Abstract

Nonlinear reflection and diffraction measurements have been performed on a GaAs/AlGaAs photonic-crystal waveguide patterned with a square lattice: The basis in the two-dimensional unit cell consists of rings of air in the dielectric matrix. The measured angles of diffracted second-harmonic beams agree with those predicted for nonlinear diffraction conditions. Results for second-harmonic intensities as a function of incidence angle, polarization, and pump wavelength show that the reflected second-harmonic signal is dominated by the crystalline symmetry of GaAs, whereas nonlinear diffraction is determined by the photonic-crystal structure.

© 2002 Optical Society of America

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    [CrossRef]
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  23. M. Galli, M. Agio, L. C. Andreani, L. Atzeni, D. Bajoni, G. Guizzeti, L. Businaro, E. D. Fabrizio, F. Romanato, and A. Passaseo, “Optical properties and photonic bands of GaAs photonic crystal waveguides with a tilted square lattice,” Eur. Phys. J. B 27, 79–87 (2002).
    [CrossRef]
  24. V. N. Astratov, D. M. Whittaker, I. S. Culshaw, R. M. Stevenson, M. S. Skolnick, T. F. Krauss, and R. M. De La Rue, “Photonic band-structure effects in the reflectivity of periodically patterned waveguides,” Phys. Rev. B 60, R16255–R16258 (1999).
    [CrossRef]
  25. N. Bloembergen and P. S. Pershan, “Light waves at the boundary of nonlinear media,” Phys. Rev. 128, 606–622 (1962).
    [CrossRef]
  26. J. Ducuing and N. Bloembergen, “Observation of reflected light harmonics at the boundary of piezoelectric crystals,” Phys. Rev. Lett. 10, 474–476 (1963).
    [CrossRef]
  27. R. K. Chang, J. Ducuing, and N. Bloembergen, “Dispersion of the optical nonlinearity in semiconductors,” Phys. Rev. Lett. 15, 415–418 (1965).
    [CrossRef]

2002

M. Galli, M. Agio, L. C. Andreani, L. Atzeni, D. Bajoni, G. Guizzeti, L. Businaro, E. D. Fabrizio, F. Romanato, and A. Passaseo, “Optical properties and photonic bands of GaAs photonic crystal waveguides with a tilted square lattice,” Eur. Phys. J. B 27, 79–87 (2002).
[CrossRef]

2000

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]

1999

V. N. Astratov, D. M. Whittaker, I. S. Culshaw, R. M. Stevenson, M. S. Skolnick, T. F. Krauss, and R. M. De La Rue, “Photonic band-structure effects in the reflectivity of periodically patterned waveguides,” Phys. Rev. B 60, R16255–R16258 (1999).
[CrossRef]

H. Benisty, C. Weisbuch, D. Labilloy, M. Rattier, C. J. M. Smith, T. F. Krauss, R. M. De La Rue, R. Houdré, U. Oesterle, C. Jouanin, and D. Cassagne, “Optical and confinement properties of two-dimensional photonic crystals,” J. Lightwave Technol. 17, 2063–2077 (1999).
[CrossRef]

1998

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

1997

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

1996

A. C. R. Pipino, R. P. Van Duyne, and G. C. Schatz, “Surface-enhanced second-harmonic diffraction: experimental investigation of selective enhancement,” Phys. Rev. B 53, 4162–4169 (1996).
[CrossRef]

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

1995

1994

A. C. R. Pipino, G. R. Schatz, and R. P. Van Duyne, “Surface-enhanced second-harmonic diffraction: selective enhancement by spatial harmonics,” Phys. Rev. B 49, 8320–8330 (1994).
[CrossRef]

1992

X. Xiao, X. D. Zhu, W. Daum, and Y. R. Shen, “Optical second-harmonic diffraction study of anisotropic surface diffusion: CO on Ni(110),” Phys. Rev. B 46, 9732–9743 (1992).
[CrossRef]

