Abstract

A numerical iteration technique starting from the analytical solution of the fundamental wave and the second harmonic wave propagation equations in undepleted-pump approximation is presented for analysis of second harmonic generation in one-dimensional nonlinear photonic-crystal microcavities under pump light incidence at an arbitrary angle, accounting for pump depletion. Numerical results are in good agreement with experimental observation and theoretical predication by transfer matrix method. Analysis of the conversion efficiency of second harmonic generation in nonlinear photonic-crystal microcavities shows that dramatic enhancement of second harmonic generation occurs in the microcavities which have the optimal numbers of distributed Bragg reflector layers. The enhancement of nonlinear interactions is ascribed to mode resonance and localization of high intensity fundamental field, corresponding to the defect mode within the forbidden band of the photonic-crystal microcavities.

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    [CrossRef]
  2. S. Lettieri, S. D. Finizio, P. Maddalena, V. Ballarini, and F. Giorgis, “Second-hamonic generation in amorphous silicon nitride microcavities,” Appl. Phys. Lett. 81(25), 4706 (2002).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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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 Stat. Nonlin. Soft Matter Phys. 75(5), 056606 (2007).
[CrossRef] [PubMed]

2006 (2)

L. Zhao and B. Gu, “Giant enhancement of second harmonic generation in multiple photonic quantum well structures made of nonlinear material,” Appl. Phys. Lett. 88(12), 122904 (2006).
[CrossRef]

L. M. Zhao and B. Y. Gu, “Enhanced second-harmonic generation for multiple wavelengths by defect modes in one-dimensional photonic crystals,” Opt. Lett. 31(10), 1510–1512 (2006).
[CrossRef] [PubMed]

2005 (2)

T. Ochiai and K. Sakoda, “Scaling law of enhanced second harmonic generation in finite Bragg stacks,” Opt. Express 13(22), 9094–9114 (2005).
[CrossRef] [PubMed]

I. V. Soboleva, E. M. Murchikova, A. A. Fedyanin, and O. A. Aktsipetrov, “Second- and third-harmonic generation in birefringent photonic crystals and microcavities based on anisotropic porous silicon,” Appl. Phys. Lett. 87(24), 241110 (2005).
[CrossRef]

2003 (1)

V. Y. Timoshenko, L. A. Osminkina, A. I. Efimova, L. A. Golovan, P. K. Kashkarov, D. Kovalev, N. Kunzner, E. Gross, J. Diener, and F. Koch, “Anisotropy of optical absorption in birefringent porous silicon,” Phys. Rev. B 67(11), 113405 (2003).
[CrossRef]

2002 (5)

2001 (1)

T. V. Dolgova, A. I. Maidikovskii, M. G. Martem’yanov, G. Marovsky, G. Mattei, D. Schuhmacher, V. A. Yakovlev, A. A. Fedyanin, and O. A. Aktsipetrov, “Giant second harmonic generation in microcavities based on porous silicon photonic crystals,” JETP Lett. 73(1), 6–9 (2001).
[CrossRef]

1998 (1)

1995 (1)

Akhouayri, H.

Aktsipetrov, O. A.

I. V. Soboleva, E. M. Murchikova, A. A. Fedyanin, and O. A. Aktsipetrov, “Second- and third-harmonic generation in birefringent photonic crystals and microcavities based on anisotropic porous silicon,” Appl. Phys. Lett. 87(24), 241110 (2005).
[CrossRef]

T. V. Dolgova, A. I. Maidykovski, M. G. Martemyanov, A. A. Fedyanin, O. A. Aktsipetrov, G. Marowsky, V. A. Yakovlev, G. Mattei, N. Ohta, and S. Nakabayashi, “Giant optical second-harmonic generation in single and coupled microcavities formed from one-dimensional photonic crystals,” J. Opt. Soc. Am. B 19(9), 2129–2140 (2002).
[CrossRef]

