Abstract

The canonical boundary-value problem of wave propagation guided by the planar interface of an isotropic homogeneous metal and a dielectric rugate filter with a refractive index that varies periodically normal to the interface may admit more than one solution, at a specific frequency. The different solutions indicate surface plasmon-polariton (SPP) waves that differ in phase speed, attenuation rate, linear polarization state, and field distribution. The multiplicity of SPP waves can only be attributed to the periodic nonhomogeneity of the rugate filter.

© 2010 Optical Society of America

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  3. D. A. Hill and J. R. Wait, “On the excitation of the Zenneck surface wave over the ground at 10 MHz,” Ann. Telecommun. 35, 179–182 (1980).
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    [CrossRef]
  5. S. A. Maier, Plasmonics: Fundamentals and Applications (Springer, 2007).
  6. M. Dragoman and D. Dragoman, “Plasmonics: Applications to nanoscale terahertz and optical devices,” Prog. Quantum Electron. 32, 1–41 (2008).
    [CrossRef]
  7. M. G. Blaber, M. D. Arnold, and M. J. Ford, “A review of the optical properties of alloys and intermetallics for plasmonics,” J. Phys. Condens. Matter 22, 143201 (2010).
    [CrossRef]
  8. P. R. West, S. Ishii, G. V. Naik, N. K. Emani, V. M. Shalaev, and A. Boltasseva, “Searching for better plasmonic materials,” Laser Photonics Rev. (2010), doi:10.1002/lpor.200900055.
    [CrossRef]
  9. J. A. Polo, Jr. and A. Lakhtakia, “Surface electromagnetic waves: A review,” Laser Photonics Rev. (2010), doi:10.1002/lpor.200900050.
    [CrossRef]
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    [CrossRef]
  12. S. J. Elston and J. R. Sambles, “Surface plasmon-polaritons on an anisotropic substrate,” J. Mod. Opt. 37, 1895–1902 (1990).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  18. M. Faryad, J. A. Polo, Jr., and A. Lakhtakia, “Multiple trains of same-color of surface plasmon-polaritons guided by the planar interface of a metal and a sculptured nematic thin film. Part IV: Canonical problem,” J. Nanophotonics 4, 043505 (2010).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  25. V. A. Yakubovich and V. M. Starzhinskii, Linear Differential Equations with Periodic Coefficients (Wiley, 1975).
  26. A. Lakhtakia, “Reflection of an obliquely incident plane wave by a half space filled by a helicoidal bianisotropic medium,” Phys. Lett. A 374, 3887–3894 (2010).
    [CrossRef]
  27. M. Faryad and A. Lakhtakia, “Surface plasmon-polariton wave propagation guided by a metal slab in a sculptured nematic thin film,” J. Opt. 12, 085102 (2010).
    [CrossRef]
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    [CrossRef] [PubMed]
  30. Y.-J. Jen, A. Lakhtakia, C.-W. Yu, and T.-Y. Chan, “Multilayered structures for p- and s-polarized long-range surface-plasmon-polariton propagation,” J. Opt. Soc. Am. A 26, 2600–2606 (2009).
    [CrossRef]
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    [CrossRef]

2010 (5)

M. G. Blaber, M. D. Arnold, and M. J. Ford, “A review of the optical properties of alloys and intermetallics for plasmonics,” J. Phys. Condens. Matter 22, 143201 (2010).
[CrossRef]

T. G. Mackay and A. Lakhtakia, “Modeling columnar thin films as platforms for surface-plasmonic-polaritonic optical sensing,” Photonics Nanostruct. Fundam. Appl. 8, 140–149 (2010).
[CrossRef]

M. Faryad, J. A. Polo, Jr., and A. Lakhtakia, “Multiple trains of same-color of surface plasmon-polaritons guided by the planar interface of a metal and a sculptured nematic thin film. Part IV: Canonical problem,” J. Nanophotonics 4, 043505 (2010).
[CrossRef]

A. Lakhtakia, “Reflection of an obliquely incident plane wave by a half space filled by a helicoidal bianisotropic medium,” Phys. Lett. A 374, 3887–3894 (2010).
[CrossRef]

M. Faryad and A. Lakhtakia, “Surface plasmon-polariton wave propagation guided by a metal slab in a sculptured nematic thin film,” J. Opt. 12, 085102 (2010).
[CrossRef]

2009 (6)

