Abstract

A second-harmonic superprism effect in 2D photonic crystals is demonstrated numerically. A full control of the second-harmonic emission is achieved by tailoring the photonic dispersion curves. This effect is demonstrated by using a multiple scattering method generalized to the second-harmonic generation. We show that small angular variations or a wavelength tuning of the fundamental field induce large shifts of the second-harmonic emission (90°).

© 2006 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. C.M.Soukoulis, ed., Photonic Band Gap Materials, Vol. 315 of the NATO Advanced Study Institute Series E: Applied Sciences (Kluwer, 1996).
  2. J. D. Joannopoulos, R. Meade, and J. Winn, Photonic Crystals (Princeton U. Press, 1995).
  3. E. Yablonovitch, "Inhibited spontaneous emission in solid-state physics and electronics," Phys. Rev. Lett. 58, 2059-2062 (1987).
    [CrossRef] [PubMed]
  4. S. John, "Strong localization of photons in certain disordered dielectric superlattices," Phys. Rev. Lett. 58, 2486-2489 (1987).
    [CrossRef] [PubMed]
  5. A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, "High transmission through sharp bends in photonic crystal waveguides," Phys. Rev. Lett. 77, 3787-3790 (1996).
    [CrossRef] [PubMed]
  6. S. Y. Lin, E. Chow, S. G. Johnson, and J. D. Joannopoulos, "Demonstration of highly efficient waveguiding in a photonic crystal slab at the 1.5-μm wavelength," Opt. Lett. 25, 1297-1299 (2000).
    [CrossRef]
  7. A. Talneau, L. Le Gouezigou, N. Bouadma, M. Kafesaki, C. M. Soukoulis, and M. Agio, "Photonic-crystal ultrashort bends with improved transmission and low reflection at 1.55μm," Appl. Phys. Lett. 80, 547-549 (2002).
    [CrossRef]
  8. E. Ozbay, I. Bulu, K. Aydin, H. Caglayan, and K. Guven, "Physics and applications of photonic crystals," Photonics Nanostruct. Fundam. Appl. 2, 87-95 (2004).
    [CrossRef]
  9. S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and H. A. Hauss, "Channel drop tunneling through localized states," Phys. Rev. Lett. 80, 960-963 (1998).
    [CrossRef]
  10. S. Noda, "Three-dimensional photonic crystals operating at optical wavelength region," Physica B 279, 142-149 (2000).
    [CrossRef]
  11. H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, "Superprism phenomena in photonic crystal," Phys. Rev. B 58, R10096-R10099 (1998).
    [CrossRef]
  12. H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, "Photonic crystals for micro lightwave circuits using wavelength-dependent angular beam steering," Appl. Phys. Lett. 74, 1370-1372 (1999).
    [CrossRef]
  13. T. Matsumoto, S. Fujita, and T. Baba, "Wavelength demultiplexer consisting of photonic crystal superprism and superlens," Opt. Express 13, 10768-10776 (2005).
    [CrossRef] [PubMed]
  14. B. Momeni and B. A. Adibi, "Optimization of photonic crystal demultiplexers based on the superprism effect," Appl. Phys. B 77, 555-560 (2003).
    [CrossRef]
  15. A. Lupu, E. Cassan, S. Laval, L. El. Melhaoui, P. Lyan, J. M. Fedeli, "Experimental evidence for superprism phenomena in SOI photonic crystals," Opt. Express 12, 5690-5696 (2004).
    [CrossRef] [PubMed]
  16. V. Berger, "Nonlinear photonic crystals," Phys. Rev. Lett. 81, 4136-4139 (1998).
    [CrossRef]
  17. A. R Cowan and J. F. Young, "Mode matching for second-harmonic generation in photonic crystal waveguides," Phys. Rev. B 65, 85106-85112 (2002).
    [CrossRef]
  18. J. Torres, D. Coquillat, R. Legros, J. P. Lascaray, F. Teppe, D. Scalbert, D. Peyrade, Y. Chen, O. Briot, M. Le Vassor d'Yerville, E. Centeno, D. Cassagne, and J. P. Albert, "Giant second-harmonic generation in a one-dimensional GaN photonic crystal," Phys. Rev. B 69, 085105-085113 (2004).
    [CrossRef]
  19. M. Yamada, N. Nada, M. Saitoh, and K. Watanabe, "First-order quasi-phase matched LiNbO3 waveguide periodically poled by applying an external field for efficient blue second-harmonic generation," Appl. Phys. Lett. 62, 435-436 (1993).
    [CrossRef]
  20. S. N. Zhu, Y. Y. Zhu, and N. B. Ming, "Quasi-phase-matched third-harmonic generation in a quasi-periodic optical superlattice," Science 278, 843-846 (1997).
    [CrossRef]
  21. 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 structures," Phys. Rev. A 56, 3166-3174 (1997).
    [CrossRef]
  22. M. Centini, C. Sibilia, M. Scalora, G. D'Aguanno, M. Bertolotti, M. J. Bloemer, C. M. Bowden, and I. Nefedov, "Dispersive properties of finite one-dimensional photonic bandgap structures: applications to nonlinear quadratic interactions," Phys. Rev. E 60, 4891-4898 (1999).
    [CrossRef]
  23. Y. Dumeige, I. Sagnes, P. Monnier, P. Vidakovic, I. Abram, C. Mériadec, and A. Levenson, "Phase-matched frequency doubling at photonic band edges: efficiency scaling as the fifth power of the length," Phys. Rev. Lett. 89, 43901-43904 (2002).
    [CrossRef]
  24. J. Martorell, R. Vilaseca, and R. Corbolan, "Second-harmonic generation in a photonic crystal," Appl. Phys. Lett. 70, 702-704 (1997).
    [CrossRef]
  25. J. Trull, R. Vilaseca, J. Martorell, and R. Cordobàn "Second-harmonic generation in local modes of a truncated periodic structure," Opt. Lett. 20, 1746-1750 (1995).
    [CrossRef] [PubMed]
  26. F. Ren, R. Li, C. Cheng, H. Wang, J. Qiu, J. Si, and K. Hirao, "Giant enhancement of second harmonic generation in a finite photonic crystal with a single defect and dual-localized modes," Phys. Rev. B 70, 245109-245113 (2004).
    [CrossRef]
  27. A. M. Malvezzi, G. Vecchi, M. Patrini, G. Guizetti, L. C. Andreani, F. Romanato, L. Businaro, E. DiFabrizio, A. Passaseo, and M. De Vittorio, "Resonant second-harmonic generation in a GaAs photonic crystal waveguide," Phys. Rev. B 68, 161306-161310 (2003).
    [CrossRef]
  28. G. D'Aguanno, M. Centini, M. Scalora, C. Sibilia, Y. Dumeige, P. Vidakovic, J. A. Levenson, M. J. Bloemer, C. M. Bowden, J. W. Haus, and M. Bertolotti, "Photonic band edge effects in finite structures and applications to chi(2) interactions," Phys. Rev. E 64, 016609-016618 (2001).
    [CrossRef]
  29. B. Shi, Z. M. Jiang, X. F. Zhou, and X. Wang, "A two-dimensional nonlinear photonic crystal for strong second-harmonic generation," J. Appl. Phys. 91, 6769-6771 (2002).
    [CrossRef]
  30. E. Centeno, "Second-harmonic superprism effect in photonic crystals," Opt. Lett. 30, 1054-1056 (2005).
    [CrossRef] [PubMed]
  31. E. Centeno and D. Felbacq, "Rigorous vector diffraction of electromagnetic waves by bidimensional photonic crystals," J. Opt. Soc. Am. A 17, 320-327 (2000).
    [CrossRef]
  32. D. Felbacq, G. Tayeb, and D. Maystre, "Scattering by a random set of parallel cylinders," J. Opt. Soc. Am. A 11, 2526-2533 (1994).
    [CrossRef]
  33. H. A. Yousif and S. Kohler, "Scattering by two penetrable cylinders at oblique incidence," J. Opt. Soc. Am. A 5, 1085-1096 (1988).
    [CrossRef]
  34. L.-M. Li and Z.-Q. Zhang, "Multiple-scattering approach to finite-sized photonic bandgap materials," Phys. Rev. B 58, 9587-9590 (1998).
    [CrossRef]
  35. E. Centeno and D. Felbacq, "Optical bistability in finite-size nonlinear bidimensional photonic crystals doped by a microcavity," Phys. Rev. B 62, R7683-R7686 (2000).
    [CrossRef]
  36. P. Xie and Z.-Q. Zhang, "Multifrequency gap solitons in nonlinear photonic crystals," Phys. Rev. Lett. 91, 213904-213908 (2003).
    [CrossRef] [PubMed]
  37. C. I. Valencia, E. R. Méndez, and B. S. Mendoza, "Second-harmonic generation in the scattering of light by an infinite cylinder," J. Opt. Soc. Am. B 21, 36-44 (2004).
    [CrossRef]
  38. M. Abramovitz and I. Stegun, Handbook of Mathematical Functions (Dover, 1970).
  39. H. Schmidt, A. C. Abare, J. E. Bowers, S. P. Denbaars, and A. Imamoglu, "Large interband second-order susceptibilities in InxGa1−xN/GaN quantum wells," Appl. Phys. Lett. 75, 3611-3613 (1999).
    [CrossRef]
  40. S. Johnson and J. Joannopoulos, "Block-iterative frequency-domain methods for Maxwell's equations in a planewave basis," Opt. Express 8, 173-190 (2001).
    [CrossRef] [PubMed]
  41. N. Antoine-Vincent, N. Natali, M. Mihailovic, A. Vasson, J. Leymarie, P. Disseix, D. Byrne, F. Semond, and J. Massies, "Determination of the refractive indices of AlN, GaN, and AlxGa1−xN grown on (111)Si substrates," J. Appl. Phys. 93, 5222-5226 (2003).
    [CrossRef]
  42. A. L. Cabuz, E. Centeno, and D. Cassagne, "Superprism effect in bidimensional rectangular photonic crystals," Appl. Phys. Lett. 84, 2031-2033 (2004).
    [CrossRef]
  43. E. Centeno and D. Cassagne, "Graded photonic crystals," Opt. Lett. 30, 2278-2280 (2005).
    [CrossRef] [PubMed]

