Abstract

A computational study of the second-harmonic generation in one-dimensional photonic crystals made of GaAs and AlAs with quadratic optical nonlinearity and material dispersion is presented. The computational approach uses a shooting method to solve nonlinear wave equations for coupled fundamental and second-harmonic fields and the invariant imbedding method to obtain the linear transmittance and group index spectra. The photonic crystal is built with an elementary cell consisting of four sublayers whose thicknesses are systematically varied. Doubly-resonant second harmonic generation with high conversion efficiency is achieved by choosing the geometrical parameters of the elementary cell optimally and controlling the band structure.

© 2009 Optical Society of America

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    [CrossRef]
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    [CrossRef]
  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 band gap structures: Applications to nonlinear quadratic interactions," Phys. Rev. E 60, 4891-4898 (1999).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  18. K. Kim, H. Lim, and D.-H. Lee, "Invariant imbedding equations for electromagnetic waves in stratified magnetic media: Applications to one-dimensional photonic crystals," J. Korean Phys. Soc. 39, L956-L960 (2001).
  19. K. Kim, D. K. Phung, F. Rotermund, and H. Lim, "Propagation of electromagnetic waves in stratified media with nonlinearity in both dielectric and magnetic responses," Opt. Express 16, 1150-1164 (2008).
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    [CrossRef]
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    [CrossRef] [PubMed]

2009 (2)

2008 (1)

2007 (1)

J.-J. Li, Z.-Y. Li, and D.-Z. Zhang, "Second harmonic generation in one-dimensional nonlinear photonic crystals solved by the transfer matrix method," Phys. Rev. E 75, 056606 (2007).
[CrossRef]

2006 (1)

M. Liscidini and L. C. Andreani, "Second-harmonic generation in doubly resonant microcavities with periodic dielectric mirrors," Phys. Rev. E 73, 016613 (2006).
[CrossRef]

2004 (1)

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. sagne, and J. P. Albert, "Giant second-harmonic generation in a onedimensional GaN photonic crystal," Phys. Rev. B 69, 085105 (2004).
[CrossRef]

2003 (2)

G. D’Aguanno, M. Centini, M. Scalora, C. Sibilia, M. Bertolotti, M. J. Bloemer, and C. M. Bowden, "Energy exchange properties during second-harmonic generation in finite one-dimensional photonic band-gap structures with deep gratings," Phys. Rev. E 67, 016606 (2003).
[CrossRef]

A. Chowdhury, H. M. Ng, M. Bhardwaj, and N. G. Weimann, "Second-harmonic generation in periodically poled GaN," Appl. Phys. Lett. 83, 1077-1079 (2003).
[CrossRef]

2002 (5)

2001 (3)

M. Midrio, "Shooting technique for the computation of plane-wave reflection and transmission through onedimensional nonlinear inhomogeneous dielectric structures," J. Opt. Soc. Am. B 18, 1866-1871 (2001).
[CrossRef]

K. Kim, H. Lim, and D.-H. Lee, "Invariant imbedding equations for electromagnetic waves in stratified magnetic media: Applications to one-dimensional photonic crystals," J. Korean Phys. Soc. 39, L956-L960 (2001).

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]

1999 (2)

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. T. Kiehne, A. E. Kryukov, and J. B. Ketterson, "A numerical study of optical second-harmonic generation in a one-dimensional photonic structure," Appl. Phys. Lett. 75, 1676-1678 (1999).
[CrossRef]

1997 (2)

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]

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

1996 (1)

J. M. Bendickson, J. P. Dowling, and M. Scalora, "Analytic expressions for the electromagnetic mode density in finite, one-dimensional, photonic band-gap structures," Phys. Rev. E 53, 4107-4121 (1996).
[CrossRef]

1992 (2)

M. Ohashi, T. Kondo, K. Kumata, S. Fukatsu, S. S. Kano, Y. Shiraki, and R. Ito, "Nonlinear optical coefficient of AlAs thin film on GaAs substrate," Jpn. J. Appl. Phys. 31, L843-L845 (1992).
[CrossRef]

M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, "Quasi-phase-matched second harmonic generation: Tuning and tolerances," IEEE J. Quantum Electron. 28, 2631-2654 (1992).
[CrossRef]

1987 (1)

W. Chen and D. L. Mills, "Gap solitons and the nonlinear optical response of superlattices," Phys. Rev. Lett. 58, 160-163 (1987).
[CrossRef] [PubMed]

Abram, I.

