Abstract

The spectral and dispersive behaviors of anisotropic layered structures forming a one-dimensional polarization-dependent photonic bandgap are discussed. The finite dimension of the structure is taken into account. Interesting field-localization properties are found when the optical axes of layers are not aligned each with each other, i.e., principal axes of layers are rotated with respect to each other. The field-localization behavior is also discussed through a suitable definition of density of modes for the anisotropic layered structure. A discussion about the behavior of the dispersion law for such a finite periodical structure is also presented.

© 2003 Optical Society of America

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    [CrossRef] [PubMed]
  2. S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 58, 2486–2488 (1987).
    [CrossRef] [PubMed]
  3. E. Yablonovitch and K. M. Leung, “Hope for photonic band gaps,” Phys. Rev. Lett. 351, 278–280 (1991).
  4. E. Yablonovitch, “Liquid versus photonic crystals,” Nature 401, 539–541 (1999).
    [CrossRef]
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    [CrossRef]
  8. G. D’Aguanno, M. Centini, M. Scalora, C. Sibilia, M. J. Bloemer, C. M. Bowden, J. W. Haus, and M. Bertolotti, “Group velocity, energy velocity, and superluminal propagation in finite photonic band-gap structures,” Phys. Rev. E 63, 036610–036615 (2001).
    [CrossRef]
  9. Y. Dumeige, P. Vidakovic, S. Sauvage, I. Sagnes, J. A. Levenson, C. Sibilia, M. Centini, G. D’Aguanno, and M. Scalora, “Enhancement of second-harmonic generation in a one-dimensional semiconductor photonic band gap,” Appl. Phys. Lett. 78, 3021–3023 (2001).
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  19. J. M. Bendickson, J. P. Dowling, and M. Sclora, “Analytic expression for the electromagnetic mode density in finite one-dimensional photonic band gap structures,” Phys. Rev. E 53, 4107–4112 (1996).
    [CrossRef]

2001 (3)

G. D’Aguanno, M. Centini, M. Scalora, C. Sibilia, M. J. Bloemer, C. M. Bowden, J. W. Haus, and M. Bertolotti, “Group velocity, energy velocity, and superluminal propagation in finite photonic band-gap structures,” Phys. Rev. E 63, 036610–036615 (2001).
[CrossRef]

Y. Dumeige, P. Vidakovic, S. Sauvage, I. Sagnes, J. A. Levenson, C. Sibilia, M. Centini, G. D’Aguanno, and M. Scalora, “Enhancement of second-harmonic generation in a one-dimensional semiconductor photonic band gap,” Appl. Phys. Lett. 78, 3021–3023 (2001).
[CrossRef]

E. Rugolo, G. Daguanno, C. Sibilia, M. Centini, M. Scalora, and M. Bertolotti, “Phase independent nonlinear amplifica-tion regime in one dimensional photonic band gap,” Pure Appl. Opt. 3, 6(11), S196–S200 (2001).
[CrossRef]

1999 (3)

M. Centini, C. Sibilia, M. Scalora, G. D’Aguanno, M. Bloemer, C. Bowden, and M. Bertolotti, “Dispersive properties of finite, one-dimensional photonic band gap structures: applications to nonlinear quadratic interactions,” Phys. Rev. E 60, 4891–4895 (1999).
[CrossRef]

V. Balakin, D. Boucher, V. A. Bushev, N. I. Koroteev, B. I. Mantsyzov, P. Masselin, I. A. Ozheredov, and A. P. Shurinov, “Enhancement of second-harmonic generation with femtosecond laser pulses near the photonic band edge for different polarizations of incident light,” Opt. Lett. 24, 793–795 (1999).
[CrossRef]

E. Yablonovitch, “Liquid versus photonic crystals,” Nature 401, 539–541 (1999).
[CrossRef]

1997 (4)

J. Martorell, R. Vilaseca, and R. Corbalan, “Second harmonic generation in a photonic crystal,” Appl. Phys. Lett. 70, 702–704 (1997).
[CrossRef]

