Abstract

The nonlinear optical properties of one-dimensional all-solid-state photonic-crystal microcavities (MCs) are experimentally studied by second-harmonic generation (SHG) spectroscopy in both the frequency and the wave-vector domains. The studied single and coupled MCs are formed by the alternating of mesoporous silicon layers of different porosities. When the fundamental radiation is in resonance with the MC mode the second-harmonic intensity is enhanced by a factor of approximately 102. The resonant SHG response is compared with the off-resonance response, as the fundamental wavelength is outside the photonic bandgap. The splitting of the modes of two identical coupled MCs is observed in the wave-vector domain spectrum of enhanced SHG. The SHG enhancement is attributed to the combined effects of the spatial localization of the fundamental field in the MC spacer and the fulfillment of the phase-matching conditions. The confinement of the resonant fundamental field is probed directly at the MC cleavage by a scanning near-field optical microscope. The role of the phase matching that is associated with the giant effective dispersion in the spectral vicinity of the MC mode is deduced from a comparison with the SHG peaks at both edges of the photonic bandgap.

© 2002 Optical Society of America

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2001 (6)

F. Genereux, S. W. Leonard, H. M. van Driel, A. Birner, and U. Gösele, “Large birefringence in two-dimensional silicon photonic crystals,” Phys. Rev. B 63, 161101(R)–161104(R) (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]

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, 016609–016609–9 (2001).
[CrossRef]

A. V. Balakin, V. A. Bushuev, B. I. Mantsyzov, I. A. Ozheredov, E. V. Petrov, A. P. Shkurinov, P. Masselin, and G. Mouret, “Enhancement of sum frequency generation near the photonic band gap edge under the quasiphase matching conditions,” Phys. Rev. E 63, 046609–0466011 (2001).
[CrossRef]

M. Falasconi, L. C. Andreani, A. M. Malvezzi, M. Patrini, V. Mulloni, and L. Pavesi, “Bulk and surface contributions to second-order susceptibility in crystalline and porous silicon by second-harmonic generation,” Surf. Sci. 481, 105–112 (2001).
[CrossRef]

H. Cao, D. B. Hall, J. M. Torkelson, and C.-Q. Cao, “Large enhancement of second harmonic generation in polymer films by microcavities,” Appl. Phys. Lett. 76, 538–540 (2001).
[CrossRef]

2000 (4)

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]

O. Bisi, S. Ossicini, and L. Pavesi, “Porous silicon: a quantum sponge structure for silicon based optoelectronics,” Surf. Sci. Rep. 38, 1–126 (2000).
[CrossRef]

N. G. R. Broderick, G. W. Ross, H. L. Offerhaus, D. J. Richardson, and D. C. Hanna, “Hexagonally poled lithium niobate: a two-dimensional nonlinear photonic crystal,” Phys. Rev. Lett. 84, 4345–4348 (2000).
[CrossRef] [PubMed]

A. Ortigosa-Blanch, J. C. Knight, W. J. Wadsworth, J. Arriaga, B. J. Managan, T. A. Birks, and P. St. J. Russell, “Highly birefringent photonic-crystal fibers,” Opt. Lett. 25, 1325–1327 (2000).
[CrossRef]

1999 (5)

A. Imhof, W. Vos, R. Sprik, and A. Lagendijk, “Large dispersive effects near the band edges of photonic crystals,” Phys. Rev. Lett. 83, 2942–2945 (1999).
[CrossRef]

L. A. Kuzik, V. A. Yakovlev, and G. Mattei, “Raman scattering enhancement in porous silicon microcavity,” Appl. Phys. Lett. 75, 1830–1832 (1999).
[CrossRef]

V. Pellegrini, R. Colombelli, I. Carusotto, F. Beltram, S. Rubini, R. Lantier, A. Franciosi, C. Vinegoni, and L. Pavesi, “Resonant second harmonic generation in ZnSe bulk microcavity,” Appl. Phys. Lett. 74, 1945–1947 (1999).
[CrossRef]

A. Yariv, Y. Xu, R. K. Lee, and A. Scherer, “Coupled-resonator optical waveguide: a proposal and analysis,” Opt. Lett. 24, 711–713 (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]

1998 (2)

L. Pavesi, G. Panzarini, and L. C. Andreani, “All-porous silicon-coupled microcavities: experiment versus theory,” Phys. Rev. B 58, 15794–15800 (1998).
[CrossRef]

V. Berger, “Nonlinear photonic crystals,” Phys. Rev. Lett. 81, 4136–4139 (1998).
[CrossRef]

1997 (3)

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]

W. Theiss, “Optical properties of porous silicon,” Surf. Sci. Rep. 29, 91–192 (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 (2)

M. J. Steel and C. Martijn de Sterke, “Second-harmonic generation in second-harmonic fiber Bragg gratings,” Appl. Opt. 35, 3211–3222 (1996).
[CrossRef] [PubMed]

S. J. B. Yoo, C. Caneau, R. Bhat, M. A. Koza, A. Rajhel, and N. Antoniades, “Wavelength conversion by difference frequency generation in AlGaAs waveguides with periodic domain inversion achieved by wafer bonding,” Appl. Phys. Lett. 68, 2609–2611 (1996).
[CrossRef]

1995 (6)

C. Mazzoleni and L. Pavesi, “Application to optical components of dielectric porous silicon multilayers,” Appl. Phys. Lett. 67, 2983–2985 (1995).
[CrossRef]

