Abstract

For the first time, to the best of our knowledge, the existence of a surface wave at the one-dimensional photonic crystal (PC)–metal interface is verified experimentally. That surface mode is excited for both transverse electric and transverse magnetic polarizations in the frequency region where one of the bandgaps of the PC overlaps with the region below the plasma frequency of the metal in the frequency wave-vector space and is observed even under normal incidence from vacuum. For a fixed frequency its angular position is very sensitive to the thickness of the one-dimensional photonic-crystal layer adjacent to the metal.

© 2008 Optical Society of America

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References

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  1. H. Raether, Surface Plasmon on Smooth and Rough Surfaces and on Gratings (Springer-Verlag, 1988).
  2. R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, “Electromagnetic Bloch waves at the surface of a photonic crystal,” Phys. Rev. B 44, 10961-10964 (1991).
    [CrossRef]
  3. J. A. Gaspar-Armenta and F. Villa, “Photonic surface-wave excitation: photonic crystal-metal interface,” J. Opt. Soc. Am. B 20, 2349-2354 (2003).
    [CrossRef]
  4. H. J. Simon, D. E. Mitchell, and J. G. Watson, “Optical second-harmonic generation with surface plasmons in silver films,” Phys. Rev. Lett. 33, 1531-1534 (1974).
    [CrossRef]
  5. J. Homola, S. S. Yee, and G. Gauglitz, “Surface plasmon resonance sensors,” Sens. Actuators B 54, 3-15 (1999).
    [CrossRef]
  6. E. Ozbay, “Plasmonics: merging photonics and electronics at nanoscale dimensions,” Science 311, 189-193 (2006).
    [CrossRef] [PubMed]
  7. M. Quinten, A. Leitner, J. R. Krenn, and F. R. Aussenegg, “Electromagnetic energy transport via linear chains of silver nanoparticles,” Opt. Lett. 23, 1331-1333 (1998).
    [CrossRef]
  8. S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, J. Y. Laluet, and T. W. Ebbesen, “Channel plasmon subwavelength waveguide components including interferometers and ring resonators,” Nature (London) 440, 508-511 (2006).
    [CrossRef]
  9. C. Ciminelli, F. Peluso, and M. N. Ármense, “Modeling and design of two-dimensional guided-wave photonic band-gap-devices,” J. Lightwave Technol. 23, 886-901 (2005).
    [CrossRef]
  10. F. Ramos-Mendieta and P. Halevi, “Electromagnetic surface modes of a dielectric superlattice: the supercell method,” J. Opt. Soc. Am. B 14, 370-381 (1997).
    [CrossRef]
  11. 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]
  12. B. Wang, W. Dai, A. Fang, L. Zhang, G. Tuttle, Th. Koschny, and C. M. Soukoulis, “Surface wave in photonic crystal slabs,” Phys. Rev. B 74, 195104-195108 (2006).
    [CrossRef]
  13. F. Ramos-Mendieta and P. Halevi, “Propagation constant-limited surface modes in dielectric superlattices,” Opt. Commun. 129, 1-5 (1996).
    [CrossRef]
  14. W. M. Robertson, “Experimental measurement of the effect of termination on surface electromagnetic waves in one-dimensional photonic bandgap arrays,” J. Lightwave Technol. 17, 2013-2017 (1999).
    [CrossRef]
  15. F. Villa, L. E. Regalado, F. Ramos-Mendieta, J. A. Gaspar-Armenta, and T. Lóopez-Ríos, “Photonic crystal sensor based on surface waves for thin-film characterization,” Opt. Lett. 27, 646-648 (2002).
    [CrossRef]
  16. A. Shinn and W. M. Robertson, “Surface plasmon-like sensor based on surface electromagnetic wave in a photonic band-gap material,” Sens. Actuators B 105, 360-364 (2005).
    [CrossRef]
  17. M. Carras and A. De Rossi, “Photonic modes of metallodielectric periodic waveguides in the midinfrared spectral range,” Phys. Rev. B 74, 235120-235123 (2006).
    [CrossRef]
  18. 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, 253904-253907 (2006).
    [CrossRef]
  19. A. S. Ramírez-Duverger, J. Gaspar-Armenta, and R. García-Llamas, “Surface wave effect on light scattering from one-dimensional photonic crystals,” Opt. Commun. 277, 302-309 (2007).
    [CrossRef]
  20. E. D. Palik, Handbook of Optical Constants of Solids I (Academic, 1985).
  21. A. S. Ramírez-Duverger and R. García-Llamas, “Diseño y construcción de un esparcímetro de luz,” Rev. Mex. Fis. 50, 541-548 (2004).
  22. E. Hecht, Optics (Addison-Wesley Iberoamericana, 2000).
  23. A. S. Ramírez-Duverger and R. García-Llamas, “Light scattering from a multimode waveguide of planar metallic walls,” Opt. Commun. 227, 227-235 (2003).
    [CrossRef]

