Abstract

We suggest a geometrical framework in which to discuss periodic layered structures in the unit disk. Bandgaps appear when the point representing the system approaches the unit circle. We show that the trace of the matrix describing the basic period allows for a classification in three families of orbits with quite different properties. The laws of convergence of the iterates to the unit circle can then be considered universal features of the reflection.

© 2003 Optical Society of America

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  1. A complete and up-to-date bibliography on the subject can be found at http://home.earthlink.net/~jpdowling/pbgbib.html.
  2. E. Centeno and D. Felbacq, J. Opt. Soc. Am. A 17, 320 (2000).
  3. Y. Fink, J. N. Winn, S. Fan, C. Chen, J. Michel, J. D. Joannopoulos, and E. L. Thomas, Science 282, 1679 (1998).
  4. J. P. Dowling, Science 282, 1841 (1998).
  5. E. Yablonovitch, Opt. Lett. 23, 1648 (1998).
  6. D. N. Chigrin, A. V. Lavrinenko, D. A. Yarotsky, and S. V. Gaponenko, Appl. Phys. A 68, 25 (1999).
  7. J. Lekner, J. Opt. A 2, 349 (2000).
  8. B. Gralak, G. Tayeb, and S. Enoch, J. Opt. Soc. Am. A 17, 1012 (2000).
  9. M. Notomi, Phys. Rev. B 62, 10696 (2000).
  10. T. Yonte, J. J. Monzón, L. L. Sánchez-Soto, J. F. Cariñena, and C. López-Lacasta, J. Opt. Soc. Am. A 19, 603 (2002).
  11. J. J. Monzón, T. Yonte, L. L. Sánchez-Soto, and J. F. Cariñena, J. Opt. Soc. Am. A 19, 985 (2002).
  12. J. J. Monzón and L. L. Sánchez-Soto, Opt. Commun. 162, 1 (1999).
  13. J. J. Monzón and L. L. Sánchez-Soto, J. Opt. Soc. Am. A 16, 2013 (1999).
  14. L. L. Sánchez-Soto, J. J. Monzón, T. Yonte, and J. F. Cariñena, Opt. Lett. 26, 1400 (2001).
  15. J. J. Monzón, T. Yonte, and L. L. Sánchez-Soto, Opt. Lett. 26, 370 (2001).
  16. D. Felbacq, J. Phys. A 33, 7137 (2000).
  17. D. Felbacq, B. Guizal, and F. Zolla, “Do Fresnel coefficients exist?” April 23, 2001, arXiv.org e-Print archive, Preprint physics/0104074, http://xxx.lanl.gov.
  18. J. Kapeluszny, T. Kuczumow, and S. Reich, Adv. Math. 143, 111 (1999).
  19. J. J. Monzón, T. Yonte, and L. L. Sánchez-Soto, Opt. Commun. 218, 43 (2003).
  20. P. Yeh, Optical Waves in Layered Media (Wiley, New York, 1988).
  21. J. Lekner, Theory of Reflection (Kluwer Academic, Dordrecht, The Netherlands, 1987).

2003 (1)

J. J. Monzón, T. Yonte, and L. L. Sánchez-Soto, Opt. Commun. 218, 43 (2003).

2002 (2)

2001 (2)

2000 (5)

D. Felbacq, J. Phys. A 33, 7137 (2000).

E. Centeno and D. Felbacq, J. Opt. Soc. Am. A 17, 320 (2000).

B. Gralak, G. Tayeb, and S. Enoch, J. Opt. Soc. Am. A 17, 1012 (2000).

J. Lekner, J. Opt. A 2, 349 (2000).

M. Notomi, Phys. Rev. B 62, 10696 (2000).

1999 (4)

J. J. Monzón and L. L. Sánchez-Soto, Opt. Commun. 162, 1 (1999).

J. J. Monzón and L. L. Sánchez-Soto, J. Opt. Soc. Am. A 16, 2013 (1999).

J. Kapeluszny, T. Kuczumow, and S. Reich, Adv. Math. 143, 111 (1999).

D. N. Chigrin, A. V. Lavrinenko, D. A. Yarotsky, and S. V. Gaponenko, Appl. Phys. A 68, 25 (1999).

1998 (3)

E. Yablonovitch, Opt. Lett. 23, 1648 (1998).

Y. Fink, J. N. Winn, S. Fan, C. Chen, J. Michel, J. D. Joannopoulos, and E. L. Thomas, Science 282, 1679 (1998).

J. P. Dowling, Science 282, 1841 (1998).

Cariñena, J. F.

Centeno, E.

Chen, C.

Y. Fink, J. N. Winn, S. Fan, C. Chen, J. Michel, J. D. Joannopoulos, and E. L. Thomas, Science 282, 1679 (1998).

Chigrin, D. N.

D. N. Chigrin, A. V. Lavrinenko, D. A. Yarotsky, and S. V. Gaponenko, Appl. Phys. A 68, 25 (1999).

Dowling, J. P.

J. P. Dowling, Science 282, 1841 (1998).

Enoch, S.

Fan, S.

Y. Fink, J. N. Winn, S. Fan, C. Chen, J. Michel, J. D. Joannopoulos, and E. L. Thomas, Science 282, 1679 (1998).

Felbacq, D.