Y.-J. Jen, A. Lakhtakia, C.-W. Yu, and T.-Y. Chan, “Multilayered structures for p- and s-polarized long-range surface-plasmon-polariton propagation,” J. Opt. Soc. Am. A 26, 2600–2606 (2009).
[CrossRef]

J. A. Polo, Jr. and A. Lakhtakia, “Energy flux in a surface-plasmon-polariton wave bound to the planar interface of a metal and a structurally chiral material,” J. Opt. Soc. Am. A 26, 1696–1703 (2009).
[CrossRef]

Devender, D. P. Pulsifer, and A. Lakhtakia, “Multiple surface plasmon polariton waves,” Electron. Lett. 45, 1137–1138 (2009).
[CrossRef]

A. Lakhtakia, Y.-J. Jen, and C.-F. Lin, “Multiple trains of same-color surface plasmon-polaritons guided by the planar interface of a metal and a sculptured nematic thin film. Part III: Experimental evidence,” J. Nanophotonics 3, 033506 (2009).
[CrossRef]

J. A. Polo, Jr. and A. Lakhtakia, “On the surface plasmon polariton wave at the planar interface of a metal and a chiral sculptured thin film,” Proc. R. Soc. London, Ser. A 465, 87–107 (2009).
[CrossRef]

I. Abdulhalim, “Surface plasmon TE and TM waves at the anisotropic film-metal interface,” J. Opt. A, Pure Appl. Opt. 11, 015002 (2009).
[CrossRef]

2008 (3)

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

V. N. Datsko and A. A. Kopylov, “On surface electromagnetic waves,” Sov. Phys. Usp. 51, 101–102 (2008).
[CrossRef]

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

2007 (1)

A. Lakhtakia, “Surface-plasmon wave at the planar interface of a metal film and a structurally chiral medium,” Opt. Commun. 279, 291–297 (2007).
[CrossRef]

1997 (1)

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

1995 (2)

R. A. Depine and M. L. Gigli, “Excitation of surface plasmons and total absorption of light at the flat boundary between a metal and a uniaxial crystal,” Opt. Lett. 20, 2243–2245 (1995).
[CrossRef] [PubMed]

H. Wang, “Excitation of surface plasmon oscillations at an interface between anisotropic dielectric and metallic media,” Opt. Mater. 4, 651–656 (1995).
[CrossRef]

1993 (1)

1990 (1)

S. J. Elston and J. R. Sambles, “Surface plasmon-polaritons on an anisotropic substrate,” J. Mod. Opt. 37, 1895–1902 (1990).
[CrossRef]

1980 (1)

D. A. Hill and J. R. Wait, “On the excitation of the Zenneck surface wave over the ground at 10 MHz,” Ann. Telecommun. 35, 179–182 (1980).

1909 (1)

A. Sommerfeld, “Über die Ausbreitung der Wellen in der drahtlosen Telegraphie,” Ann. Phys. (Leipzig) 28, 665–736 (1909).

1907 (1)

J. Zenneck, “Über die Fortpflanzung ebener elektromagnetischer Wellen längs einer ebenen Lieterfläche und ihre Beziehung zur drahtlosen Telegraphie,” Ann. Phys. (Leipzig) 23, 846–866 (1907).

Abdulhalim, I.

I. Abdulhalim, “Surface plasmon TE and TM waves at the anisotropic film-metal interface,” J. Opt. A, Pure Appl. Opt. 11, 015002 (2009).
[CrossRef]

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

Arnold, M. D.

M. G. Blaber, M. D. Arnold, and M. J. Ford, “A review of the optical properties of alloys and intermetallics for plasmonics,” J. Phys. Condens. Matter 22, 143201 (2010).
[CrossRef]

Baumeister, P. W.

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

Blaber, M. G.

M. G. Blaber, M. D. Arnold, and M. J. Ford, “A review of the optical properties of alloys and intermetallics for plasmonics,” J. Phys. Condens. Matter 22, 143201 (2010).
[CrossRef]

Boltasseva, A.

P. R. West, S. Ishii, G. V. Naik, N. K. Emani, V. M. Shalaev, and A. Boltasseva, “Searching for better plasmonic materials,” Laser Photonics Rev. (2010), doi:10.1002/lpor.200900055.
[CrossRef]

Bovard, B. G.

Chan, T. -Y.

Datsko, V. N.

V. N. Datsko and A. A. Kopylov, “On surface electromagnetic waves,” Sov. Phys. Usp. 51, 101–102 (2008).
[CrossRef]

Depine, R. A.