2007

A. S. Ramírez-Duverger, J. Gaspar-Armenta, and R. García-Llamas, “Surface wave effect on light scattering from one-dimensional photonic crystals,” Opt. Commun. 277, 302-309 (2007).
[CrossRef]

2006

E. Ozbay, “Plasmonics: merging photonics and electronics at nanoscale dimensions,” Science 311, 189-193 (2006).
[CrossRef] [PubMed]

S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, J. Y. Laluet, and T. W. Ebbesen, “Channel plasmon subwavelength waveguide components including interferometers and ring resonators,” Nature (London) 440, 508-511 (2006).
[CrossRef]

B. Wang, W. Dai, A. Fang, L. Zhang, G. Tuttle, Th. Koschny, and C. M. Soukoulis, “Surface wave in photonic crystal slabs,” Phys. Rev. B 74, 195104-195108 (2006).
[CrossRef]

M. Carras and A. De Rossi, “Photonic modes of metallodielectric periodic waveguides in the midinfrared spectral range,” Phys. Rev. B 74, 235120-235123 (2006).
[CrossRef]

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, 253904-253907 (2006).
[CrossRef]

2005

A. Shinn and W. M. Robertson, “Surface plasmon-like sensor based on surface electromagnetic wave in a photonic band-gap material,” Sens. Actuators B 105, 360-364 (2005).
[CrossRef]

C. Ciminelli, F. Peluso, and M. N. Ármense, “Modeling and design of two-dimensional guided-wave photonic band-gap-devices,” J. Lightwave Technol. 23, 886-901 (2005).
[CrossRef]

2004

A. S. Ramírez-Duverger and R. García-Llamas, “Diseño y construcción de un esparcímetro de luz,” Rev. Mex. Fis. 50, 541-548 (2004).

2003

A. S. Ramírez-Duverger and R. García-Llamas, “Light scattering from a multimode waveguide of planar metallic walls,” Opt. Commun. 227, 227-235 (2003).
[CrossRef]

J. A. Gaspar-Armenta and F. Villa, “Photonic surface-wave excitation: photonic crystal-metal interface,” J. Opt. Soc. Am. B 20, 2349-2354 (2003).
[CrossRef]

2002

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]

W. M. Robertson, “Experimental measurement of the effect of termination on surface electromagnetic waves in one-dimensional photonic bandgap arrays,” J. Lightwave Technol. 17, 2013-2017 (1999).
[CrossRef]

J. Homola, S. S. Yee, and G. Gauglitz, “Surface plasmon resonance sensors,” Sens. Actuators B 54, 3-15 (1999).
[CrossRef]

1998

1997

1996

F. Ramos-Mendieta and P. Halevi, “Propagation constant-limited surface modes in dielectric superlattices,” Opt. Commun. 129, 1-5 (1996).
[CrossRef]

1991

R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, “Electromagnetic Bloch waves at the surface of a photonic crystal,” Phys. Rev. B 44, 10961-10964 (1991).
[CrossRef]

1974

H. J. Simon, D. E. Mitchell, and J. G. Watson, “Optical second-harmonic generation with surface plasmons in silver films,” Phys. Rev. Lett. 33, 1531-1534 (1974).
[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, 253904-253907 (2006).
[CrossRef]

Ármense, M. N.

Aussenegg, F. R.

Bozhevolnyi, S. I.

S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, J. Y. Laluet, and T. W. Ebbesen, “Channel plasmon subwavelength waveguide components including interferometers and ring resonators,” Nature (London) 440, 508-511 (2006).
[CrossRef]

Brommer, K. D.

R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, “Electromagnetic Bloch waves at the surface of a photonic crystal,” Phys. Rev. B 44, 10961-10964 (1991).
[CrossRef]

Carras, M.

M. Carras and A. De Rossi, “Photonic modes of metallodielectric periodic waveguides in the midinfrared spectral range,” Phys. Rev. B 74, 235120-235123 (2006).
[CrossRef]

Ciminelli, C.

Dai, W.

B. Wang, W. Dai, A. Fang, L. Zhang, G. Tuttle, Th. Koschny, and C. M. Soukoulis, “Surface wave in photonic crystal slabs,” Phys. Rev. B 74, 195104-195108 (2006).
[CrossRef]

De Rossi, A.