2005 (3)

2004 (6)

C. I. Valencia, E. R. Méndez, and B. S. Mendoza, "Second-harmonic generation in the scattering of light by an infinite cylinder," J. Opt. Soc. Am. B 21, 36-44 (2004).
[CrossRef]

A. Lupu, E. Cassan, S. Laval, L. El. Melhaoui, P. Lyan, J. M. Fedeli, "Experimental evidence for superprism phenomena in SOI photonic crystals," Opt. Express 12, 5690-5696 (2004).
[CrossRef] [PubMed]

E. Ozbay, I. Bulu, K. Aydin, H. Caglayan, and K. Guven, "Physics and applications of photonic crystals," Photonics Nanostruct. Fundam. Appl. 2, 87-95 (2004).
[CrossRef]

J. Torres, D. Coquillat, R. Legros, J. P. Lascaray, F. Teppe, D. Scalbert, D. Peyrade, Y. Chen, O. Briot, M. Le Vassor d'Yerville, E. Centeno, D. Cassagne, and J. P. Albert, "Giant second-harmonic generation in a one-dimensional GaN photonic crystal," Phys. Rev. B 69, 085105-085113 (2004).
[CrossRef]

F. Ren, R. Li, C. Cheng, H. Wang, J. Qiu, J. Si, and K. Hirao, "Giant enhancement of second harmonic generation in a finite photonic crystal with a single defect and dual-localized modes," Phys. Rev. B 70, 245109-245113 (2004).
[CrossRef]

A. L. Cabuz, E. Centeno, and D. Cassagne, "Superprism effect in bidimensional rectangular photonic crystals," Appl. Phys. Lett. 84, 2031-2033 (2004).
[CrossRef]

2003 (4)

P. Xie and Z.-Q. Zhang, "Multifrequency gap solitons in nonlinear photonic crystals," Phys. Rev. Lett. 91, 213904-213908 (2003).
[CrossRef] [PubMed]

N. Antoine-Vincent, N. Natali, M. Mihailovic, A. Vasson, J. Leymarie, P. Disseix, D. Byrne, F. Semond, and J. Massies, "Determination of the refractive indices of AlN, GaN, and AlxGa1−xN grown on (111)Si substrates," J. Appl. Phys. 93, 5222-5226 (2003).
[CrossRef]

A. M. Malvezzi, G. Vecchi, M. Patrini, G. Guizetti, L. C. Andreani, F. Romanato, L. Businaro, E. DiFabrizio, A. Passaseo, and M. De Vittorio, "Resonant second-harmonic generation in a GaAs photonic crystal waveguide," Phys. Rev. B 68, 161306-161310 (2003).
[CrossRef]

B. Momeni and B. A. Adibi, "Optimization of photonic crystal demultiplexers based on the superprism effect," Appl. Phys. B 77, 555-560 (2003).
[CrossRef]

2002 (4)

B. Shi, Z. M. Jiang, X. F. Zhou, and X. Wang, "A two-dimensional nonlinear photonic crystal for strong second-harmonic generation," J. Appl. Phys. 91, 6769-6771 (2002).
[CrossRef]

Y. Dumeige, I. Sagnes, P. Monnier, P. Vidakovic, I. Abram, C. Mériadec, and A. Levenson, "Phase-matched frequency doubling at photonic band edges: efficiency scaling as the fifth power of the length," Phys. Rev. Lett. 89, 43901-43904 (2002).
[CrossRef]

A. R Cowan and J. F. Young, "Mode matching for second-harmonic generation in photonic crystal waveguides," Phys. Rev. B 65, 85106-85112 (2002).
[CrossRef]

A. Talneau, L. Le Gouezigou, N. Bouadma, M. Kafesaki, C. M. Soukoulis, and M. Agio, "Photonic-crystal ultrashort bends with improved transmission and low reflection at 1.55μm," Appl. Phys. Lett. 80, 547-549 (2002).
[CrossRef]

2001 (2)

G. D'Aguanno, M. Centini, M. Scalora, C. Sibilia, Y. Dumeige, P. Vidakovic, J. A. Levenson, M. J. Bloemer, C. M. Bowden, J. W. Haus, and M. Bertolotti, "Photonic band edge effects in finite structures and applications to chi(2) interactions," Phys. Rev. E 64, 016609-016618 (2001).
[CrossRef]

S. Johnson and J. Joannopoulos, "Block-iterative frequency-domain methods for Maxwell's equations in a planewave basis," Opt. Express 8, 173-190 (2001).
[CrossRef] [PubMed]

2000 (4)

E. Centeno and D. Felbacq, "Optical bistability in finite-size nonlinear bidimensional photonic crystals doped by a microcavity," Phys. Rev. B 62, R7683-R7686 (2000).
[CrossRef]

S. Y. Lin, E. Chow, S. G. Johnson, and J. D. Joannopoulos, "Demonstration of highly efficient waveguiding in a photonic crystal slab at the 1.5-μm wavelength," Opt. Lett. 25, 1297-1299 (2000).
[CrossRef]

E. Centeno and D. Felbacq, "Rigorous vector diffraction of electromagnetic waves by bidimensional photonic crystals," J. Opt. Soc. Am. A 17, 320-327 (2000).
[CrossRef]

S. Noda, "Three-dimensional photonic crystals operating at optical wavelength region," Physica B 279, 142-149 (2000).
[CrossRef]

1999 (3)

M. Centini, C. Sibilia, M. Scalora, G. D'Aguanno, M. Bertolotti, M. J. Bloemer, C. M. Bowden, and I. Nefedov, "Dispersive properties of finite one-dimensional photonic bandgap structures: applications to nonlinear quadratic interactions," Phys. Rev. E 60, 4891-4898 (1999).
[CrossRef]

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, "Photonic crystals for micro lightwave circuits using wavelength-dependent angular beam steering," Appl. Phys. Lett. 74, 1370-1372 (1999).
[CrossRef]

H. Schmidt, A. C. Abare, J. E. Bowers, S. P. Denbaars, and A. Imamoglu, "Large interband second-order susceptibilities in InxGa1−xN/GaN quantum wells," Appl. Phys. Lett. 75, 3611-3613 (1999).
[CrossRef]

1998 (4)

L.-M. Li and Z.-Q. Zhang, "Multiple-scattering approach to finite-sized photonic bandgap materials," Phys. Rev. B 58, 9587-9590 (1998).
[CrossRef]

V. Berger, "Nonlinear photonic crystals," Phys. Rev. Lett. 81, 4136-4139 (1998).
[CrossRef]

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, "Superprism phenomena in photonic crystal," Phys. Rev. B 58, R10096-R10099 (1998).
[CrossRef]

S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and H. A. Hauss, "Channel drop tunneling through localized states," Phys. Rev. Lett. 80, 960-963 (1998).
[CrossRef]

1997 (3)

S. N. Zhu, Y. Y. Zhu, and N. B. Ming, "Quasi-phase-matched third-harmonic generation in a quasi-periodic optical superlattice," Science 278, 843-846 (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 structures," Phys. Rev. A 56, 3166-3174 (1997).
[CrossRef]

J. Martorell, R. Vilaseca, and R. Corbolan, "Second-harmonic generation in a photonic crystal," Appl. Phys. Lett. 70, 702-704 (1997).
[CrossRef]

1996 (1)

A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, "High transmission through sharp bends in photonic crystal waveguides," Phys. Rev. Lett. 77, 3787-3790 (1996).
[CrossRef] [PubMed]

1995 (1)

1994 (1)

1993 (1)

M. Yamada, N. Nada, M. Saitoh, and K. Watanabe, "First-order quasi-phase matched LiNbO3 waveguide periodically poled by applying an external field for efficient blue second-harmonic generation," Appl. Phys. Lett. 62, 435-436 (1993).
[CrossRef]

1988 (1)

1987 (2)

E. Yablonovitch, "Inhibited spontaneous emission in solid-state physics and electronics," Phys. Rev. Lett. 58, 2059-2062 (1987).
[CrossRef] [PubMed]

S. John, "Strong localization of photons in certain disordered dielectric superlattices," Phys. Rev. Lett. 58, 2486-2489 (1987).
[CrossRef] [PubMed]

Abare, A. C.

H. Schmidt, A. C. Abare, J. E. Bowers, S. P. Denbaars, and A. Imamoglu, "Large interband second-order susceptibilities in InxGa1−xN/GaN quantum wells," Appl. Phys. Lett. 75, 3611-3613 (1999).
[CrossRef]

Abram, I.

Y. Dumeige, I. Sagnes, P. Monnier, P. Vidakovic, I. Abram, C. Mériadec, and A. Levenson, "Phase-matched frequency doubling at photonic band edges: efficiency scaling as the fifth power of the length," Phys. Rev. Lett. 89, 43901-43904 (2002).
[CrossRef]

Abramovitz, M.