L. E. Myers, R. C. Eckardt, M. M. Fejer, R. L. Byer, W. R. Bosenberg, and J. W. Pierce, “Quasi-phase-matched optical parametric oscillators in bulk periodically poled LiNbO3,” J. Opt. Soc. Am. B 12, 2102–2116 (1995).
[CrossRef]

J. Trull, R. Vilaseca, J. Martorell, and R. Corbalan, “Second-harmonic generation in local modes of a truncated periodic structure,” Opt. Lett. 20, 1746–1748 (1995).
[CrossRef] [PubMed]

S. Nakagawa, N. Yamada, N. Mikoshiba, and D. E. Mars, “Second-harmonic generation from GaAs/AlAs vertical cavity,” Appl. Phys. Lett. 66, 2159–2161 (1995).
[CrossRef]

O. A. Aktsipetrov, A. V. Melnikov, Yu. N. Moiseev, T. V. Murzina, C. W. van Hasselt, Th. Rasing, and G. Rikken, “Second harmonic generation and atomic-force microscopy studies of porous silicon,” Appl. Phys. Lett. 67, 1191–1193 (1995).
[CrossRef]

V. Pellegrini, A. Tredicucci, C. Mazzoleni, and L. Pavesi, “Enhanced optical properties in porous silicon microcavities,” Phys. Rev. B 52, R14328–R14331 (1995).
[CrossRef]

1994 (2)

J. P. Dowling, M. Scalora, M. J. Bloemer, and C. M. Bowden, “The photonic band edge laser: a new approach to gain enhancement,” J. Appl. Phys. 75, 1896–1899 (1994).
[CrossRef]

M. Scalora, J. P. Dowling, C. M. Bowden, and M. J. Bloemer, “Optical limiting and switching of ultrashort pulses in nonlinear photonic band gap materials,” Phys. Rev. Lett. 73, 1368–1371 (1994).
[CrossRef] [PubMed]

1989 (1)

1987 (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]

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

1976 (1)

J. P. van der Ziel and M. Ilegems, “Optical second harmonic generation in periodic multilayer GaAs–Al0.3Ga0.7As structures,” Appl. Phys. Lett. 28, 437–439 (1976).
[CrossRef]

1970 (1)

N. Bloembergen and J. Sievers, “Nonlinear optical properties of periodic laminar structures,” Appl. Phys. Lett. 17, 483–486 (1970).
[CrossRef]

1968 (1)

N. Bloembergen, R. K. Chang, S. S. Jha, and C. H. Lee, “Optical second-harmonic generation in reflection from media with inversion symmetry,” Phys. Rev. 174, 813–822 (1968).
[CrossRef]

1962 (2)

N. Bloembergen and P. S. Pershan, “Light waves at the boundary of nonlinear media,” Phys. Rev. 128, 606–622 (1962).
[CrossRef]

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, “Interactions between light waves in a nonlinear dielectric,” Phys. Rev. 127, 1918–1939 (1962).
[CrossRef]

Aktsipetrov, O. A.

O. A. Aktsipetrov, A. V. Melnikov, Yu. N. Moiseev, T. V. Murzina, C. W. van Hasselt, Th. Rasing, and G. Rikken, “Second harmonic generation and atomic-force microscopy studies of porous silicon,” Appl. Phys. Lett. 67, 1191–1193 (1995).
[CrossRef]

Andreani, L. C.

M. Falasconi, L. C. Andreani, A. M. Malvezzi, M. Patrini, V. Mulloni, and L. Pavesi, “Bulk and surface contributions to second-order susceptibility in crystalline and porous silicon by second-harmonic generation,” Surf. Sci. 481, 105–112 (2001).
[CrossRef]

L. Pavesi, G. Panzarini, and L. C. Andreani, “All-porous silicon-coupled microcavities: experiment versus theory,” Phys. Rev. B 58, 15794–15800 (1998).
[CrossRef]

Antoniades, N.

S. J. B. Yoo, C. Caneau, R. Bhat, M. A. Koza, A. Rajhel, and N. Antoniades, “Wavelength conversion by difference frequency generation in AlGaAs waveguides with periodic domain inversion achieved by wafer bonding,” Appl. Phys. Lett. 68, 2609–2611 (1996).
[CrossRef]

Armstrong, J. A.

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, “Interactions between light waves in a nonlinear dielectric,” Phys. Rev. 127, 1918–1939 (1962).
[CrossRef]

Arriaga, J.

Balakin, A. V.

A. V. Balakin, V. A. Bushuev, B. I. Mantsyzov, I. A. Ozheredov, E. V. Petrov, A. P. Shkurinov, P. Masselin, and G. Mouret, “Enhancement of sum frequency generation near the photonic band gap edge under the quasiphase matching conditions,” Phys. Rev. E 63, 046609–0466011 (2001).
[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]

Beltram, F.

V. Pellegrini, R. Colombelli, I. Carusotto, F. Beltram, S. Rubini, R. Lantier, A. Franciosi, C. Vinegoni, and L. Pavesi, “Resonant second harmonic generation in ZnSe bulk microcavity,” Appl. Phys. Lett. 74, 1945–1947 (1999).
[CrossRef]

Berger, V.

V. Berger, “Nonlinear photonic crystals,” Phys. Rev. Lett. 81, 4136–4139 (1998).
[CrossRef]

Bertolotti, M.

G. D’Aguanno, M. Centini, M. Scalora, C. Sibilia, Y. Dumeige, P. Vidakovic, J. A. Levenson, M. J. Bloemer, C. M. Bowden, J. W. Haus, and M. Bertolotti, “Photonic band edge effects in finite structures and applications to χ(2) interactions,” Phys. Rev. E 64, 016609–016609–9 (2001).
[CrossRef]

Bethune, D. S.

