=nZE(n)(z)exp(ikx(n)x),z[0,d3],
H(r)=nZH(n)(z)exp(ikx(n)x),z[0,d3].
Rp=n=NtNt|rp(n)|2Re(kz(n)kz(0))
Tp=n=NtNt|tp(n)|2Re(kz(n)kz(0))
Rs=n=NtNt|rs(n)|2Re(kz(n)kz(0))
Ts=n=NtNt|ts(n)|2Re(kz(n)kz(0)),

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