Y. Dumeige, I. Sagnes, P. Monnier, P. Vidakovic, I. Abram, C. M’eriadec, and A. Levenson, "Phase-matched frequency doubling at photonic band edges: Efficiency scaling as the fifth power of the length," Phys. Rev. Lett. 89, 043901 (2002).
[CrossRef] [PubMed]

Aktsipetrov, O. A.

Andreani, L. C.

M. Liscidini and L. C. Andreani, "Second-harmonic generation in doubly resonant microcavities with periodic dielectric mirrors," Phys. Rev. E 73, 016613 (2006).
[CrossRef]

Bendickson, J. M.

J. M. Bendickson, J. P. Dowling, and M. Scalora, "Analytic expressions for the electromagnetic mode density in finite, one-dimensional, photonic band-gap structures," Phys. Rev. E 53, 4107-4121 (1996).
[CrossRef]

Bertolotti, M.

G. D’Aguanno, M. Centini, M. Scalora, C. Sibilia, M. Bertolotti, M. J. Bloemer, and C. M. Bowden, "Energy exchange properties during second-harmonic generation in finite one-dimensional photonic band-gap structures with deep gratings," Phys. Rev. E 67, 016606 (2003).
[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]

Bhardwaj, M.

A. Chowdhury, H. M. Ng, M. Bhardwaj, and N. G. Weimann, "Second-harmonic generation in periodically poled GaN," Appl. Phys. Lett. 83, 1077-1079 (2003).
[CrossRef]

Bloemer, M. J.

G. D’Aguanno, M. Centini, M. Scalora, C. Sibilia, M. Bertolotti, M. J. Bloemer, and C. M. Bowden, "Energy exchange properties during second-harmonic generation in finite one-dimensional photonic band-gap structures with deep gratings," Phys. Rev. E 67, 016606 (2003).
[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]

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]

Bowden, C. M.

G. D’Aguanno, M. Centini, M. Scalora, C. Sibilia, M. Bertolotti, M. J. Bloemer, and C. M. Bowden, "Energy exchange properties during second-harmonic generation in finite one-dimensional photonic band-gap structures with deep gratings," Phys. Rev. E 67, 016606 (2003).
[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]

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]

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. sagne, and J. P. Albert, "Giant second-harmonic generation in a onedimensional GaN photonic crystal," Phys. Rev. B 69, 085105 (2004).
[CrossRef]

Byer, R. L.

M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, "Quasi-phase-matched second harmonic generation: Tuning and tolerances," IEEE J. Quantum Electron. 28, 2631-2654 (1992).
[CrossRef]

Centini, M.

G. D’Aguanno, M. Centini, M. Scalora, C. Sibilia, M. Bertolotti, M. J. Bloemer, and C. M. Bowden, "Energy exchange properties during second-harmonic generation in finite one-dimensional photonic band-gap structures with deep gratings," Phys. Rev. E 67, 016606 (2003).
[CrossRef]

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

M. Centini, C. Sibilia, M. Scalora, G. D’Aguanno, M. 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]

Chen, W.

W. Chen and D. L. Mills, "Gap solitons and the nonlinear optical response of superlattices," Phys. Rev. Lett. 58, 160-163 (1987).
[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. sagne, and J. P. Albert, "Giant second-harmonic generation in a onedimensional GaN photonic crystal," Phys. Rev. B 69, 085105 (2004).
[CrossRef]

Chowdhury, A.