Devender,

Devender, D. P. Pulsifer, and A. Lakhtakia, “Multiple surface plasmon polariton waves,” Electron. Lett. 45, 1137–1138 (2009).
[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]

Elston, S. J.

S. J. Elston and J. R. Sambles, “Surface plasmon-polaritons on an anisotropic substrate,” J. Mod. Opt. 37, 1895–1902 (1990).
[CrossRef]

Emani, N. K.

P. R. West, S. Ishii, G. V. Naik, N. K. Emani, V. M. Shalaev, and A. Boltasseva, “Searching for better plasmonic materials,” Laser Photonics Rev. (2010), doi:10.1002/lpor.200900055.
[CrossRef]

Faryad, M.

M. Faryad, J. A. Polo, Jr., and A. Lakhtakia, “Multiple trains of same-color of surface plasmon-polaritons guided by the planar interface of a metal and a sculptured nematic thin film. Part IV: Canonical problem,” J. Nanophotonics 4, 043505 (2010).
[CrossRef]

M. Faryad and A. Lakhtakia, “Surface plasmon-polariton wave propagation guided by a metal slab in a sculptured nematic thin film,” J. Opt. 12, 085102 (2010).
[CrossRef]

Ford, M. J.

M. G. Blaber, M. D. Arnold, and M. J. Ford, “A review of the optical properties of alloys and intermetallics for plasmonics,” J. Phys. Condens. Matter 22, 143201 (2010).
[CrossRef]

Gigli, M. L.

Hill, D. A.

D. A. Hill and J. R. Wait, “On the excitation of the Zenneck surface wave over the ground at 10 MHz,” Ann. Telecommun. 35, 179–182 (1980).

Ishii, S.

P. R. West, S. Ishii, G. V. Naik, N. K. Emani, V. M. Shalaev, and A. Boltasseva, “Searching for better plasmonic materials,” Laser Photonics Rev. (2010), doi:10.1002/lpor.200900055.
[CrossRef]

Jaluria, Y.

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

Jen, Y. -J.

Y.-J. Jen, A. Lakhtakia, C.-W. Yu, and T.-Y. Chan, “Multilayered structures for p- and s-polarized long-range surface-plasmon-polariton propagation,” J. Opt. Soc. Am. A 26, 2600–2606 (2009).
[CrossRef]

A. Lakhtakia, Y.-J. Jen, and C.-F. Lin, “Multiple trains of same-color surface plasmon-polaritons guided by the planar interface of a metal and a sculptured nematic thin film. Part III: Experimental evidence,” J. Nanophotonics 3, 033506 (2009).
[CrossRef]

Kopylov, A. A.

V. N. Datsko and A. A. Kopylov, “On surface electromagnetic waves,” Sov. Phys. Usp. 51, 101–102 (2008).
[CrossRef]

Lakhtakia, A.

T. G. Mackay and A. Lakhtakia, “Modeling columnar thin films as platforms for surface-plasmonic-polaritonic optical sensing,” Photonics Nanostruct. Fundam. Appl. 8, 140–149 (2010).
[CrossRef]

M. Faryad, J. A. Polo, Jr., and A. Lakhtakia, “Multiple trains of same-color of surface plasmon-polaritons guided by the planar interface of a metal and a sculptured nematic thin film. Part IV: Canonical problem,” J. Nanophotonics 4, 043505 (2010).
[CrossRef]

A. Lakhtakia, “Reflection of an obliquely incident plane wave by a half space filled by a helicoidal bianisotropic medium,” Phys. Lett. A 374, 3887–3894 (2010).
[CrossRef]

M. Faryad and A. Lakhtakia, “Surface plasmon-polariton wave propagation guided by a metal slab in a sculptured nematic thin film,” J. Opt. 12, 085102 (2010).
[CrossRef]

Y.-J. Jen, A. Lakhtakia, C.-W. Yu, and T.-Y. Chan, “Multilayered structures for p- and s-polarized long-range surface-plasmon-polariton propagation,” J. Opt. Soc. Am. A 26, 2600–2606 (2009).
[CrossRef]

J. A. Polo, Jr. and A. Lakhtakia, “Energy flux in a surface-plasmon-polariton wave bound to the planar interface of a metal and a structurally chiral material,” J. Opt. Soc. Am. A 26, 1696–1703 (2009).
[CrossRef]

Devender, D. P. Pulsifer, and A. Lakhtakia, “Multiple surface plasmon polariton waves,” Electron. Lett. 45, 1137–1138 (2009).
[CrossRef]