1991

G. A. Reider, U. Höfer, and T. F. Heinz, “Surface diffusion of hydrogen on Si(111)7×7,” Phys. Rev. Lett. 66, 1994–1997 (1991).
[CrossRef] [PubMed]

1990

R. W. J. Hollering, Q. H. F. Vrehen, and G. Marowsky, “Angular dependence of optical second-harmonic generation from a monolayer grating,” Opt. Commun. 78, 387–392 (1990).
[CrossRef]

1989

H. J. Simon and Z. Chen, “Optical second-harmonic generation with grating-coupled surface plasmons from a quartz–silver–quartz grating structure,” Phys. Rev. B 39, 3077–3085 (1989).
[CrossRef]

T. Suzuki and T. F. Heinz, “Surface-harmonic diffraction from a monolayer grating,” Opt. Lett. 14, 1201–1203 (1989).
[CrossRef] [PubMed]

1988

M. Nevière, P. Vincent, D. Maystre, R. Reinisch, and J. Coutaz, “Differential theory for metallic gratings in nonlinear optics. Second-harmonic generation,” J. Opt. Soc. Am. B 5, 330–337 (1988).
[CrossRef]

X. D. Zhu, Th. Rasing, and Y. R. Shen, “Surface diffusion of CO on Ni(111) studied by diffraction of optical second-harmonic generation off a monolayer grating,” Phys. Rev. Lett. 61, 2883–2885 (1988).
[CrossRef] [PubMed]

G. A. Reider, M. Huemer, and A. J. Schmidt, “Surface second harmonic generation spectroscopy without interference of substrate contributions,” Opt. Commun. 68, 149–152 (1988).
[CrossRef]

1985

J. L. Coutaz, M. Nevière, E. Pic, and R. Reinisch, “Experi-mental study of surface-enhanced second-harmonic generation on silver gratings,” Phys. Rev. B 32, 2227–2232 (1985).
[CrossRef]

M. Nevière, R. Reinisch, and D. Maystre, “Surface-enhanced second-harmonic generation at a silver grating: a numerical study,” Phys. Rev. B 32, 3634–3641 (1985).
[CrossRef]

1983

R. Reinisch and M. Nevière, “Electromagnetic theory of diffraction in nonlinear optics and surface-enhanced nonlinear optical effects,” Phys. Rev. B 28, 1870–1885 (1983).
[CrossRef]

1968

I. Freund, “Nonlinear diffraction,” Phys. Rev. Lett. 21, 1404–1406 (1968).
[CrossRef]

1965

R. K. Chang, J. Ducuing, and N. Bloembergen, “Dispersion of the optical nonlinearity in semiconductors,” Phys. Rev. Lett. 15, 415–418 (1965).
[CrossRef]

1963

J. Ducuing and N. Bloembergen, “Observation of reflected light harmonics at the boundary of piezoelectric crystals,” Phys. Rev. Lett. 10, 474–476 (1963).
[CrossRef]

1962

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

Agio, M.

M. Galli, M. Agio, L. C. Andreani, L. Atzeni, D. Bajoni, G. Guizzeti, L. Businaro, E. D. Fabrizio, F. Romanato, and A. Passaseo, “Optical properties and photonic bands of GaAs photonic crystal waveguides with a tilted square lattice,” Eur. Phys. J. B 27, 79–87 (2002).
[CrossRef]

Andreani, L. C.

M. Galli, M. Agio, L. C. Andreani, L. Atzeni, D. Bajoni, G. Guizzeti, L. Businaro, E. D. Fabrizio, F. Romanato, and A. Passaseo, “Optical properties and photonic bands of GaAs photonic crystal waveguides with a tilted square lattice,” Eur. Phys. J. B 27, 79–87 (2002).
[CrossRef]

Astratov, V. N.

V. N. Astratov, D. M. Whittaker, I. S. Culshaw, R. M. Stevenson, M. S. Skolnick, T. F. Krauss, and R. M. De La Rue, “Photonic band-structure effects in the reflectivity of periodically patterned waveguides,” Phys. Rev. B 60, R16255–R16258 (1999).
[CrossRef]

Atzeni, L.

