Abstract

Using the multiple-scale approach, we derive an analytical expression for the conversion efficiency of second-harmonic generation (SHG) in a one-dimensional photonic crystal. The results, obtained in the undepleted pump limit for the continuous-wave case, allow us to describe the role played by the feedback and the dispersion introduced by the periodic structure and hence to optimize the SHG process. Numerical simulations are then used to explore the pulsed pump case, proving that the obtained results retain their validity up to a pump field bandwidth of less than approximately 12% of the stack transmission bandwidth. Shorter pulses experience both a reduced conversion efficiency and shape distortions.

© 2003 Optical Society of America

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2002 (5)

A. Locatelli, F. M. Pigozzo, D. Modotto, A. D. Capobianco, and C. De Angelis, “Bidirectional beam propagation method for multilayered dielectrics with quadratic nonlinearity,” IEEE J. Sel. Top. Quantum Electron. 8, 440–447 (2002).
[CrossRef]

A. Locatelli, F. M. Pigozzo, D. Modotto, A. D. Capobianco, and C. De Angelis, “Novel bidirectional propagation method for quadratic nonlinear multilayers,” IEEE Photon. Technol. Lett. 14, 1536–1538 (2002).
[CrossRef]

S. Mookherjea and A. Yariv, “Second-harmonic generation with pulses in a coupled-resonator optical waveguide,” Phys. Rev. E 65, 026607 (2002).
[CrossRef]

G. D’Aguanno, M. Centini, M. Scalora, C. Sibilia, M. Bertolotti, M. J. Bloemer, and C. M. Bowden, “Generalized coupled-mode theory for χ(2) interactions in finite multilayered structures,” J. Opt. Soc. Am. B 19, 2111–2121 (2002).
[CrossRef]

J. W. Haus, B. Y. Soon, M. Scalora, C. Sibilia, and I. V. Mel’nikov, “Coupled-mode equations for Kerr media with periodically modulated linear and nonlinear coefficients,” J. Opt. Soc. Am. B 19, 2282–2291 (2002).
[CrossRef]

2001 (3)

C. De Angelis, F. Gringoli, M. Midrio, D. Modotto, J. S. Aitchison, and G. F. Nalesso, “Conversion efficiency for second-harmonic generation in photonic crystals,” J. Opt. Soc. Am. B 18, 348–351 (2001).
[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 χ(2) interactions,” Phys. Rev. E 64, 016609 (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]

2000 (3)

S. G. Johnson, P. R. Villeneuve, S. Fan, and J. D. Joannopoulos, “Linear waveguides in photonic-crystal slabs,” Phys. Rev. B 62, 8212–8222 (2000).
[CrossRef]

Y. Xu, R. K. Lee, and A. Yariv, “Propagation and second-harmonic generation of electromagnetic waves in a coupled resonator optical waveguide,” J. Opt. Soc. Am. B 17, 387–400 (2000).
[CrossRef]

T. Iizuka and C. M. de Sterke, “Corrections to coupled mode theory for deep gratings,” Phys. Rev. E 61, 4491–4499 (2000).
[CrossRef]

1999 (6)

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 band gap structures: applications to nonlinear quadratic interactions,” Phys. Rev. E 60, 4891–4898 (1999).
[CrossRef]

A. V. Balakin, V. A. Bushuev, N. I. Koroteev, B. I. Mantsyzov, I. A. Ozheredov, A. P. Shkurinov, D. Boucher, and P. Masselin, “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]

G. D’Aguanno, M. Centini, C. Sibilia, M. Bertolotti, M. Scalora, M. J. Bloemer, and C. M. Bowden, “Enhancement of χ(2) cascading processes in one-dimensional photonic bandgap structures,” Opt. Lett. 24, 1663–1665 (1999).
[CrossRef]

H. Rao, R. Scarmozzino, and R. M. Osgood, Jr., “A bidirectional beam propagation method for multiple dielectric interfaces,” IEEE Photon. Technol. Lett. 11, 830–832 (1999).
[CrossRef]

T. F. Krauss and R. M. De La Rue, “Photonic crystals in the optical regime—past, present and future,” Prog. Quantum Electron. 23, 51–96 (1999).
[CrossRef]

S. G. Johnson, S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and L. A. Kolodziejski, “Guided modes in photonic crystal slabs,” Phys. Rev. B 60, 5751–5758 (1999).
[CrossRef]

1998 (3)

A. Arraf and C. M. de Sterke, “Coupled-mode equations for quadratically nonlinear deep gratings,” Phys. Rev. E 58, 7951–7958 (1998).
[CrossRef]

J. W. Haus, R. Viswanathan, M. Scalora, A. G. Kalocsai, J. D. Cole, and J. Theimer, “Enhanced second-harmonic generation in media with a weak periodicity,” Phys. Rev. A 57, 2120–2128 (1998).
[CrossRef]

K. Busch and S. John, “Photonic band gap formation in certain self-organizing systems,” Phys. Rev. E 58, 3896–3908 (1998).
[CrossRef]

1997 (5)

J. D. Joannopoulos, P. R. Villeneuve, and S. Fan, “Photonic crystals: putting a new twist on light,” Nature (London) 387, 143–149 (1997).
[CrossRef]

D. Labilloy, H. Benitsy, C. Weisbuch, T. F. Krauss, R. M. De La Rue, V. Bardinal, R. Houdré, U. Oesterle, D. Cassagne, and C. Jouanin, “Quantitative measurement of transmission, reflection, and diffraction of two-dimensional photonic band gap structures at near-infrared wavelengths,” Phys. Rev. Lett. 79, 4147–4150 (1997).
[CrossRef]

J. S. Aitchison, D. C. Hutchings, J. U. Kang, G. I. Stegeman, and A. Villeneuve, “Nonlinear optical properties of AlGaAs at the half band gap,” IEEE J. Quantum Electron. 33, 341–348 (1997).
[CrossRef]

R. M. Joseph and A. Taflove, “FDTD Maxwell’s equations models for nonlinear electrodynamics and optics,” IEEE Trans. Antennas Propag. 45, 364–374 (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]

1996 (2)

T. F. Krauss, R. M. De La Rue, and S. Brand, “Two-dimensional photonic bandgap structures operating at near-infrared wavelengths,” Nature (London) 383, 699–702 (1996).
[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,” Phys. Rev. Lett. 77, 3787–3790 (1996).
[CrossRef] [PubMed]

1994 (1)

R. D. Meade, A. Devenyl, J. D. Joannopoulos, O. L. Alerhand, D. A. Smith, and K. Kash, “Novel applications of photonic band gap materials: low-loss bends and high Q cavities,” J. Appl. Phys. 75, 4753–4755 (1994).
[CrossRef]

1993 (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]

1985 (1)

S. Adachi, “Ga As, Al As and AlxGa1−xAs: material parameters for use in research and device applications,” J. Appl. Phys. 58, R1–R29 (1985).
[CrossRef]

1977 (1)

1976 (1)

J. P. van der Ziel, M. Ilegemes, P. W. Foy, and R. M. Mikulyak, “Phase-matched second harmonic generation in a periodic AlGaAs waveguide,” Appl. Phys. Lett. 29, 775–777 (1976).
[CrossRef]

1973 (1)

C. L. Tang and P. P. Bey, “Phase matching in second harmonic generation using artificial periodic structures,” IEEE J. Quantum Electron. QE-9, 9–17 (1973).
[CrossRef]

1972 (1)

S. Somekh and A. Yariv, “Phase-matchable nonlinear optical interactions in periodic thin films,” Appl. Phys. Lett. 21, 140–141 (1972).
[CrossRef]

1970 (1)

N. Bloembergen and A. J. Sievers, “Nonlinear optical properties of periodic laminar structures,” Appl. Phys. Lett. 17, 483–485 (1970).
[CrossRef]

Adachi, S.