T. V. Dolgova, A. I. Maidykovski, M. G. Martemyanov, A. A. Fedyanin, O. A. Aktsipetrov, G. Marowsky, V. A. Yakovlev, and G. Mattei, “Giant microcavity enhancement of second-harmonic generation in all-silicon photonic crystals,” Appl. Phys. Lett. 81(15), 2725 (2002).
[CrossRef]

T. V. Dolgova, A. I. Maidikovskii, M. G. Martem’yanov, G. Marovsky, G. Mattei, D. Schuhmacher, V. A. Yakovlev, A. A. Fedyanin, and O. A. Aktsipetrov, “Giant second harmonic generation in microcavities based on porous silicon photonic crystals,” JETP Lett. 73(1), 6–9 (2001).
[CrossRef]

Ballarini, V.

S. Lettieri, S. D. Finizio, P. Maddalena, V. Ballarini, and F. Giorgis, “Second-hamonic generation in amorphous silicon nitride microcavities,” Appl. Phys. Lett. 81(25), 4706 (2002).
[CrossRef]

Bertolotti, M.

Bloemer, M. J.

Bowden, C. M.

Centini, M.

Corbalan, R.

D'Aguanno, G.

Dal Negro, L.

Diener, J.

V. Y. Timoshenko, L. A. Osminkina, A. I. Efimova, L. A. Golovan, P. K. Kashkarov, D. Kovalev, N. Kunzner, E. Gross, J. Diener, and F. Koch, “Anisotropy of optical absorption in birefringent porous silicon,” Phys. Rev. B 67(11), 113405 (2003).
[CrossRef]

Dolgova, T. V.

T. V. Dolgova, A. I. Maidykovski, M. G. Martemyanov, A. A. Fedyanin, O. A. Aktsipetrov, G. Marowsky, V. A. Yakovlev, and G. Mattei, “Giant microcavity enhancement of second-harmonic generation in all-silicon photonic crystals,” Appl. Phys. Lett. 81(15), 2725 (2002).
[CrossRef]

T. V. Dolgova, A. I. Maidykovski, M. G. Martemyanov, A. A. Fedyanin, O. A. Aktsipetrov, G. Marowsky, V. A. Yakovlev, G. Mattei, N. Ohta, and S. Nakabayashi, “Giant optical second-harmonic generation in single and coupled microcavities formed from one-dimensional photonic crystals,” J. Opt. Soc. Am. B 19(9), 2129–2140 (2002).
[CrossRef]

T. V. Dolgova, A. I. Maidikovskii, M. G. Martem’yanov, G. Marovsky, G. Mattei, D. Schuhmacher, V. A. Yakovlev, A. A. Fedyanin, and O. A. Aktsipetrov, “Giant second harmonic generation in microcavities based on porous silicon photonic crystals,” JETP Lett. 73(1), 6–9 (2001).
[CrossRef]

Efimova, A. I.

V. Y. Timoshenko, L. A. Osminkina, A. I. Efimova, L. A. Golovan, P. K. Kashkarov, D. Kovalev, N. Kunzner, E. Gross, J. Diener, and F. Koch, “Anisotropy of optical absorption in birefringent porous silicon,” Phys. Rev. B 67(11), 113405 (2003).
[CrossRef]

Enoch, S.

Fainman, Y.

Fedyanin, A. A.

I. V. Soboleva, E. M. Murchikova, A. A. Fedyanin, and O. A. Aktsipetrov, “Second- and third-harmonic generation in birefringent photonic crystals and microcavities based on anisotropic porous silicon,” Appl. Phys. Lett. 87(24), 241110 (2005).
[CrossRef]

T. V. Dolgova, A. I. Maidykovski, M. G. Martemyanov, A. A. Fedyanin, O. A. Aktsipetrov, G. Marowsky, V. A. Yakovlev, G. Mattei, N. Ohta, and S. Nakabayashi, “Giant optical second-harmonic generation in single and coupled microcavities formed from one-dimensional photonic crystals,” J. Opt. Soc. Am. B 19(9), 2129–2140 (2002).
[CrossRef]