M. Galli, M. Agio, L. C. Andreani, L. Atzeni, D. Bajoni, G. Guizzeti, L. Businaro, E. D. Fabrizio, F. Romanato, and A. Passaseo, “Optical properties and photonic bands of GaAs photonic crystal waveguides with a tilted square lattice,” Eur. Phys. J. B 27, 79–87 (2002).
[CrossRef]

Bajoni, D.

M. Galli, M. Agio, L. C. Andreani, L. Atzeni, D. Bajoni, G. Guizzeti, L. Businaro, E. D. Fabrizio, F. Romanato, and A. Passaseo, “Optical properties and photonic bands of GaAs photonic crystal waveguides with a tilted square lattice,” Eur. Phys. J. B 27, 79–87 (2002).
[CrossRef]

Bardinal, V.

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

Benisty, H.

H. Benisty, C. Weisbuch, D. Labilloy, M. Rattier, C. J. M. Smith, T. F. Krauss, R. M. De La Rue, R. Houdré, U. Oesterle, C. Jouanin, and D. Cassagne, “Optical and confinement properties of two-dimensional photonic crystals,” J. Lightwave Technol. 17, 2063–2077 (1999).
[CrossRef]

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

Berger, V.

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

Blau, G.

Bloembergen, N.

R. K. Chang, J. Ducuing, and N. Bloembergen, “Dispersion of the optical nonlinearity in semiconductors,” Phys. Rev. Lett. 15, 415–418 (1965).
[CrossRef]

J. Ducuing and N. Bloembergen, “Observation of reflected light harmonics at the boundary of piezoelectric crystals,” Phys. Rev. Lett. 10, 474–476 (1963).
[CrossRef]

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

Brand, S.

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

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]

Businaro, L.

M. Galli, M. Agio, L. C. Andreani, L. Atzeni, D. Bajoni, G. Guizzeti, L. Businaro, E. D. Fabrizio, F. Romanato, and A. Passaseo, “Optical properties and photonic bands of GaAs photonic crystal waveguides with a tilted square lattice,” Eur. Phys. J. B 27, 79–87 (2002).
[CrossRef]

Cassagne, D.

H. Benisty, C. Weisbuch, D. Labilloy, M. Rattier, C. J. M. Smith, T. F. Krauss, R. M. De La Rue, R. Houdré, U. Oesterle, C. Jouanin, and D. Cassagne, “Optical and confinement properties of two-dimensional photonic crystals,” J. Lightwave Technol. 17, 2063–2077 (1999).
[CrossRef]

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

Chang, R. K.

R. K. Chang, J. Ducuing, and N. Bloembergen, “Dispersion of the optical nonlinearity in semiconductors,” Phys. Rev. Lett. 15, 415–418 (1965).
[CrossRef]

Chen, Z.

H. J. Simon and Z. Chen, “Optical second-harmonic generation with grating-coupled surface plasmons from a quartz–silver–quartz grating structure,” Phys. Rev. B 39, 3077–3085 (1989).
[CrossRef]

Coutaz, J.

Coutaz, J. L.

J. L. Coutaz, M. Nevière, E. Pic, and R. Reinisch, “Experi-mental study of surface-enhanced second-harmonic generation on silver gratings,” Phys. Rev. B 32, 2227–2232 (1985).
[CrossRef]

Culshaw, I. S.

V. N. Astratov, D. M. Whittaker, I. S. Culshaw, R. M. Stevenson, M. S. Skolnick, T. F. Krauss, and R. M. De La Rue, “Photonic band-structure effects in the reflectivity of periodically patterned waveguides,” Phys. Rev. B 60, R16255–R16258 (1999).
[CrossRef]

Daum, W.

X. Xiao, X. D. Zhu, W. Daum, and Y. R. Shen, “Optical second-harmonic diffraction study of anisotropic surface diffusion: CO on Ni(110),” Phys. Rev. B 46, 9732–9743 (1992).
[CrossRef]

De La Rue, R. M.