S. Adachi, “Ga As, Al As and AlxGa1−xAs: material parameters for use in research and device applications,” J. Appl. Phys. 58, R1–R29 (1985).
[CrossRef]

Aitchison, J. S.

C. De Angelis, F. Gringoli, M. Midrio, D. Modotto, J. S. Aitchison, and G. F. Nalesso, “Conversion efficiency for second-harmonic generation in photonic crystals,” J. Opt. Soc. Am. B 18, 348–351 (2001).
[CrossRef]

J. S. Aitchison, D. C. Hutchings, J. U. Kang, G. I. Stegeman, and A. Villeneuve, “Nonlinear optical properties of AlGaAs at the half band gap,” IEEE J. Quantum Electron. 33, 341–348 (1997).
[CrossRef]

Alerhand, O. L.

R. D. Meade, A. Devenyl, J. D. Joannopoulos, O. L. Alerhand, D. A. Smith, and K. Kash, “Novel applications of photonic band gap materials: low-loss bends and high Q cavities,” J. Appl. Phys. 75, 4753–4755 (1994).
[CrossRef]

Arraf, A.

A. Arraf and C. M. de Sterke, “Coupled-mode equations for quadratically nonlinear deep gratings,” Phys. Rev. E 58, 7951–7958 (1998).
[CrossRef]

Balakin, A. V.

Bardinal, V.

D. Labilloy, H. Benitsy, C. Weisbuch, T. F. Krauss, R. M. De La Rue, V. Bardinal, R. Houdré, U. Oesterle, D. Cassagne, and C. Jouanin, “Quantitative measurement of transmission, reflection, and diffraction of two-dimensional photonic band gap structures at near-infrared wavelengths,” Phys. Rev. Lett. 79, 4147–4150 (1997).
[CrossRef]

Benitsy, H.

D. Labilloy, H. Benitsy, C. Weisbuch, T. F. Krauss, R. M. De La Rue, V. Bardinal, R. Houdré, U. Oesterle, D. Cassagne, and C. Jouanin, “Quantitative measurement of transmission, reflection, and diffraction of two-dimensional photonic band gap structures at near-infrared wavelengths,” Phys. Rev. Lett. 79, 4147–4150 (1997).
[CrossRef]

Bertolotti, M.

G. D’Aguanno, M. Centini, M. Scalora, C. Sibilia, M. Bertolotti, M. J. Bloemer, and C. M. Bowden, “Generalized coupled-mode theory for χ(2) interactions in finite multilayered structures,” J. Opt. Soc. Am. B 19, 2111–2121 (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 χ(2) interactions,” Phys. Rev. E 64, 016609 (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 band gap structures: applications to nonlinear quadratic interactions,” Phys. Rev. E 60, 4891–4898 (1999).
[CrossRef]

G. D’Aguanno, M. Centini, C. Sibilia, M. Bertolotti, M. Scalora, M. J. Bloemer, and C. M. Bowden, “Enhancement of χ(2) cascading processes in one-dimensional photonic bandgap structures,” Opt. Lett. 24, 1663–1665 (1999).
[CrossRef]

Bey, P. P.

C. L. Tang and P. P. Bey, “Phase matching in second harmonic generation using artificial periodic structures,” IEEE J. Quantum Electron. QE-9, 9–17 (1973).
[CrossRef]

Bloembergen, N.

N. Bloembergen and A. J. Sievers, “Nonlinear optical properties of periodic laminar structures,” Appl. Phys. Lett. 17, 483–485 (1970).
[CrossRef]

Bloemer, M. J.

G. D’Aguanno, M. Centini, M. Scalora, C. Sibilia, M. Bertolotti, M. J. Bloemer, and C. M. Bowden, “Generalized coupled-mode theory for χ(2) interactions in finite multilayered structures,” J. Opt. Soc. Am. B 19, 2111–2121 (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 χ(2) interactions,” Phys. Rev. E 64, 016609 (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 band gap structures: applications to nonlinear quadratic interactions,” Phys. Rev. E 60, 4891–4898 (1999).
[CrossRef]

G. D’Aguanno, M. Centini, C. Sibilia, M. Bertolotti, M. Scalora, M. J. Bloemer, and C. M. Bowden, “Enhancement of χ(2) cascading processes in one-dimensional photonic bandgap structures,” Opt. Lett. 24, 1663–1665 (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]

Boucher, D.

Bowden, C. M.

G. D’Aguanno, M. Centini, M. Scalora, C. Sibilia, M. Bertolotti, M. J. Bloemer, and C. M. Bowden, “Generalized coupled-mode theory for χ(2) interactions in finite multilayered structures,” J. Opt. Soc. Am. B 19, 2111–2121 (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 χ(2) interactions,” Phys. Rev. E 64, 016609 (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 band gap structures: applications to nonlinear quadratic interactions,” Phys. Rev. E 60, 4891–4898 (1999).
[CrossRef]

G. D’Aguanno, M. Centini, C. Sibilia, M. Bertolotti, M. Scalora, M. J. Bloemer, and C. M. Bowden, “Enhancement of χ(2) cascading processes in one-dimensional photonic bandgap structures,” Opt. Lett. 24, 1663–1665 (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]

Brand, S.

T. F. Krauss, R. M. De La Rue, and S. Brand, “Two-dimensional photonic bandgap structures operating at near-infrared wavelengths,” Nature (London) 383, 699–702 (1996).
[CrossRef]

Busch, K.

K. Busch and S. John, “Photonic band gap formation in certain self-organizing systems,” Phys. Rev. E 58, 3896–3908 (1998).
[CrossRef]

Bushuev, V. A.

Capobianco, A. D.

A. Locatelli, F. M. Pigozzo, D. Modotto, A. D. Capobianco, and C. De Angelis, “Novel bidirectional propagation method for quadratic nonlinear multilayers,” IEEE Photon. Technol. Lett. 14, 1536–1538 (2002).
[CrossRef]

A. Locatelli, F. M. Pigozzo, D. Modotto, A. D. Capobianco, and C. De Angelis, “Bidirectional beam propagation method for multilayered dielectrics with quadratic nonlinearity,” IEEE J. Sel. Top. Quantum Electron. 8, 440–447 (2002).
[CrossRef]

Cassagne, D.