Bhat, R.

S. J. B. Yoo, C. Caneau, R. Bhat, M. A. Koza, A. Rajhel, and N. Antoniades, “Wavelength conversion by difference frequency generation in AlGaAs waveguides with periodic domain inversion achieved by wafer bonding,” Appl. Phys. Lett. 68, 2609–2611 (1996).
[CrossRef]

Birks, T. A.

Birner, A.

F. Genereux, S. W. Leonard, H. M. van Driel, A. Birner, and U. Gösele, “Large birefringence in two-dimensional silicon photonic crystals,” Phys. Rev. B 63, 161101(R)–161104(R) (2001).
[CrossRef]

Bisi, O.

O. Bisi, S. Ossicini, and L. Pavesi, “Porous silicon: a quantum sponge structure for silicon based optoelectronics,” Surf. Sci. Rep. 38, 1–126 (2000).
[CrossRef]

Bloembergen, N.

N. Bloembergen and J. Sievers, “Nonlinear optical properties of periodic laminar structures,” Appl. Phys. Lett. 17, 483–486 (1970).
[CrossRef]

N. Bloembergen, R. K. Chang, S. S. Jha, and C. H. Lee, “Optical second-harmonic generation in reflection from media with inversion symmetry,” Phys. Rev. 174, 813–822 (1968).
[CrossRef]

N. Bloembergen and P. S. Pershan, “Light waves at the boundary of nonlinear media,” Phys. Rev. 128, 606–622 (1962).
[CrossRef]

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, “Interactions between light waves in a nonlinear dielectric,” Phys. Rev. 127, 1918–1939 (1962).
[CrossRef]

Bloemer, M. J.

G. D’Aguanno, M. Centini, M. Scalora, C. Sibilia, Y. Dumeige, P. Vidakovic, J. A. Levenson, M. J. Bloemer, C. M. Bowden, J. W. Haus, and M. Bertolotti, “Photonic band edge effects in finite structures and applications to χ(2) interactions,” Phys. Rev. E 64, 016609–016609–9 (2001).
[CrossRef]

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

J. P. Dowling, M. Scalora, M. J. Bloemer, and C. M. Bowden, “The photonic band edge laser: a new approach to gain enhancement,” J. Appl. Phys. 75, 1896–1899 (1994).
[CrossRef]

M. Scalora, J. P. Dowling, C. M. Bowden, and M. J. Bloemer, “Optical limiting and switching of ultrashort pulses in nonlinear photonic band gap materials,” Phys. Rev. Lett. 73, 1368–1371 (1994).
[CrossRef] [PubMed]

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Boucher, D.

Bowden, C. M.

G. D’Aguanno, M. Centini, M. Scalora, C. Sibilia, Y. Dumeige, P. Vidakovic, J. A. Levenson, M. J. Bloemer, C. M. Bowden, J. W. Haus, and M. Bertolotti, “Photonic band edge effects in finite structures and applications to χ(2) interactions,” Phys. Rev. E 64, 016609–016609–9 (2001).
[CrossRef]

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

J. P. Dowling, M. Scalora, M. J. Bloemer, and C. M. Bowden, “The photonic band edge laser: a new approach to gain enhancement,” J. Appl. Phys. 75, 1896–1899 (1994).
[CrossRef]

M. Scalora, J. P. Dowling, C. M. Bowden, and M. J. Bloemer, “Optical limiting and switching of ultrashort pulses in nonlinear photonic band gap materials,” Phys. Rev. Lett. 73, 1368–1371 (1994).
[CrossRef] [PubMed]

Broderick, N. G. R.

N. G. R. Broderick, G. W. Ross, H. L. Offerhaus, D. J. Richardson, and D. C. Hanna, “Hexagonally poled lithium niobate: a two-dimensional nonlinear photonic crystal,” Phys. Rev. Lett. 84, 4345–4348 (2000).
[CrossRef] [PubMed]

Bushuev, V. A.

A. V. Balakin, V. A. Bushuev, B. I. Mantsyzov, I. A. Ozheredov, E. V. Petrov, A. P. Shkurinov, P. Masselin, and G. Mouret, “Enhancement of sum frequency generation near the photonic band gap edge under the quasiphase matching conditions,” Phys. Rev. E 63, 046609–0466011 (2001).
[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]

Byer, R. L.

Caneau, C.

S. J. B. Yoo, C. Caneau, R. Bhat, M. A. Koza, A. Rajhel, and N. Antoniades, “Wavelength conversion by difference frequency generation in AlGaAs waveguides with periodic domain inversion achieved by wafer bonding,” Appl. Phys. Lett. 68, 2609–2611 (1996).
[CrossRef]

Cao, C.-Q.

H. Cao, D. B. Hall, J. M. Torkelson, and C.-Q. Cao, “Large enhancement of second harmonic generation in polymer films by microcavities,” Appl. Phys. Lett. 76, 538–540 (2001).
[CrossRef]

Cao, H.

H. Cao, D. B. Hall, J. M. Torkelson, and C.-Q. Cao, “Large enhancement of second harmonic generation in polymer films by microcavities,” Appl. Phys. Lett. 76, 538–540 (2001).
[CrossRef]

Carusotto, I.