M. Abramovitz and I. Stegun, Handbook of Mathematical Functions (Dover, 1970).

Adibi, B. A.

B. Momeni and B. A. Adibi, "Optimization of photonic crystal demultiplexers based on the superprism effect," Appl. Phys. B 77, 555-560 (2003).
[CrossRef]

Agio, M.

A. Talneau, L. Le Gouezigou, N. Bouadma, M. Kafesaki, C. M. Soukoulis, and M. Agio, "Photonic-crystal ultrashort bends with improved transmission and low reflection at 1.55μm," Appl. Phys. Lett. 80, 547-549 (2002).
[CrossRef]

Albert, J. P.

J. Torres, D. Coquillat, R. Legros, J. P. Lascaray, F. Teppe, D. Scalbert, D. Peyrade, Y. Chen, O. Briot, M. Le Vassor d'Yerville, E. Centeno, D. Cassagne, and J. P. Albert, "Giant second-harmonic generation in a one-dimensional GaN photonic crystal," Phys. Rev. B 69, 085105-085113 (2004).
[CrossRef]

Andreani, L. C.

A. M. Malvezzi, G. Vecchi, M. Patrini, G. Guizetti, L. C. Andreani, F. Romanato, L. Businaro, E. DiFabrizio, A. Passaseo, and M. De Vittorio, "Resonant second-harmonic generation in a GaAs photonic crystal waveguide," Phys. Rev. B 68, 161306-161310 (2003).
[CrossRef]

Antoine-Vincent, N.

N. Antoine-Vincent, N. Natali, M. Mihailovic, A. Vasson, J. Leymarie, P. Disseix, D. Byrne, F. Semond, and J. Massies, "Determination of the refractive indices of AlN, GaN, and AlxGa1−xN grown on (111)Si substrates," J. Appl. Phys. 93, 5222-5226 (2003).
[CrossRef]

Aydin, K.

E. Ozbay, I. Bulu, K. Aydin, H. Caglayan, and K. Guven, "Physics and applications of photonic crystals," Photonics Nanostruct. Fundam. Appl. 2, 87-95 (2004).
[CrossRef]

Baba, T.

Berger, V.

V. Berger, "Nonlinear photonic crystals," Phys. Rev. Lett. 81, 4136-4139 (1998).
[CrossRef]

Bertolotti, M.

G. D'Aguanno, M. Centini, M. Scalora, C. Sibilia, Y. Dumeige, P. Vidakovic, J. A. Levenson, M. J. Bloemer, C. M. Bowden, J. W. Haus, and M. Bertolotti, "Photonic band edge effects in finite structures and applications to chi(2) interactions," Phys. Rev. E 64, 016609-016618 (2001).
[CrossRef]

M. Centini, C. Sibilia, M. Scalora, G. D'Aguanno, M. Bertolotti, M. J. Bloemer, C. M. Bowden, and I. Nefedov, "Dispersive properties of finite one-dimensional photonic bandgap structures: applications to nonlinear quadratic interactions," Phys. Rev. E 60, 4891-4898 (1999).
[CrossRef]

Bloemer, M. J.

G. D'Aguanno, M. Centini, M. Scalora, C. Sibilia, Y. Dumeige, P. Vidakovic, J. A. Levenson, M. J. Bloemer, C. M. Bowden, J. W. Haus, and M. Bertolotti, "Photonic band edge effects in finite structures and applications to chi(2) interactions," Phys. Rev. E 64, 016609-016618 (2001).
[CrossRef]

M. Centini, C. Sibilia, M. Scalora, G. D'Aguanno, M. Bertolotti, M. J. Bloemer, C. M. Bowden, and I. Nefedov, "Dispersive properties of finite one-dimensional photonic bandgap structures: applications to nonlinear quadratic interactions," Phys. Rev. E 60, 4891-4898 (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 structures," Phys. Rev. A 56, 3166-3174 (1997).
[CrossRef]

Bouadma, N.

A. Talneau, L. Le Gouezigou, N. Bouadma, M. Kafesaki, C. M. Soukoulis, and M. Agio, "Photonic-crystal ultrashort bends with improved transmission and low reflection at 1.55μm," Appl. Phys. Lett. 80, 547-549 (2002).
[CrossRef]

Bowden, C. M.

G. D'Aguanno, M. Centini, M. Scalora, C. Sibilia, Y. Dumeige, P. Vidakovic, J. A. Levenson, M. J. Bloemer, C. M. Bowden, J. W. Haus, and M. Bertolotti, "Photonic band edge effects in finite structures and applications to chi(2) interactions," Phys. Rev. E 64, 016609-016618 (2001).
[CrossRef]

M. Centini, C. Sibilia, M. Scalora, G. D'Aguanno, M. Bertolotti, M. J. Bloemer, C. M. Bowden, and I. Nefedov, "Dispersive properties of finite one-dimensional photonic bandgap structures: applications to nonlinear quadratic interactions," Phys. Rev. E 60, 4891-4898 (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 structures," Phys. Rev. A 56, 3166-3174 (1997).
[CrossRef]

Bowers, J. E.

H. Schmidt, A. C. Abare, J. E. Bowers, S. P. Denbaars, and A. Imamoglu, "Large interband second-order susceptibilities in InxGa1−xN/GaN quantum wells," Appl. Phys. Lett. 75, 3611-3613 (1999).
[CrossRef]

Briot, O.

J. Torres, D. Coquillat, R. Legros, J. P. Lascaray, F. Teppe, D. Scalbert, D. Peyrade, Y. Chen, O. Briot, M. Le Vassor d'Yerville, E. Centeno, D. Cassagne, and J. P. Albert, "Giant second-harmonic generation in a one-dimensional GaN photonic crystal," Phys. Rev. B 69, 085105-085113 (2004).
[CrossRef]

Bulu, I.

E. Ozbay, I. Bulu, K. Aydin, H. Caglayan, and K. Guven, "Physics and applications of photonic crystals," Photonics Nanostruct. Fundam. Appl. 2, 87-95 (2004).
[CrossRef]

Businaro, L.

A. M. Malvezzi, G. Vecchi, M. Patrini, G. Guizetti, L. C. Andreani, F. Romanato, L. Businaro, E. DiFabrizio, A. Passaseo, and M. De Vittorio, "Resonant second-harmonic generation in a GaAs photonic crystal waveguide," Phys. Rev. B 68, 161306-161310 (2003).
[CrossRef]

Byrne, D.

N. Antoine-Vincent, N. Natali, M. Mihailovic, A. Vasson, J. Leymarie, P. Disseix, D. Byrne, F. Semond, and J. Massies, "Determination of the refractive indices of AlN, GaN, and AlxGa1−xN grown on (111)Si substrates," J. Appl. Phys. 93, 5222-5226 (2003).
[CrossRef]

Cabuz, A. L.

A. L. Cabuz, E. Centeno, and D. Cassagne, "Superprism effect in bidimensional rectangular photonic crystals," Appl. Phys. Lett. 84, 2031-2033 (2004).
[CrossRef]

Caglayan, H.

E. Ozbay, I. Bulu, K. Aydin, H. Caglayan, and K. Guven, "Physics and applications of photonic crystals," Photonics Nanostruct. Fundam. Appl. 2, 87-95 (2004).
[CrossRef]

Cassagne, D.

E. Centeno and D. Cassagne, "Graded photonic crystals," Opt. Lett. 30, 2278-2280 (2005).
[CrossRef] [PubMed]

A. L. Cabuz, E. Centeno, and D. Cassagne, "Superprism effect in bidimensional rectangular photonic crystals," Appl. Phys. Lett. 84, 2031-2033 (2004).
[CrossRef]

J. Torres, D. Coquillat, R. Legros, J. P. Lascaray, F. Teppe, D. Scalbert, D. Peyrade, Y. Chen, O. Briot, M. Le Vassor d'Yerville, E. Centeno, D. Cassagne, and J. P. Albert, "Giant second-harmonic generation in a one-dimensional GaN photonic crystal," Phys. Rev. B 69, 085105-085113 (2004).
[CrossRef]

Cassan, E.

Centeno, E.

E. Centeno, "Second-harmonic superprism effect in photonic crystals," Opt. Lett. 30, 1054-1056 (2005).
[CrossRef] [PubMed]

E. Centeno and D. Cassagne, "Graded photonic crystals," Opt. Lett. 30, 2278-2280 (2005).
[CrossRef] [PubMed]

J. Torres, D. Coquillat, R. Legros, J. P. Lascaray, F. Teppe, D. Scalbert, D. Peyrade, Y. Chen, O. Briot, M. Le Vassor d'Yerville, E. Centeno, D. Cassagne, and J. P. Albert, "Giant second-harmonic generation in a one-dimensional GaN photonic crystal," Phys. Rev. B 69, 085105-085113 (2004).
[CrossRef]

A. L. Cabuz, E. Centeno, and D. Cassagne, "Superprism effect in bidimensional rectangular photonic crystals," Appl. Phys. Lett. 84, 2031-2033 (2004).
[CrossRef]

E. Centeno and D. Felbacq, "Rigorous vector diffraction of electromagnetic waves by bidimensional photonic crystals," J. Opt. Soc. Am. A 17, 320-327 (2000).
[CrossRef]

E. Centeno and D. Felbacq, "Optical bistability in finite-size nonlinear bidimensional photonic crystals doped by a microcavity," Phys. Rev. B 62, R7683-R7686 (2000).
[CrossRef]

Centini, M.