V. N. Astratov, D. M. Whittaker, I. S. Culshaw, R. M. Stevenson, M. S. Skolnick, T. F. Krauss, and R. M. De La Rue, “Photonic band-structure effects in the reflectivity of periodically patterned waveguides,” Phys. Rev. B 60, R16255–R16258 (1999).
[CrossRef]

H. Benisty, C. Weisbuch, D. Labilloy, M. Rattier, C. J. M. Smith, T. F. Krauss, R. M. De La Rue, R. Houdré, U. Oesterle, C. Jouanin, and D. Cassagne, “Optical and confinement properties of two-dimensional photonic crystals,” J. Lightwave Technol. 17, 2063–2077 (1999).
[CrossRef]

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

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

Ducuing, J.

R. K. Chang, J. Ducuing, and N. Bloembergen, “Dispersion of the optical nonlinearity in semiconductors,” Phys. Rev. Lett. 15, 415–418 (1965).
[CrossRef]

J. Ducuing and N. Bloembergen, “Observation of reflected light harmonics at the boundary of piezoelectric crystals,” Phys. Rev. Lett. 10, 474–476 (1963).
[CrossRef]

Fabrizio, E. D.

M. Galli, M. Agio, L. C. Andreani, L. Atzeni, D. Bajoni, G. Guizzeti, L. Businaro, E. D. Fabrizio, F. Romanato, and A. Passaseo, “Optical properties and photonic bands of GaAs photonic crystal waveguides with a tilted square lattice,” Eur. Phys. J. B 27, 79–87 (2002).
[CrossRef]

Freund, I.

I. Freund, “Nonlinear diffraction,” Phys. Rev. Lett. 21, 1404–1406 (1968).
[CrossRef]

Galli, M.

M. Galli, M. Agio, L. C. Andreani, L. Atzeni, D. Bajoni, G. Guizzeti, L. Businaro, E. D. Fabrizio, F. Romanato, and A. Passaseo, “Optical properties and photonic bands of GaAs photonic crystal waveguides with a tilted square lattice,” Eur. Phys. J. B 27, 79–87 (2002).
[CrossRef]

Guizzeti, G.

M. Galli, M. Agio, L. C. Andreani, L. Atzeni, D. Bajoni, G. Guizzeti, L. Businaro, E. D. Fabrizio, F. Romanato, and A. Passaseo, “Optical properties and photonic bands of GaAs photonic crystal waveguides with a tilted square lattice,” Eur. Phys. J. B 27, 79–87 (2002).
[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]

Heinz, T. F.

G. A. Reider, U. Höfer, and T. F. Heinz, “Surface diffusion of hydrogen on Si(111)7×7,” Phys. Rev. Lett. 66, 1994–1997 (1991).
[CrossRef] [PubMed]

T. Suzuki and T. F. Heinz, “Surface-harmonic diffraction from a monolayer grating,” Opt. Lett. 14, 1201–1203 (1989).
[CrossRef] [PubMed]

Höfer, U.

G. A. Reider, U. Höfer, and T. F. Heinz, “Surface diffusion of hydrogen on Si(111)7×7,” Phys. Rev. Lett. 66, 1994–1997 (1991).
[CrossRef] [PubMed]

Hollering, R. W. J.

R. W. J. Hollering, Q. H. F. Vrehen, and G. Marowsky, “Angular dependence of optical second-harmonic generation from a monolayer grating,” Opt. Commun. 78, 387–392 (1990).
[CrossRef]

Houdré, R.

H. Benisty, C. Weisbuch, D. Labilloy, M. Rattier, C. J. M. Smith, T. F. Krauss, R. M. De La Rue, R. Houdré, U. Oesterle, C. Jouanin, and D. Cassagne, “Optical and confinement properties of two-dimensional photonic crystals,” J. Lightwave Technol. 17, 2063–2077 (1999).
[CrossRef]

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

Huemer, M.