A. Chowdhury, H. M. Ng, M. Bhardwaj, and N. G. Weimann, "Second-harmonic generation in periodically poled GaN," Appl. Phys. Lett. 83, 1077-1079 (2003).
[CrossRef]

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. sagne, and J. P. Albert, "Giant second-harmonic generation in a onedimensional GaN photonic crystal," Phys. Rev. B 69, 085105 (2004).
[CrossRef]

D’Aguanno, G.

G. D’Aguanno, M. Centini, M. Scalora, C. Sibilia, M. Bertolotti, M. J. Bloemer, and C. M. Bowden, "Energy exchange properties during second-harmonic generation in finite one-dimensional photonic band-gap structures with deep gratings," Phys. Rev. E 67, 016606 (2003).
[CrossRef]

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

M. Centini, C. Sibilia, M. Scalora, G. D’Aguanno, M. 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]

Debray, J. P.

Dolgova, T. V.

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]

J. M. Bendickson, J. P. Dowling, and M. Scalora, "Analytic expressions for the electromagnetic mode density in finite, one-dimensional, photonic band-gap structures," Phys. Rev. E 53, 4107-4121 (1996).
[CrossRef]

Dumeige, Y.

Y. Dumeige, I. Sagnes, P. Monnier, P. Vidakovic, C. M’eriadec, and A. Levenson, "c(2) semiconductor photonic crystals," J. Opt. Soc. Am. B 19, 2094-2101 (2002).
[CrossRef]

Y. Dumeige, I. Sagnes, P. Monnier, P. Vidakovic, I. Abram, C. M’eriadec, and A. Levenson, "Phase-matched frequency doubling at photonic band edges: Efficiency scaling as the fifth power of the length," Phys. Rev. Lett. 89, 043901 (2002).
[CrossRef] [PubMed]

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]

Fainman, Y.

Fedyanin, A. A.

Fejer, M. M.

M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, "Quasi-phase-matched second harmonic generation: Tuning and tolerances," IEEE J. Quantum Electron. 28, 2631-2654 (1992).
[CrossRef]

Fukatsu, S.

M. Ohashi, T. Kondo, K. Kumata, S. Fukatsu, S. S. Kano, Y. Shiraki, and R. Ito, "Nonlinear optical coefficient of AlAs thin film on GaAs substrate," Jpn. J. Appl. Phys. 31, L843-L845 (1992).
[CrossRef]

Harmand, J. C.

Haus, J. W.

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]

Ito, R.

M. Ohashi, T. Kondo, K. Kumata, S. Fukatsu, S. S. Kano, Y. Shiraki, and R. Ito, "Nonlinear optical coefficient of AlAs thin film on GaAs substrate," Jpn. J. Appl. Phys. 31, L843-L845 (1992).
[CrossRef]

Jundt, D. H.

M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, "Quasi-phase-matched second harmonic generation: Tuning and tolerances," IEEE J. Quantum Electron. 28, 2631-2654 (1992).
[CrossRef]

Kano, S. S.

M. Ohashi, T. Kondo, K. Kumata, S. Fukatsu, S. S. Kano, Y. Shiraki, and R. Ito, "Nonlinear optical coefficient of AlAs thin film on GaAs substrate," Jpn. J. Appl. Phys. 31, L843-L845 (1992).
[CrossRef]

Ketterson, J. B.

G. T. Kiehne, A. E. Kryukov, and J. B. Ketterson, "A numerical study of optical second-harmonic generation in a one-dimensional photonic structure," Appl. Phys. Lett. 75, 1676-1678 (1999).
[CrossRef]

Kiehne, G. T.

G. T. Kiehne, A. E. Kryukov, and J. B. Ketterson, "A numerical study of optical second-harmonic generation in a one-dimensional photonic structure," Appl. Phys. Lett. 75, 1676-1678 (1999).
[CrossRef]

Kim, K.

K. Kim, D. K. Phung, F. Rotermund, and H. Lim, "Propagation of electromagnetic waves in stratified media with nonlinearity in both dielectric and magnetic responses," Opt. Express 16, 1150-1164 (2008).
[CrossRef] [PubMed]

K. Kim, H. Lim, and D.-H. Lee, "Invariant imbedding equations for electromagnetic waves in stratified magnetic media: Applications to one-dimensional photonic crystals," J. Korean Phys. Soc. 39, L956-L960 (2001).