J. Martorell, R. Vilaseca, and R. Corbalan, “Scattering of second-harmonic light from small spherical particles ordered in a crystalline lattice,” Phys. Rev. A 55, 4520–4525 (1997).
[CrossRef]

C. Simonneau, J. P. Debray, J. C. Harmand, P. Vidakovic, D. J. Lovering, and J. A. Levenson, “Second-harmonic generation in a doubly resonant semiconductor microcavity,” Opt. Lett. 22, 1775–1777 (1997).
[CrossRef]

M. Scalora, M. J. Bloemer, A. S. Manka, J. P. Dowling, C. M. Bowden, R. Viswanathan, and J. W. Haus, “Pulsed second-harmonic generation in nonlinear, one-dimensional, periodic structure,” Phys. Rev. A 56, 3166–3174 (1997).
[CrossRef]

1996 (1)

J. M. Bendickson, J. P. Dowling, and M. Sclora, “Analytic expression for the electromagnetic mode density in finite one-dimensional photonic band gap structures,” Phys. Rev. E 53, 4107–4112 (1996).
[CrossRef]

1991 (1)

E. Yablonovitch and K. M. Leung, “Hope for photonic band gaps,” Phys. Rev. Lett. 351, 278–280 (1991).

1990 (1)

J. Martorell and N. M. Lawandy, “Observation of inhibited spontaneous emission in a periodic dielectric structure,” Phys. Rev. Lett. 65, 1877–1879 (1990).
[CrossRef] [PubMed]

1987 (2)

E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58, 2059–2061 (1987).
[CrossRef] [PubMed]

S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 58, 2486–2488 (1987).
[CrossRef] [PubMed]

1977 (2)

Balakin, V.

Bendickson, J. M.

J. M. Bendickson, J. P. Dowling, and M. Sclora, “Analytic expression for the electromagnetic mode density in finite one-dimensional photonic band gap structures,” Phys. Rev. E 53, 4107–4112 (1996).
[CrossRef]

Bertolotti, M.

E. Rugolo, G. Daguanno, C. Sibilia, M. Centini, M. Scalora, and M. Bertolotti, “Phase independent nonlinear amplifica-tion regime in one dimensional photonic band gap,” Pure Appl. Opt. 3, 6(11), S196–S200 (2001).
[CrossRef]

G. D’Aguanno, M. Centini, M. Scalora, C. Sibilia, M. J. Bloemer, C. M. Bowden, J. W. Haus, and M. Bertolotti, “Group velocity, energy velocity, and superluminal propagation in finite photonic band-gap structures,” Phys. Rev. E 63, 036610–036615 (2001).
[CrossRef]

M. Centini, C. Sibilia, M. Scalora, G. D’Aguanno, M. Bloemer, C. Bowden, and M. Bertolotti, “Dispersive properties of finite, one-dimensional photonic band gap structures: applications to nonlinear quadratic interactions,” Phys. Rev. E 60, 4891–4895 (1999).
[CrossRef]

Bloemer, M.

M. Centini, C. Sibilia, M. Scalora, G. D’Aguanno, M. Bloemer, C. Bowden, and M. Bertolotti, “Dispersive properties of finite, one-dimensional photonic band gap structures: applications to nonlinear quadratic interactions,” Phys. Rev. E 60, 4891–4895 (1999).
[CrossRef]

Bloemer, M. J.

G. D’Aguanno, M. Centini, M. Scalora, C. Sibilia, M. J. Bloemer, C. M. Bowden, J. W. Haus, and M. Bertolotti, “Group velocity, energy velocity, and superluminal propagation in finite photonic band-gap structures,” Phys. Rev. E 63, 036610–036615 (2001).
[CrossRef]

M. Scalora, M. J. Bloemer, A. S. Manka, J. P. Dowling, C. M. Bowden, R. Viswanathan, and J. W. Haus, “Pulsed second-harmonic generation in nonlinear, one-dimensional, periodic structure,” Phys. Rev. A 56, 3166–3174 (1997).
[CrossRef]

Boucher, D.

Bowden, C.