D. Labilloy, H. Benitsy, C. Weisbuch, T. F. Krauss, R. M. De La Rue, V. Bardinal, R. Houdré, U. Oesterle, D. Cassagne, and C. Jouanin, “Quantitative measurement of transmission, reflection, and diffraction of two-dimensional photonic band gap structures at near-infrared wavelengths,” Phys. Rev. Lett. 79, 4147–4150 (1997).
[CrossRef]

Centini, M.

G. D’Aguanno, M. Centini, M. Scalora, C. Sibilia, M. Bertolotti, M. J. Bloemer, and C. M. Bowden, “Generalized coupled-mode theory for χ(2) interactions in finite multilayered structures,” J. Opt. Soc. Am. B 19, 2111–2121 (2002).
[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]

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 χ(2) interactions,” Phys. Rev. E 64, 016609 (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 band gap structures: applications to nonlinear quadratic interactions,” Phys. Rev. E 60, 4891–4898 (1999).
[CrossRef]

G. D’Aguanno, M. Centini, C. Sibilia, M. Bertolotti, M. Scalora, M. J. Bloemer, and C. M. Bowden, “Enhancement of χ(2) cascading processes in one-dimensional photonic bandgap structures,” Opt. Lett. 24, 1663–1665 (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,” Phys. Rev. Lett. 77, 3787–3790 (1996).
[CrossRef] [PubMed]

Cole, J. D.

J. W. Haus, R. Viswanathan, M. Scalora, A. G. Kalocsai, J. D. Cole, and J. Theimer, “Enhanced second-harmonic generation in media with a weak periodicity,” Phys. Rev. A 57, 2120–2128 (1998).
[CrossRef]

D’Aguanno, G.

G. D’Aguanno, M. Centini, M. Scalora, C. Sibilia, M. Bertolotti, M. J. Bloemer, and C. M. Bowden, “Generalized coupled-mode theory for χ(2) interactions in finite multilayered structures,” J. Opt. Soc. Am. B 19, 2111–2121 (2002).
[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]

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 χ(2) interactions,” Phys. Rev. E 64, 016609 (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 band gap structures: applications to nonlinear quadratic interactions,” Phys. Rev. E 60, 4891–4898 (1999).
[CrossRef]

G. D’Aguanno, M. Centini, C. Sibilia, M. Bertolotti, M. Scalora, M. J. Bloemer, and C. M. Bowden, “Enhancement of χ(2) cascading processes in one-dimensional photonic bandgap structures,” Opt. Lett. 24, 1663–1665 (1999).
[CrossRef]

De Angelis, C.

A. Locatelli, F. M. Pigozzo, D. Modotto, A. D. Capobianco, and C. De Angelis, “Novel bidirectional propagation method for quadratic nonlinear multilayers,” IEEE Photon. Technol. Lett. 14, 1536–1538 (2002).
[CrossRef]

A. Locatelli, F. M. Pigozzo, D. Modotto, A. D. Capobianco, and C. De Angelis, “Bidirectional beam propagation method for multilayered dielectrics with quadratic nonlinearity,” IEEE J. Sel. Top. Quantum Electron. 8, 440–447 (2002).
[CrossRef]

C. De Angelis, F. Gringoli, M. Midrio, D. Modotto, J. S. Aitchison, and G. F. Nalesso, “Conversion efficiency for second-harmonic generation in photonic crystals,” J. Opt. Soc. Am. B 18, 348–351 (2001).
[CrossRef]

De La Rue, R. M.

T. F. Krauss and R. M. De La Rue, “Photonic crystals in the optical regime—past, present and future,” Prog. Quantum Electron. 23, 51–96 (1999).
[CrossRef]

D. Labilloy, H. Benitsy, C. Weisbuch, T. F. Krauss, R. M. De La Rue, V. Bardinal, R. Houdré, U. Oesterle, D. Cassagne, and C. Jouanin, “Quantitative measurement of transmission, reflection, and diffraction of two-dimensional photonic band gap structures at near-infrared wavelengths,” Phys. Rev. Lett. 79, 4147–4150 (1997).
[CrossRef]

T. F. Krauss, R. M. De La Rue, and S. Brand, “Two-dimensional photonic bandgap structures operating at near-infrared wavelengths,” Nature (London) 383, 699–702 (1996).
[CrossRef]

de Sterke, C. M.

T. Iizuka and C. M. de Sterke, “Corrections to coupled mode theory for deep gratings,” Phys. Rev. E 61, 4491–4499 (2000).
[CrossRef]

A. Arraf and C. M. de Sterke, “Coupled-mode equations for quadratically nonlinear deep gratings,” Phys. Rev. E 58, 7951–7958 (1998).
[CrossRef]

Devenyl, A.

R. D. Meade, A. Devenyl, J. D. Joannopoulos, O. L. Alerhand, D. A. Smith, and K. Kash, “Novel applications of photonic band gap materials: low-loss bends and high Q cavities,” J. Appl. Phys. 75, 4753–4755 (1994).
[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.

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 χ(2) interactions,” Phys. Rev. E 64, 016609 (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]

Fan, S.

S. G. Johnson, P. R. Villeneuve, S. Fan, and J. D. Joannopoulos, “Linear waveguides in photonic-crystal slabs,” Phys. Rev. B 62, 8212–8222 (2000).
[CrossRef]

S. G. Johnson, S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and L. A. Kolodziejski, “Guided modes in photonic crystal slabs,” Phys. Rev. B 60, 5751–5758 (1999).
[CrossRef]

J. D. Joannopoulos, P. R. Villeneuve, and S. Fan, “Photonic crystals: putting a new twist on light,” Nature (London) 387, 143–149 (1997).
[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,” Phys. Rev. Lett. 77, 3787–3790 (1996).
[CrossRef] [PubMed]

Foy, P. W.

J. P. van der Ziel, M. Ilegemes, P. W. Foy, and R. M. Mikulyak, “Phase-matched second harmonic generation in a periodic AlGaAs waveguide,” Appl. Phys. Lett. 29, 775–777 (1976).
[CrossRef]

Gringoli, F.

Haus, J. W.

J. W. Haus, B. Y. Soon, M. Scalora, C. Sibilia, and I. V. Mel’nikov, “Coupled-mode equations for Kerr media with periodically modulated linear and nonlinear coefficients,” J. Opt. Soc. Am. B 19, 2282–2291 (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 χ(2) interactions,” Phys. Rev. E 64, 016609 (2001).
[CrossRef]

J. W. Haus, R. Viswanathan, M. Scalora, A. G. Kalocsai, J. D. Cole, and J. Theimer, “Enhanced second-harmonic generation in media with a weak periodicity,” Phys. Rev. A 57, 2120–2128 (1998).
[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]

Hong, C. S.