A. Lakhtakia, Y.-J. Jen, and C.-F. Lin, “Multiple trains of same-color surface plasmon-polaritons guided by the planar interface of a metal and a sculptured nematic thin film. Part III: Experimental evidence,” J. Nanophotonics 3, 033506 (2009).
[CrossRef]

J. A. Polo, Jr. and A. Lakhtakia, “On the surface plasmon polariton wave at the planar interface of a metal and a chiral sculptured thin film,” Proc. R. Soc. London, Ser. A 465, 87–107 (2009).
[CrossRef]

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

A. Lakhtakia, “Surface-plasmon wave at the planar interface of a metal film and a structurally chiral medium,” Opt. Commun. 279, 291–297 (2007).
[CrossRef]

A. Lakhtakia and R. Messier, Sculptured Thin Films: Nanoengineered Morphology and Optics (SPIE, 2005).
[CrossRef]

J. A. Polo, Jr. and A. Lakhtakia, “Surface electromagnetic waves: A review,” Laser Photonics Rev. (2010), doi:10.1002/lpor.200900050.
[CrossRef]

Lin, C. -F.

A. Lakhtakia, Y.-J. Jen, and C.-F. Lin, “Multiple trains of same-color surface plasmon-polaritons guided by the planar interface of a metal and a sculptured nematic thin film. Part III: Experimental evidence,” J. Nanophotonics 3, 033506 (2009).
[CrossRef]

Mackay, T. G.

T. G. Mackay and A. Lakhtakia, “Modeling columnar thin films as platforms for surface-plasmonic-polaritonic optical sensing,” Photonics Nanostruct. Fundam. Appl. 8, 140–149 (2010).
[CrossRef]

Macleod, H. A.

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

Maier, S. A.

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

Messier, R.

A. Lakhtakia and R. Messier, Sculptured Thin Films: Nanoengineered Morphology and Optics (SPIE, 2005).
[CrossRef]

Naik, G. V.

P. R. West, S. Ishii, G. V. Naik, N. K. Emani, V. M. Shalaev, and A. Boltasseva, “Searching for better plasmonic materials,” Laser Photonics Rev. (2010), doi:10.1002/lpor.200900055.
[CrossRef]

Polo, J. A.

M. Faryad, J. A. Polo, Jr., and A. Lakhtakia, “Multiple trains of same-color of surface plasmon-polaritons guided by the planar interface of a metal and a sculptured nematic thin film. Part IV: Canonical problem,” J. Nanophotonics 4, 043505 (2010).
[CrossRef]

J. A. Polo, Jr. and A. Lakhtakia, “On the surface plasmon polariton wave at the planar interface of a metal and a chiral sculptured thin film,” Proc. R. Soc. London, Ser. A 465, 87–107 (2009).
[CrossRef]

J. A. Polo, Jr. and A. Lakhtakia, “Energy flux in a surface-plasmon-polariton wave bound to the planar interface of a metal and a structurally chiral material,” J. Opt. Soc. Am. A 26, 1696–1703 (2009).
[CrossRef]

J. A. Polo, Jr. and A. Lakhtakia, “Surface electromagnetic waves: A review,” Laser Photonics Rev. (2010), doi:10.1002/lpor.200900050.
[CrossRef]

Pulsifer, D. P.

Devender, D. P. Pulsifer, and A. Lakhtakia, “Multiple surface plasmon polariton waves,” Electron. Lett. 45, 1137–1138 (2009).
[CrossRef]

Salamon, Z.

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

Sambles, J. R.

S. J. Elston and J. R. Sambles, “Surface plasmon-polaritons on an anisotropic substrate,” J. Mod. Opt. 37, 1895–1902 (1990).
[CrossRef]

Shalaev, V. M.

P. R. West, S. Ishii, G. V. Naik, N. K. Emani, V. M. Shalaev, and A. Boltasseva, “Searching for better plasmonic materials,” Laser Photonics Rev. (2010), doi:10.1002/lpor.200900055.
[CrossRef]

Sommerfeld, A.

A. Sommerfeld, “Über die Ausbreitung der Wellen in der drahtlosen Telegraphie,” Ann. Phys. (Leipzig) 28, 665–736 (1909).

Starzhinskii, V. M.

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

Tollin, G.

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

Wait, J. R.

D. A. Hill and J. R. Wait, “On the excitation of the Zenneck surface wave over the ground at 10 MHz,” Ann. Telecommun. 35, 179–182 (1980).