M. Centini, C. Sibilia, M. Scalora, G. D’Aguanno, M. Bloemer, C. Bowden, and M. Bertolotti, “Dispersive properties of finite, one-dimensional photonic band gap structures: applications to nonlinear quadratic interactions,” Phys. Rev. E 60, 4891–4895 (1999).
[CrossRef]

Bowden, C. M.

G. D’Aguanno, M. Centini, M. Scalora, C. Sibilia, M. J. Bloemer, C. M. Bowden, J. W. Haus, and M. Bertolotti, “Group velocity, energy velocity, and superluminal propagation in finite photonic band-gap structures,” Phys. Rev. E 63, 036610–036615 (2001).
[CrossRef]

M. Scalora, M. J. Bloemer, A. S. Manka, J. P. Dowling, C. M. Bowden, R. Viswanathan, and J. W. Haus, “Pulsed second-harmonic generation in nonlinear, one-dimensional, periodic structure,” Phys. Rev. A 56, 3166–3174 (1997).
[CrossRef]

Bushev, V. A.

Centini, M.

E. Rugolo, G. Daguanno, C. Sibilia, M. Centini, M. Scalora, and M. Bertolotti, “Phase independent nonlinear amplifica-tion regime in one dimensional photonic band gap,” Pure Appl. Opt. 3, 6(11), S196–S200 (2001).
[CrossRef]

G. D’Aguanno, M. Centini, M. Scalora, C. Sibilia, M. J. Bloemer, C. M. Bowden, J. W. Haus, and M. Bertolotti, “Group velocity, energy velocity, and superluminal propagation in finite photonic band-gap structures,” Phys. Rev. E 63, 036610–036615 (2001).
[CrossRef]

Y. Dumeige, P. Vidakovic, S. Sauvage, I. Sagnes, J. A. Levenson, C. Sibilia, M. Centini, G. D’Aguanno, and M. Scalora, “Enhancement of second-harmonic generation in a one-dimensional semiconductor photonic band gap,” Appl. Phys. Lett. 78, 3021–3023 (2001).
[CrossRef]

M. Centini, C. Sibilia, M. Scalora, G. D’Aguanno, M. Bloemer, C. Bowden, and M. Bertolotti, “Dispersive properties of finite, one-dimensional photonic band gap structures: applications to nonlinear quadratic interactions,” Phys. Rev. E 60, 4891–4895 (1999).
[CrossRef]

Corbalan, R.

J. Martorell, R. Vilaseca, and R. Corbalan, “Second harmonic generation in a photonic crystal,” Appl. Phys. Lett. 70, 702–704 (1997).
[CrossRef]

J. Martorell, R. Vilaseca, and R. Corbalan, “Scattering of second-harmonic light from small spherical particles ordered in a crystalline lattice,” Phys. Rev. A 55, 4520–4525 (1997).
[CrossRef]

D’Aguanno, G.

Y. Dumeige, P. Vidakovic, S. Sauvage, I. Sagnes, J. A. Levenson, C. Sibilia, M. Centini, G. D’Aguanno, and M. Scalora, “Enhancement of second-harmonic generation in a one-dimensional semiconductor photonic band gap,” Appl. Phys. Lett. 78, 3021–3023 (2001).
[CrossRef]

G. D’Aguanno, M. Centini, M. Scalora, C. Sibilia, M. J. Bloemer, C. M. Bowden, J. W. Haus, and M. Bertolotti, “Group velocity, energy velocity, and superluminal propagation in finite photonic band-gap structures,” Phys. Rev. E 63, 036610–036615 (2001).
[CrossRef]

M. Centini, C. Sibilia, M. Scalora, G. D’Aguanno, M. Bloemer, C. Bowden, and M. Bertolotti, “Dispersive properties of finite, one-dimensional photonic band gap structures: applications to nonlinear quadratic interactions,” Phys. Rev. E 60, 4891–4895 (1999).
[CrossRef]

Daguanno, G.

E. Rugolo, G. Daguanno, C. Sibilia, M. Centini, M. Scalora, and M. Bertolotti, “Phase independent nonlinear amplifica-tion regime in one dimensional photonic band gap,” Pure Appl. Opt. 3, 6(11), S196–S200 (2001).
[CrossRef]

Debray, J. P.