G. D'Aguanno, M. Centini, M. Scalora, C. Sibilia, Y. Dumeige, P. Vidakovic, J. A. Levenson, M. J. Bloemer, C. M. Bowden, J. W. Haus, and M. Bertolotti, "Photonic band edge effects in finite structures and applications to chi(2) interactions," Phys. Rev. E 64, 016609-016618 (2001).
[CrossRef]

M. Centini, C. Sibilia, M. Scalora, G. D'Aguanno, M. Bertolotti, M. J. Bloemer, C. M. Bowden, and I. Nefedov, "Dispersive properties of finite one-dimensional photonic bandgap structures: applications to nonlinear quadratic interactions," Phys. Rev. E 60, 4891-4898 (1999).
[CrossRef]

Chen, J. C.

A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, "High transmission through sharp bends in photonic crystal waveguides," Phys. Rev. Lett. 77, 3787-3790 (1996).
[CrossRef] [PubMed]

Chen, Y.

J. Torres, D. Coquillat, R. Legros, J. P. Lascaray, F. Teppe, D. Scalbert, D. Peyrade, Y. Chen, O. Briot, M. Le Vassor d'Yerville, E. Centeno, D. Cassagne, and J. P. Albert, "Giant second-harmonic generation in a one-dimensional GaN photonic crystal," Phys. Rev. B 69, 085105-085113 (2004).
[CrossRef]

Cheng, C.

F. Ren, R. Li, C. Cheng, H. Wang, J. Qiu, J. Si, and K. Hirao, "Giant enhancement of second harmonic generation in a finite photonic crystal with a single defect and dual-localized modes," Phys. Rev. B 70, 245109-245113 (2004).
[CrossRef]

Chow, E.

Coquillat, D.

J. Torres, D. Coquillat, R. Legros, J. P. Lascaray, F. Teppe, D. Scalbert, D. Peyrade, Y. Chen, O. Briot, M. Le Vassor d'Yerville, E. Centeno, D. Cassagne, and J. P. Albert, "Giant second-harmonic generation in a one-dimensional GaN photonic crystal," Phys. Rev. B 69, 085105-085113 (2004).
[CrossRef]

Corbolan, R.

J. Martorell, R. Vilaseca, and R. Corbolan, "Second-harmonic generation in a photonic crystal," Appl. Phys. Lett. 70, 702-704 (1997).
[CrossRef]

Cordobàn, R.

Cowan, A. R

A. R Cowan and J. F. Young, "Mode matching for second-harmonic generation in photonic crystal waveguides," Phys. Rev. B 65, 85106-85112 (2002).
[CrossRef]

D'Aguanno, G.

G. D'Aguanno, M. Centini, M. Scalora, C. Sibilia, Y. Dumeige, P. Vidakovic, J. A. Levenson, M. J. Bloemer, C. M. Bowden, J. W. Haus, and M. Bertolotti, "Photonic band edge effects in finite structures and applications to chi(2) interactions," Phys. Rev. E 64, 016609-016618 (2001).
[CrossRef]

M. Centini, C. Sibilia, M. Scalora, G. D'Aguanno, M. Bertolotti, M. J. Bloemer, C. M. Bowden, and I. Nefedov, "Dispersive properties of finite one-dimensional photonic bandgap structures: applications to nonlinear quadratic interactions," Phys. Rev. E 60, 4891-4898 (1999).
[CrossRef]

Denbaars, S. P.

H. Schmidt, A. C. Abare, J. E. Bowers, S. P. Denbaars, and A. Imamoglu, "Large interband second-order susceptibilities in InxGa1−xN/GaN quantum wells," Appl. Phys. Lett. 75, 3611-3613 (1999).
[CrossRef]

DiFabrizio, E.

A. M. Malvezzi, G. Vecchi, M. Patrini, G. Guizetti, L. C. Andreani, F. Romanato, L. Businaro, E. DiFabrizio, A. Passaseo, and M. De Vittorio, "Resonant second-harmonic generation in a GaAs photonic crystal waveguide," Phys. Rev. B 68, 161306-161310 (2003).
[CrossRef]

Disseix, P.

N. Antoine-Vincent, N. Natali, M. Mihailovic, A. Vasson, J. Leymarie, P. Disseix, D. Byrne, F. Semond, and J. Massies, "Determination of the refractive indices of AlN, GaN, and AlxGa1−xN grown on (111)Si substrates," J. Appl. Phys. 93, 5222-5226 (2003).
[CrossRef]

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 structures," Phys. Rev. A 56, 3166-3174 (1997).
[CrossRef]

Dumeige, Y.

Y. Dumeige, I. Sagnes, P. Monnier, P. Vidakovic, I. Abram, C. Mériadec, and A. Levenson, "Phase-matched frequency doubling at photonic band edges: efficiency scaling as the fifth power of the length," Phys. Rev. Lett. 89, 43901-43904 (2002).
[CrossRef]

G. D'Aguanno, M. Centini, M. Scalora, C. Sibilia, Y. Dumeige, P. Vidakovic, J. A. Levenson, M. J. Bloemer, C. M. Bowden, J. W. Haus, and M. Bertolotti, "Photonic band edge effects in finite structures and applications to chi(2) interactions," Phys. Rev. E 64, 016609-016618 (2001).
[CrossRef]

Fan, S.

S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and H. A. Hauss, "Channel drop tunneling through localized states," Phys. Rev. Lett. 80, 960-963 (1998).
[CrossRef]

A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, "High transmission through sharp bends in photonic crystal waveguides," Phys. Rev. Lett. 77, 3787-3790 (1996).
[CrossRef] [PubMed]

Fedeli, J. M.

Felbacq, D.

Fujita, S.

Gouezigou, L. Le

A. Talneau, L. Le Gouezigou, N. Bouadma, M. Kafesaki, C. M. Soukoulis, and M. Agio, "Photonic-crystal ultrashort bends with improved transmission and low reflection at 1.55μm," Appl. Phys. Lett. 80, 547-549 (2002).
[CrossRef]

Guizetti, G.

A. M. Malvezzi, G. Vecchi, M. Patrini, G. Guizetti, L. C. Andreani, F. Romanato, L. Businaro, E. DiFabrizio, A. Passaseo, and M. De Vittorio, "Resonant second-harmonic generation in a GaAs photonic crystal waveguide," Phys. Rev. B 68, 161306-161310 (2003).
[CrossRef]

Guven, K.

E. Ozbay, I. Bulu, K. Aydin, H. Caglayan, and K. Guven, "Physics and applications of photonic crystals," Photonics Nanostruct. Fundam. Appl. 2, 87-95 (2004).
[CrossRef]

Haus, J. W.

G. D'Aguanno, M. Centini, M. Scalora, C. Sibilia, Y. Dumeige, P. Vidakovic, J. A. Levenson, M. J. Bloemer, C. M. Bowden, J. W. Haus, and M. Bertolotti, "Photonic band edge effects in finite structures and applications to chi(2) interactions," Phys. Rev. E 64, 016609-016618 (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 structures," Phys. Rev. A 56, 3166-3174 (1997).
[CrossRef]

Hauss, H. A.

S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and H. A. Hauss, "Channel drop tunneling through localized states," Phys. Rev. Lett. 80, 960-963 (1998).
[CrossRef]

Hirao, K.

F. Ren, R. Li, C. Cheng, H. Wang, J. Qiu, J. Si, and K. Hirao, "Giant enhancement of second harmonic generation in a finite photonic crystal with a single defect and dual-localized modes," Phys. Rev. B 70, 245109-245113 (2004).
[CrossRef]

Imamoglu, A.

H. Schmidt, A. C. Abare, J. E. Bowers, S. P. Denbaars, and A. Imamoglu, "Large interband second-order susceptibilities in InxGa1−xN/GaN quantum wells," Appl. Phys. Lett. 75, 3611-3613 (1999).
[CrossRef]

Jiang, Z. M.

B. Shi, Z. M. Jiang, X. F. Zhou, and X. Wang, "A two-dimensional nonlinear photonic crystal for strong second-harmonic generation," J. Appl. Phys. 91, 6769-6771 (2002).
[CrossRef]

Joannopoulos, J.

Joannopoulos, J. D.

S. Y. Lin, E. Chow, S. G. Johnson, and J. D. Joannopoulos, "Demonstration of highly efficient waveguiding in a photonic crystal slab at the 1.5-μm wavelength," Opt. Lett. 25, 1297-1299 (2000).
[CrossRef]

S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and H. A. Hauss, "Channel drop tunneling through localized states," Phys. Rev. Lett. 80, 960-963 (1998).
[CrossRef]

A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, "High transmission through sharp bends in photonic crystal waveguides," Phys. Rev. Lett. 77, 3787-3790 (1996).
[CrossRef] [PubMed]

J. D. Joannopoulos, R. Meade, and J. Winn, Photonic Crystals (Princeton U. Press, 1995).

John, S.

S. John, "Strong localization of photons in certain disordered dielectric superlattices," Phys. Rev. Lett. 58, 2486-2489 (1987).
[CrossRef] [PubMed]

Johnson, S.

Johnson, S. G.

Kafesaki, M.

A. Talneau, L. Le Gouezigou, N. Bouadma, M. Kafesaki, C. M. Soukoulis, and M. Agio, "Photonic-crystal ultrashort bends with improved transmission and low reflection at 1.55μm," Appl. Phys. Lett. 80, 547-549 (2002).
[CrossRef]

Kawakami, S.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, "Photonic crystals for micro lightwave circuits using wavelength-dependent angular beam steering," Appl. Phys. Lett. 74, 1370-1372 (1999).
[CrossRef]

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, "Superprism phenomena in photonic crystal," Phys. Rev. B 58, R10096-R10099 (1998).
[CrossRef]

Kawashima, T.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, "Photonic crystals for micro lightwave circuits using wavelength-dependent angular beam steering," Appl. Phys. Lett. 74, 1370-1372 (1999).
[CrossRef]

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, "Superprism phenomena in photonic crystal," Phys. Rev. B 58, R10096-R10099 (1998).
[CrossRef]

Kohler, S.