T. V. Dolgova, A. I. Maidykovski, M. G. Martemyanov, A. A. Fedyanin, O. A. Aktsipetrov, G. Marowsky, V. A. Yakovlev, and G. Mattei, “Giant microcavity enhancement of second-harmonic generation in all-silicon photonic crystals,” Appl. Phys. Lett. 81(15), 2725 (2002).
[CrossRef]

T. V. Dolgova, A. I. Maidikovskii, M. G. Martem’yanov, G. Marovsky, G. Mattei, D. Schuhmacher, V. A. Yakovlev, A. A. Fedyanin, and O. A. Aktsipetrov, “Giant second harmonic generation in microcavities based on porous silicon photonic crystals,” JETP Lett. 73(1), 6–9 (2001).
[CrossRef]

Finizio, S. D.

S. Lettieri, S. D. Finizio, P. Maddalena, V. Ballarini, and F. Giorgis, “Second-hamonic generation in amorphous silicon nitride microcavities,” Appl. Phys. Lett. 81(25), 4706 (2002).
[CrossRef]

Giorgis, F.

S. Lettieri, S. D. Finizio, P. Maddalena, V. Ballarini, and F. Giorgis, “Second-hamonic generation in amorphous silicon nitride microcavities,” Appl. Phys. Lett. 81(25), 4706 (2002).
[CrossRef]

Golovan, L. A.

V. Y. Timoshenko, L. A. Osminkina, A. I. Efimova, L. A. Golovan, P. K. Kashkarov, D. Kovalev, N. Kunzner, E. Gross, J. Diener, and F. Koch, “Anisotropy of optical absorption in birefringent porous silicon,” Phys. Rev. B 67(11), 113405 (2003).
[CrossRef]

Gross, E.

V. Y. Timoshenko, L. A. Osminkina, A. I. Efimova, L. A. Golovan, P. K. Kashkarov, D. Kovalev, N. Kunzner, E. Gross, J. Diener, and F. Koch, “Anisotropy of optical absorption in birefringent porous silicon,” Phys. Rev. B 67(11), 113405 (2003).
[CrossRef]

Gu, B.

L. Zhao and B. Gu, “Giant enhancement of second harmonic generation in multiple photonic quantum well structures made of nonlinear material,” Appl. Phys. Lett. 88(12), 122904 (2006).
[CrossRef]

Gu, B. Y.

Kashkarov, P. K.

V. Y. Timoshenko, L. A. Osminkina, A. I. Efimova, L. A. Golovan, P. K. Kashkarov, D. Kovalev, N. Kunzner, E. Gross, J. Diener, and F. Koch, “Anisotropy of optical absorption in birefringent porous silicon,” Phys. Rev. B 67(11), 113405 (2003).
[CrossRef]

Koch, F.

V. Y. Timoshenko, L. A. Osminkina, A. I. Efimova, L. A. Golovan, P. K. Kashkarov, D. Kovalev, N. Kunzner, E. Gross, J. Diener, and F. Koch, “Anisotropy of optical absorption in birefringent porous silicon,” Phys. Rev. B 67(11), 113405 (2003).
[CrossRef]

Kovalev, D.

V. Y. Timoshenko, L. A. Osminkina, A. I. Efimova, L. A. Golovan, P. K. Kashkarov, D. Kovalev, N. Kunzner, E. Gross, J. Diener, and F. Koch, “Anisotropy of optical absorption in birefringent porous silicon,” Phys. Rev. B 67(11), 113405 (2003).
[CrossRef]

Kunzner, N.

V. Y. Timoshenko, L. A. Osminkina, A. I. Efimova, L. A. Golovan, P. K. Kashkarov, D. Kovalev, N. Kunzner, E. Gross, J. Diener, and F. Koch, “Anisotropy of optical absorption in birefringent porous silicon,” Phys. Rev. B 67(11), 113405 (2003).
[CrossRef]

Lettieri, S.