V. Pellegrini, R. Colombelli, I. Carusotto, F. Beltram, S. Rubini, R. Lantier, A. Franciosi, C. Vinegoni, and L. Pavesi, “Resonant second harmonic generation in ZnSe bulk microcavity,” Appl. Phys. Lett. 74, 1945–1947 (1999).
[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, 016609–016609–9 (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]

Chang, R. K.

N. Bloembergen, R. K. Chang, S. S. Jha, and C. H. Lee, “Optical second-harmonic generation in reflection from media with inversion symmetry,” Phys. Rev. 174, 813–822 (1968).
[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]

Colombelli, R.

V. Pellegrini, R. Colombelli, I. Carusotto, F. Beltram, S. Rubini, R. Lantier, A. Franciosi, C. Vinegoni, and L. Pavesi, “Resonant second harmonic generation in ZnSe bulk microcavity,” Appl. Phys. Lett. 74, 1945–1947 (1999).
[CrossRef]

Corbalan, R.

D’Aguanno, G.

G. D’Aguanno, M. Centini, M. Scalora, C. Sibilia, Y. Dumeige, P. Vidakovic, J. A. Levenson, M. J. Bloemer, C. M. Bowden, J. W. Haus, and M. Bertolotti, “Photonic band edge effects in finite structures and applications to χ(2) interactions,” Phys. Rev. E 64, 016609–016609–9 (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]

de Sterke, C. Martijn

Debray, J. P.

Dowling, J. P.

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

J. P. Dowling, M. Scalora, M. J. Bloemer, and C. M. Bowden, “The photonic band edge laser: a new approach to gain enhancement,” J. Appl. Phys. 75, 1896–1899 (1994).
[CrossRef]

M. Scalora, J. P. Dowling, C. M. Bowden, and M. J. Bloemer, “Optical limiting and switching of ultrashort pulses in nonlinear photonic band gap materials,” Phys. Rev. Lett. 73, 1368–1371 (1994).
[CrossRef] [PubMed]

Ducuing, J.

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, “Interactions between light waves in a nonlinear dielectric,” Phys. Rev. 127, 1918–1939 (1962).
[CrossRef]

Dumeige, Y.

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

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, 016609–016609–9 (2001).
[CrossRef]

Eckardt, R. C.

Falasconi, M.

M. Falasconi, L. C. Andreani, A. M. Malvezzi, M. Patrini, V. Mulloni, and L. Pavesi, “Bulk and surface contributions to second-order susceptibility in crystalline and porous silicon by second-harmonic generation,” Surf. Sci. 481, 105–112 (2001).
[CrossRef]

Fejer, M. M.

Franciosi, A.

V. Pellegrini, R. Colombelli, I. Carusotto, F. Beltram, S. Rubini, R. Lantier, A. Franciosi, C. Vinegoni, and L. Pavesi, “Resonant second harmonic generation in ZnSe bulk microcavity,” Appl. Phys. Lett. 74, 1945–1947 (1999).
[CrossRef]

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F. Genereux, S. W. Leonard, H. M. van Driel, A. Birner, and U. Gösele, “Large birefringence in two-dimensional silicon photonic crystals,” Phys. Rev. B 63, 161101(R)–161104(R) (2001).
[CrossRef]

Gösele, U.

F. Genereux, S. W. Leonard, H. M. van Driel, A. Birner, and U. Gösele, “Large birefringence in two-dimensional silicon photonic crystals,” Phys. Rev. B 63, 161101(R)–161104(R) (2001).
[CrossRef]

Hall, D. B.

H. Cao, D. B. Hall, J. M. Torkelson, and C.-Q. Cao, “Large enhancement of second harmonic generation in polymer films by microcavities,” Appl. Phys. Lett. 76, 538–540 (2001).
[CrossRef]

Hanna, D. C.

N. G. R. Broderick, G. W. Ross, H. L. Offerhaus, D. J. Richardson, and D. C. Hanna, “Hexagonally poled lithium niobate: a two-dimensional nonlinear photonic crystal,” Phys. Rev. Lett. 84, 4345–4348 (2000).
[CrossRef] [PubMed]

Harmand, J. C.

Haus, J. W.

G. D’Aguanno, M. Centini, M. Scalora, C. Sibilia, Y. Dumeige, P. Vidakovic, J. A. Levenson, M. J. Bloemer, C. M. Bowden, J. W. Haus, and M. Bertolotti, “Photonic band edge effects in finite structures and applications to χ(2) interactions,” Phys. Rev. E 64, 016609–016609–9 (2001).
[CrossRef]

M. Scalora, M. J. Bloemer, A. S. Manka, J. P. Dowling, C. M. Bowden, R. Viswanathan, and J. W. Haus, “Pulsed second-harmonic generation in nonlinear, one-dimensional, periodic structures,” Phys. Rev. A 56, 3166–3174 (1997).
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J. P. van der Ziel and M. Ilegems, “Optical second harmonic generation in periodic multilayer GaAs–Al0.3Ga0.7As structures,” Appl. Phys. Lett. 28, 437–439 (1976).
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A. Imhof, W. Vos, R. Sprik, and A. Lagendijk, “Large dispersive effects near the band edges of photonic crystals,” Phys. Rev. Lett. 83, 2942–2945 (1999).
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Jha, S. S.

N. Bloembergen, R. K. Chang, S. S. Jha, and C. H. Lee, “Optical second-harmonic generation in reflection from media with inversion symmetry,” Phys. Rev. 174, 813–822 (1968).
[CrossRef]

Knight, J. C.

Koroteev, N. I.

Koza, M. A.