Wang, H.

H. Wang, “Excitation of surface plasmon oscillations at an interface between anisotropic dielectric and metallic media,” Opt. Mater. 4, 651–656 (1995).
[CrossRef]

West, P. R.

P. R. West, S. Ishii, G. V. Naik, N. K. Emani, V. M. Shalaev, and A. Boltasseva, “Searching for better plasmonic materials,” Laser Photonics Rev. (2010), doi:10.1002/lpor.200900055.
[CrossRef]

Yakubovich, V. A.

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

Yu, C. -W.

Zenneck, J.

J. Zenneck, “Über die Fortpflanzung ebener elektromagnetischer Wellen längs einer ebenen Lieterfläche und ihre Beziehung zur drahtlosen Telegraphie,” Ann. Phys. (Leipzig) 23, 846–866 (1907).

Zourob, M.

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

Ann. Phys. (Leipzig) (2)

J. Zenneck, “Über die Fortpflanzung ebener elektromagnetischer Wellen längs einer ebenen Lieterfläche und ihre Beziehung zur drahtlosen Telegraphie,” Ann. Phys. (Leipzig) 23, 846–866 (1907).

A. Sommerfeld, “Über die Ausbreitung der Wellen in der drahtlosen Telegraphie,” Ann. Phys. (Leipzig) 28, 665–736 (1909).

Ann. Telecommun. (1)

D. A. Hill and J. R. Wait, “On the excitation of the Zenneck surface wave over the ground at 10 MHz,” Ann. Telecommun. 35, 179–182 (1980).

Appl. Opt. (1)

Biophys. J. (1)

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

Electromagnetics (1)

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

Electron. Lett. (1)

Devender, D. P. Pulsifer, and A. Lakhtakia, “Multiple surface plasmon polariton waves,” Electron. Lett. 45, 1137–1138 (2009).
[CrossRef]

J. Mod. Opt. (1)

S. J. Elston and J. R. Sambles, “Surface plasmon-polaritons on an anisotropic substrate,” J. Mod. Opt. 37, 1895–1902 (1990).
[CrossRef]

J. Nanophotonics (2)

M. Faryad, J. A. Polo, Jr., and A. Lakhtakia, “Multiple trains of same-color of surface plasmon-polaritons guided by the planar interface of a metal and a sculptured nematic thin film. Part IV: Canonical problem,” J. Nanophotonics 4, 043505 (2010).
[CrossRef]

A. Lakhtakia, Y.-J. Jen, and C.-F. Lin, “Multiple trains of same-color surface plasmon-polaritons guided by the planar interface of a metal and a sculptured nematic thin film. Part III: Experimental evidence,” J. Nanophotonics 3, 033506 (2009).
[CrossRef]

J. Opt. (1)

M. Faryad and A. Lakhtakia, “Surface plasmon-polariton wave propagation guided by a metal slab in a sculptured nematic thin film,” J. Opt. 12, 085102 (2010).
[CrossRef]

J. Opt. A, Pure Appl. Opt. (1)

I. Abdulhalim, “Surface plasmon TE and TM waves at the anisotropic film-metal interface,” J. Opt. A, Pure Appl. Opt. 11, 015002 (2009).
[CrossRef]

J. Opt. Soc. Am. A (2)

J. Phys. Condens. Matter (1)

M. G. Blaber, M. D. Arnold, and M. J. Ford, “A review of the optical properties of alloys and intermetallics for plasmonics,” J. Phys. Condens. Matter 22, 143201 (2010).
[CrossRef]

Opt. Commun. (1)

A. Lakhtakia, “Surface-plasmon wave at the planar interface of a metal film and a structurally chiral medium,” Opt. Commun. 279, 291–297 (2007).
[CrossRef]

Opt. Lett. (1)

Opt. Mater. (1)

H. Wang, “Excitation of surface plasmon oscillations at an interface between anisotropic dielectric and metallic media,” Opt. Mater. 4, 651–656 (1995).
[CrossRef]

Photonics Nanostruct. Fundam. Appl. (1)

T. G. Mackay and A. Lakhtakia, “Modeling columnar thin films as platforms for surface-plasmonic-polaritonic optical sensing,” Photonics Nanostruct. Fundam. Appl. 8, 140–149 (2010).
[CrossRef]

Phys. Lett. A (1)

A. Lakhtakia, “Reflection of an obliquely incident plane wave by a half space filled by a helicoidal bianisotropic medium,” Phys. Lett. A 374, 3887–3894 (2010).
[CrossRef]

Proc. R. Soc. London, Ser. A (1)

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Figures (5)

Fig. 1
Fig. 1

(left) Real and (right) imaginary parts of κ / k 0 as functions of Ω / λ 0 for SPP-wave propagation guided by the planar interface of aluminum and a rugate filter described by Eq. (1) with n a = 1.45 and n b = 2.32 .