Kosaka, H.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, "Photonic crystals for micro lightwave circuits using wavelength-dependent angular beam steering," Appl. Phys. Lett. 74, 1370-1372 (1999).
[CrossRef]

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, "Superprism phenomena in photonic crystal," Phys. Rev. B 58, R10096-R10099 (1998).
[CrossRef]

Kurland, I.

A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, "High transmission through sharp bends in photonic crystal waveguides," Phys. Rev. Lett. 77, 3787-3790 (1996).
[CrossRef] [PubMed]

Lascaray, J. P.

J. Torres, D. Coquillat, R. Legros, J. P. Lascaray, F. Teppe, D. Scalbert, D. Peyrade, Y. Chen, O. Briot, M. Le Vassor d'Yerville, E. Centeno, D. Cassagne, and J. P. Albert, "Giant second-harmonic generation in a one-dimensional GaN photonic crystal," Phys. Rev. B 69, 085105-085113 (2004).
[CrossRef]

Laval, S.

Legros, R.

J. Torres, D. Coquillat, R. Legros, J. P. Lascaray, F. Teppe, D. Scalbert, D. Peyrade, Y. Chen, O. Briot, M. Le Vassor d'Yerville, E. Centeno, D. Cassagne, and J. P. Albert, "Giant second-harmonic generation in a one-dimensional GaN photonic crystal," Phys. Rev. B 69, 085105-085113 (2004).
[CrossRef]

Levenson, A.

Y. Dumeige, I. Sagnes, P. Monnier, P. Vidakovic, I. Abram, C. Mériadec, and A. Levenson, "Phase-matched frequency doubling at photonic band edges: efficiency scaling as the fifth power of the length," Phys. Rev. Lett. 89, 43901-43904 (2002).
[CrossRef]

Levenson, J. A.

G. D'Aguanno, M. Centini, M. Scalora, C. Sibilia, Y. Dumeige, P. Vidakovic, J. A. Levenson, M. J. Bloemer, C. M. Bowden, J. W. Haus, and M. Bertolotti, "Photonic band edge effects in finite structures and applications to chi(2) interactions," Phys. Rev. E 64, 016609-016618 (2001).
[CrossRef]

Leymarie, J.

N. Antoine-Vincent, N. Natali, M. Mihailovic, A. Vasson, J. Leymarie, P. Disseix, D. Byrne, F. Semond, and J. Massies, "Determination of the refractive indices of AlN, GaN, and AlxGa1−xN grown on (111)Si substrates," J. Appl. Phys. 93, 5222-5226 (2003).
[CrossRef]

Li, L.-M.

L.-M. Li and Z.-Q. Zhang, "Multiple-scattering approach to finite-sized photonic bandgap materials," Phys. Rev. B 58, 9587-9590 (1998).
[CrossRef]

Li, R.

F. Ren, R. Li, C. Cheng, H. Wang, J. Qiu, J. Si, and K. Hirao, "Giant enhancement of second harmonic generation in a finite photonic crystal with a single defect and dual-localized modes," Phys. Rev. B 70, 245109-245113 (2004).
[CrossRef]

Lin, S. Y.

Lupu, A.

Lyan, P.

Malvezzi, A. M.

A. M. Malvezzi, G. Vecchi, M. Patrini, G. Guizetti, L. C. Andreani, F. Romanato, L. Businaro, E. DiFabrizio, A. Passaseo, and M. De Vittorio, "Resonant second-harmonic generation in a GaAs photonic crystal waveguide," Phys. Rev. B 68, 161306-161310 (2003).
[CrossRef]

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 structures," Phys. Rev. A 56, 3166-3174 (1997).
[CrossRef]

Martorell, J.

J. Martorell, R. Vilaseca, and R. Corbolan, "Second-harmonic generation in a photonic crystal," Appl. Phys. Lett. 70, 702-704 (1997).
[CrossRef]

J. Trull, R. Vilaseca, J. Martorell, and R. Cordobàn "Second-harmonic generation in local modes of a truncated periodic structure," Opt. Lett. 20, 1746-1750 (1995).
[CrossRef] [PubMed]

Massies, J.

N. Antoine-Vincent, N. Natali, M. Mihailovic, A. Vasson, J. Leymarie, P. Disseix, D. Byrne, F. Semond, and J. Massies, "Determination of the refractive indices of AlN, GaN, and AlxGa1−xN grown on (111)Si substrates," J. Appl. Phys. 93, 5222-5226 (2003).
[CrossRef]

Matsumoto, T.

Maystre, D.

Meade, R.

J. D. Joannopoulos, R. Meade, and J. Winn, Photonic Crystals (Princeton U. Press, 1995).

Mekis, A.

A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, "High transmission through sharp bends in photonic crystal waveguides," Phys. Rev. Lett. 77, 3787-3790 (1996).
[CrossRef] [PubMed]

Melhaoui, L. El.

Méndez, E. R.

Mendoza, B. S.

Mériadec, C.

Y. Dumeige, I. Sagnes, P. Monnier, P. Vidakovic, I. Abram, C. Mériadec, and A. Levenson, "Phase-matched frequency doubling at photonic band edges: efficiency scaling as the fifth power of the length," Phys. Rev. Lett. 89, 43901-43904 (2002).
[CrossRef]

Mihailovic, M.

N. Antoine-Vincent, N. Natali, M. Mihailovic, A. Vasson, J. Leymarie, P. Disseix, D. Byrne, F. Semond, and J. Massies, "Determination of the refractive indices of AlN, GaN, and AlxGa1−xN grown on (111)Si substrates," J. Appl. Phys. 93, 5222-5226 (2003).
[CrossRef]

Ming, N. B.

S. N. Zhu, Y. Y. Zhu, and N. B. Ming, "Quasi-phase-matched third-harmonic generation in a quasi-periodic optical superlattice," Science 278, 843-846 (1997).
[CrossRef]

Momeni, B.

B. Momeni and B. A. Adibi, "Optimization of photonic crystal demultiplexers based on the superprism effect," Appl. Phys. B 77, 555-560 (2003).
[CrossRef]

Monnier, P.

Y. Dumeige, I. Sagnes, P. Monnier, P. Vidakovic, I. Abram, C. Mériadec, and A. Levenson, "Phase-matched frequency doubling at photonic band edges: efficiency scaling as the fifth power of the length," Phys. Rev. Lett. 89, 43901-43904 (2002).
[CrossRef]

Nada, N.

M. Yamada, N. Nada, M. Saitoh, and K. Watanabe, "First-order quasi-phase matched LiNbO3 waveguide periodically poled by applying an external field for efficient blue second-harmonic generation," Appl. Phys. Lett. 62, 435-436 (1993).
[CrossRef]

Natali, N.

N. Antoine-Vincent, N. Natali, M. Mihailovic, A. Vasson, J. Leymarie, P. Disseix, D. Byrne, F. Semond, and J. Massies, "Determination of the refractive indices of AlN, GaN, and AlxGa1−xN grown on (111)Si substrates," J. Appl. Phys. 93, 5222-5226 (2003).
[CrossRef]

Nefedov, I.

M. Centini, C. Sibilia, M. Scalora, G. D'Aguanno, M. Bertolotti, M. J. Bloemer, C. M. Bowden, and I. Nefedov, "Dispersive properties of finite one-dimensional photonic bandgap structures: applications to nonlinear quadratic interactions," Phys. Rev. E 60, 4891-4898 (1999).
[CrossRef]

Noda, S.

S. Noda, "Three-dimensional photonic crystals operating at optical wavelength region," Physica B 279, 142-149 (2000).
[CrossRef]

Notomi, M.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, "Photonic crystals for micro lightwave circuits using wavelength-dependent angular beam steering," Appl. Phys. Lett. 74, 1370-1372 (1999).
[CrossRef]

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, "Superprism phenomena in photonic crystal," Phys. Rev. B 58, R10096-R10099 (1998).
[CrossRef]

Ozbay, E.

E. Ozbay, I. Bulu, K. Aydin, H. Caglayan, and K. Guven, "Physics and applications of photonic crystals," Photonics Nanostruct. Fundam. Appl. 2, 87-95 (2004).
[CrossRef]

Passaseo, A.

A. M. Malvezzi, G. Vecchi, M. Patrini, G. Guizetti, L. C. Andreani, F. Romanato, L. Businaro, E. DiFabrizio, A. Passaseo, and M. De Vittorio, "Resonant second-harmonic generation in a GaAs photonic crystal waveguide," Phys. Rev. B 68, 161306-161310 (2003).
[CrossRef]

Patrini, M.

A. M. Malvezzi, G. Vecchi, M. Patrini, G. Guizetti, L. C. Andreani, F. Romanato, L. Businaro, E. DiFabrizio, A. Passaseo, and M. De Vittorio, "Resonant second-harmonic generation in a GaAs photonic crystal waveguide," Phys. Rev. B 68, 161306-161310 (2003).
[CrossRef]

Peyrade, D.

J. Torres, D. Coquillat, R. Legros, J. P. Lascaray, F. Teppe, D. Scalbert, D. Peyrade, Y. Chen, O. Briot, M. Le Vassor d'Yerville, E. Centeno, D. Cassagne, and J. P. Albert, "Giant second-harmonic generation in a one-dimensional GaN photonic crystal," Phys. Rev. B 69, 085105-085113 (2004).
[CrossRef]

Qiu, J.