Dowling, J. P.

M. Scalora, M. J. Bloemer, A. S. Manka, J. P. Dowling, C. M. Bowden, R. Viswanathan, and J. W. Haus, “Pulsed second-harmonic generation in nonlinear, one-dimensional, periodic structure,” Phys. Rev. A 56, 3166–3174 (1997).
[CrossRef]

J. M. Bendickson, J. P. Dowling, and M. Sclora, “Analytic expression for the electromagnetic mode density in finite one-dimensional photonic band gap structures,” Phys. Rev. E 53, 4107–4112 (1996).
[CrossRef]

Dumeige, Y.

Y. Dumeige, P. Vidakovic, S. Sauvage, I. Sagnes, J. A. Levenson, C. Sibilia, M. Centini, G. D’Aguanno, and M. Scalora, “Enhancement of second-harmonic generation in a one-dimensional semiconductor photonic band gap,” Appl. Phys. Lett. 78, 3021–3023 (2001).
[CrossRef]

Harmand, J. C.

Haus, J. W.

G. D’Aguanno, M. Centini, M. Scalora, C. Sibilia, M. J. Bloemer, C. M. Bowden, J. W. Haus, and M. Bertolotti, “Group velocity, energy velocity, and superluminal propagation in finite photonic band-gap structures,” Phys. Rev. E 63, 036610–036615 (2001).
[CrossRef]

M. Scalora, M. J. Bloemer, A. S. Manka, J. P. Dowling, C. M. Bowden, R. Viswanathan, and J. W. Haus, “Pulsed second-harmonic generation in nonlinear, one-dimensional, periodic structure,” Phys. Rev. A 56, 3166–3174 (1997).
[CrossRef]

Hong, C. S.

John, S.

S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 58, 2486–2488 (1987).
[CrossRef] [PubMed]

Koroteev, N. I.

Lawandy, N. M.

J. Martorell and N. M. Lawandy, “Observation of inhibited spontaneous emission in a periodic dielectric structure,” Phys. Rev. Lett. 65, 1877–1879 (1990).
[CrossRef] [PubMed]

Leung, K. M.

E. Yablonovitch and K. M. Leung, “Hope for photonic band gaps,” Phys. Rev. Lett. 351, 278–280 (1991).

Levenson, J. A.

Y. Dumeige, P. Vidakovic, S. Sauvage, I. Sagnes, J. A. Levenson, C. Sibilia, M. Centini, G. D’Aguanno, and M. Scalora, “Enhancement of second-harmonic generation in a one-dimensional semiconductor photonic band gap,” Appl. Phys. Lett. 78, 3021–3023 (2001).
[CrossRef]

C. Simonneau, J. P. Debray, J. C. Harmand, P. Vidakovic, D. J. Lovering, and J. A. Levenson, “Second-harmonic generation in a doubly resonant semiconductor microcavity,” Opt. Lett. 22, 1775–1777 (1997).
[CrossRef]

Lovering, D. J.

Manka, A. S.

M. Scalora, M. J. Bloemer, A. S. Manka, J. P. Dowling, C. M. Bowden, R. Viswanathan, and J. W. Haus, “Pulsed second-harmonic generation in nonlinear, one-dimensional, periodic structure,” Phys. Rev. A 56, 3166–3174 (1997).
[CrossRef]

Mantsyzov, B. I.

Martorell, J.

J. Martorell, R. Vilaseca, and R. Corbalan, “Second harmonic generation in a photonic crystal,” Appl. Phys. Lett. 70, 702–704 (1997).
[CrossRef]

J. Martorell, R. Vilaseca, and R. Corbalan, “Scattering of second-harmonic light from small spherical particles ordered in a crystalline lattice,” Phys. Rev. A 55, 4520–4525 (1997).
[CrossRef]

J. Martorell and N. M. Lawandy, “Observation of inhibited spontaneous emission in a periodic dielectric structure,” Phys. Rev. Lett. 65, 1877–1879 (1990).
[CrossRef] [PubMed]

Masselin, P.

Ozheredov, I. A.

Rugolo, E.