Fig. 2
Fig. 2

Variations with z of the Cartesian components of e, h, and P along the line { x = 0 , y = 0 } . 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 were computed by setting a p = 1   V   m 1 . (left) Ω / λ 0 = 0.1 , κ / k 0 = 2.009 43 + 0.044 68 i and (right) Ω / λ 0 = 1 , κ / k 0 = 2.214 56 + 0.002 46 i . Both solutions lie on the branch labeled p 8 in Fig. 1.

Fig. 3
Fig. 3

Same as Fig. 2 except for (left) Ω / λ 0 = 1 , κ / k 0 = 1.4864 + 0.0013203 i and (right) Ω / λ 0 = 1.5 , κ / k 0 = 1.7873 + 0.000 780 1 i , and the data were computed by setting a s = 1   V   m 1 . Both solutions lie on the branch labeled s 2 in Fig. 1.

Fig. 4
Fig. 4

(left) Real and (right) imaginary parts of κ / k 0 as functions of γ [ 1 , 0.001 ] , with Ω = 2 λ 0 for SPP-wave propagation guided by the planar interface of aluminum and a rugate filter described by Eq. (17) with n a = 1.45 , n b = 2.32 , and Ω = 2 λ 0 .

Fig. 5
Fig. 5

Same as Fig. 2 except for (left) γ = 0.5 and κ / k 0 = 1.781 42 + 0.002 88 i on the branch labeled p 3 in Fig. 4, and (right) γ = 0.1 and κ / k 0 = 1.9515 + 0.019 43 i on the branch labeled p 10 in Fig. 4.

Equations (17)

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ϵ r ( z ) = [ ( n b + n a 2 ) + ( n b n a 2 ) sin ( π z Ω ) ] 2 ,
k met = κ u ̂ x α met u ̂ z ,
E ( r ) = [ a p ( α met k 0 u ̂ x + κ k 0 u ̂ z ) + a s u ̂ y ] exp ( i k met r ) ,     z 0 ,
H ( r ) = η 0 1 [ a p ϵ met u ̂ y + a s ( α met k 0 u ̂ x + κ k 0 u ̂ z ) ] exp ( i k met r ) ,     z 0.
e z ( z ) = κ ω ϵ 0 ϵ r ( z ) h y ( z ) ,     z > 0 ,
h z ( z ) = κ ω μ 0 e y ( z ) ,     z > 0.
[ f ( z ) ] = [ e x ( z ) e y ( z ) h x ( z ) h y ( z ) ] T ,
d d z [ f ( z ) ] = i [ P ͇ ( z ) ] [ f ( z ) ] ,     z > 0 ,
[ P ͇ ( z ) ] = ω [ 0 0 0 μ 0 0 0 μ 0 0 0 ϵ 0 ϵ r ( z ) 0 0 ϵ 0 ϵ r ( z ) 0 0 0 ] + κ 2 ω ϵ 0 ϵ r ( z ) μ 0 [ 0 0 0 μ 0 0 0 0 0 0 ϵ 0 ϵ r ( z ) 0 0 0 0 0 0 ] .
[ f ( 2 Ω ) ] = [ Q ͇ ] [ f ( 0 + ) ]
[ Q ͇ ] = exp { i 2 Ω [ Q ̃ ͇ ] } .
α n = i ln   σ n 2 Ω ,     n [ 1 , 4 ] .
[ f ( 0 + ) ] = [ [ t ] ( 1 ) [ t ] ( 2 ) ] [ b 1 b 2 ]
[ f ( 0 ) ] = [ α met k 0 0 0 1 0 α met k 0 η 0 ϵ met η 0 0 ] [ a p a s ] ,
[ Y ͇ ] [ a p a s b 1 b 2 ] = [ 0 0 0 0 ] .
det [ Y ͇ ] = 0
ϵ r ( z ) = [ ( n b + n a 2 ) + γ ( n b n a 2 ) sin ( π z Ω ) ] 2 ,     γ [ 0 , 1 ] ,

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