Houdré, R.

D. Labilloy, H. Benitsy, C. Weisbuch, T. F. Krauss, R. M. De La Rue, V. Bardinal, R. Houdré, U. Oesterle, D. Cassagne, and C. Jouanin, “Quantitative measurement of transmission, reflection, and diffraction of two-dimensional photonic band gap structures at near-infrared wavelengths,” Phys. Rev. Lett. 79, 4147–4150 (1997).
[CrossRef]

Hutchings, D. C.

J. S. Aitchison, D. C. Hutchings, J. U. Kang, G. I. Stegeman, and A. Villeneuve, “Nonlinear optical properties of AlGaAs at the half band gap,” IEEE J. Quantum Electron. 33, 341–348 (1997).
[CrossRef]

Iizuka, T.

T. Iizuka and C. M. de Sterke, “Corrections to coupled mode theory for deep gratings,” Phys. Rev. E 61, 4491–4499 (2000).
[CrossRef]

Ilegemes, M.

J. P. van der Ziel, M. Ilegemes, P. W. Foy, and R. M. Mikulyak, “Phase-matched second harmonic generation in a periodic AlGaAs waveguide,” Appl. Phys. Lett. 29, 775–777 (1976).
[CrossRef]

Joannopoulos, J. D.

S. G. Johnson, P. R. Villeneuve, S. Fan, and J. D. Joannopoulos, “Linear waveguides in photonic-crystal slabs,” Phys. Rev. B 62, 8212–8222 (2000).
[CrossRef]

S. G. Johnson, S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and L. A. Kolodziejski, “Guided modes in photonic crystal slabs,” Phys. Rev. B 60, 5751–5758 (1999).
[CrossRef]

J. D. Joannopoulos, P. R. Villeneuve, and S. Fan, “Photonic crystals: putting a new twist on light,” Nature (London) 387, 143–149 (1997).
[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,” Phys. Rev. Lett. 77, 3787–3790 (1996).
[CrossRef] [PubMed]

R. D. Meade, A. Devenyl, J. D. Joannopoulos, O. L. Alerhand, D. A. Smith, and K. Kash, “Novel applications of photonic band gap materials: low-loss bends and high Q cavities,” J. Appl. Phys. 75, 4753–4755 (1994).
[CrossRef]

John, S.

K. Busch and S. John, “Photonic band gap formation in certain self-organizing systems,” Phys. Rev. E 58, 3896–3908 (1998).
[CrossRef]

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

Johnson, S. G.

S. G. Johnson, P. R. Villeneuve, S. Fan, and J. D. Joannopoulos, “Linear waveguides in photonic-crystal slabs,” Phys. Rev. B 62, 8212–8222 (2000).
[CrossRef]

S. G. Johnson, S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and L. A. Kolodziejski, “Guided modes in photonic crystal slabs,” Phys. Rev. B 60, 5751–5758 (1999).
[CrossRef]

Joseph, R. M.

R. M. Joseph and A. Taflove, “FDTD Maxwell’s equations models for nonlinear electrodynamics and optics,” IEEE Trans. Antennas Propag. 45, 364–374 (1997).
[CrossRef]

Jouanin, C.

D. Labilloy, H. Benitsy, C. Weisbuch, T. F. Krauss, R. M. De La Rue, V. Bardinal, R. Houdré, U. Oesterle, D. Cassagne, and C. Jouanin, “Quantitative measurement of transmission, reflection, and diffraction of two-dimensional photonic band gap structures at near-infrared wavelengths,” Phys. Rev. Lett. 79, 4147–4150 (1997).
[CrossRef]

Kalocsai, A. G.

J. W. Haus, R. Viswanathan, M. Scalora, A. G. Kalocsai, J. D. Cole, and J. Theimer, “Enhanced second-harmonic generation in media with a weak periodicity,” Phys. Rev. A 57, 2120–2128 (1998).
[CrossRef]

Kang, J. U.

J. S. Aitchison, D. C. Hutchings, J. U. Kang, G. I. Stegeman, and A. Villeneuve, “Nonlinear optical properties of AlGaAs at the half band gap,” IEEE J. Quantum Electron. 33, 341–348 (1997).
[CrossRef]

Kash, K.

R. D. Meade, A. Devenyl, J. D. Joannopoulos, O. L. Alerhand, D. A. Smith, and K. Kash, “Novel applications of photonic band gap materials: low-loss bends and high Q cavities,” J. Appl. Phys. 75, 4753–4755 (1994).
[CrossRef]

Kolodziejski, L. A.

S. G. Johnson, S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and L. A. Kolodziejski, “Guided modes in photonic crystal slabs,” Phys. Rev. B 60, 5751–5758 (1999).
[CrossRef]

Koroteev, N. I.

Krauss, T. F.

T. F. Krauss and R. M. De La Rue, “Photonic crystals in the optical regime—past, present and future,” Prog. Quantum Electron. 23, 51–96 (1999).
[CrossRef]

D. Labilloy, H. Benitsy, C. Weisbuch, T. F. Krauss, R. M. De La Rue, V. Bardinal, R. Houdré, U. Oesterle, D. Cassagne, and C. Jouanin, “Quantitative measurement of transmission, reflection, and diffraction of two-dimensional photonic band gap structures at near-infrared wavelengths,” Phys. Rev. Lett. 79, 4147–4150 (1997).
[CrossRef]

T. F. Krauss, R. M. De La Rue, and S. Brand, “Two-dimensional photonic bandgap structures operating at near-infrared wavelengths,” Nature (London) 383, 699–702 (1996).
[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,” Phys. Rev. Lett. 77, 3787–3790 (1996).
[CrossRef] [PubMed]

Labilloy, D.

D. Labilloy, H. Benitsy, C. Weisbuch, T. F. Krauss, R. M. De La Rue, V. Bardinal, R. Houdré, U. Oesterle, D. Cassagne, and C. Jouanin, “Quantitative measurement of transmission, reflection, and diffraction of two-dimensional photonic band gap structures at near-infrared wavelengths,” Phys. Rev. Lett. 79, 4147–4150 (1997).
[CrossRef]

Lee, R. K.

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]

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 χ(2) interactions,” Phys. Rev. E 64, 016609 (2001).
[CrossRef]

Locatelli, A.

A. Locatelli, F. M. Pigozzo, D. Modotto, A. D. Capobianco, and C. De Angelis, “Bidirectional beam propagation method for multilayered dielectrics with quadratic nonlinearity,” IEEE J. Sel. Top. Quantum Electron. 8, 440–447 (2002).
[CrossRef]

A. Locatelli, F. M. Pigozzo, D. Modotto, A. D. Capobianco, and C. De Angelis, “Novel bidirectional propagation method for quadratic nonlinear multilayers,” IEEE Photon. Technol. Lett. 14, 1536–1538 (2002).
[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]

Mantsyzov, B. I.