S. Lettieri, S. D. Finizio, P. Maddalena, V. Ballarini, and F. Giorgis, “Second-hamonic generation in amorphous silicon nitride microcavities,” Appl. Phys. Lett. 81(25), 4706 (2002).
[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 Stat. Nonlin. Soft Matter Phys. 75(5), 056606 (2007).
[CrossRef] [PubMed]

Li, Z. Y.

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 Stat. Nonlin. Soft Matter Phys. 75(5), 056606 (2007).
[CrossRef] [PubMed]

Maddalena, P.

S. Lettieri, S. D. Finizio, P. Maddalena, V. Ballarini, and F. Giorgis, “Second-hamonic generation in amorphous silicon nitride microcavities,” Appl. Phys. Lett. 81(25), 4706 (2002).
[CrossRef]

Maidikovskii, A. I.

T. V. Dolgova, A. I. Maidikovskii, M. G. Martem’yanov, G. Marovsky, G. Mattei, D. Schuhmacher, V. A. Yakovlev, A. A. Fedyanin, and O. A. Aktsipetrov, “Giant second harmonic generation in microcavities based on porous silicon photonic crystals,” JETP Lett. 73(1), 6–9 (2001).
[CrossRef]

Maidykovski, A. I.

T. V. Dolgova, A. I. Maidykovski, M. G. Martemyanov, A. A. Fedyanin, O. A. Aktsipetrov, G. Marowsky, V. A. Yakovlev, G. Mattei, N. Ohta, and S. Nakabayashi, “Giant optical second-harmonic generation in single and coupled microcavities formed from one-dimensional photonic crystals,” J. Opt. Soc. Am. B 19(9), 2129–2140 (2002).
[CrossRef]

T. V. Dolgova, A. I. Maidykovski, M. G. Martemyanov, A. A. Fedyanin, O. A. Aktsipetrov, G. Marowsky, V. A. Yakovlev, and G. Mattei, “Giant microcavity enhancement of second-harmonic generation in all-silicon photonic crystals,” Appl. Phys. Lett. 81(15), 2725 (2002).
[CrossRef]

Marovsky, G.

T. V. Dolgova, A. I. Maidikovskii, M. G. Martem’yanov, G. Marovsky, G. Mattei, D. Schuhmacher, V. A. Yakovlev, A. A. Fedyanin, and O. A. Aktsipetrov, “Giant second harmonic generation in microcavities based on porous silicon photonic crystals,” JETP Lett. 73(1), 6–9 (2001).
[CrossRef]

Marowsky, G.

T. V. Dolgova, A. I. Maidykovski, M. G. Martemyanov, A. A. Fedyanin, O. A. Aktsipetrov, G. Marowsky, V. A. Yakovlev, G. Mattei, N. Ohta, and S. Nakabayashi, “Giant optical second-harmonic generation in single and coupled microcavities formed from one-dimensional photonic crystals,” J. Opt. Soc. Am. B 19(9), 2129–2140 (2002).
[CrossRef]

T. V. Dolgova, A. I. Maidykovski, M. G. Martemyanov, A. A. Fedyanin, O. A. Aktsipetrov, G. Marowsky, V. A. Yakovlev, and G. Mattei, “Giant microcavity enhancement of second-harmonic generation in all-silicon photonic crystals,” Appl. Phys. Lett. 81(15), 2725 (2002).
[CrossRef]

Martem’yanov, M. G.

T. V. Dolgova, A. I. Maidikovskii, M. G. Martem’yanov, G. Marovsky, G. Mattei, D. Schuhmacher, V. A. Yakovlev, A. A. Fedyanin, and O. A. Aktsipetrov, “Giant second harmonic generation in microcavities based on porous silicon photonic crystals,” JETP Lett. 73(1), 6–9 (2001).
[CrossRef]

Martemyanov, M. G.