M. Carras and A. De Rossi, “Photonic modes of metallodielectric periodic waveguides in the midinfrared spectral range,” Phys. Rev. B 74, 235120-235123 (2006).
[CrossRef]

Devaux, E.

S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, J. Y. Laluet, and T. W. Ebbesen, “Channel plasmon subwavelength waveguide components including interferometers and ring resonators,” Nature (London) 440, 508-511 (2006).
[CrossRef]

Ebbesen, T. W.

S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, J. Y. Laluet, and T. W. Ebbesen, “Channel plasmon subwavelength waveguide components including interferometers and ring resonators,” Nature (London) 440, 508-511 (2006).
[CrossRef]

Fang, A.

B. Wang, W. Dai, A. Fang, L. Zhang, G. Tuttle, Th. Koschny, and C. M. Soukoulis, “Surface wave in photonic crystal slabs,” Phys. Rev. B 74, 195104-195108 (2006).
[CrossRef]

García-Llamas, R.

A. S. Ramírez-Duverger, J. Gaspar-Armenta, and R. García-Llamas, “Surface wave effect on light scattering from one-dimensional photonic crystals,” Opt. Commun. 277, 302-309 (2007).
[CrossRef]

A. S. Ramírez-Duverger and R. García-Llamas, “Diseño y construcción de un esparcímetro de luz,” Rev. Mex. Fis. 50, 541-548 (2004).

A. S. Ramírez-Duverger and R. García-Llamas, “Light scattering from a multimode waveguide of planar metallic walls,” Opt. Commun. 227, 227-235 (2003).
[CrossRef]

Gaspar-Armenta, J.

A. S. Ramírez-Duverger, J. Gaspar-Armenta, and R. García-Llamas, “Surface wave effect on light scattering from one-dimensional photonic crystals,” Opt. Commun. 277, 302-309 (2007).
[CrossRef]

Gaspar-Armenta, J. A.

Gauglitz, G.

J. Homola, S. S. Yee, and G. Gauglitz, “Surface plasmon resonance sensors,” Sens. Actuators B 54, 3-15 (1999).
[CrossRef]

Halevi, P.

F. Ramos-Mendieta and P. Halevi, “Electromagnetic surface modes of a dielectric superlattice: the supercell method,” J. Opt. Soc. Am. B 14, 370-381 (1997).
[CrossRef]

F. Ramos-Mendieta and P. Halevi, “Propagation constant-limited surface modes in dielectric superlattices,” Opt. Commun. 129, 1-5 (1996).
[CrossRef]

Hecht, E.

E. Hecht, Optics (Addison-Wesley Iberoamericana, 2000).

Homola, J.

J. Homola, S. S. Yee, and G. Gauglitz, “Surface plasmon resonance sensors,” Sens. Actuators B 54, 3-15 (1999).
[CrossRef]

Joannopoulos, J. D.

R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, “Electromagnetic Bloch waves at the surface of a photonic crystal,” Phys. Rev. B 44, 10961-10964 (1991).
[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, 253904-253907 (2006).
[CrossRef]

Koschny, Th.

B. Wang, W. Dai, A. Fang, L. Zhang, G. Tuttle, Th. Koschny, and C. M. Soukoulis, “Surface wave in photonic crystal slabs,” Phys. Rev. B 74, 195104-195108 (2006).
[CrossRef]

Krenn, J. R.

Laluet, J. Y.

S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, J. Y. Laluet, and T. W. Ebbesen, “Channel plasmon subwavelength waveguide components including interferometers and ring resonators,” Nature (London) 440, 508-511 (2006).
[CrossRef]

Leitner, A.

Lóopez-Ríos, T.

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]

Meade, R. D.

R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, “Electromagnetic Bloch waves at the surface of a photonic crystal,” Phys. Rev. B 44, 10961-10964 (1991).
[CrossRef]

Mitchell, D. E.

H. J. Simon, D. E. Mitchell, and J. G. Watson, “Optical second-harmonic generation with surface plasmons in silver films,” Phys. Rev. Lett. 33, 1531-1534 (1974).
[CrossRef]

Ozbay, E.

E. Ozbay, “Plasmonics: merging photonics and electronics at nanoscale dimensions,” Science 311, 189-193 (2006).
[CrossRef] [PubMed]

Palik, E. D.

E. D. Palik, Handbook of Optical Constants of Solids I (Academic, 1985).

Peluso, F.

Quinten, M.

Raether, H.

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

Ramírez-Duverger, A. S.

A. S. Ramírez-Duverger, J. Gaspar-Armenta, and R. García-Llamas, “Surface wave effect on light scattering from one-dimensional photonic crystals,” Opt. Commun. 277, 302-309 (2007).
[CrossRef]

A. S. Ramírez-Duverger and R. García-Llamas, “Diseño y construcción de un esparcímetro de luz,” Rev. Mex. Fis. 50, 541-548 (2004).