Masselin, P.

Meade, R. D.

R. D. Meade, A. Devenyl, J. D. Joannopoulos, O. L. Alerhand, D. A. Smith, and K. Kash, “Novel applications of photonic band gap materials: low-loss bends and high Q cavities,” J. Appl. Phys. 75, 4753–4755 (1994).
[CrossRef]

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,” Phys. Rev. Lett. 77, 3787–3790 (1996).
[CrossRef] [PubMed]

Mel’nikov, I. V.

Midrio, M.

Mikulyak, R. M.

J. P. van der Ziel, M. Ilegemes, P. W. Foy, and R. M. Mikulyak, “Phase-matched second harmonic generation in a periodic AlGaAs waveguide,” Appl. Phys. Lett. 29, 775–777 (1976).
[CrossRef]

Modotto, D.

A. Locatelli, F. M. Pigozzo, D. Modotto, A. D. Capobianco, and C. De Angelis, “Novel bidirectional propagation method for quadratic nonlinear multilayers,” IEEE Photon. Technol. Lett. 14, 1536–1538 (2002).
[CrossRef]

A. Locatelli, F. M. Pigozzo, D. Modotto, A. D. Capobianco, and C. De Angelis, “Bidirectional beam propagation method for multilayered dielectrics with quadratic nonlinearity,” IEEE J. Sel. Top. Quantum Electron. 8, 440–447 (2002).
[CrossRef]

C. De Angelis, F. Gringoli, M. Midrio, D. Modotto, J. S. Aitchison, and G. F. Nalesso, “Conversion efficiency for second-harmonic generation in photonic crystals,” J. Opt. Soc. Am. B 18, 348–351 (2001).
[CrossRef]

Mookherjea, S.

S. Mookherjea and A. Yariv, “Second-harmonic generation with pulses in a coupled-resonator optical waveguide,” Phys. Rev. E 65, 026607 (2002).
[CrossRef]

Nalesso, G. F.

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 band gap structures: applications to nonlinear quadratic interactions,” Phys. Rev. E 60, 4891–4898 (1999).
[CrossRef]

Oesterle, U.

D. Labilloy, H. Benitsy, C. Weisbuch, T. F. Krauss, R. M. De La Rue, V. Bardinal, R. Houdré, U. Oesterle, D. Cassagne, and C. Jouanin, “Quantitative measurement of transmission, reflection, and diffraction of two-dimensional photonic band gap structures at near-infrared wavelengths,” Phys. Rev. Lett. 79, 4147–4150 (1997).
[CrossRef]

Osgood Jr., R. M.

H. Rao, R. Scarmozzino, and R. M. Osgood, Jr., “A bidirectional beam propagation method for multiple dielectric interfaces,” IEEE Photon. Technol. Lett. 11, 830–832 (1999).
[CrossRef]

Ozheredov, I. A.

Pigozzo, F. M.

A. Locatelli, F. M. Pigozzo, D. Modotto, A. D. Capobianco, and C. De Angelis, “Novel bidirectional propagation method for quadratic nonlinear multilayers,” IEEE Photon. Technol. Lett. 14, 1536–1538 (2002).
[CrossRef]

A. Locatelli, F. M. Pigozzo, D. Modotto, A. D. Capobianco, and C. De Angelis, “Bidirectional beam propagation method for multilayered dielectrics with quadratic nonlinearity,” IEEE J. Sel. Top. Quantum Electron. 8, 440–447 (2002).
[CrossRef]

Rao, H.

H. Rao, R. Scarmozzino, and R. M. Osgood, Jr., “A bidirectional beam propagation method for multiple dielectric interfaces,” IEEE Photon. Technol. Lett. 11, 830–832 (1999).
[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.

J. W. Haus, B. Y. Soon, M. Scalora, C. Sibilia, and I. V. Mel’nikov, “Coupled-mode equations for Kerr media with periodically modulated linear and nonlinear coefficients,” J. Opt. Soc. Am. B 19, 2282–2291 (2002).
[CrossRef]

G. D’Aguanno, M. Centini, M. Scalora, C. Sibilia, M. Bertolotti, M. J. Bloemer, and C. M. Bowden, “Generalized coupled-mode theory for χ(2) interactions in finite multilayered structures,” J. Opt. Soc. Am. B 19, 2111–2121 (2002).
[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]

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 χ(2) interactions,” Phys. Rev. E 64, 016609 (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 band gap structures: applications to nonlinear quadratic interactions,” Phys. Rev. E 60, 4891–4898 (1999).
[CrossRef]

G. D’Aguanno, M. Centini, C. Sibilia, M. Bertolotti, M. Scalora, M. J. Bloemer, and C. M. Bowden, “Enhancement of χ(2) cascading processes in one-dimensional photonic bandgap structures,” Opt. Lett. 24, 1663–1665 (1999).
[CrossRef]

J. W. Haus, R. Viswanathan, M. Scalora, A. G. Kalocsai, J. D. Cole, and J. Theimer, “Enhanced second-harmonic generation in media with a weak periodicity,” Phys. Rev. A 57, 2120–2128 (1998).
[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]

Scarmozzino, R.

H. Rao, R. Scarmozzino, and R. M. Osgood, Jr., “A bidirectional beam propagation method for multiple dielectric interfaces,” IEEE Photon. Technol. Lett. 11, 830–832 (1999).
[CrossRef]

Shkurinov, A. P.

Sibilia, C.

G. D’Aguanno, M. Centini, M. Scalora, C. Sibilia, M. Bertolotti, M. J. Bloemer, and C. M. Bowden, “Generalized coupled-mode theory for χ(2) interactions in finite multilayered structures,” J. Opt. Soc. Am. B 19, 2111–2121 (2002).
[CrossRef]

J. W. Haus, B. Y. Soon, M. Scalora, C. Sibilia, and I. V. Mel’nikov, “Coupled-mode equations for Kerr media with periodically modulated linear and nonlinear coefficients,” J. Opt. Soc. Am. B 19, 2282–2291 (2002).
[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]

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 χ(2) interactions,” Phys. Rev. E 64, 016609 (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 band gap structures: applications to nonlinear quadratic interactions,” Phys. Rev. E 60, 4891–4898 (1999).
[CrossRef]

G. D’Aguanno, M. Centini, C. Sibilia, M. Bertolotti, M. Scalora, M. J. Bloemer, and C. M. Bowden, “Enhancement of χ(2) cascading processes in one-dimensional photonic bandgap structures,” Opt. Lett. 24, 1663–1665 (1999).
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Sievers, A. J.

N. Bloembergen and A. J. Sievers, “Nonlinear optical properties of periodic laminar structures,” Appl. Phys. Lett. 17, 483–485 (1970).
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Smith, D. A.

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[CrossRef]

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[CrossRef]

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C. L. Tang and P. P. Bey, “Phase matching in second harmonic generation using artificial periodic structures,” IEEE J. Quantum Electron. QE-9, 9–17 (1973).
[CrossRef]

Theimer, J.