T. V. Dolgova, A. I. Maidykovski, M. G. Martemyanov, A. A. Fedyanin, O. A. Aktsipetrov, G. Marowsky, V. A. Yakovlev, G. Mattei, N. Ohta, and S. Nakabayashi, “Giant optical second-harmonic generation in single and coupled microcavities formed from one-dimensional photonic crystals,” J. Opt. Soc. Am. B 19(9), 2129–2140 (2002).
[CrossRef]

T. V. Dolgova, A. I. Maidykovski, M. G. Martemyanov, A. A. Fedyanin, O. A. Aktsipetrov, G. Marowsky, V. A. Yakovlev, and G. Mattei, “Giant microcavity enhancement of second-harmonic generation in all-silicon photonic crystals,” Appl. Phys. Lett. 81(15), 2725 (2002).
[CrossRef]

Martorell, J.

Mattei, G.

T. V. Dolgova, A. I. Maidykovski, M. G. Martemyanov, A. A. Fedyanin, O. A. Aktsipetrov, G. Marowsky, V. A. Yakovlev, and G. Mattei, “Giant microcavity enhancement of second-harmonic generation in all-silicon photonic crystals,” Appl. Phys. Lett. 81(15), 2725 (2002).
[CrossRef]

T. V. Dolgova, A. I. Maidykovski, M. G. Martemyanov, A. A. Fedyanin, O. A. Aktsipetrov, G. Marowsky, V. A. Yakovlev, G. Mattei, N. Ohta, and S. Nakabayashi, “Giant optical second-harmonic generation in single and coupled microcavities formed from one-dimensional photonic crystals,” J. Opt. Soc. Am. B 19(9), 2129–2140 (2002).
[CrossRef]

T. V. Dolgova, A. I. Maidikovskii, M. G. Martem’yanov, G. Marovsky, G. Mattei, D. Schuhmacher, V. A. Yakovlev, A. A. Fedyanin, and O. A. Aktsipetrov, “Giant second harmonic generation in microcavities based on porous silicon photonic crystals,” JETP Lett. 73(1), 6–9 (2001).
[CrossRef]

Murchikova, E. M.

I. V. Soboleva, E. M. Murchikova, A. A. Fedyanin, and O. A. Aktsipetrov, “Second- and third-harmonic generation in birefringent photonic crystals and microcavities based on anisotropic porous silicon,” Appl. Phys. Lett. 87(24), 241110 (2005).
[CrossRef]

Nakabayashi, S.

Nakagawa, W.

Ochiai, T.

Ohta, N.

Osminkina, L. A.

V. Y. Timoshenko, L. A. Osminkina, A. I. Efimova, L. A. Golovan, P. K. Kashkarov, D. Kovalev, N. Kunzner, E. Gross, J. Diener, and F. Koch, “Anisotropy of optical absorption in birefringent porous silicon,” Phys. Rev. B 67(11), 113405 (2003).
[CrossRef]

Sakoda, K.

Saleh, B. E.

Saleh, M. F.

Scalora, M.

Schuhmacher, D.

T. V. Dolgova, A. I. Maidikovskii, M. G. Martem’yanov, G. Marovsky, G. Mattei, D. Schuhmacher, V. A. Yakovlev, A. A. Fedyanin, and O. A. Aktsipetrov, “Giant second harmonic generation in microcavities based on porous silicon photonic crystals,” JETP Lett. 73(1), 6–9 (2001).
[CrossRef]

Sibilia, C.

Soboleva, I. V.

I. V. Soboleva, E. M. Murchikova, A. A. Fedyanin, and O. A. Aktsipetrov, “Second- and third-harmonic generation in birefringent photonic crystals and microcavities based on anisotropic porous silicon,” Appl. Phys. Lett. 87(24), 241110 (2005).
[CrossRef]

Timoshenko, V. Y.

V. Y. Timoshenko, L. A. Osminkina, A. I. Efimova, L. A. Golovan, P. K. Kashkarov, D. Kovalev, N. Kunzner, E. Gross, J. Diener, and F. Koch, “Anisotropy of optical absorption in birefringent porous silicon,” Phys. Rev. B 67(11), 113405 (2003).
[CrossRef]

Trull, J.