E. Centeno and D. Felbacq, J. Opt. Soc. Am. A 17, 320 (2000).

D. Felbacq, J. Phys. A 33, 7137 (2000).

D. Felbacq, B. Guizal, and F. Zolla, “Do Fresnel coefficients exist?” April 23, 2001, arXiv.org e-Print archive, Preprint physics/0104074, http://xxx.lanl.gov.

Fink, Y.

Y. Fink, J. N. Winn, S. Fan, C. Chen, J. Michel, J. D. Joannopoulos, and E. L. Thomas, Science 282, 1679 (1998).

Gaponenko, S. V.

D. N. Chigrin, A. V. Lavrinenko, D. A. Yarotsky, and S. V. Gaponenko, Appl. Phys. A 68, 25 (1999).

Gralak, B.

Guizal, B.

D. Felbacq, B. Guizal, and F. Zolla, “Do Fresnel coefficients exist?” April 23, 2001, arXiv.org e-Print archive, Preprint physics/0104074, http://xxx.lanl.gov.

Joannopoulos, J. D.

Y. Fink, J. N. Winn, S. Fan, C. Chen, J. Michel, J. D. Joannopoulos, and E. L. Thomas, Science 282, 1679 (1998).

Kapeluszny, J.

J. Kapeluszny, T. Kuczumow, and S. Reich, Adv. Math. 143, 111 (1999).

Kuczumow, T.

J. Kapeluszny, T. Kuczumow, and S. Reich, Adv. Math. 143, 111 (1999).

Lavrinenko, A. V.

D. N. Chigrin, A. V. Lavrinenko, D. A. Yarotsky, and S. V. Gaponenko, Appl. Phys. A 68, 25 (1999).

Lekner, J.

J. Lekner, J. Opt. A 2, 349 (2000).

J. Lekner, Theory of Reflection (Kluwer Academic, Dordrecht, The Netherlands, 1987).

López-Lacasta, C.

Michel, J.

Y. Fink, J. N. Winn, S. Fan, C. Chen, J. Michel, J. D. Joannopoulos, and E. L. Thomas, Science 282, 1679 (1998).

Monzón, J. J.

Notomi, M.

M. Notomi, Phys. Rev. B 62, 10696 (2000).

Reich, S.

J. Kapeluszny, T. Kuczumow, and S. Reich, Adv. Math. 143, 111 (1999).

Sánchez-Soto, L. L.

Tayeb, G.

Thomas, E. L.

Y. Fink, J. N. Winn, S. Fan, C. Chen, J. Michel, J. D. Joannopoulos, and E. L. Thomas, Science 282, 1679 (1998).

Winn, J. N.

Y. Fink, J. N. Winn, S. Fan, C. Chen, J. Michel, J. D. Joannopoulos, and E. L. Thomas, Science 282, 1679 (1998).

Yablonovitch, E.

Yarotsky, D. A.

D. N. Chigrin, A. V. Lavrinenko, D. A. Yarotsky, and S. V. Gaponenko, Appl. Phys. A 68, 25 (1999).

Yeh, P.

P. Yeh, Optical Waves in Layered Media (Wiley, New York, 1988).

Yonte, T.

Zolla, F.

D. Felbacq, B. Guizal, and F. Zolla, “Do Fresnel coefficients exist?” April 23, 2001, arXiv.org e-Print archive, Preprint physics/0104074, http://xxx.lanl.gov.

Adv. Math. (1)

J. Kapeluszny, T. Kuczumow, and S. Reich, Adv. Math. 143, 111 (1999).

Appl. Phys. A (1)

D. N. Chigrin, A. V. Lavrinenko, D. A. Yarotsky, and S. V. Gaponenko, Appl. Phys. A 68, 25 (1999).

J. Opt. A (1)

J. Lekner, J. Opt. A 2, 349 (2000).

J. Opt. Soc. Am. A (5)

J. Phys. A (1)

D. Felbacq, J. Phys. A 33, 7137 (2000).

Opt. Commun. (2)

J. J. Monzón and L. L. Sánchez-Soto, Opt. Commun. 162, 1 (1999).

J. J. Monzón, T. Yonte, and L. L. Sánchez-Soto, Opt. Commun. 218, 43 (2003).

Opt. Lett. (3)

Phys. Rev. B (1)

M. Notomi, Phys. Rev. B 62, 10696 (2000).

Science (2)

Y. Fink, J. N. Winn, S. Fan, C. Chen, J. Michel, J. D. Joannopoulos, and E. L. Thomas, Science 282, 1679 (1998).

J. P. Dowling, Science 282, 1841 (1998).

Other (4)

P. Yeh, Optical Waves in Layered Media (Wiley, New York, 1988).

J. Lekner, Theory of Reflection (Kluwer Academic, Dordrecht, The Netherlands, 1987).

A complete and up-to-date bibliography on the subject can be found at http://home.earthlink.net/~jpdowling/pbgbib.html.

D. Felbacq, B. Guizal, and F. Zolla, “Do Fresnel coefficients exist?” April 23, 2001, arXiv.org e-Print archive, Preprint physics/0104074, http://xxx.lanl.gov.

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