G. A. Reider, M. Huemer, and A. J. Schmidt, “Surface second harmonic generation spectroscopy without interference of substrate contributions,” Opt. Commun. 68, 149–152 (1988).
[CrossRef]

Jouanin, C.

H. Benisty, C. Weisbuch, D. Labilloy, M. Rattier, C. J. M. Smith, T. F. Krauss, R. M. De La Rue, R. Houdré, U. Oesterle, C. Jouanin, and D. Cassagne, “Optical and confinement properties of two-dimensional photonic crystals,” J. Lightwave Technol. 17, 2063–2077 (1999).
[CrossRef]

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

Krauss, T. F.

H. Benisty, C. Weisbuch, D. Labilloy, M. Rattier, C. J. M. Smith, T. F. Krauss, R. M. De La Rue, R. Houdré, U. Oesterle, C. Jouanin, and D. Cassagne, “Optical and confinement properties of two-dimensional photonic crystals,” J. Lightwave Technol. 17, 2063–2077 (1999).
[CrossRef]

V. N. Astratov, D. M. Whittaker, I. S. Culshaw, R. M. Stevenson, M. S. Skolnick, T. F. Krauss, and R. M. De La Rue, “Photonic band-structure effects in the reflectivity of periodically patterned waveguides,” Phys. Rev. B 60, R16255–R16258 (1999).
[CrossRef]

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

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

Labilloy, D.

H. Benisty, C. Weisbuch, D. Labilloy, M. Rattier, C. J. M. Smith, T. F. Krauss, R. M. De La Rue, R. Houdré, U. Oesterle, C. Jouanin, and D. Cassagne, “Optical and confinement properties of two-dimensional photonic crystals,” J. Lightwave Technol. 17, 2063–2077 (1999).
[CrossRef]

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

Marowsky, G.

R. W. J. Hollering, Q. H. F. Vrehen, and G. Marowsky, “Angular dependence of optical second-harmonic generation from a monolayer grating,” Opt. Commun. 78, 387–392 (1990).
[CrossRef]

Maystre, D.

M. Nevière, P. Vincent, D. Maystre, R. Reinisch, and J. Coutaz, “Differential theory for metallic gratings in nonlinear optics. Second-harmonic generation,” J. Opt. Soc. Am. B 5, 330–337 (1988).
[CrossRef]

M. Nevière, R. Reinisch, and D. Maystre, “Surface-enhanced second-harmonic generation at a silver grating: a numerical study,” Phys. Rev. B 32, 3634–3641 (1985).
[CrossRef]

Nevière, M.

M. Nevière, E. Popov, and R. Reinisch, “Electromagnetic resonances in linear and nonlinear optics: phenomenological study of grating behavior through the poles and zeros of the scattering operator,” J. Opt. Soc. Am. A 12, 513–523 (1995).
[CrossRef]

E. Popov, M. Nevière, G. Blau, and R. Reinisch, “Numerical optimization of grating-enhanced second-harmonic genera-tion in optical waveguides,” J. Opt. Soc. Am. B 12, 2390–2397 (1995).
[CrossRef]

M. Nevière, P. Vincent, D. Maystre, R. Reinisch, and J. Coutaz, “Differential theory for metallic gratings in nonlinear optics. Second-harmonic generation,” J. Opt. Soc. Am. B 5, 330–337 (1988).
[CrossRef]

J. L. Coutaz, M. Nevière, E. Pic, and R. Reinisch, “Experi-mental study of surface-enhanced second-harmonic generation on silver gratings,” Phys. Rev. B 32, 2227–2232 (1985).
[CrossRef]

M. Nevière, R. Reinisch, and D. Maystre, “Surface-enhanced second-harmonic generation at a silver grating: a numerical study,” Phys. Rev. B 32, 3634–3641 (1985).
[CrossRef]

R. Reinisch and M. Nevière, “Electromagnetic theory of diffraction in nonlinear optics and surface-enhanced nonlinear optical effects,” Phys. Rev. B 28, 1870–1885 (1983).
[CrossRef]

Oesterle, U.