A. S. Ramírez-Duverger and R. García-Llamas, “Light scattering from a multimode waveguide of planar metallic walls,” Opt. Commun. 227, 227-235 (2003).
[CrossRef]

Ramos-Mendieta, F.

Rappe, A. M.

R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, “Electromagnetic Bloch waves at the surface of a photonic crystal,” Phys. Rev. B 44, 10961-10964 (1991).
[CrossRef]

Regalado, L. E.

Robertson, W. M.

A. Shinn and W. M. Robertson, “Surface plasmon-like sensor based on surface electromagnetic wave in a photonic band-gap material,” Sens. Actuators B 105, 360-364 (2005).
[CrossRef]

W. M. Robertson, “Experimental measurement of the effect of termination on surface electromagnetic waves in one-dimensional photonic bandgap arrays,” J. Lightwave Technol. 17, 2013-2017 (1999).
[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]

Shinn, A.

A. Shinn and W. M. Robertson, “Surface plasmon-like sensor based on surface electromagnetic wave in a photonic band-gap material,” Sens. Actuators B 105, 360-364 (2005).
[CrossRef]

Simon, H. J.

H. J. Simon, D. E. Mitchell, and J. G. Watson, “Optical second-harmonic generation with surface plasmons in silver films,” Phys. Rev. Lett. 33, 1531-1534 (1974).
[CrossRef]

Soukoulis, C. M.

B. Wang, W. Dai, A. Fang, L. Zhang, G. Tuttle, Th. Koschny, and C. M. Soukoulis, “Surface wave in photonic crystal slabs,” Phys. Rev. B 74, 195104-195108 (2006).
[CrossRef]

Tuttle, G.

B. Wang, W. Dai, A. Fang, L. Zhang, G. Tuttle, Th. Koschny, and C. M. Soukoulis, “Surface wave in photonic crystal slabs,” Phys. Rev. B 74, 195104-195108 (2006).
[CrossRef]

Villa, F.

Volkov, V. S.

S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, J. Y. Laluet, and T. W. Ebbesen, “Channel plasmon subwavelength waveguide components including interferometers and ring resonators,” Nature (London) 440, 508-511 (2006).
[CrossRef]

Wang, B.

B. Wang, W. Dai, A. Fang, L. Zhang, G. Tuttle, Th. Koschny, and C. M. Soukoulis, “Surface wave in photonic crystal slabs,” Phys. Rev. B 74, 195104-195108 (2006).
[CrossRef]

Watson, J. G.

H. J. Simon, D. E. Mitchell, and J. G. Watson, “Optical second-harmonic generation with surface plasmons in silver films,” Phys. Rev. Lett. 33, 1531-1534 (1974).
[CrossRef]

Yee, S. S.

J. Homola, S. S. Yee, and G. Gauglitz, “Surface plasmon resonance sensors,” Sens. Actuators B 54, 3-15 (1999).
[CrossRef]

Zhang, L.

B. Wang, W. Dai, A. Fang, L. Zhang, G. Tuttle, Th. Koschny, and C. M. Soukoulis, “Surface wave in photonic crystal slabs,” Phys. Rev. B 74, 195104-195108 (2006).
[CrossRef]

Appl. Phys. Lett.

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]

J. Lightwave Technol.

J. Opt. Soc. Am. B

Nature (London)

S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, J. Y. Laluet, and T. W. Ebbesen, “Channel plasmon subwavelength waveguide components including interferometers and ring resonators,” Nature (London) 440, 508-511 (2006).
[CrossRef]

Opt. Commun.

F. Ramos-Mendieta and P. Halevi, “Propagation constant-limited surface modes in dielectric superlattices,” Opt. Commun. 129, 1-5 (1996).
[CrossRef]

A. S. Ramírez-Duverger, J. Gaspar-Armenta, and R. García-Llamas, “Surface wave effect on light scattering from one-dimensional photonic crystals,” Opt. Commun. 277, 302-309 (2007).
[CrossRef]

A. S. Ramírez-Duverger and R. García-Llamas, “Light scattering from a multimode waveguide of planar metallic walls,” Opt. Commun. 227, 227-235 (2003).
[CrossRef]

Opt. Lett.