E. Rugolo, G. Daguanno, C. Sibilia, M. Centini, M. Scalora, and M. Bertolotti, “Phase independent nonlinear amplifica-tion regime in one dimensional photonic band gap,” Pure Appl. Opt. 3, 6(11), S196–S200 (2001).
[CrossRef]

Sagnes, I.

Y. Dumeige, P. Vidakovic, S. Sauvage, I. Sagnes, J. A. Levenson, C. Sibilia, M. Centini, G. D’Aguanno, and M. Scalora, “Enhancement of second-harmonic generation in a one-dimensional semiconductor photonic band gap,” Appl. Phys. Lett. 78, 3021–3023 (2001).
[CrossRef]

Sauvage, S.

Y. Dumeige, P. Vidakovic, S. Sauvage, I. Sagnes, J. A. Levenson, C. Sibilia, M. Centini, G. D’Aguanno, and M. Scalora, “Enhancement of second-harmonic generation in a one-dimensional semiconductor photonic band gap,” Appl. Phys. Lett. 78, 3021–3023 (2001).
[CrossRef]

Scalora, M.

Y. Dumeige, P. Vidakovic, S. Sauvage, I. Sagnes, J. A. Levenson, C. Sibilia, M. Centini, G. D’Aguanno, and M. Scalora, “Enhancement of second-harmonic generation in a one-dimensional semiconductor photonic band gap,” Appl. Phys. Lett. 78, 3021–3023 (2001).
[CrossRef]

G. D’Aguanno, M. Centini, M. Scalora, C. Sibilia, M. J. Bloemer, C. M. Bowden, J. W. Haus, and M. Bertolotti, “Group velocity, energy velocity, and superluminal propagation in finite photonic band-gap structures,” Phys. Rev. E 63, 036610–036615 (2001).
[CrossRef]

E. Rugolo, G. Daguanno, C. Sibilia, M. Centini, M. Scalora, and M. Bertolotti, “Phase independent nonlinear amplifica-tion regime in one dimensional photonic band gap,” Pure Appl. Opt. 3, 6(11), S196–S200 (2001).
[CrossRef]

M. Centini, C. Sibilia, M. Scalora, G. D’Aguanno, M. Bloemer, C. Bowden, and M. Bertolotti, “Dispersive properties of finite, one-dimensional photonic band gap structures: applications to nonlinear quadratic interactions,” Phys. Rev. E 60, 4891–4895 (1999).
[CrossRef]

M. Scalora, M. J. Bloemer, A. S. Manka, J. P. Dowling, C. M. Bowden, R. Viswanathan, and J. W. Haus, “Pulsed second-harmonic generation in nonlinear, one-dimensional, periodic structure,” Phys. Rev. A 56, 3166–3174 (1997).
[CrossRef]

Sclora, M.

J. M. Bendickson, J. P. Dowling, and M. Sclora, “Analytic expression for the electromagnetic mode density in finite one-dimensional photonic band gap structures,” Phys. Rev. E 53, 4107–4112 (1996).
[CrossRef]

Shurinov, A. P.

Sibilia, C.

E. Rugolo, G. Daguanno, C. Sibilia, M. Centini, M. Scalora, and M. Bertolotti, “Phase independent nonlinear amplifica-tion regime in one dimensional photonic band gap,” Pure Appl. Opt. 3, 6(11), S196–S200 (2001).
[CrossRef]

G. D’Aguanno, M. Centini, M. Scalora, C. Sibilia, M. J. Bloemer, C. M. Bowden, J. W. Haus, and M. Bertolotti, “Group velocity, energy velocity, and superluminal propagation in finite photonic band-gap structures,” Phys. Rev. E 63, 036610–036615 (2001).
[CrossRef]

Y. Dumeige, P. Vidakovic, S. Sauvage, I. Sagnes, J. A. Levenson, C. Sibilia, M. Centini, G. D’Aguanno, and M. Scalora, “Enhancement of second-harmonic generation in a one-dimensional semiconductor photonic band gap,” Appl. Phys. Lett. 78, 3021–3023 (2001).
[CrossRef]

M. Centini, C. Sibilia, M. Scalora, G. D’Aguanno, M. Bloemer, C. Bowden, and M. Bertolotti, “Dispersive properties of finite, one-dimensional photonic band gap structures: applications to nonlinear quadratic interactions,” Phys. Rev. E 60, 4891–4895 (1999).
[CrossRef]

Simonneau, C.