S. J. B. Yoo, C. Caneau, R. Bhat, M. A. Koza, A. Rajhel, and N. Antoniades, “Wavelength conversion by difference frequency generation in AlGaAs waveguides with periodic domain inversion achieved by wafer bonding,” Appl. Phys. Lett. 68, 2609–2611 (1996).
[CrossRef]

Kuzik, L. A.

L. A. Kuzik, V. A. Yakovlev, and G. Mattei, “Raman scattering enhancement in porous silicon microcavity,” Appl. Phys. Lett. 75, 1830–1832 (1999).
[CrossRef]

Lagendijk, A.

A. Imhof, W. Vos, R. Sprik, and A. Lagendijk, “Large dispersive effects near the band edges of photonic crystals,” Phys. Rev. Lett. 83, 2942–2945 (1999).
[CrossRef]

Lantier, R.

V. Pellegrini, R. Colombelli, I. Carusotto, F. Beltram, S. Rubini, R. Lantier, A. Franciosi, C. Vinegoni, and L. Pavesi, “Resonant second harmonic generation in ZnSe bulk microcavity,” Appl. Phys. Lett. 74, 1945–1947 (1999).
[CrossRef]

Lee, C. H.

N. Bloembergen, R. K. Chang, S. S. Jha, and C. H. Lee, “Optical second-harmonic generation in reflection from media with inversion symmetry,” Phys. Rev. 174, 813–822 (1968).
[CrossRef]

Lee, R. K.

Leonard, S. W.

F. Genereux, S. W. Leonard, H. M. van Driel, A. Birner, and U. Gösele, “Large birefringence in two-dimensional silicon photonic crystals,” Phys. Rev. B 63, 161101(R)–161104(R) (2001).
[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]

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, 016609–016609–9 (2001).
[CrossRef]

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

Lovering, D. J.

Malvezzi, A. M.

M. Falasconi, L. C. Andreani, A. M. Malvezzi, M. Patrini, V. Mulloni, and L. Pavesi, “Bulk and surface contributions to second-order susceptibility in crystalline and porous silicon by second-harmonic generation,” Surf. Sci. 481, 105–112 (2001).
[CrossRef]

Managan, B. J.

Manka, A. S.

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

Mantsyzov, B. I.

A. V. Balakin, V. A. Bushuev, B. I. Mantsyzov, I. A. Ozheredov, E. V. Petrov, A. P. Shkurinov, P. Masselin, and G. Mouret, “Enhancement of sum frequency generation near the photonic band gap edge under the quasiphase matching conditions,” Phys. Rev. E 63, 046609–0466011 (2001).
[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]

Mars, D. E.

S. Nakagawa, N. Yamada, N. Mikoshiba, and D. E. Mars, “Second-harmonic generation from GaAs/AlAs vertical cavity,” Appl. Phys. Lett. 66, 2159–2161 (1995).
[CrossRef]

Martorell, J.

Masselin, P.

A. V. Balakin, V. A. Bushuev, B. I. Mantsyzov, I. A. Ozheredov, E. V. Petrov, A. P. Shkurinov, P. Masselin, and G. Mouret, “Enhancement of sum frequency generation near the photonic band gap edge under the quasiphase matching conditions,” Phys. Rev. E 63, 046609–0466011 (2001).
[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]

Mattei, G.

L. A. Kuzik, V. A. Yakovlev, and G. Mattei, “Raman scattering enhancement in porous silicon microcavity,” Appl. Phys. Lett. 75, 1830–1832 (1999).
[CrossRef]

Mazzoleni, C.

V. Pellegrini, A. Tredicucci, C. Mazzoleni, and L. Pavesi, “Enhanced optical properties in porous silicon microcavities,” Phys. Rev. B 52, R14328–R14331 (1995).
[CrossRef]

C. Mazzoleni and L. Pavesi, “Application to optical components of dielectric porous silicon multilayers,” Appl. Phys. Lett. 67, 2983–2985 (1995).
[CrossRef]

Melnikov, A. V.

O. A. Aktsipetrov, A. V. Melnikov, Yu. N. Moiseev, T. V. Murzina, C. W. van Hasselt, Th. Rasing, and G. Rikken, “Second harmonic generation and atomic-force microscopy studies of porous silicon,” Appl. Phys. Lett. 67, 1191–1193 (1995).
[CrossRef]

Mikoshiba, N.

S. Nakagawa, N. Yamada, N. Mikoshiba, and D. E. Mars, “Second-harmonic generation from GaAs/AlAs vertical cavity,” Appl. Phys. Lett. 66, 2159–2161 (1995).
[CrossRef]

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]

Moiseev, Yu. N.

O. A. Aktsipetrov, A. V. Melnikov, Yu. N. Moiseev, T. V. Murzina, C. W. van Hasselt, Th. Rasing, and G. Rikken, “Second harmonic generation and atomic-force microscopy studies of porous silicon,” Appl. Phys. Lett. 67, 1191–1193 (1995).
[CrossRef]

Mouret, G.

A. V. Balakin, V. A. Bushuev, B. I. Mantsyzov, I. A. Ozheredov, E. V. Petrov, A. P. Shkurinov, P. Masselin, and G. Mouret, “Enhancement of sum frequency generation near the photonic band gap edge under the quasiphase matching conditions,” Phys. Rev. E 63, 046609–0466011 (2001).
[CrossRef]

Mulloni, V.

M. Falasconi, L. C. Andreani, A. M. Malvezzi, M. Patrini, V. Mulloni, and L. Pavesi, “Bulk and surface contributions to second-order susceptibility in crystalline and porous silicon by second-harmonic generation,” Surf. Sci. 481, 105–112 (2001).
[CrossRef]

Murzina, T. V.