Phys. Rev. B

R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, “Electromagnetic Bloch waves at the surface of a photonic crystal,” Phys. Rev. B 44, 10961-10964 (1991).
[CrossRef]

M. Carras and A. De Rossi, “Photonic modes of metallodielectric periodic waveguides in the midinfrared spectral range,” Phys. Rev. B 74, 235120-235123 (2006).
[CrossRef]

B. Wang, W. Dai, A. Fang, L. Zhang, G. Tuttle, Th. Koschny, and C. M. Soukoulis, “Surface wave in photonic crystal slabs,” Phys. Rev. B 74, 195104-195108 (2006).
[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, 253904-253907 (2006).
[CrossRef]

H. J. Simon, D. E. Mitchell, and J. G. Watson, “Optical second-harmonic generation with surface plasmons in silver films,” Phys. Rev. Lett. 33, 1531-1534 (1974).
[CrossRef]

Rev. Mex. Fis.

A. S. Ramírez-Duverger and R. García-Llamas, “Diseño y construcción de un esparcímetro de luz,” Rev. Mex. Fis. 50, 541-548 (2004).

Science

E. Ozbay, “Plasmonics: merging photonics and electronics at nanoscale dimensions,” Science 311, 189-193 (2006).
[CrossRef] [PubMed]

Sens. Actuators B

J. Homola, S. S. Yee, and G. Gauglitz, “Surface plasmon resonance sensors,” Sens. Actuators B 54, 3-15 (1999).
[CrossRef]

A. Shinn and W. M. Robertson, “Surface plasmon-like sensor based on surface electromagnetic wave in a photonic band-gap material,” Sens. Actuators B 105, 360-364 (2005).
[CrossRef]

Other

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

E. Hecht, Optics (Addison-Wesley Iberoamericana, 2000).

E. D. Palik, Handbook of Optical Constants of Solids I (Academic, 1985).

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Figures (7)

Fig. 1
Fig. 1

Multilayer system composed of a glass substrate of ten periods of the bilayer SiO 2 ( 115 nm ) TiO 2 ( 59 nm ) , with the last film of TiO 2 reduced to 39 nm , then a 42 nm metal film of Ag, and finally air. Light impinges on the air side with an amplitude of u and an angle θ i and finally exits into the air with the reflection angle θ r . The y z plane is the incidence plane.

Fig. 2
Fig. 2

(a) Reflection versus wavelength for an incident angle θ i = 20.0 ° for p polarization of the incident light. The circles represent the experimental result for the metal film 1DPC system, and the triangles represent the experimental results without a metal film. The solid curve (with Ag) and the dashed curve (without Ag) correspond to the theoretical data. The minima detected at λ i min = 594.4 nm correspond to excitation of the surface mode. (b) Same as 2a, but for s polarization of the incident light. The minima detected at λ i min = 590.0 nm correspond to excitation of the surface mode.

Fig. 3
Fig. 3

Square E-field amplitude as a function of thickness in the multilayer for the surface mode. The position of the surface occurs for zero in the thickness coordinate.

Fig. 4
Fig. 4

(a) Transmission versus wavelength for an incident angle θ i = 20.0 ° for p polarization of the incident light. The circles represent the experiment, and the solid curve represents the theory. (b) Same as (a), but for s polarization of the incident light.

Fig. 5
Fig. 5

(a) Dispersion relation of the electromagnetic surface modes for p polarization. Circles represent the experiment; squares represent theoretical spectral reflection; and the solid curves represent the air light line. Clear and gray regions represent the bandgaps and allowed bands of the system, respectively. (b) Same as (a), but for s polarization of the incident light.

Fig. 6
Fig. 6

Reflection as a function of the angle of incidence for a wavelength of λ i = 532 nm . The system was described in Section 2. The circles and the triangles represent the experimental results for p and s polarization of the incident light, respectively. The solid and the dashed curves correspond to the theoretical data for p and s polarizations, respectively. The minima at (circles) θ i = 62.2 ° and (triangles) θ i = 61.1 ° correspond to excitation of the surface mode for p and s polarizations, respectively.

Fig. 7
Fig. 7

Angular position of the surface mode as a function of the thickness of the trunk TiO 2 film. The incident wavelength was λ i = 532 nm . For p polarization, open circles and squares represent experiment and theory, respectively. For s polarization, open triangles and crosses represent experiment and theory, respectively. The angular position at 58.02 ° ( d = 36 nm ) , 62.2 ° ( d = 39 nm ) , and 65.82 ° ( d = 42 nm ) for p polarization; and at 53.46 ° ( d = 36 nm ) , 61.1 ° ( d = 39 nm ) , and 70.01 ° ( d = 42 nm ) for s polarization correspond to excitation of the surface mode.

Equations (1)

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ε TiO 2 ( ω ) = 1 ω p 2 ( ω 2 ω 0 2 ) + i Γ ω ,

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