Vidakovic, P.

Y. Dumeige, P. Vidakovic, S. Sauvage, I. Sagnes, J. A. Levenson, C. Sibilia, M. Centini, G. D’Aguanno, and M. Scalora, “Enhancement of second-harmonic generation in a one-dimensional semiconductor photonic band gap,” Appl. Phys. Lett. 78, 3021–3023 (2001).
[CrossRef]

C. Simonneau, J. P. Debray, J. C. Harmand, P. Vidakovic, D. J. Lovering, and J. A. Levenson, “Second-harmonic generation in a doubly resonant semiconductor microcavity,” Opt. Lett. 22, 1775–1777 (1997).
[CrossRef]

Vilaseca, R.

J. Martorell, R. Vilaseca, and R. Corbalan, “Second harmonic generation in a photonic crystal,” Appl. Phys. Lett. 70, 702–704 (1997).
[CrossRef]

J. Martorell, R. Vilaseca, and R. Corbalan, “Scattering of second-harmonic light from small spherical particles ordered in a crystalline lattice,” Phys. Rev. A 55, 4520–4525 (1997).
[CrossRef]

Viswanathan, R.

M. Scalora, M. J. Bloemer, A. S. Manka, J. P. Dowling, C. M. Bowden, R. Viswanathan, and J. W. Haus, “Pulsed second-harmonic generation in nonlinear, one-dimensional, periodic structure,” Phys. Rev. A 56, 3166–3174 (1997).
[CrossRef]

Yablonovitch, E.

E. Yablonovitch, “Liquid versus photonic crystals,” Nature 401, 539–541 (1999).
[CrossRef]

E. Yablonovitch and K. M. Leung, “Hope for photonic band gaps,” Phys. Rev. Lett. 351, 278–280 (1991).

E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58, 2059–2061 (1987).
[CrossRef] [PubMed]

Yariv, A.

Yeh, P.

Appl. Phys. Lett. (2)

Y. Dumeige, P. Vidakovic, S. Sauvage, I. Sagnes, J. A. Levenson, C. Sibilia, M. Centini, G. D’Aguanno, and M. Scalora, “Enhancement of second-harmonic generation in a one-dimensional semiconductor photonic band gap,” Appl. Phys. Lett. 78, 3021–3023 (2001).
[CrossRef]

J. Martorell, R. Vilaseca, and R. Corbalan, “Second harmonic generation in a photonic crystal,” Appl. Phys. Lett. 70, 702–704 (1997).
[CrossRef]

J. Opt. Soc. Am. (2)

Nature (1)

E. Yablonovitch, “Liquid versus photonic crystals,” Nature 401, 539–541 (1999).
[CrossRef]

Opt. Lett. (2)

Phys. Rev. A (2)

J. Martorell, R. Vilaseca, and R. Corbalan, “Scattering of second-harmonic light from small spherical particles ordered in a crystalline lattice,” Phys. Rev. A 55, 4520–4525 (1997).
[CrossRef]

M. Scalora, M. J. Bloemer, A. S. Manka, J. P. Dowling, C. M. Bowden, R. Viswanathan, and J. W. Haus, “Pulsed second-harmonic generation in nonlinear, one-dimensional, periodic structure,” Phys. Rev. A 56, 3166–3174 (1997).
[CrossRef]

Phys. Rev. E (3)

G. D’Aguanno, M. Centini, M. Scalora, C. Sibilia, M. J. Bloemer, C. M. Bowden, J. W. Haus, and M. Bertolotti, “Group velocity, energy velocity, and superluminal propagation in finite photonic band-gap structures,” Phys. Rev. E 63, 036610–036615 (2001).
[CrossRef]