Kondo, T.

M. Ohashi, T. Kondo, K. Kumata, S. Fukatsu, S. S. Kano, Y. Shiraki, and R. Ito, "Nonlinear optical coefficient of AlAs thin film on GaAs substrate," Jpn. J. Appl. Phys. 31, L843-L845 (1992).
[CrossRef]

Kryukov, A. E.

G. T. Kiehne, A. E. Kryukov, and J. B. Ketterson, "A numerical study of optical second-harmonic generation in a one-dimensional photonic structure," Appl. Phys. Lett. 75, 1676-1678 (1999).
[CrossRef]

Kumata, K.

M. Ohashi, T. Kondo, K. Kumata, S. Fukatsu, S. S. Kano, Y. Shiraki, and R. Ito, "Nonlinear optical coefficient of AlAs thin film on GaAs substrate," Jpn. J. Appl. Phys. 31, L843-L845 (1992).
[CrossRef]

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. sagne, and J. P. Albert, "Giant second-harmonic generation in a onedimensional GaN photonic crystal," Phys. Rev. B 69, 085105 (2004).
[CrossRef]

Lee, D.-H.

K. Kim, H. Lim, and D.-H. Lee, "Invariant imbedding equations for electromagnetic waves in stratified magnetic media: Applications to one-dimensional photonic crystals," J. Korean Phys. Soc. 39, L956-L960 (2001).

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. sagne, and J. P. Albert, "Giant second-harmonic generation in a onedimensional GaN photonic crystal," Phys. Rev. B 69, 085105 (2004).
[CrossRef]

Levenson, J. A.

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

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

Li, J.-J.

J.-J. Li, Z.-Y. Li, and D.-Z. Zhang, "Second harmonic generation in one-dimensional nonlinear photonic crystals solved by the transfer matrix method," Phys. Rev. E 75, 056606 (2007).
[CrossRef]

Li, Z.-Y.

M.-L. Ren and Z.-Y. Li, "Giant enhancement of second harmonic generation in nonlinear photonic crystals with distributed Bragg reflector mirrors," Opt. Express 17, 14502-14510 (2009).
[CrossRef] [PubMed]

J.-J. Li, Z.-Y. Li, and D.-Z. Zhang, "Second harmonic generation in one-dimensional nonlinear photonic crystals solved by the transfer matrix method," Phys. Rev. E 75, 056606 (2007).
[CrossRef]

Lim, H.

K. Kim, D. K. Phung, F. Rotermund, and H. Lim, "Propagation of electromagnetic waves in stratified media with nonlinearity in both dielectric and magnetic responses," Opt. Express 16, 1150-1164 (2008).
[CrossRef] [PubMed]

K. Kim, H. Lim, and D.-H. Lee, "Invariant imbedding equations for electromagnetic waves in stratified magnetic media: Applications to one-dimensional photonic crystals," J. Korean Phys. Soc. 39, L956-L960 (2001).

Liscidini, M.

M. Liscidini and L. C. Andreani, "Second-harmonic generation in doubly resonant microcavities with periodic dielectric mirrors," Phys. Rev. E 73, 016613 (2006).
[CrossRef]

Lovering, D. J.

Magel, G. A.

M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, "Quasi-phase-matched second harmonic generation: Tuning and tolerances," IEEE J. Quantum Electron. 28, 2631-2654 (1992).
[CrossRef]

Maidykovski, A. I.

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]

Marowsky, G.

Martemyanov, M. G.

Mattei, G.

Midrio, M.

Mills, D. L.

W. Chen and D. L. Mills, "Gap solitons and the nonlinear optical response of superlattices," Phys. Rev. Lett. 58, 160-163 (1987).
[CrossRef] [PubMed]

Monnier, P.