H. Benisty, C. Weisbuch, D. Labilloy, M. Rattier, C. J. M. Smith, T. F. Krauss, R. M. De La Rue, R. Houdré, U. Oesterle, C. Jouanin, and D. Cassagne, “Optical and confinement properties of two-dimensional photonic crystals,” J. Lightwave Technol. 17, 2063–2077 (1999).
[CrossRef]

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

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]

Passaseo, A.

M. Galli, M. Agio, L. C. Andreani, L. Atzeni, D. Bajoni, G. Guizzeti, L. Businaro, E. D. Fabrizio, F. Romanato, and A. Passaseo, “Optical properties and photonic bands of GaAs photonic crystal waveguides with a tilted square lattice,” Eur. Phys. J. B 27, 79–87 (2002).
[CrossRef]

Pershan, P. S.

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

Pic, E.

J. L. Coutaz, M. Nevière, E. Pic, and R. Reinisch, “Experi-mental study of surface-enhanced second-harmonic generation on silver gratings,” Phys. Rev. B 32, 2227–2232 (1985).
[CrossRef]

Pipino, A. C. R.

A. C. R. Pipino, R. P. Van Duyne, and G. C. Schatz, “Surface-enhanced second-harmonic diffraction: experimental investigation of selective enhancement,” Phys. Rev. B 53, 4162–4169 (1996).
[CrossRef]

A. C. R. Pipino, G. R. Schatz, and R. P. Van Duyne, “Surface-enhanced second-harmonic diffraction: selective enhancement by spatial harmonics,” Phys. Rev. B 49, 8320–8330 (1994).
[CrossRef]

Popov, E.

Rasing, Th.

X. D. Zhu, Th. Rasing, and Y. R. Shen, “Surface diffusion of CO on Ni(111) studied by diffraction of optical second-harmonic generation off a monolayer grating,” Phys. Rev. Lett. 61, 2883–2885 (1988).
[CrossRef] [PubMed]

Rattier, M.

Reider, G. A.

G. A. Reider, U. Höfer, and T. F. Heinz, “Surface diffusion of hydrogen on Si(111)7×7,” Phys. Rev. Lett. 66, 1994–1997 (1991).
[CrossRef] [PubMed]

G. A. Reider, M. Huemer, and A. J. Schmidt, “Surface second harmonic generation spectroscopy without interference of substrate contributions,” Opt. Commun. 68, 149–152 (1988).
[CrossRef]

Reinisch, R.

M. Nevière, E. Popov, and R. Reinisch, “Electromagnetic resonances in linear and nonlinear optics: phenomenological study of grating behavior through the poles and zeros of the scattering operator,” J. Opt. Soc. Am. A 12, 513–523 (1995).
[CrossRef]

E. Popov, M. Nevière, G. Blau, and R. Reinisch, “Numerical optimization of grating-enhanced second-harmonic genera-tion in optical waveguides,” J. Opt. Soc. Am. B 12, 2390–2397 (1995).
[CrossRef]

M. Nevière, P. Vincent, D. Maystre, R. Reinisch, and J. Coutaz, “Differential theory for metallic gratings in nonlinear optics. Second-harmonic generation,” J. Opt. Soc. Am. B 5, 330–337 (1988).
[CrossRef]

J. L. Coutaz, M. Nevière, E. Pic, and R. Reinisch, “Experi-mental study of surface-enhanced second-harmonic generation on silver gratings,” Phys. Rev. B 32, 2227–2232 (1985).
[CrossRef]

M. Nevière, R. Reinisch, and D. Maystre, “Surface-enhanced second-harmonic generation at a silver grating: a numerical study,” Phys. Rev. B 32, 3634–3641 (1985).
[CrossRef]

R. Reinisch and M. Nevière, “Electromagnetic theory of diffraction in nonlinear optics and surface-enhanced nonlinear optical effects,” Phys. Rev. B 28, 1870–1885 (1983).
[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]

Romanato, F.