O. A. Aktsipetrov, A. V. Melnikov, Yu. N. Moiseev, T. V. Murzina, C. W. van Hasselt, Th. Rasing, and G. Rikken, “Second harmonic generation and atomic-force microscopy studies of porous silicon,” Appl. Phys. Lett. 67, 1191–1193 (1995).
[CrossRef]

Myers, L. E.

Nakagawa, S.

S. Nakagawa, N. Yamada, N. Mikoshiba, and D. E. Mars, “Second-harmonic generation from GaAs/AlAs vertical cavity,” Appl. Phys. Lett. 66, 2159–2161 (1995).
[CrossRef]

Offerhaus, H. L.

N. G. R. Broderick, G. W. Ross, H. L. Offerhaus, D. J. Richardson, and D. C. Hanna, “Hexagonally poled lithium niobate: a two-dimensional nonlinear photonic crystal,” Phys. Rev. Lett. 84, 4345–4348 (2000).
[CrossRef] [PubMed]

Ortigosa-Blanch, A.

Ossicini, S.

O. Bisi, S. Ossicini, and L. Pavesi, “Porous silicon: a quantum sponge structure for silicon based optoelectronics,” Surf. Sci. Rep. 38, 1–126 (2000).
[CrossRef]

Ozheredov, I. A.

A. V. Balakin, V. A. Bushuev, B. I. Mantsyzov, I. A. Ozheredov, E. V. Petrov, A. P. Shkurinov, P. Masselin, and G. Mouret, “Enhancement of sum frequency generation near the photonic band gap edge under the quasiphase matching conditions,” Phys. Rev. E 63, 046609–0466011 (2001).
[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]

Panzarini, G.

L. Pavesi, G. Panzarini, and L. C. Andreani, “All-porous silicon-coupled microcavities: experiment versus theory,” Phys. Rev. B 58, 15794–15800 (1998).
[CrossRef]

Patrini, M.

M. Falasconi, L. C. Andreani, A. M. Malvezzi, M. Patrini, V. Mulloni, and L. Pavesi, “Bulk and surface contributions to second-order susceptibility in crystalline and porous silicon by second-harmonic generation,” Surf. Sci. 481, 105–112 (2001).
[CrossRef]

Pavesi, L.

M. Falasconi, L. C. Andreani, A. M. Malvezzi, M. Patrini, V. Mulloni, and L. Pavesi, “Bulk and surface contributions to second-order susceptibility in crystalline and porous silicon by second-harmonic generation,” Surf. Sci. 481, 105–112 (2001).
[CrossRef]

O. Bisi, S. Ossicini, and L. Pavesi, “Porous silicon: a quantum sponge structure for silicon based optoelectronics,” Surf. Sci. Rep. 38, 1–126 (2000).
[CrossRef]

V. Pellegrini, R. Colombelli, I. Carusotto, F. Beltram, S. Rubini, R. Lantier, A. Franciosi, C. Vinegoni, and L. Pavesi, “Resonant second harmonic generation in ZnSe bulk microcavity,” Appl. Phys. Lett. 74, 1945–1947 (1999).
[CrossRef]

L. Pavesi, G. Panzarini, and L. C. Andreani, “All-porous silicon-coupled microcavities: experiment versus theory,” Phys. Rev. B 58, 15794–15800 (1998).
[CrossRef]

V. Pellegrini, A. Tredicucci, C. Mazzoleni, and L. Pavesi, “Enhanced optical properties in porous silicon microcavities,” Phys. Rev. B 52, R14328–R14331 (1995).
[CrossRef]

C. Mazzoleni and L. Pavesi, “Application to optical components of dielectric porous silicon multilayers,” Appl. Phys. Lett. 67, 2983–2985 (1995).
[CrossRef]

Pellegrini, V.

V. Pellegrini, R. Colombelli, I. Carusotto, F. Beltram, S. Rubini, R. Lantier, A. Franciosi, C. Vinegoni, and L. Pavesi, “Resonant second harmonic generation in ZnSe bulk microcavity,” Appl. Phys. Lett. 74, 1945–1947 (1999).
[CrossRef]

V. Pellegrini, A. Tredicucci, C. Mazzoleni, and L. Pavesi, “Enhanced optical properties in porous silicon microcavities,” Phys. Rev. B 52, R14328–R14331 (1995).
[CrossRef]

Pershan, P. S.

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, “Interactions between light waves in a nonlinear dielectric,” Phys. Rev. 127, 1918–1939 (1962).
[CrossRef]

N. Bloembergen and P. S. Pershan, “Light waves at the boundary of nonlinear media,” Phys. Rev. 128, 606–622 (1962).
[CrossRef]

Petrov, E. V.

A. V. Balakin, V. A. Bushuev, B. I. Mantsyzov, I. A. Ozheredov, E. V. Petrov, A. P. Shkurinov, P. Masselin, and G. Mouret, “Enhancement of sum frequency generation near the photonic band gap edge under the quasiphase matching conditions,” Phys. Rev. E 63, 046609–0466011 (2001).
[CrossRef]

Pierce, J. W.

Rajhel, A.

S. J. B. Yoo, C. Caneau, R. Bhat, M. A. Koza, A. Rajhel, and N. Antoniades, “Wavelength conversion by difference frequency generation in AlGaAs waveguides with periodic domain inversion achieved by wafer bonding,” Appl. Phys. Lett. 68, 2609–2611 (1996).
[CrossRef]

Rasing, Th.