Y. Dumeige, I. Sagnes, P. Monnier, P. Vidakovic, I. Abram, C. M’eriadec, and A. Levenson, "Phase-matched frequency doubling at photonic band edges: Efficiency scaling as the fifth power of the length," Phys. Rev. Lett. 89, 043901 (2002).
[CrossRef] [PubMed]

Y. Dumeige, I. Sagnes, P. Monnier, P. Vidakovic, C. M’eriadec, and A. Levenson, "c(2) semiconductor photonic crystals," J. Opt. Soc. Am. B 19, 2094-2101 (2002).
[CrossRef]

Nakabayashi, S.

Nakagawa, W.

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]

Ng, H. M.

A. Chowdhury, H. M. Ng, M. Bhardwaj, and N. G. Weimann, "Second-harmonic generation in periodically poled GaN," Appl. Phys. Lett. 83, 1077-1079 (2003).
[CrossRef]

Ohashi, M.

M. Ohashi, T. Kondo, K. Kumata, S. Fukatsu, S. S. Kano, Y. Shiraki, and R. Ito, "Nonlinear optical coefficient of AlAs thin film on GaAs substrate," Jpn. J. Appl. Phys. 31, L843-L845 (1992).
[CrossRef]

Ohta, N.

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. sagne, and J. P. Albert, "Giant second-harmonic generation in a onedimensional GaN photonic crystal," Phys. Rev. B 69, 085105 (2004).
[CrossRef]

Phung, D. K.

Ren, M.-L.

Romagnoli, M.

Rotermund, F.

Sagnes, I.

Y. Dumeige, I. Sagnes, P. Monnier, P. Vidakovic, I. Abram, C. M’eriadec, and A. Levenson, "Phase-matched frequency doubling at photonic band edges: Efficiency scaling as the fifth power of the length," Phys. Rev. Lett. 89, 043901 (2002).
[CrossRef] [PubMed]

Y. Dumeige, I. Sagnes, P. Monnier, P. Vidakovic, C. M’eriadec, and A. Levenson, "c(2) semiconductor photonic crystals," J. Opt. Soc. Am. B 19, 2094-2101 (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]

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]

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. sagne, and J. P. Albert, "Giant second-harmonic generation in a onedimensional GaN photonic crystal," Phys. Rev. B 69, 085105 (2004).
[CrossRef]

Scalora, M.

G. D’Aguanno, M. Centini, M. Scalora, C. Sibilia, M. Bertolotti, M. J. Bloemer, and C. M. Bowden, "Energy exchange properties during second-harmonic generation in finite one-dimensional photonic band-gap structures with deep gratings," Phys. Rev. E 67, 016606 (2003).
[CrossRef]

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

M. Centini, C. Sibilia, M. Scalora, G. D’Aguanno, M. 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]

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. M. Bendickson, J. P. Dowling, and M. Scalora, "Analytic expressions for the electromagnetic mode density in finite, one-dimensional, photonic band-gap structures," Phys. Rev. E 53, 4107-4121 (1996).
[CrossRef]

Shiraki, Y.

M. Ohashi, T. Kondo, K. Kumata, S. Fukatsu, S. S. Kano, Y. Shiraki, and R. Ito, "Nonlinear optical coefficient of AlAs thin film on GaAs substrate," Jpn. J. Appl. Phys. 31, L843-L845 (1992).
[CrossRef]

Sibilia, C.

G. D’Aguanno, M. Centini, M. Scalora, C. Sibilia, M. Bertolotti, M. J. Bloemer, and C. M. Bowden, "Energy exchange properties during second-harmonic generation in finite one-dimensional photonic band-gap structures with deep gratings," Phys. Rev. E 67, 016606 (2003).
[CrossRef]

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

M. Centini, C. Sibilia, M. Scalora, G. D’Aguanno, M. 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]

Simonneau, C.

Socci, L.

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. sagne, and J. P. Albert, "Giant second-harmonic generation in a onedimensional GaN photonic crystal," Phys. Rev. B 69, 085105 (2004).
[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. sagne, and J. P. Albert, "Giant second-harmonic generation in a onedimensional GaN photonic crystal," Phys. Rev. B 69, 085105 (2004).
[CrossRef]

Tyan, R.-C.