J. W. Haus, R. Viswanathan, M. Scalora, A. G. Kalocsai, J. D. Cole, and J. Theimer, “Enhanced second-harmonic generation in media with a weak periodicity,” Phys. Rev. A 57, 2120–2128 (1998).
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J. P. van der Ziel, M. Ilegemes, P. W. Foy, and R. M. Mikulyak, “Phase-matched second harmonic generation in a periodic AlGaAs waveguide,” Appl. Phys. Lett. 29, 775–777 (1976).
[CrossRef]

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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 χ(2) interactions,” Phys. Rev. E 64, 016609 (2001).
[CrossRef]

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J. S. Aitchison, D. C. Hutchings, J. U. Kang, G. I. Stegeman, and A. Villeneuve, “Nonlinear optical properties of AlGaAs at the half band gap,” IEEE J. Quantum Electron. 33, 341–348 (1997).
[CrossRef]

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S. G. Johnson, P. R. Villeneuve, S. Fan, and J. D. Joannopoulos, “Linear waveguides in photonic-crystal slabs,” Phys. Rev. B 62, 8212–8222 (2000).
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J. D. Joannopoulos, P. R. Villeneuve, and S. Fan, “Photonic crystals: putting a new twist on light,” Nature (London) 387, 143–149 (1997).
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A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “High transmission through sharp bends in photonic crystal,” Phys. Rev. Lett. 77, 3787–3790 (1996).
[CrossRef] [PubMed]

Viswanathan, R.

J. W. Haus, R. Viswanathan, M. Scalora, A. G. Kalocsai, J. D. Cole, and J. Theimer, “Enhanced second-harmonic generation in media with a weak periodicity,” Phys. Rev. A 57, 2120–2128 (1998).
[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]

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D. Labilloy, H. Benitsy, C. Weisbuch, T. F. Krauss, R. M. De La Rue, V. Bardinal, R. Houdré, U. Oesterle, D. Cassagne, and C. Jouanin, “Quantitative measurement of transmission, reflection, and diffraction of two-dimensional photonic band gap structures at near-infrared wavelengths,” Phys. Rev. Lett. 79, 4147–4150 (1997).
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S. Mookherjea and A. Yariv, “Second-harmonic generation with pulses in a coupled-resonator optical waveguide,” Phys. Rev. E 65, 026607 (2002).
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S. Somekh and A. Yariv, “Phase-matchable nonlinear optical interactions in periodic thin films,” Appl. Phys. Lett. 21, 140–141 (1972).
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Appl. Phys. Lett. (4)

J. P. van der Ziel, M. Ilegemes, P. W. Foy, and R. M. Mikulyak, “Phase-matched second harmonic generation in a periodic AlGaAs waveguide,” Appl. Phys. Lett. 29, 775–777 (1976).
[CrossRef]

N. Bloembergen and A. J. Sievers, “Nonlinear optical properties of periodic laminar structures,” Appl. Phys. Lett. 17, 483–485 (1970).
[CrossRef]

S. Somekh and A. Yariv, “Phase-matchable nonlinear optical interactions in periodic thin films,” Appl. Phys. Lett. 21, 140–141 (1972).
[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]

IEEE J. Quantum Electron. (2)

J. S. Aitchison, D. C. Hutchings, J. U. Kang, G. I. Stegeman, and A. Villeneuve, “Nonlinear optical properties of AlGaAs at the half band gap,” IEEE J. Quantum Electron. 33, 341–348 (1997).
[CrossRef]

C. L. Tang and P. P. Bey, “Phase matching in second harmonic generation using artificial periodic structures,” IEEE J. Quantum Electron. QE-9, 9–17 (1973).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (1)

A. Locatelli, F. M. Pigozzo, D. Modotto, A. D. Capobianco, and C. De Angelis, “Bidirectional beam propagation method for multilayered dielectrics with quadratic nonlinearity,” IEEE J. Sel. Top. Quantum Electron. 8, 440–447 (2002).
[CrossRef]

IEEE Photon. Technol. Lett. (2)

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[CrossRef]

H. Rao, R. Scarmozzino, and R. M. Osgood, Jr., “A bidirectional beam propagation method for multiple dielectric interfaces,” IEEE Photon. Technol. Lett. 11, 830–832 (1999).
[CrossRef]

IEEE Trans. Antennas Propag. (1)

R. M. Joseph and A. Taflove, “FDTD Maxwell’s equations models for nonlinear electrodynamics and optics,” IEEE Trans. Antennas Propag. 45, 364–374 (1997).
[CrossRef]

J. Appl. Phys. (2)

R. D. Meade, A. Devenyl, J. D. Joannopoulos, O. L. Alerhand, D. A. Smith, and K. Kash, “Novel applications of photonic band gap materials: low-loss bends and high Q cavities,” J. Appl. Phys. 75, 4753–4755 (1994).
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J. Opt. Soc. Am. (1)

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Nature (London) (2)

T. F. Krauss, R. M. De La Rue, and S. Brand, “Two-dimensional photonic bandgap structures operating at near-infrared wavelengths,” Nature (London) 383, 699–702 (1996).
[CrossRef]

J. D. Joannopoulos, P. R. Villeneuve, and S. Fan, “Photonic crystals: putting a new twist on light,” Nature (London) 387, 143–149 (1997).
[CrossRef]

Opt. Lett. (2)

Phys. Rev. A (2)

J. W. Haus, R. Viswanathan, M. Scalora, A. G. Kalocsai, J. D. Cole, and J. Theimer, “Enhanced second-harmonic generation in media with a weak periodicity,” Phys. Rev. A 57, 2120–2128 (1998).
[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]

Phys. Rev. B (2)

S. G. Johnson, S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and L. A. Kolodziejski, “Guided modes in photonic crystal slabs,” Phys. Rev. B 60, 5751–5758 (1999).
[CrossRef]

S. G. Johnson, P. R. Villeneuve, S. Fan, and J. D. Joannopoulos, “Linear waveguides in photonic-crystal slabs,” Phys. Rev. B 62, 8212–8222 (2000).
[CrossRef]

Phys. Rev. E (6)

K. Busch and S. John, “Photonic band gap formation in certain self-organizing systems,” Phys. Rev. E 58, 3896–3908 (1998).
[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 band gap structures: applications to nonlinear quadratic interactions,” Phys. Rev. E 60, 4891–4898 (1999).
[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 χ(2) interactions,” Phys. Rev. E 64, 016609 (2001).
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T. Iizuka and C. M. de Sterke, “Corrections to coupled mode theory for deep gratings,” Phys. Rev. E 61, 4491–4499 (2000).
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A. Arraf and C. M. de Sterke, “Coupled-mode equations for quadratically nonlinear deep gratings,” Phys. Rev. E 58, 7951–7958 (1998).
[CrossRef]

