Abstract

The study of the dependence of surface mode dispersion on the termination of multilayer stacks reveals interesting features. For stratified media with high-refractive-index contrasts, surface modes can shift across several bandgaps if the thickness of the final layer is changed. The distance to the photonic band edge influences the decay length of the mode inside the multilayer stack. In the middle of the bandgap, the electromagnetic energy is concentrated in the final layer of the crystal, while near bandgap edges the decay length extends over several periods. Additional evidence suggests that surface modes behave like guided modes that can couple with the extended Bloch modes and give rise to evanescent field profiles oscillating along several periods.

© 2008 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. P. Yeh, A. Yariv, and A. Y. Cho, Appl. Phys. Lett. 32, 104 (1978).
    [CrossRef]
  2. F. Villa, L. E. Regaldo, F. Ramos-Mendieta, J. A. Gaspar-Armenta, and T. Lopez-Ríos, Opt. Lett. 27, 646 (2002).
    [CrossRef]
  3. F. Villa and J. A. Gaspar-Armenta, Opt. Express 12, 2338 (2004).
    [CrossRef] [PubMed]
  4. B. J. Lee, C. J. Fu, and Z. M. Zhang, Appl. Phys. Lett. 87, 071904 (2005).
    [CrossRef]
  5. M. L. Bah, A. Akjouj, E. H. El Boudouti, B. Djafari-Rouhani, and L. Dobrzynski, J. Phys. Condens. Matter 8, 4171 (1996).
    [CrossRef]
  6. F. Ramos-Mendieta and P. Halevi, J. Opt. Soc. Am. B 14, 370 (1997).
    [CrossRef]
  7. M. L. H. Lahlaouti, A. Akjouj, B. Djafari-Rouhani, and L. Dobrzynski, Phys. Rev. B 61, 2059 (2000).
    [CrossRef]
  8. W. M. Robertson and M. S. May, Appl. Phys. Lett. 74, 1800 (1999).
    [CrossRef]
  9. A. D. Boardman, Electromagnetic Surface Modes (Wiley, 1982).
  10. A. Dereux, J. P. Vigneron, P. Lambin, and A. A. Lucas, Phys. Rev. B 38, 5438 (1988).
    [CrossRef]
  11. V. Lousse and J. P. Vigneron, Proc. SPIE 5733, 257 (2005).
    [CrossRef]
  12. O. Painter, K. Srinivasan, and P. E. Barclay, Phys. Rev. B 68, 035214 (2003).
    [CrossRef]
  13. P. Yeh, Optical Waves in Layered Media, 2nd ed. (Wiley, 2005).

2005 (2)

B. J. Lee, C. J. Fu, and Z. M. Zhang, Appl. Phys. Lett. 87, 071904 (2005).
[CrossRef]

V. Lousse and J. P. Vigneron, Proc. SPIE 5733, 257 (2005).
[CrossRef]

2004 (1)

2003 (1)

O. Painter, K. Srinivasan, and P. E. Barclay, Phys. Rev. B 68, 035214 (2003).
[CrossRef]

2002 (1)

2000 (1)

M. L. H. Lahlaouti, A. Akjouj, B. Djafari-Rouhani, and L. Dobrzynski, Phys. Rev. B 61, 2059 (2000).
[CrossRef]

1999 (1)

W. M. Robertson and M. S. May, Appl. Phys. Lett. 74, 1800 (1999).
[CrossRef]

1997 (1)

1996 (1)

M. L. Bah, A. Akjouj, E. H. El Boudouti, B. Djafari-Rouhani, and L. Dobrzynski, J. Phys. Condens. Matter 8, 4171 (1996).
[CrossRef]

1988 (1)

A. Dereux, J. P. Vigneron, P. Lambin, and A. A. Lucas, Phys. Rev. B 38, 5438 (1988).
[CrossRef]

1978 (1)

P. Yeh, A. Yariv, and A. Y. Cho, Appl. Phys. Lett. 32, 104 (1978).
[CrossRef]

Akjouj, A.