F. Ren, R. Li, C. Cheng, H. Wang, J. Qiu, J. Si, and K. Hirao, "Giant enhancement of second harmonic generation in a finite photonic crystal with a single defect and dual-localized modes," Phys. Rev. B 70, 245109-245113 (2004).
[CrossRef]

Ren, F.

F. Ren, R. Li, C. Cheng, H. Wang, J. Qiu, J. Si, and K. Hirao, "Giant enhancement of second harmonic generation in a finite photonic crystal with a single defect and dual-localized modes," Phys. Rev. B 70, 245109-245113 (2004).
[CrossRef]

Romanato, F.

A. M. Malvezzi, G. Vecchi, M. Patrini, G. Guizetti, L. C. Andreani, F. Romanato, L. Businaro, E. DiFabrizio, A. Passaseo, and M. De Vittorio, "Resonant second-harmonic generation in a GaAs photonic crystal waveguide," Phys. Rev. B 68, 161306-161310 (2003).
[CrossRef]

Sagnes, I.

Y. Dumeige, I. Sagnes, P. Monnier, P. Vidakovic, I. Abram, C. Mériadec, and A. Levenson, "Phase-matched frequency doubling at photonic band edges: efficiency scaling as the fifth power of the length," Phys. Rev. Lett. 89, 43901-43904 (2002).
[CrossRef]

Saitoh, M.

M. Yamada, N. Nada, M. Saitoh, and K. Watanabe, "First-order quasi-phase matched LiNbO3 waveguide periodically poled by applying an external field for efficient blue second-harmonic generation," Appl. Phys. Lett. 62, 435-436 (1993).
[CrossRef]

Sato, T.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, "Photonic crystals for micro lightwave circuits using wavelength-dependent angular beam steering," Appl. Phys. Lett. 74, 1370-1372 (1999).
[CrossRef]

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, "Superprism phenomena in photonic crystal," Phys. Rev. B 58, R10096-R10099 (1998).
[CrossRef]

Scalbert, D.

J. Torres, D. Coquillat, R. Legros, J. P. Lascaray, F. Teppe, D. Scalbert, D. Peyrade, Y. Chen, O. Briot, M. Le Vassor d'Yerville, E. Centeno, D. Cassagne, and J. P. Albert, "Giant second-harmonic generation in a one-dimensional GaN photonic crystal," Phys. Rev. B 69, 085105-085113 (2004).
[CrossRef]

Scalora, M.

G. D'Aguanno, M. Centini, M. Scalora, C. Sibilia, Y. Dumeige, P. Vidakovic, J. A. Levenson, M. J. Bloemer, C. M. Bowden, J. W. Haus, and M. Bertolotti, "Photonic band edge effects in finite structures and applications to chi(2) interactions," Phys. Rev. E 64, 016609-016618 (2001).
[CrossRef]

M. Centini, C. Sibilia, M. Scalora, G. D'Aguanno, M. Bertolotti, M. J. Bloemer, C. M. Bowden, and I. Nefedov, "Dispersive properties of finite one-dimensional photonic bandgap structures: applications to nonlinear quadratic interactions," Phys. Rev. E 60, 4891-4898 (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 structures," Phys. Rev. A 56, 3166-3174 (1997).
[CrossRef]

Schmidt, H.

H. Schmidt, A. C. Abare, J. E. Bowers, S. P. Denbaars, and A. Imamoglu, "Large interband second-order susceptibilities in InxGa1−xN/GaN quantum wells," Appl. Phys. Lett. 75, 3611-3613 (1999).
[CrossRef]

Semond, F.

N. Antoine-Vincent, N. Natali, M. Mihailovic, A. Vasson, J. Leymarie, P. Disseix, D. Byrne, F. Semond, and J. Massies, "Determination of the refractive indices of AlN, GaN, and AlxGa1−xN grown on (111)Si substrates," J. Appl. Phys. 93, 5222-5226 (2003).
[CrossRef]

Shi, B.

B. Shi, Z. M. Jiang, X. F. Zhou, and X. Wang, "A two-dimensional nonlinear photonic crystal for strong second-harmonic generation," J. Appl. Phys. 91, 6769-6771 (2002).
[CrossRef]

Si, J.

F. Ren, R. Li, C. Cheng, H. Wang, J. Qiu, J. Si, and K. Hirao, "Giant enhancement of second harmonic generation in a finite photonic crystal with a single defect and dual-localized modes," Phys. Rev. B 70, 245109-245113 (2004).
[CrossRef]

Sibilia, C.

G. D'Aguanno, M. Centini, M. Scalora, C. Sibilia, Y. Dumeige, P. Vidakovic, J. A. Levenson, M. J. Bloemer, C. M. Bowden, J. W. Haus, and M. Bertolotti, "Photonic band edge effects in finite structures and applications to chi(2) interactions," Phys. Rev. E 64, 016609-016618 (2001).
[CrossRef]

M. Centini, C. Sibilia, M. Scalora, G. D'Aguanno, M. Bertolotti, M. J. Bloemer, C. M. Bowden, and I. Nefedov, "Dispersive properties of finite one-dimensional photonic bandgap structures: applications to nonlinear quadratic interactions," Phys. Rev. E 60, 4891-4898 (1999).
[CrossRef]

Soukoulis, C. M.

A. Talneau, L. Le Gouezigou, N. Bouadma, M. Kafesaki, C. M. Soukoulis, and M. Agio, "Photonic-crystal ultrashort bends with improved transmission and low reflection at 1.55μm," Appl. Phys. Lett. 80, 547-549 (2002).
[CrossRef]

Stegun, I.

M. Abramovitz and I. Stegun, Handbook of Mathematical Functions (Dover, 1970).

Talneau, A.

A. Talneau, L. Le Gouezigou, N. Bouadma, M. Kafesaki, C. M. Soukoulis, and M. Agio, "Photonic-crystal ultrashort bends with improved transmission and low reflection at 1.55μm," Appl. Phys. Lett. 80, 547-549 (2002).
[CrossRef]

Tamamura, T.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, "Photonic crystals for micro lightwave circuits using wavelength-dependent angular beam steering," Appl. Phys. Lett. 74, 1370-1372 (1999).
[CrossRef]

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, "Superprism phenomena in photonic crystal," Phys. Rev. B 58, R10096-R10099 (1998).
[CrossRef]

Tayeb, G.

Teppe, F.

J. Torres, D. Coquillat, R. Legros, J. P. Lascaray, F. Teppe, D. Scalbert, D. Peyrade, Y. Chen, O. Briot, M. Le Vassor d'Yerville, E. Centeno, D. Cassagne, and J. P. Albert, "Giant second-harmonic generation in a one-dimensional GaN photonic crystal," Phys. Rev. B 69, 085105-085113 (2004).
[CrossRef]

Tomita, A.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, "Photonic crystals for micro lightwave circuits using wavelength-dependent angular beam steering," Appl. Phys. Lett. 74, 1370-1372 (1999).
[CrossRef]

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, "Superprism phenomena in photonic crystal," Phys. Rev. B 58, R10096-R10099 (1998).
[CrossRef]

Torres, J.

J. Torres, D. Coquillat, R. Legros, J. P. Lascaray, F. Teppe, D. Scalbert, D. Peyrade, Y. Chen, O. Briot, M. Le Vassor d'Yerville, E. Centeno, D. Cassagne, and J. P. Albert, "Giant second-harmonic generation in a one-dimensional GaN photonic crystal," Phys. Rev. B 69, 085105-085113 (2004).
[CrossRef]

Trull, J.

Valencia, C. I.

Vasson, A.

N. Antoine-Vincent, N. Natali, M. Mihailovic, A. Vasson, J. Leymarie, P. Disseix, D. Byrne, F. Semond, and J. Massies, "Determination of the refractive indices of AlN, GaN, and AlxGa1−xN grown on (111)Si substrates," J. Appl. Phys. 93, 5222-5226 (2003).
[CrossRef]

Vassor d'Yerville, M. Le

J. Torres, D. Coquillat, R. Legros, J. P. Lascaray, F. Teppe, D. Scalbert, D. Peyrade, Y. Chen, O. Briot, M. Le Vassor d'Yerville, E. Centeno, D. Cassagne, and J. P. Albert, "Giant second-harmonic generation in a one-dimensional GaN photonic crystal," Phys. Rev. B 69, 085105-085113 (2004).
[CrossRef]

Vecchi, G.

A. M. Malvezzi, G. Vecchi, M. Patrini, G. Guizetti, L. C. Andreani, F. Romanato, L. Businaro, E. DiFabrizio, A. Passaseo, and M. De Vittorio, "Resonant second-harmonic generation in a GaAs photonic crystal waveguide," Phys. Rev. B 68, 161306-161310 (2003).
[CrossRef]

Vidakovic, P.

Y. Dumeige, I. Sagnes, P. Monnier, P. Vidakovic, I. Abram, C. Mériadec, and A. Levenson, "Phase-matched frequency doubling at photonic band edges: efficiency scaling as the fifth power of the length," Phys. Rev. Lett. 89, 43901-43904 (2002).
[CrossRef]

G. D'Aguanno, M. Centini, M. Scalora, C. Sibilia, Y. Dumeige, P. Vidakovic, J. A. Levenson, M. J. Bloemer, C. M. Bowden, J. W. Haus, and M. Bertolotti, "Photonic band edge effects in finite structures and applications to chi(2) interactions," Phys. Rev. E 64, 016609-016618 (2001).
[CrossRef]

Vilaseca, R.