S. Mookherjea and A. Yariv, “Second-harmonic generation with pulses in a coupled-resonator optical waveguide,” Phys. Rev. E 65, 026607 (2002).
[CrossRef]

Phys. Rev. Lett. (4)

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]

D. Labilloy, H. Benitsy, C. Weisbuch, T. F. Krauss, R. M. De La Rue, V. Bardinal, R. Houdré, U. Oesterle, D. Cassagne, and C. Jouanin, “Quantitative measurement of transmission, reflection, and diffraction of two-dimensional photonic band gap structures at near-infrared wavelengths,” Phys. Rev. Lett. 79, 4147–4150 (1997).
[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,” Phys. Rev. Lett. 77, 3787–3790 (1996).
[CrossRef] [PubMed]

Prog. Quantum Electron. (1)

T. F. Krauss and R. M. De La Rue, “Photonic crystals in the optical regime—past, present and future,” Prog. Quantum Electron. 23, 51–96 (1999).
[CrossRef]

Other (2)

A. Nayfeh, Introduction to Perturbation Techniques (Wiley-Interscience, New York, 1993).

A. Yariv, Optical Electronics in Modern Communications (Oxford U. Press, Oxford, UK, 1997).

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Figures (11)

Fig. 1
Fig. 1

Fundamental frequency (FF) (|F1|) and second-harmonic (SH) (|F2|) forward-traveling waves inside the sinusoidal grating composed of ten periods. The SH (dashed curve) has been multiplied by a factor of 100 in order to make easier the comparison. The dotted curve is the analytical result from Eq. (30). The thin solid curve shows the periodic variation of the refractive index at the fundamental wavelength. The period is Λ=230.36 nm, and at the SH it is Λ/2.

Fig. 2
Fig. 2

Period (Λ) and thickness of the air layer (W) necessary to fulfill the resonance conditions in the square wave grating as functions of number of periods (N) of the photonic crystal.

Fig. 3
Fig. 3

FF (|F1|) and SH (|F2|) forward-traveling waves inside a square wave grating composed of ten periods. The SH (dashed curve) has been multiplied by a factor of 100 in order to make easier the comparison. The thin solid curve shows the refractive index at the FF, which oscillates between 3.3426 (AlGaAs) and 1 (air); the period is Λ=234.59 nm, and the air layer thickness is W=91.55 nm.

Fig. 4
Fig. 4

|F1(L)|, |F2(L)|, and |B2(0)| as functions of the fundamental wavelength in a square wave grating (ten periods long) designed to be phase matched at 1550 nm. The solid curve refers to the forward FF traveling wave, and the dashed curves apply to the forward and backward SH waves.

Fig. 5
Fig. 5

Forward [F2(L), squares] and backward [B2(0), circles] output SH for optimized square wave gratings as functions of length of the grating itself. The squares and the circles are from the numerical solution of the system, and the solid and dotted–dashed curves are the theoretical predictions. The dashed line is the SH that could be obtained at the end of a bulk phase-matched semiconductor.

Fig. 6
Fig. 6

Comparison between the solution of the coupled wave equations for the FF field (thick solid curves) and the exact results obtained by means of the BiBPM code (dashed curves). The forward waves (|F1|) are displayed in (a) and the backward waves (|B1|) in (b).

Fig. 7
Fig. 7

Comparison of the results at the SH. The thick solid curves are the solutions of the coupled wave equations, and the dashed curves are the results of the BiBPM. The forward waves (|F2|) are displayed in (a) and the backward waves (|B2|) in (b).

Fig. 8
Fig. 8

Total FF field (|E1|): results from the coupled equations (thick solid curve) and from the BiBPM (dashed curve); the two curves are perfectly overlapped. The thin solid curve is the refractive index at the FF.

Fig. 9
Fig. 9

Total SH field (|E2|): results from the coupled equations (thick solid curve) and from the BiBPM (dashed curve); the two curves differ only near the local maxima. The thin solid curve shows the refractive index at the SH.

Fig. 10
Fig. 10

Temporal shapes of input and output FF fields (dotted and solid curves, respectively) and of output SH field (dashed curves) through the ten-period stack of Fig. 3. Input pulse widths are as follows: ΔTFWHM(in,FF)=4.94 ps in (a), 1.23 ps in (b), and 0.62 ps in (c).

Fig. 11
Fig. 11

Energy and power ratios in the conversion process of pulsed fields through the ten-period stack of Fig. 3. The solid curve with solid diamonds is the energy ratio RE,(dB), the solid curve with solid circles is the maximum power ratio RP,(dB), and the dashed curve with unfilled circles is drawn by adding 1.5 dB to RE,(dB).

Equations (75)