Vidakovic, P.

Y. Dumeige, I. Sagnes, P. Monnier, P. Vidakovic, I. Abram, C. M’eriadec, and A. Levenson, "Phase-matched frequency doubling at photonic band edges: Efficiency scaling as the fifth power of the length," Phys. Rev. Lett. 89, 043901 (2002).
[CrossRef] [PubMed]

Y. Dumeige, I. Sagnes, P. Monnier, P. Vidakovic, C. M’eriadec, and A. Levenson, "c(2) semiconductor photonic crystals," J. Opt. Soc. Am. B 19, 2094-2101 (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]

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

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]

Weimann, N. G.

A. Chowdhury, H. M. Ng, M. Bhardwaj, and N. G. Weimann, "Second-harmonic generation in periodically poled GaN," Appl. Phys. Lett. 83, 1077-1079 (2003).
[CrossRef]

Yakovlev, V. A.

Yuan, J.

J. Yuan, "Computing for second harmonic generation in one-dimensional nonlinear photonic crystals," Opt. Comm. 282, 2628-2633 (2009).
[CrossRef]

Zhang, D.-Z.

J.-J. Li, Z.-Y. Li, and D.-Z. Zhang, "Second harmonic generation in one-dimensional nonlinear photonic crystals solved by the transfer matrix method," Phys. Rev. E 75, 056606 (2007).
[CrossRef]

Appl. Phys. Lett. (3)

G. T. Kiehne, A. E. Kryukov, and J. B. Ketterson, "A numerical study of optical second-harmonic generation in a one-dimensional photonic structure," Appl. Phys. Lett. 75, 1676-1678 (1999).
[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]

A. Chowdhury, H. M. Ng, M. Bhardwaj, and N. G. Weimann, "Second-harmonic generation in periodically poled GaN," Appl. Phys. Lett. 83, 1077-1079 (2003).
[CrossRef]

IEEE J. Quantum Electron. (1)

M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, "Quasi-phase-matched second harmonic generation: Tuning and tolerances," IEEE J. Quantum Electron. 28, 2631-2654 (1992).
[CrossRef]

J. Korean Phys. Soc. (1)

K. Kim, H. Lim, and D.-H. Lee, "Invariant imbedding equations for electromagnetic waves in stratified magnetic media: Applications to one-dimensional photonic crystals," J. Korean Phys. Soc. 39, L956-L960 (2001).

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

J. Opt. Soc. Am. B (4)

Jpn. J. Appl. Phys. (1)

M. Ohashi, T. Kondo, K. Kumata, S. Fukatsu, S. S. Kano, Y. Shiraki, and R. Ito, "Nonlinear optical coefficient of AlAs thin film on GaAs substrate," Jpn. J. Appl. Phys. 31, L843-L845 (1992).
[CrossRef]

Opt. Comm. (1)

J. Yuan, "Computing for second harmonic generation in one-dimensional nonlinear photonic crystals," Opt. Comm. 282, 2628-2633 (2009).
[CrossRef]

Opt. Express (2)

Opt. Lett. (1)

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 (1)

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. sagne, and J. P. Albert, "Giant second-harmonic generation in a onedimensional GaN photonic crystal," Phys. Rev. B 69, 085105 (2004).
[CrossRef]

Phys. Rev. E (5)

M. Liscidini and L. C. Andreani, "Second-harmonic generation in doubly resonant microcavities with periodic dielectric mirrors," Phys. Rev. E 73, 016613 (2006).
[CrossRef]

J.-J. Li, Z.-Y. Li, and D.-Z. Zhang, "Second harmonic generation in one-dimensional nonlinear photonic crystals solved by the transfer matrix method," Phys. Rev. E 75, 056606 (2007).
[CrossRef]

G. D’Aguanno, M. Centini, M. Scalora, C. Sibilia, M. Bertolotti, M. J. Bloemer, and C. M. Bowden, "Energy exchange properties during second-harmonic generation in finite one-dimensional photonic band-gap structures with deep gratings," Phys. Rev. E 67, 016606 (2003).
[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]