Tyan, R. C.

Vilaseca, R.

Yakovlev, V. A.

T. V. Dolgova, A. I. Maidykovski, M. G. Martemyanov, A. A. Fedyanin, O. A. Aktsipetrov, G. Marowsky, V. A. Yakovlev, and G. Mattei, “Giant microcavity enhancement of second-harmonic generation in all-silicon photonic crystals,” Appl. Phys. Lett. 81(15), 2725 (2002).
[CrossRef]

T. V. Dolgova, A. I. Maidykovski, M. G. Martemyanov, A. A. Fedyanin, O. A. Aktsipetrov, G. Marowsky, V. A. Yakovlev, G. Mattei, N. Ohta, and S. Nakabayashi, “Giant optical second-harmonic generation in single and coupled microcavities formed from one-dimensional photonic crystals,” J. Opt. Soc. Am. B 19(9), 2129–2140 (2002).
[CrossRef]

T. V. Dolgova, A. I. Maidikovskii, M. G. Martem’yanov, G. Marovsky, G. Mattei, D. Schuhmacher, V. A. Yakovlev, A. A. Fedyanin, and O. A. Aktsipetrov, “Giant second harmonic generation in microcavities based on porous silicon photonic crystals,” JETP Lett. 73(1), 6–9 (2001).
[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 Stat. Nonlin. Soft Matter Phys. 75(5), 056606 (2007).
[CrossRef] [PubMed]

Zhao, L.

L. Zhao and B. Gu, “Giant enhancement of second harmonic generation in multiple photonic quantum well structures made of nonlinear material,” Appl. Phys. Lett. 88(12), 122904 (2006).
[CrossRef]

Zhao, L. M.

Appl. Phys. Lett. (4)

I. V. Soboleva, E. M. Murchikova, A. A. Fedyanin, and O. A. Aktsipetrov, “Second- and third-harmonic generation in birefringent photonic crystals and microcavities based on anisotropic porous silicon,” Appl. Phys. Lett. 87(24), 241110 (2005).
[CrossRef]

S. Lettieri, S. D. Finizio, P. Maddalena, V. Ballarini, and F. Giorgis, “Second-hamonic generation in amorphous silicon nitride microcavities,” Appl. Phys. Lett. 81(25), 4706 (2002).
[CrossRef]

T. V. Dolgova, A. I. Maidykovski, M. G. Martemyanov, A. A. Fedyanin, O. A. Aktsipetrov, G. Marowsky, V. A. Yakovlev, and G. Mattei, “Giant microcavity enhancement of second-harmonic generation in all-silicon photonic crystals,” Appl. Phys. Lett. 81(15), 2725 (2002).
[CrossRef]

L. Zhao and B. Gu, “Giant enhancement of second harmonic generation in multiple photonic quantum well structures made of nonlinear material,” Appl. Phys. Lett. 88(12), 122904 (2006).
[CrossRef]

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

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

JETP Lett. (1)

T. V. Dolgova, A. I. Maidikovskii, M. G. Martem’yanov, G. Marovsky, G. Mattei, D. Schuhmacher, V. A. Yakovlev, A. A. Fedyanin, and O. A. Aktsipetrov, “Giant second harmonic generation in microcavities based on porous silicon photonic crystals,” JETP Lett. 73(1), 6–9 (2001).
[CrossRef]

Opt. Express (2)

Opt. Lett. (2)

Phys. Rev. B (1)

V. Y. Timoshenko, L. A. Osminkina, A. I. Efimova, L. A. Golovan, P. K. Kashkarov, D. Kovalev, N. Kunzner, E. Gross, J. Diener, and F. Koch, “Anisotropy of optical absorption in birefringent porous silicon,” Phys. Rev. B 67(11), 113405 (2003).
[CrossRef]

Phys. Rev. E Stat. Nonlin. Soft Matter Phys. (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 Stat. Nonlin. Soft Matter Phys. 75(5), 056606 (2007).
[CrossRef] [PubMed]

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Figures (5)

Fig. 1
Fig. 1

Schematic of a MC structure, showing the coordinate axes and incident angles. White block: low index layer; grey block: high index layer.