J. Martorell, R. Vilaseca, and R. Corbolan, "Second-harmonic generation in a photonic crystal," Appl. Phys. Lett. 70, 702-704 (1997).
[CrossRef]

J. Trull, R. Vilaseca, J. Martorell, and R. Cordobàn "Second-harmonic generation in local modes of a truncated periodic structure," Opt. Lett. 20, 1746-1750 (1995).
[CrossRef] [PubMed]

Villeneuve, P. R.

S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and H. A. Hauss, "Channel drop tunneling through localized states," Phys. Rev. Lett. 80, 960-963 (1998).
[CrossRef]

A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, "High transmission through sharp bends in photonic crystal waveguides," Phys. Rev. Lett. 77, 3787-3790 (1996).
[CrossRef] [PubMed]

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 structures," Phys. Rev. A 56, 3166-3174 (1997).
[CrossRef]

Vittorio, M. De

A. M. Malvezzi, G. Vecchi, M. Patrini, G. Guizetti, L. C. Andreani, F. Romanato, L. Businaro, E. DiFabrizio, A. Passaseo, and M. De Vittorio, "Resonant second-harmonic generation in a GaAs photonic crystal waveguide," Phys. Rev. B 68, 161306-161310 (2003).
[CrossRef]

Wang, H.

F. Ren, R. Li, C. Cheng, H. Wang, J. Qiu, J. Si, and K. Hirao, "Giant enhancement of second harmonic generation in a finite photonic crystal with a single defect and dual-localized modes," Phys. Rev. B 70, 245109-245113 (2004).
[CrossRef]

Wang, X.

B. Shi, Z. M. Jiang, X. F. Zhou, and X. Wang, "A two-dimensional nonlinear photonic crystal for strong second-harmonic generation," J. Appl. Phys. 91, 6769-6771 (2002).
[CrossRef]

Watanabe, K.

M. Yamada, N. Nada, M. Saitoh, and K. Watanabe, "First-order quasi-phase matched LiNbO3 waveguide periodically poled by applying an external field for efficient blue second-harmonic generation," Appl. Phys. Lett. 62, 435-436 (1993).
[CrossRef]

Winn, J.

J. D. Joannopoulos, R. Meade, and J. Winn, Photonic Crystals (Princeton U. Press, 1995).

Xie, P.

P. Xie and Z.-Q. Zhang, "Multifrequency gap solitons in nonlinear photonic crystals," Phys. Rev. Lett. 91, 213904-213908 (2003).
[CrossRef] [PubMed]

Yablonovitch, E.

E. Yablonovitch, "Inhibited spontaneous emission in solid-state physics and electronics," Phys. Rev. Lett. 58, 2059-2062 (1987).
[CrossRef] [PubMed]

Yamada, M.

M. Yamada, N. Nada, M. Saitoh, and K. Watanabe, "First-order quasi-phase matched LiNbO3 waveguide periodically poled by applying an external field for efficient blue second-harmonic generation," Appl. Phys. Lett. 62, 435-436 (1993).
[CrossRef]

Young, J. F.

A. R Cowan and J. F. Young, "Mode matching for second-harmonic generation in photonic crystal waveguides," Phys. Rev. B 65, 85106-85112 (2002).
[CrossRef]

Yousif, H. A.

Zhang, Z.-Q.

P. Xie and Z.-Q. Zhang, "Multifrequency gap solitons in nonlinear photonic crystals," Phys. Rev. Lett. 91, 213904-213908 (2003).
[CrossRef] [PubMed]

L.-M. Li and Z.-Q. Zhang, "Multiple-scattering approach to finite-sized photonic bandgap materials," Phys. Rev. B 58, 9587-9590 (1998).
[CrossRef]

Zhou, X. F.

B. Shi, Z. M. Jiang, X. F. Zhou, and X. Wang, "A two-dimensional nonlinear photonic crystal for strong second-harmonic generation," J. Appl. Phys. 91, 6769-6771 (2002).
[CrossRef]

Zhu, S. N.

S. N. Zhu, Y. Y. Zhu, and N. B. Ming, "Quasi-phase-matched third-harmonic generation in a quasi-periodic optical superlattice," Science 278, 843-846 (1997).
[CrossRef]

Zhu, Y. Y.

S. N. Zhu, Y. Y. Zhu, and N. B. Ming, "Quasi-phase-matched third-harmonic generation in a quasi-periodic optical superlattice," Science 278, 843-846 (1997).
[CrossRef]

Appl. Phys. B (1)

B. Momeni and B. A. Adibi, "Optimization of photonic crystal demultiplexers based on the superprism effect," Appl. Phys. B 77, 555-560 (2003).
[CrossRef]

Appl. Phys. Lett. (6)

J. Martorell, R. Vilaseca, and R. Corbolan, "Second-harmonic generation in a photonic crystal," Appl. Phys. Lett. 70, 702-704 (1997).
[CrossRef]

H. Schmidt, A. C. Abare, J. E. Bowers, S. P. Denbaars, and A. Imamoglu, "Large interband second-order susceptibilities in InxGa1−xN/GaN quantum wells," Appl. Phys. Lett. 75, 3611-3613 (1999).
[CrossRef]

A. L. Cabuz, E. Centeno, and D. Cassagne, "Superprism effect in bidimensional rectangular photonic crystals," Appl. Phys. Lett. 84, 2031-2033 (2004).
[CrossRef]

A. Talneau, L. Le Gouezigou, N. Bouadma, M. Kafesaki, C. M. Soukoulis, and M. Agio, "Photonic-crystal ultrashort bends with improved transmission and low reflection at 1.55μm," Appl. Phys. Lett. 80, 547-549 (2002).
[CrossRef]

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, "Photonic crystals for micro lightwave circuits using wavelength-dependent angular beam steering," Appl. Phys. Lett. 74, 1370-1372 (1999).
[CrossRef]

M. Yamada, N. Nada, M. Saitoh, and K. Watanabe, "First-order quasi-phase matched LiNbO3 waveguide periodically poled by applying an external field for efficient blue second-harmonic generation," Appl. Phys. Lett. 62, 435-436 (1993).
[CrossRef]

J. Appl. Phys. (2)

N. Antoine-Vincent, N. Natali, M. Mihailovic, A. Vasson, J. Leymarie, P. Disseix, D. Byrne, F. Semond, and J. Massies, "Determination of the refractive indices of AlN, GaN, and AlxGa1−xN grown on (111)Si substrates," J. Appl. Phys. 93, 5222-5226 (2003).
[CrossRef]

B. Shi, Z. M. Jiang, X. F. Zhou, and X. Wang, "A two-dimensional nonlinear photonic crystal for strong second-harmonic generation," J. Appl. Phys. 91, 6769-6771 (2002).
[CrossRef]

J. Opt. Soc. Am. A (3)

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

Opt. Express (3)

Opt. Lett. (4)

Photonics Nanostruct. Fundam. Appl. (1)

E. Ozbay, I. Bulu, K. Aydin, H. Caglayan, and K. Guven, "Physics and applications of photonic crystals," Photonics Nanostruct. Fundam. Appl. 2, 87-95 (2004).
[CrossRef]

Phys. Rev. A (1)

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 structures," Phys. Rev. A 56, 3166-3174 (1997).
[CrossRef]

Phys. Rev. B (7)

A. R Cowan and J. F. Young, "Mode matching for second-harmonic generation in photonic crystal waveguides," Phys. Rev. B 65, 85106-85112 (2002).
[CrossRef]

J. Torres, D. Coquillat, R. Legros, J. P. Lascaray, F. Teppe, D. Scalbert, D. Peyrade, Y. Chen, O. Briot, M. Le Vassor d'Yerville, E. Centeno, D. Cassagne, and J. P. Albert, "Giant second-harmonic generation in a one-dimensional GaN photonic crystal," Phys. Rev. B 69, 085105-085113 (2004).
[CrossRef]

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, "Superprism phenomena in photonic crystal," Phys. Rev. B 58, R10096-R10099 (1998).
[CrossRef]

F. Ren, R. Li, C. Cheng, H. Wang, J. Qiu, J. Si, and K. Hirao, "Giant enhancement of second harmonic generation in a finite photonic crystal with a single defect and dual-localized modes," Phys. Rev. B 70, 245109-245113 (2004).
[CrossRef]

A. M. Malvezzi, G. Vecchi, M. Patrini, G. Guizetti, L. C. Andreani, F. Romanato, L. Businaro, E. DiFabrizio, A. Passaseo, and M. De Vittorio, "Resonant second-harmonic generation in a GaAs photonic crystal waveguide," Phys. Rev. B 68, 161306-161310 (2003).
[CrossRef]

L.-M. Li and Z.-Q. Zhang, "Multiple-scattering approach to finite-sized photonic bandgap materials," Phys. Rev. B 58, 9587-9590 (1998).
[CrossRef]

E. Centeno and D. Felbacq, "Optical bistability in finite-size nonlinear bidimensional photonic crystals doped by a microcavity," Phys. Rev. B 62, R7683-R7686 (2000).
[CrossRef]

Phys. Rev. E (2)

G. D'Aguanno, M. Centini, M. Scalora, C. Sibilia, Y. Dumeige, P. Vidakovic, J. A. Levenson, M. J. Bloemer, C. M. Bowden, J. W. Haus, and M. Bertolotti, "Photonic band edge effects in finite structures and applications to chi(2) interactions," Phys. Rev. E 64, 016609-016618 (2001).
[CrossRef]