M. L. H. Lahlaouti, A. Akjouj, B. Djafari-Rouhani, and L. Dobrzynski, Phys. Rev. B 61, 2059 (2000).
[CrossRef]

M. L. Bah, A. Akjouj, E. H. El Boudouti, B. Djafari-Rouhani, and L. Dobrzynski, J. Phys. Condens. Matter 8, 4171 (1996).
[CrossRef]

Bah, M. L.

M. L. Bah, A. Akjouj, E. H. El Boudouti, B. Djafari-Rouhani, and L. Dobrzynski, J. Phys. Condens. Matter 8, 4171 (1996).
[CrossRef]

Barclay, P. E.

O. Painter, K. Srinivasan, and P. E. Barclay, Phys. Rev. B 68, 035214 (2003).
[CrossRef]

Boardman, A. D.

A. D. Boardman, Electromagnetic Surface Modes (Wiley, 1982).

Cho, A. Y.

P. Yeh, A. Yariv, and A. Y. Cho, Appl. Phys. Lett. 32, 104 (1978).
[CrossRef]

Dereux, A.

A. Dereux, J. P. Vigneron, P. Lambin, and A. A. Lucas, Phys. Rev. B 38, 5438 (1988).
[CrossRef]

Djafari-Rouhani, B.

M. L. H. Lahlaouti, A. Akjouj, B. Djafari-Rouhani, and L. Dobrzynski, Phys. Rev. B 61, 2059 (2000).
[CrossRef]

M. L. Bah, A. Akjouj, E. H. El Boudouti, B. Djafari-Rouhani, and L. Dobrzynski, J. Phys. Condens. Matter 8, 4171 (1996).
[CrossRef]

Dobrzynski, L.

M. L. H. Lahlaouti, A. Akjouj, B. Djafari-Rouhani, and L. Dobrzynski, Phys. Rev. B 61, 2059 (2000).
[CrossRef]

M. L. Bah, A. Akjouj, E. H. El Boudouti, B. Djafari-Rouhani, and L. Dobrzynski, J. Phys. Condens. Matter 8, 4171 (1996).
[CrossRef]

El Boudouti, E. H.

M. L. Bah, A. Akjouj, E. H. El Boudouti, B. Djafari-Rouhani, and L. Dobrzynski, J. Phys. Condens. Matter 8, 4171 (1996).
[CrossRef]

Fu, C. J.

B. J. Lee, C. J. Fu, and Z. M. Zhang, Appl. Phys. Lett. 87, 071904 (2005).
[CrossRef]

Gaspar-Armenta, J. A.

Halevi, P.

Lahlaouti, M. L. H.

M. L. H. Lahlaouti, A. Akjouj, B. Djafari-Rouhani, and L. Dobrzynski, Phys. Rev. B 61, 2059 (2000).
[CrossRef]

Lambin, P.

A. Dereux, J. P. Vigneron, P. Lambin, and A. A. Lucas, Phys. Rev. B 38, 5438 (1988).
[CrossRef]

Lee, B. J.

B. J. Lee, C. J. Fu, and Z. M. Zhang, Appl. Phys. Lett. 87, 071904 (2005).
[CrossRef]

Lopez-Ríos, T.

Lousse, V.

V. Lousse and J. P. Vigneron, Proc. SPIE 5733, 257 (2005).
[CrossRef]

Lucas, A. A.

A. Dereux, J. P. Vigneron, P. Lambin, and A. A. Lucas, Phys. Rev. B 38, 5438 (1988).
[CrossRef]

May, M. S.

W. M. Robertson and M. S. May, Appl. Phys. Lett. 74, 1800 (1999).
[CrossRef]

Painter, O.

O. Painter, K. Srinivasan, and P. E. Barclay, Phys. Rev. B 68, 035214 (2003).
[CrossRef]

Ramos-Mendieta, F.

Regaldo, L. E.

Robertson, W. M.

W. M. Robertson and M. S. May, Appl. Phys. Lett. 74, 1800 (1999).
[CrossRef]

Srinivasan, K.

O. Painter, K. Srinivasan, and P. E. Barclay, Phys. Rev. B 68, 035214 (2003).
[CrossRef]

Vigneron, J. P.