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d2EdZ2+ω2μ0n02E=-ω2μ0Δn2(Z)E-PL(Z),
n2(Z, ω)=n02(ω)+Δn2(Z, ω),
Δn2(Z, ω)=Δn2(Z+Λ, ω),
P˜nl(Z, t)=0χ(2)E˜2(Z, t),
d2E(Z, ω)dZ2+ωc2n102E(Z, ω)
=-ωc2χ(2)E*(Z, ω)E(Z, 2ω)-ωc2Δn2(Z)E(Z, ω),
d2E(Z, 2ω)dZ2+2ωc2n202E(Z, 2ω)
=-2ωc2χ(2)E2(Z, ω)-2ωc2Δn2(Z)E(Z, 2ω).
k1=ωn10c,k2=2ωn20c,
km=k2+2k12,ks=k2-2k12,
d2E(z, ω)dz2+k1km2E(z, ω)+k1kmA1(z)E(z, ω)
=-P1(z),
d2E(z, 2ω)dz2+k2km2E(z, 2ω)+k2kmA2(z)E(z, 2ω)
=-P2(z),
P1(z)=k1kmD1(z)E*(z, ω)E(z, 2ω),
P2(z)=k22kmD2(z)E2(z, ω),
Aq(z)=kqkmnq02l=-δl(qω)expj kdkm lz,
q={1, 2}.
Δn2(z, qω)=l=-δl(qω)expj kdkm lz,
Dq(z)=l=-dl(q)expj kdkm lz=kqkmnq02χ(2)(z),
2k1km=1-=O(1),k2km=1+=O(1).
kdkm=1+αwithα=O(1).
δ±1(ω)n102=O(),δ±2(2ω)n202=O().
|χ(2)E(2ω)|=O(m)
E2(2ω)E2(ω)=O(m-1)
E(ω, z0, z1,)=E0(ω, z0, z1,)+E1(ω, z0, z1,)+.
d2E0(ω, z0, z1,)dz02+ωn10kmc2E0(ω, z0, z1,)=0,
E0(ω, z0, z1,)=Ef0(ω, z1,)exp-j k1km z0+Eb0(ω, z1,)expj k1km z0.
d2dz02 E1(ω, z0, z1,)+k1km2E1(ω, z0, z1,)
- 2jk1kmddz1Ef0(ω, z1,)exp-j k1km z0
+Eb0(ω, z1,)expj k1km z0
+k1km2l=-+δl(ω)expjl kdkm z0n102  
×Ef0(ω, z1,)exp-j k1km z0
+Eb0(ω, z1,)expj k1km z0
=-η1mk1kmD1(ω, z0)E0*(ω, z0, z1,)×E0(2ω, z0, z1,)
-2 j ddz1 Ef0(ω, z1,)+k1δ-1kmn102  
×exp[-j(1+α)z1]Eb0(ω, z1,)=0,
2j ddz1 Eb0(ω, z1,)+k1δ1kmn102  
×exp[j(1+α)z1]Ef0(ω, z1,)=0.
-2j ddz Ef0(ω, z)+k1δ-1kmn102exp(jΔ˜1z)Eb0(ω, z)=0,
2j ddz Eb0(ω, z)+k1δ1kmn102exp(-jΔ˜1z)Ef0(ω, z)=0
E1(ω, z0, z1,)=Ef1(ω, z0, z1,)exp-j k1km z0+Eb1(ω, z0, z1,)expj k1km z0,
Ef1(ω, z0, z1,)
=Ψf1(ω)+k12kml1δln102×expjl kdkm z0-1lkdkmEf0(ω, z)+l-1δln102×expj 2k1+lkdkm z0-12k1+lkdkm  Eb0(ω, z),
Eb1(ω, z0, z1,)
=Ψb1(ω)-k12kml1δln102×exp-j 2k1-lkdkm z0-1-2k1-lkdkmEf0(ω, z)+l-1δln102expjl kdkm z0-1lkdkmEb0(ω, z).
-2j ddz Ef0(2ω, z)+k2kmδ-2n202exp(jΔ˜2z)Eb0(2ω, z)
=-d0exp(jΔ˜kz)Ef02(ω, z)+2d-1expj Δ˜22 zEf0(ω, z)Eb0(ω, z)+d-2expjΔ˜22+Δ˜1zEb02(ω, z),
2j ddz Eb0(2ω, z)+k2kmδ2n202exp(-jΔ˜2z)Ef0(2ω, z)
=-d0exp(-jΔ˜kz)Eb02(ω, z)+2d1exp-j Δ˜22 zEf0(ω, z)Eb0(ω, z)+d2exp-jΔ˜22+Δ˜1zEf02(ω, z).
E1(2ω, z0, z1,)=Ef1(2ω, z0, z1,)exp-j k2km z0+Eb1(2ω, z0, z1,)expj k2km z0,
Ef1(2ω, z0, z1,)
=Ψf1(2ω)+12k2kml2δln202expjl kdkm z0-1lkdkmEf0(2ω, z)+l-2δln202expj 2k2+lkdkm z0-12k2+lkdkm  Eb0(2ω, z)-l0,2dl4expj k2-2k1+lkdkm z0-1k2-2k1+lkdkm  Ef02(ω, z)-l0,-2dl4expj k2+2k1+lkdkm z0-1k2+2k1+lkdkm  Eb02(ω, z)-l1,-1dl4expj k2+lkdkm z0-1k2+lkdkm  2Ef0(ω, z)Eb0(ω, z),
Eb1(2ω, z0, z1,)
=Ψb1(2ω)+12k2kml2δln202exp-j 2k2-lkdkm z0-12k2-lkdkm  Ef0(2ω, z)-l-2δln202expjl kdkm z0-1lkdkm  Eb0(2ω, z)+l0,2dl4exp-j k2+2k1-lkdkm z0-1k2+2k1-lkdkm  Ef02(ω, z)+l0,-2dl4exp-j k2-2k1-lkdkm z0-1k2-2k1-lkdkm  Eb02(ω, z)+l1,-1dl4exp-j k2-lkdkm z0-1k2-lkdkm  2Ef0(ω, z)Eb0(ω, z).
C±1=k1km12n102 δ±1(ω),Φ1=Δ124-C1C-11/2,
Ef0(ω, z)
=cos(Φ1z)+jΦ1sin(Φ1L)+(Δ˜1/2)cos(Φ1L)-(Δ˜1/2)sin(Φ1L)+jΦ1cos(Φ1L)×sin(Φ1z)exp[j(Δ˜1/2)z]E0=F1(ω, z)exp[j(Δ˜1/2)z],
Eb0(ω, z)
=C1sin(Φ1L)cos(Φ1z)-cos(Φ1L)sin(Φ1z)-(Δ˜1/2)sin(Φ1L)+jΦ1cos(Φ1L)×exp[-j(Δ˜1/2)z]E0=B1(ω, z)exp[-j(Δ˜1/2)z].
Eb1(ω, 0)=Ψb1(ω)k12k1+kdδ-1n102Ef0(ω, L).
C±2=k2km12n202 δ±2(2ω),Φ2=Δ224-C2C-21/2,
Ef0(2ω, z)=exp[j(Δ˜2/2)z]A sin(Φ2z)+0zcos[Φ2(z-τ)]-j Δ22Φ2×sin[Φ2(z-τ)]Γ1(τ)dτ-0zj C-2Φ2sin[Φ2(z-τ)]Γ2(τ)dτ=F2(2ω, z)exp[j(Δ˜2/2)z],
Eb0(2ω, z)=exp[-j(Δ˜2/2)z]AC-2 [-(Δ2/2)sin(Φ2z)+jΦ2cos(Φ2z)]+0zcos[Φ2(z-τ)]+j Δ22Φ2sin[Φ2(z-τ)]Γ2(τ)dτ+0zj C2Φ2sin[Φ2(z-τ)]Γ1(τ)dτ=B2(2ω, z)exp[-j(Δ˜2/2)z],
Γ1(z)=-j[d0F12(ω, z)+2d-1F1(ω, z)B1(ω, z)+d-2B12(ω, z)],
Γ2(z)=j[d0B12(ω, z)+2d1F1(ω, z)B1(ω, z)+d2F12(ω, z)]
F2(2ω, L)=E02L4d0Δ1L2πΔ2L2π+d01+Δ1L2π2+d1C1LπC2Lπ-Δ2L2π-2Δ1L2π+d2C1Lπ2-C2LπΔ1L2π,
B2(2ω, 0)=E02L4C2Lπd0Δ1L2π-d1C1Lπ+C1Lπd1Δ2L2π-2d1Δ1L2π+d0C1Lπ+d21+Δ1L2π2-Δ2L2πΔ1L2π,
F2(2ω, L)=deff E02L,
|Ef1(2ω, L)|d1km2kd-ΔkEf02(ω, L)|d1E02|.
Ef1(2ω, L)Ef0(2ω, L)d1deffL1.
EFF(t, z=0)=AFFexp-t22T02
ESH(t, z=L)=ASHexp-t2T02.
RE=|ESH(t, z=L)|2dt|EFF(t, z=0)|2dt,
RP,(dB)=RE,(dB)+1.5.

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