Fig. 2
Fig. 2

(a). Intensity of backward SH radiation as a function of wavelength for s-polarized fundamental wave at different angles of incidence: θ0 = 45°, 40 o, and 30 o. (b) The linear reflection spectra for the s-polarized fundamental wave at different angles of incidence: θ 0 = 45°, 40 o, and 30 o.

Fig. 3
Fig. 3

Efficiencies of backward SHG (solid line) and forward SHG (dashed line) as a function of pair number of bottom DBR in the MC for s-polarized pump incidence at the wavelength of 0.783 μm and the angle of incidence: θ 0 = 45°, top DBRs consisting of 12 pairs of high and low index layers.

Fig. 4
Fig. 4

(a). Electrical field intensity distribution of FWs in the MCs for the s-polarized pump incidence at the wavelength of 0.783 μm and the angle of incidence: θ 0 = 45°. The peaks are located at the centers of the spacer layers in the MCs. (b) Electrical field intensity distribution of SHWs.

Fig. 5
Fig. 5

Wavelength dependence of SHG conversion efficiency of the MC consisting of 12 and 15 pairs of high and low index layers in top and bottom DBRs at the pump pulses of 20 mJ, 4 ns and the angle of incidence: θ 0 = 45°. (a) for the backward SHG, (b) for the forward SHG. Insert is the reflection spectrum of the MC indicating a defect mode at the wavelength of 0.783 μm.

Equations (16)

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d2Ey(1)dz2+β(1)2Ey(1)=2k102χ(2)Ey*(1)Ey(2),
d2Ey(2)dz2+β(2)2Ey(2)=k202χ(2)Ey(1)2,
β(1)=[k(1)2k0(1)2sin2θ0(1)]12,β(2)=[k(2)2k0(2)2sin2θ0(2)]12,
Ey,l(1)(z)=Eundepleted,l(1)(z)+Ep,l(z),
Eundepleted,l(1)(z)=Aundepleted,l(1)ejβl(1)(zzl1)+Bundepleted,l(1)ejβl(1)(zzl1),
d2Ey(1)dz2+β(1)2Ey(1)=0.
Ep,l(z)=2k102χl(2)Ey,l*(1)(z)Ey,l(2)(z)βl(1)2=2χl(2)Ey,l*(1)(z)Ey,l(2)(z)[nl(1)2n0(1)2sin2θ0(1)].
Ey,l(1)(z)=Al(1)ejβl(1)(zzl1)+Bl(1)ejβl(1)(zzl1),
Al(1)=(1+Δ)Aundepleted,l(1),Bl(1)=(1+Δ)Bundepleted,l(1),
Δ=2χl(2)Ey,l*(1)(z)Ey,l(2)(z)[nl(1)2n0(1)2sin2θ0(1)]Eundepleted,l(1)(z),
Ey,l(2)=Al(2)ejβl(2)(zzl1)+Bl(2)ejβl(2)(zzl1)+C21ej2βl(1)(zzl1)+C22ej2βl(1)(zzl1)2k202χl(2)βl(2)2Al(1)Bl(1),
C21=k202χl(2)Al(1)2βl(2)24βl(1)2,C22=k202χl(2)Bl(1)2βl(2)24βl(1)2.
|Iz,new(2)Iz(2)|Iz(2)Err,
ηforth=Iforth,N(2)I0,ηback=Iback,1(2)I0,
d2Hy(1)dz2+β(1)2Hy(1)=jωrot(PNL(1))y^,
d2Hy(2)dz2+β(2)2Hy(2)=2jωrot(PNL(2))y^,

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