M. Centini, C. Sibilia, M. Scalora, G. D'Aguanno, M. Bertolotti, M. J. Bloemer, C. M. Bowden, and I. Nefedov, "Dispersive properties of finite one-dimensional photonic bandgap structures: applications to nonlinear quadratic interactions," Phys. Rev. E 60, 4891-4898 (1999).
[CrossRef]

Phys. Rev. Lett. (7)

Y. Dumeige, I. Sagnes, P. Monnier, P. Vidakovic, I. Abram, C. Mériadec, and A. Levenson, "Phase-matched frequency doubling at photonic band edges: efficiency scaling as the fifth power of the length," Phys. Rev. Lett. 89, 43901-43904 (2002).
[CrossRef]

V. Berger, "Nonlinear photonic crystals," Phys. Rev. Lett. 81, 4136-4139 (1998).
[CrossRef]

S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and H. A. Hauss, "Channel drop tunneling through localized states," Phys. Rev. Lett. 80, 960-963 (1998).
[CrossRef]

E. Yablonovitch, "Inhibited spontaneous emission in solid-state physics and electronics," Phys. Rev. Lett. 58, 2059-2062 (1987).
[CrossRef] [PubMed]

S. John, "Strong localization of photons in certain disordered dielectric superlattices," Phys. Rev. Lett. 58, 2486-2489 (1987).
[CrossRef] [PubMed]

A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, "High transmission through sharp bends in photonic crystal waveguides," Phys. Rev. Lett. 77, 3787-3790 (1996).
[CrossRef] [PubMed]

P. Xie and Z.-Q. Zhang, "Multifrequency gap solitons in nonlinear photonic crystals," Phys. Rev. Lett. 91, 213904-213908 (2003).
[CrossRef] [PubMed]

Physica B (1)

S. Noda, "Three-dimensional photonic crystals operating at optical wavelength region," Physica B 279, 142-149 (2000).
[CrossRef]

Science (1)

S. N. Zhu, Y. Y. Zhu, and N. B. Ming, "Quasi-phase-matched third-harmonic generation in a quasi-periodic optical superlattice," Science 278, 843-846 (1997).
[CrossRef]

Other (3)

C.M.Soukoulis, ed., Photonic Band Gap Materials, Vol. 315 of the NATO Advanced Study Institute Series E: Applied Sciences (Kluwer, 1996).

J. D. Joannopoulos, R. Meade, and J. Winn, Photonic Crystals (Princeton U. Press, 1995).

M. Abramovitz and I. Stegun, Handbook of Mathematical Functions (Dover, 1970).

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 (6)

Fig. 1
Fig. 1

Illustration of the second harmonic scattering problem. The gray area, D, depicts the nonlinear domain containing N d rods labeled C j . The coordinates of the rods are ( r j , φ j ) in the cylindrical basis represented by ( O , r , φ ) . The thick arrow represents the incident field F ω inc at the fundamental frequency that enlightens the set of rods.

Fig. 2
Fig. 2

The blue curve represents the IFCs for the fundamental wavelength λ 1 = 1518 nm . The black curves are the SH IFCs for λ 1 2 and for k 2 ω 2 . At points A and B the QPM conditions are fulfilled for the angle of incidence θ A = 8.3 ° and θ B = 21.7 ° . The blue and the black arrows represent the group velocities of the fundamental and the SH fields, respectively.

Fig. 3
Fig. 3

IFCs for the fundamental wavelength λ 2 = 1600 nm (blue curve) and for the half wavelength λ 2 2 (black curves). The blue and the black arrows represents the group velocities v g ( ω ) and v g ( 2 ω ) . The QPM conditions are satisfied at points C and D. At point C the incident angle is equal to θ A = 8.3 ° .

Fig. 4
Fig. 4

(a) Fundamental and (b) SH modulus of the electric fields for the wavelengths λ 1 and λ 1 2 , respectively. The incident angle is θ A = 8.3 ° , corresponding to the QPM conditions at points A. The dashed arrows indicate the direction of propagation of light inside the PCs and the black box represents the boundaries of the 2D PC.

Fig. 5
Fig. 5

(a) and (b) represent the modulus of the electric field at the wavelengths, λ 1 and λ 1 2 , respectively and for an angle θ B = 21.7 ° . These parameters correspond to the QPM conditions at point B.

Fig. 6
Fig. 6

(a) Fundamental and (b) SH for λ 2 and for an incident angle θ A = 8.3 ° . These conditions correspond to the quasi-phase-matched point C.

Equations (36)

Equations on this page are rendered with MathJax. Learn more.

ε ( r , ω ) = { ε j ( ω ) inside rod C j ε m ( ω ) outside rods .
χ ( 2 ) ( r , ω ) = { χ ( 2 ) ( ω ) for r D { C j } , j = [ 1 , , N D ] 0 elsewhere .
Δ E ( r , Ω ) + k Ω 2 ε ( r , Ω ) E ( r , Ω ) = k Ω 2 ε 0 P ( 2 ) ( r , Ω ) ,
Δ H ( r , Ω ) + k Ω 2 ε ( r , Ω ) H ( r , Ω ) = i Ω P ( 2 ) ( r , Ω ) .
P ( 2 ) ( r , ω ) = ε 0 χ ( 2 ) ( r , ω ) : E ( r , 2 ω ) E ( r , ω ) ,
P ( 2 ) ( r , 2 ω ) = ε 0 χ ( 2 ) ( r , 2 ω ) : E ( r , ω ) E ( r , ω ) .
Δ E z ( r , ω ) + k ω 2 ε ( r , ω ) E z ( r , ω ) = 0 ,
Δ E z ( r , 2 ω ) + k 2 ω 2 ε ( r , 2 ω ) E z ( r , 2 ω ) = k 2 ω 2 ε 0 P z ( 2 ) ( r , 2 ω ) ;
Δ H z ( r , ω ) + k ω 2 ε ( r , ω ) H z ( r , ω ) = 0 ,
Δ H z ( r , 2 ω ) + k 2 ω 2 ε ( r , 2 ω ) H z ( r , 2 ω ) = 2 i ω [ P ( 2 ) ( r , 2 ω ) ] e z ,
U ( r , ω ) = U inc ( r , ω ) + U s ( r , ω ) .
Δ U inc ( r , ω ) + k ω 2 ε m ( ω ) U inc ( r , ω ) = 0 .
U inc ( P , ω ) = n = + U j , n inc J n [ k ω ε m ( ω ) r j ( P ) ] e i n φ j ( P ) .
r j ( P ) R j , U s ( P , ω ) = n = + U j , n s H n ( 2 ) [ k ω ε m ( ω ) r j ( P ) ] e i n φ j ( P ) .
F j local = F j inc + 1 j T j , l F l s .
T j , l , n , q = exp [ i ( q n ) φ j l ] H n ( 2 ) ( k ω ε m r j l ) ,
F j s = S j F j local .
j = 1 N ( δ l , j I S l T j , l ) F j s = S j F j inc , l = [ 1 , N ] ,
F ω s = S ( ω ) F ω inc .
U ( P , ω ) = U inc ( P , ω ) + j = 1 N U j s ( P , ω ) .
U ( r , 2 ω ) = U source ( r , 2 ω ) + U s ( r , 2 ω ) .
r j ( P ) R j , U s ( P , 2 ω ) = n = + U j , n s H n ( 2 ) [ k ω ε m ( 2 ω ) r j ( P ) ] e i n φ j ( P ) .
Δ E z source ( r , 2 ω ) + k 2 ω 2 ε m ( 2 ω ) E z source ( r , 2 ω ) = k 2 ω 2 ε 0 P z ( 2 ) ( r , 2 ω ) ,
Δ H z source ( r , 2 ω ) + k 2 ω 2 ε m ( 2 ω ) H z source ( r , 2 ω ) = 2 i ω [ P ( 2 ) ( r , 2 ω ) ] e z .
E z source ( P , 2 ω ) = i 4 H 0 ( 2 ) [ k 2 ω ε m ( 2 ω ) r ( P ) ] * k 2 ω 2 ε 0 P z ( 2 ) [ r ( P ) , 2 ω ] ,
H z source ( P , 2 ω ) = ω 2 H 0 ( 2 ) [ k 2 ω ε m ( 2 ω ) r ( P ) ] * { P ( 2 ) [ r ( P ) , 2 ω ] } e z
U z , j source ( R j , 2 ω ) = n = + U j , n source J n ( k 2 ω ε m ( 2 ω ) R j ) e i n φ j ( R j ) ,
U j , n source = i k 2 ω 2 4 ε 0 Γ H n ( 2 ) [ k 2 ω ε m ( 2 ω ) r r j ] e i n φ j ( r r j ) P z ( 2 ) ( r , 2 ω ) d r ;
U j , n source = i k 2 ω 2 4 ε 0 Γ H n ( 2 ) ( k 2 ω ε m ( 2 ω ) r r j ) e i n φ j ( r r j ) [ r P ( 2 ) ( r , 2 ω ) ] e z d r .
F 2 ω s = S ( 2 ω ) F 2 ω source ,
U ( P , 2 ω ) = U source ( P , 2 ω ) + j = 1 N U j s ( P , 2 ω ) .
E z ( r , 2 ω ) ,
d E z ( r , 2 ω ) d r ;
H z ( r , 2 ω ) ,
1 ε ( r , 2 ω ) [ d H z ( r , 2 ω ) d r i 2 ω P φ ( 2 ) ( r , 2 ω ) ] .
n ( λ ) = a + b λ 2 ( λ 2 c 2 ) ,

Metrics