O. A. Aktsipetrov, A. V. Melnikov, Yu. N. Moiseev, T. V. Murzina, C. W. van Hasselt, Th. Rasing, and G. Rikken, “Second harmonic generation and atomic-force microscopy studies of porous silicon,” Appl. Phys. Lett. 67, 1191–1193 (1995).
[CrossRef]

Richardson, D. J.

N. G. R. Broderick, G. W. Ross, H. L. Offerhaus, D. J. Richardson, and D. C. Hanna, “Hexagonally poled lithium niobate: a two-dimensional nonlinear photonic crystal,” Phys. Rev. Lett. 84, 4345–4348 (2000).
[CrossRef] [PubMed]

Rikken, G.

O. A. Aktsipetrov, A. V. Melnikov, Yu. N. Moiseev, T. V. Murzina, C. W. van Hasselt, Th. Rasing, and G. Rikken, “Second harmonic generation and atomic-force microscopy studies of porous silicon,” Appl. Phys. Lett. 67, 1191–1193 (1995).
[CrossRef]

Ross, G. W.

N. G. R. Broderick, G. W. Ross, H. L. Offerhaus, D. J. Richardson, and D. C. Hanna, “Hexagonally poled lithium niobate: a two-dimensional nonlinear photonic crystal,” Phys. Rev. Lett. 84, 4345–4348 (2000).
[CrossRef] [PubMed]

Rubini, S.

V. Pellegrini, R. Colombelli, I. Carusotto, F. Beltram, S. Rubini, R. Lantier, A. Franciosi, C. Vinegoni, and L. Pavesi, “Resonant second harmonic generation in ZnSe bulk microcavity,” Appl. Phys. Lett. 74, 1945–1947 (1999).
[CrossRef]

Russell, P. St. J.

Sagnes, I.

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

Sauvage, S.

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

Scalora, M.

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

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[CrossRef]

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[CrossRef]

J. P. Dowling, M. Scalora, M. J. Bloemer, and C. M. Bowden, “The photonic band edge laser: a new approach to gain enhancement,” J. Appl. Phys. 75, 1896–1899 (1994).
[CrossRef]

M. Scalora, J. P. Dowling, C. M. Bowden, and M. J. Bloemer, “Optical limiting and switching of ultrashort pulses in nonlinear photonic band gap materials,” Phys. Rev. Lett. 73, 1368–1371 (1994).
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[CrossRef]

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[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, 016609–016609–9 (2001).
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O. A. Aktsipetrov, A. V. Melnikov, Yu. N. Moiseev, T. V. Murzina, C. W. van Hasselt, Th. Rasing, and G. Rikken, “Second harmonic generation and atomic-force microscopy studies of porous silicon,” Appl. Phys. Lett. 67, 1191–1193 (1995).
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[CrossRef]

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[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]

H. Cao, D. B. Hall, J. M. Torkelson, and C.-Q. Cao, “Large enhancement of second harmonic generation in polymer films by microcavities,” Appl. Phys. Lett. 76, 538–540 (2001).
[CrossRef]

V. Pellegrini, R. Colombelli, I. Carusotto, F. Beltram, S. Rubini, R. Lantier, A. Franciosi, C. Vinegoni, and L. Pavesi, “Resonant second harmonic generation in ZnSe bulk microcavity,” Appl. Phys. Lett. 74, 1945–1947 (1999).
[CrossRef]

C. Mazzoleni and L. Pavesi, “Application to optical components of dielectric porous silicon multilayers,” Appl. Phys. Lett. 67, 2983–2985 (1995).
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J. P. Dowling, M. Scalora, M. J. Bloemer, and C. M. Bowden, “The photonic band edge laser: a new approach to gain enhancement,” J. Appl. Phys. 75, 1896–1899 (1994).
[CrossRef]

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[CrossRef]

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[CrossRef]

Phys. Rev. A (1)

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

Phys. Rev. B (3)

F. Genereux, S. W. Leonard, H. M. van Driel, A. Birner, and U. Gösele, “Large birefringence in two-dimensional silicon photonic crystals,” Phys. Rev. B 63, 161101(R)–161104(R) (2001).
[CrossRef]

V. Pellegrini, A. Tredicucci, C. Mazzoleni, and L. Pavesi, “Enhanced optical properties in porous silicon microcavities,” Phys. Rev. B 52, R14328–R14331 (1995).
[CrossRef]

L. Pavesi, G. Panzarini, and L. C. Andreani, “All-porous silicon-coupled microcavities: experiment versus theory,” Phys. Rev. B 58, 15794–15800 (1998).
[CrossRef]

Phys. Rev. E (2)

G. D’Aguanno, M. Centini, M. Scalora, C. Sibilia, Y. Dumeige, P. Vidakovic, J. A. Levenson, M. J. Bloemer, C. M. Bowden, J. W. Haus, and M. Bertolotti, “Photonic band edge effects in finite structures and applications to χ(2) interactions,” Phys. Rev. E 64, 016609–016609–9 (2001).
[CrossRef]

A. V. Balakin, V. A. Bushuev, B. I. Mantsyzov, I. A. Ozheredov, E. V. Petrov, A. P. Shkurinov, P. Masselin, and G. Mouret, “Enhancement of sum frequency generation near the photonic band gap edge under the quasiphase matching conditions,” Phys. Rev. E 63, 046609–0466011 (2001).
[CrossRef]

Phys. Rev. Lett. (6)

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[CrossRef] [PubMed]

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M. Scalora, J. P. Dowling, C. M. Bowden, and M. J. Bloemer, “Optical limiting and switching of ultrashort pulses in nonlinear photonic band gap materials,” Phys. Rev. Lett. 73, 1368–1371 (1994).
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Figures (9)

Fig. 1
Fig. 1

(a) Scanning shear-force microscope image of the MC cleavage with λMC620 nm. The scan area is 1.8 µm×1.8 µm. (b) Scanning electron microscope image of the MC cleavage with λMC1700 nm.