J. M. Bendickson, J. P. Dowling, and M. Scalora, "Analytic expressions for the electromagnetic mode density in finite, one-dimensional, photonic band-gap structures," Phys. Rev. E 53, 4107-4121 (1996).
[CrossRef]

Phys. Rev. Lett. (2)

W. Chen and D. L. Mills, "Gap solitons and the nonlinear optical response of superlattices," Phys. Rev. Lett. 58, 160-163 (1987).
[CrossRef] [PubMed]

Y. Dumeige, I. Sagnes, P. Monnier, P. Vidakovic, I. Abram, C. M’eriadec, and A. Levenson, "Phase-matched frequency doubling at photonic band edges: Efficiency scaling as the fifth power of the length," Phys. Rev. Lett. 89, 043901 (2002).
[CrossRef] [PubMed]

Other (3)

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

R. W. Boyd, Nonlinear Optics, 2nd ed. (Academic Press, 2003).

R. Waynant and M. Ediger, Electro-Optics Handbook (McGraw-Hill, 1994).

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Figures (7)

Fig. 1.
Fig. 1.

Elementary cell of the photonic crystal under study.

Fig. 2.
Fig. 2.

Transmittance T versus the normalized frequency Ω(=ω/ω 0) for the (ABCD) N structure made of GaAs and AlAs with N=40, λ 0=2πc/ω 0=2.9872 µm and α=0.313. The FF and the SH are at the lower edges of bandgaps.

Fig. 3.
Fig. 3.

(a) Group index versus normalized frequency for the (ABCD) N structure with N=40, λ 0=2.9872 µm, α=0.313 and ε 1=µ 1=1. Group index versus vacuum wavelength (b) near the fundamental frequency and (c) near the SH frequency.

Fig. 4.
Fig. 4.

Forward and backward SH conversion efficiencies, η f and ηb , versus the normalized frequency Ω for the (ABCD) N structure with N=40, λ 0=2.9872 µm and α=0.313. The incident and transmitted regions consist of GaAs. The pump intensity I FF is equal to 10 MW/cm2. Both curves are peaked at the frequency corresponding to λ FF=3.1 µm.

Fig. 5.
Fig. 5.

Spatial distributions of (a) the normalized FF field intensity, |u FF|2, and (b) the normalized SH field intensity, |u SH|2, inside the 40-period photonic crystal at double resonance, when the pump intensity I FF is equal to 10 MW/cm2. The wave is incident from the left. (c) Expanded field distributions near the center of the structure.

Fig. 6.
Fig. 6.

(a) Forward and backward SH conversion efficiencies ηf and ηb versus the pump intensity I FF. (b) Reflectance R FF and transmittance T FF of the FF wave versus I FF.

Fig. 7.
Fig. 7.

Spatial distributions of (a) the normalized FF field intensity and (b) the normalized SH field intensity inside the 40-period photonic crystal at double resonance, when the pump intensity I FF is equal to 3200 MW/cm2.

Equations (7)

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

ω0cnAdA=ω0cnDdD=(1α)π,ω0cnBdB=ω0cnCdC=α π ,
d2Edz21μ(z)dμdzdEdz+[k02ε(z)μ(z)q2]E=0,
1ipdrdl=2μ(l)μ1r(l)+12a(l)[1+r(l)]2,1ipdtdl=μ(l)μ1t(l)+12a(l)[1+r(l)]t(l),
a(l)=ε(l)ε1μ(l)μ1+[ε(l)ε1μ1μ(l)]tan2θ
ρ=1L yxxyx2+y2 ,
d2EFFdz2=ωFF2c2εFFEFF2χ(2)ωFF2c2EFF*ESH,d2ESHdz2=ωSH2c2εSHESHχ(2)ωSH2c2EFF2,
d2uFFdξ2=ωFF2c2εFFuFF2βωFF2c2uFF*uSH,d2uSHdξ2=ωSH2c2εSHuSHβωSH2c2uFF2,

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