M. Centini, C. Sibilia, M. Scalora, G. D’Aguanno, M. Bloemer, C. Bowden, and M. Bertolotti, “Dispersive properties of finite, one-dimensional photonic band gap structures: applications to nonlinear quadratic interactions,” Phys. Rev. E 60, 4891–4895 (1999).
[CrossRef]

J. M. Bendickson, J. P. Dowling, and M. Sclora, “Analytic expression for the electromagnetic mode density in finite one-dimensional photonic band gap structures,” Phys. Rev. E 53, 4107–4112 (1996).
[CrossRef]

Phys. Rev. Lett. (4)

J. Martorell and N. M. Lawandy, “Observation of inhibited spontaneous emission in a periodic dielectric structure,” Phys. Rev. Lett. 65, 1877–1879 (1990).
[CrossRef] [PubMed]

E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58, 2059–2061 (1987).
[CrossRef] [PubMed]

S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 58, 2486–2488 (1987).
[CrossRef] [PubMed]

E. Yablonovitch and K. M. Leung, “Hope for photonic band gaps,” Phys. Rev. Lett. 351, 278–280 (1991).

Pure Appl. Opt. (1)

E. Rugolo, G. Daguanno, C. Sibilia, M. Centini, M. Scalora, and M. Bertolotti, “Phase independent nonlinear amplifica-tion regime in one dimensional photonic band gap,” Pure Appl. Opt. 3, 6(11), S196–S200 (2001).
[CrossRef]

Other (2)

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

J. D. Joannopoulos, R. D. Mead, and J. N. Winn, Photonic Crystals (Princeton University, Princeton, N.J., 1994).

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Figures (8)

Fig. 1
Fig. 1

Multilayer structure with an aligned optical axis.

Fig. 2
Fig. 2

Multilayer structure with optical axis of a generic angle φ not aligned with respect to the x axis. ε1z and ε2z maintain the same alignment.

Fig. 3
Fig. 3

(a) Transmission spectrum for an input-polarized field along the x1 direction. The rotation angle among ε1x and ε2x is equal to zero. The alignment is the same for ε1z and ε2z. ε1xx=6, ε1yy=2, ε1zz=4, ε2zz=3, ε2yy=7, ε2zz=4, d1=41.7 nm, d2=125 nm, N=15. The output-polarized field is the same direction as the input. (b) Same parameters as Fig. 3. The polarization of the input field is along the y1 axis. The output field is along the same polarization direction of the input.

Fig. 4
Fig. 4

(a) Transmission spectrum for the x2-axis output with an input field polarized with the electric field parallel to the x1 axis. The geometrical parameters are the same as in Fig. 3. The spectrum is for an angle φ=20° of rotation among ε1x and ε2x. (b) Transmission spectrum for the y2-axis output with an input field polarized with the electric field parallel to the x1 axis. The geometrical parameters are the same as in Fig. 3. The spectrum is for an angle φ=20° of rotation among ε1x and ε2x. (c) Transmission spectrum for the x2-axis output with an input field polarized with the electric field parallel to the y1 axis. The geometrical parameters are the same as in Fig. 3. The spectrum is for an angle φ=20° of rotation among ε1x and ε2x. (d) Transmission spectrum for the y2-axis output with an input field polarized with the electric field parallel to the y1 axis. The geometrical parameters are the same as in Fig. 3. The spectrum is for an angle φ=20° of rotation among ε1x and ε2x.

Fig. 5
Fig. 5

(a) Three-dimensional transmission spectrum for the same geometrical parameters as in Fig. 3 as a function of the wavelength and of the rotation angle among ε1x and ε2x (φ). The input field is polarized with the electric field parallel to the x1 axis; the output field is polarized along the x2 axis. (b) Three-dimensional transmission spectrum for the same geometrical parameters as in Fig. 3, as a function of the wavelength and of the rotation angle among ε1x and ε2x (φ). The input field is polarized with the electric field parallel to the x1 axis; the output field is polarized along the y2 axis.

Fig. 6
Fig. 6

Modulus of the electric field distribution, for y1-axis input. Rotation angle: central curve, φ=19°; exponential curve, φ=0°; low-amplitude curve, φ=25°; other low-amplitude curve, φ=40°; λ=0.249 μm.