V. Lousse and J. P. Vigneron, Proc. SPIE 5733, 257 (2005).
[CrossRef]

A. Dereux, J. P. Vigneron, P. Lambin, and A. A. Lucas, Phys. Rev. B 38, 5438 (1988).
[CrossRef]

Villa, F.

Yariv, A.

P. Yeh, A. Yariv, and A. Y. Cho, Appl. Phys. Lett. 32, 104 (1978).
[CrossRef]

Yeh, P.

P. Yeh, A. Yariv, and A. Y. Cho, Appl. Phys. Lett. 32, 104 (1978).
[CrossRef]

P. Yeh, Optical Waves in Layered Media, 2nd ed. (Wiley, 2005).

Zhang, Z. M.

B. J. Lee, C. J. Fu, and Z. M. Zhang, Appl. Phys. Lett. 87, 071904 (2005).
[CrossRef]

Appl. Phys. Lett. (3)

P. Yeh, A. Yariv, and A. Y. Cho, Appl. Phys. Lett. 32, 104 (1978).
[CrossRef]

B. J. Lee, C. J. Fu, and Z. M. Zhang, Appl. Phys. Lett. 87, 071904 (2005).
[CrossRef]

W. M. Robertson and M. S. May, Appl. Phys. Lett. 74, 1800 (1999).
[CrossRef]

J. Opt. Soc. Am. B (1)

J. Phys. Condens. Matter (1)

M. L. Bah, A. Akjouj, E. H. El Boudouti, B. Djafari-Rouhani, and L. Dobrzynski, J. Phys. Condens. Matter 8, 4171 (1996).
[CrossRef]

Opt. Express (1)

Opt. Lett. (1)

Phys. Rev. B (3)

M. L. H. Lahlaouti, A. Akjouj, B. Djafari-Rouhani, and L. Dobrzynski, Phys. Rev. B 61, 2059 (2000).
[CrossRef]

A. Dereux, J. P. Vigneron, P. Lambin, and A. A. Lucas, Phys. Rev. B 38, 5438 (1988).
[CrossRef]

O. Painter, K. Srinivasan, and P. E. Barclay, Phys. Rev. B 68, 035214 (2003).
[CrossRef]

Proc. SPIE (1)

V. Lousse and J. P. Vigneron, Proc. SPIE 5733, 257 (2005).
[CrossRef]

Other (2)

P. Yeh, Optical Waves in Layered Media, 2nd ed. (Wiley, 2005).

A. D. Boardman, Electromagnetic Surface Modes (Wiley, 1982).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (4)

Fig. 1
Fig. 1

Influence of the termination of a semi-infinite 1D PC on the position of modes in the photonic band structure. τ determines the filling factor of the final layer. The PC consists in alternated layers having dielectric constants ε 1 = 2.25 and ε 2 = 13.00 . The final layer is made of the high-refractive-index material.

Fig. 2
Fig. 2

Decay length α of the evanescent mode profile against filling factor τ for the third dispersion curve starting at ω a 2 π c = 1.3765 and finishing at ω a 2 π c = 0.8726 in Fig. 1. Both (a) and (b) illustrate the field profile of the magnetic field H x 2 as a function of the depth z inside the multilayer stack. a is the length of the period.

Fig. 3
Fig. 3

Magnetic field profile H x 2 as a function of the depth z inside the multilayer stack. a is the length of the period. The parameters are τ = 0.292 and ω a 2 π c = 0.857 . Light (dark) gray areas represent high (low) index layers. The first light gray layer on the left is the final layer.

Fig. 4
Fig. 4

Comparison of the dispersion of the electromagnetic surface modes of a semi-infinite 1D PC (circles) and the guided mode (solid curve) of a waveguide ( ε 2 = 13.00 ) surrounded by vacuum and substrate ( ε 1 = 2.25 ) . The two insets give the two distinguished behaviors near the photonic bandgap: crossing (around ω a 2 π c = 0.655 ) or anticrossing (around ω a 2 π c = 0.85 ) cases.

Metrics