Fig. 2
Fig. 2

Top panels: ω-domain SH intensity spectra for MC with λMC945 nm, and bottom panels: spectra of the linear reflection coefficient of the s-polarized fundamental wave, both measured for angles of incidence of (a) θ0=45°, (b) θ0=40°, and (c) θ0=30°. Curves are fits of numerical-calculation results within a nonlinear optical transfer-matrix formalism to the data. The fit parameters are as follows: top, DBR-layer thickness of dL240 nm and dH150 nm; bottom, DBR-layer thicknesses of dL230 nm and dH140 nm, a cavity-layer thickness of dMC305 nm, and layer porosities of fL=fMC0.88 and fH0.77.

Fig. 3
Fig. 3

Top panel: k-domain SH intensity spectra of the MC sample. Bottom panel: angular spectra of the linear reflection of the s-polarized fundamental radiation.

Fig. 4
Fig. 4

Top panel: k-domain SH intensity spectrum of the coupled-MC sample. Bottom panel: angular spectrum of the linear reflection of the s-polarized fundamental radiation. Inset: ω-domain spectrum of the linear reflection coefficient from the coupled-MC sample with λMC680 nm at an angle of incidence of 30°. The arrows indicate the positions of the coupled-MC modes.

Fig. 5
Fig. 5

Top panel: spatial distribution of the light intensity at the MC cleavage measured with SNOM. Bottom panel: cross section of the intensity distribution perpendicular to the MC surface as extracted from the SNOM image (circles) and calculated by transfer-matrix formalism (curve). The dashed lines mark the cavity layer.

Fig. 6
Fig. 6

Schematic of a multilayer nonlinear medium. The wave vectors of forward- and backward-propagating homogeneous SH waves in the ith and the jth layers and of inhomogeneous SH waves in the jth layer are shown.

Fig. 7
Fig. 7

Amplitudes of outgoing partial SH fields |E0,j| generated in every jth layer of the MC plotted as functions of the layer number calculated for fundamental wavelengths at the cavity mode (top panel), near the PBG edge at the spectral position of the SHG peak (filled bars in middle panel) and outside the PBG (crosshatched bars in middle panel), and inside the PBG (bottom panel). The spectral positions are marked at the sketched linear reflection and SHG spectra in the insets. The dashed lines indicate the cavity spacer, and the topmost layer is layer 1. Details of the ideal MC sample used for calculation are given in the text.

Fig. 8
Fig. 8

Partial SH contributions E0,j presented at the complex plane and calculated for the fundamental wavelength at the cavity mode (top panel), near the PBG edge (middle panel), and inside the PBG (bottom panel).

Fig. 9
Fig. 9

Top panel: k-domain SH intensity spectra of the reference PS slab. Bottom panel: angular spectra of linear reflection of the s-polarized fundamental radiation.

Equations (27)

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

(1-fj) Si-jSi+2j=fj j-11+2j,
Pj2ω(z)=χˆj(2) : Ejω(z)Ejω(z),
χ1χxzx=χyzy=χxxz=χyyz,
χ2χzxx=χzyy,
χ3χzzz.
Ps(z)=2χ1Esω(z)Epω(z)sin θ,
Pp(z)=(P2+P2)1/2,
P=χ1(Epω)2 sin 2θ cos θ-χ2(Epω)2 cos2 θ sin θ-χ2(Esω)2 sin θ-χ3(Epω)2 sin3 θ,
P=χ1(Epω)2 sin 2θ sin θ+χ2(Epω)2 cos3 θ+χ2(Esω)2 cos θ+χ3(Epω)2 sin2 θ cos θ.
χˆj(2)=[a-b/(-Ω+2ω+iΓ)](1-fj).
Pj2ω=Ps+P+P
E(s)=4πj(ω)-j(2ω)(Ps+P)-4πj(2ω) P.
Ejω(z, t)=Ej+ exp[+ikz,jω(z-dij)+(ikxωx-iωt)]+Ej- exp[-ikz,jω(z-dij)+(ikxωx-iωt)],
Ei+Ei-=1/tijrij/tijrij/tij1/tijEj+Ej-,
Ej+Ej-=Ej
1/tijrij/tijrij/tij1/tij=Mij.
Ej(zj+ζ)=Φj(ζ)Ej(zj)
Φj(ζ)=exp(ikz,jωζ)00exp(-ikz,jωζ).
T=Ml(l-1)Φ(l-1)  M10,
Ejω(z)=Tj(z)E0ω=exp(ikz,jωz)00exp(-ikz,jωz)×Mj(j-1)Φ(j-1)  M101R.
Ei=MijEj+Mi(s)E(s),
MkjΦjEj+Mk(s)Φ(s)E(s)=Ek.
Ek=MkjΦj(MjiEi+Sj),
Sj=[Φ¯jMj(s)Φ(s)-Mj(s)]E(s)
RjlEl,j-Lj0E0,j=Sj.
RjlΦ¯jMjkΦ¯k  Φ¯(l-1)M(l-1)l,
Lj0MjiΦiMi(i-1)  Φ1M10

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