Fig. 7
Fig. 7

Effective index for different polarization of input. The geometrical parameters are the same as in Fig. 3. The DOMs are for an angle φ=20° of rotation among ε1x and ε2x: (a) obtained from transmission given in Fig. 4(a); (b) obtained from Fig. 4(b); (c) obtained from Fig. 4(c); (d) obtained from Fig. 4(d).  

Fig. 8
Fig. 8

Density of modes for different polarizations of input. The geometrical parameters are the same as in Fig. 3. The DOMs are for an angle φ=20° of rotation among ε1x and ε2x. The direction of propagation of the input beam is from the left to the right: (a) obtained from transmission given in Fig. 4(a); (b) obtained from Fig. 4(b); (c) obtained from Fig. 4(c); (d) obtained from Fig. 4(d).

Equations (29)

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ε˜=Aε1000ε2000ε3A-1,
A=cos ψ cos ϕ-cos θ sin ϕ sin ψ-sin ψ cos ϕ-cos θ sin ϕ cos ψsin θ sin ϕcos ψ sin ϕ+cos θ cos ϕ sin ψ-sin ψ sin ϕ+cos θ cos ϕ cos ψ-sin θ cos ϕsin θ sin ψsin θ cos ψcos θ.
k×(k×E)+ω2με˜E=0,
ω2μεxx-β2-γ2ω2μεxy+αβω2μεxz+αγω2μεyx+αβω2μεyy-α2-γ2ω2μεyz+βγω2μεzx+αγω2μεzy+βγω2μεzz-α2-β2×ExEyEz=0.
E=σ=14Aσpσexp[i(αx+βγ+γσz-ωt)].
ε˜=ε˜(0)z<z0ε˜(1)z0<z<z1ε˜(2)z1<z<z2ε˜(N)zN-1<z<zNε˜(s)zN<z.
E=σ=14Aσ(n)pσ(n)×exp{i[αx+βy+γσ(n)(z-zn)-ωt]}.
H=σ=14Aσ(n)qσ(n)×exp{i[αx+βy+γσ(n)(z-zn)-ωt]},
qσ(n)=ckσ(n)ωμ×pσ(n),
kσ(n)=αi+βj+γσ(n)k.
σ=14Aσ(n-1)pσ(n-1)x
=σ=14Aσ(n)pσ(n)xexp[-iγσ(n)tn],
σ=14Aσ(n-1)pσ(n-1)y
=σ=14Aσ(n)pσ(n)yexp[-iγσ(n)tn],
σ=14Aσ(n-1)qσ(n-1)x
=σ=14Aσ(n)qσ(n)xexp[-iγσ(n)tn],
σ=14Aσ(n-1)qσ(n-1)y
=σ=14Aσ(n)qσ(n)yexp[-iγσ(n)tn],
A1(n-1)A2(n-1)A3(n-1)A4(n-1)=D-1(n-1)D(n)P(n)A1(n)A2(n)A3(n)A4(n),
D(n)=xp1(n)xp2(n)xp3(n)xp4(n)yq1(n)yq2(n)yq3(n)yq4(n)yp1(n)yp2(n)yp3(n)yp4(n)xq1(n)xq2(n)xq3(n)xq4(n),
P(n)=exp[-iγ1(n)tn]0000exp[-iγ2(n)tn]0000exp[-iγ3(n)tn]0000exp[-iγ4(n)tn].
Tn-1,n=D-1(n-1)D(n)P(n).
A1(n-1)A2(n-1)A3(n-1)A4(n-1)=Tn-1,nA1(n)A2(n)A3(n)A4(n).
A1(0)A2(0)A3(0)A4(0)=T0,1T1,2TN-1,NTN,sA1(s)A2(s)A3(s)A4(s),
Ax1Rx1Ay1Ry1=TTx10x1Ty10y1,
t=x+iy=exp(lnT)exp(iφt)=exp(iφ˜),
φ˜=ωc n˜effD,
n˜eff(ω)=(c/ωD)[φt-(i/2)ln(|t|2)].
ρ=dφtDdω.

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