M. Galli, M. Agio, L. C. Andreani, L. Atzeni, D. Bajoni, G. Guizzeti, L. Businaro, E. D. Fabrizio, F. Romanato, and A. Passaseo, “Optical properties and photonic bands of GaAs photonic crystal waveguides with a tilted square lattice,” Eur. Phys. J. B 27, 79–87 (2002).
[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]

Schatz, G. C.

A. C. R. Pipino, R. P. Van Duyne, and G. C. Schatz, “Surface-enhanced second-harmonic diffraction: experimental investigation of selective enhancement,” Phys. Rev. B 53, 4162–4169 (1996).
[CrossRef]

Schatz, G. R.

A. C. R. Pipino, G. R. Schatz, and R. P. Van Duyne, “Surface-enhanced second-harmonic diffraction: selective enhancement by spatial harmonics,” Phys. Rev. B 49, 8320–8330 (1994).
[CrossRef]

Schmidt, A. J.

G. A. Reider, M. Huemer, and A. J. Schmidt, “Surface second harmonic generation spectroscopy without interference of substrate contributions,” Opt. Commun. 68, 149–152 (1988).
[CrossRef]

Shen, Y. R.

X. Xiao, X. D. Zhu, W. Daum, and Y. R. Shen, “Optical second-harmonic diffraction study of anisotropic surface diffusion: CO on Ni(110),” Phys. Rev. B 46, 9732–9743 (1992).
[CrossRef]

X. D. Zhu, Th. Rasing, and Y. R. Shen, “Surface diffusion of CO on Ni(111) studied by diffraction of optical second-harmonic generation off a monolayer grating,” Phys. Rev. Lett. 61, 2883–2885 (1988).
[CrossRef] [PubMed]

Simon, H. J.

H. J. Simon and Z. Chen, “Optical second-harmonic generation with grating-coupled surface plasmons from a quartz–silver–quartz grating structure,” Phys. Rev. B 39, 3077–3085 (1989).
[CrossRef]

Skolnick, M. S.

V. N. Astratov, D. M. Whittaker, I. S. Culshaw, R. M. Stevenson, M. S. Skolnick, T. F. Krauss, and R. M. De La Rue, “Photonic band-structure effects in the reflectivity of periodically patterned waveguides,” Phys. Rev. B 60, R16255–R16258 (1999).
[CrossRef]

Smith, C. J. M.

Stevenson, R. M.

V. N. Astratov, D. M. Whittaker, I. S. Culshaw, R. M. Stevenson, M. S. Skolnick, T. F. Krauss, and R. M. De La Rue, “Photonic band-structure effects in the reflectivity of periodically patterned waveguides,” Phys. Rev. B 60, R16255–R16258 (1999).
[CrossRef]

Suzuki, T.

Van Duyne, R. P.

A. C. R. Pipino, R. P. Van Duyne, and G. C. Schatz, “Surface-enhanced second-harmonic diffraction: experimental investigation of selective enhancement,” Phys. Rev. B 53, 4162–4169 (1996).
[CrossRef]

A. C. R. Pipino, G. R. Schatz, and R. P. Van Duyne, “Surface-enhanced second-harmonic diffraction: selective enhancement by spatial harmonics,” Phys. Rev. B 49, 8320–8330 (1994).
[CrossRef]

Vincent, P.

Vrehen, Q. H. F.

R. W. J. Hollering, Q. H. F. Vrehen, and G. Marowsky, “Angular dependence of optical second-harmonic generation from a monolayer grating,” Opt. Commun. 78, 387–392 (1990).
[CrossRef]

Weisbuch, C.

H. Benisty, C. Weisbuch, D. Labilloy, M. Rattier, C. J. M. Smith, T. F. Krauss, R. M. De La Rue, R. Houdré, U. Oesterle, C. Jouanin, and D. Cassagne, “Optical and confinement properties of two-dimensional photonic crystals,” J. Lightwave Technol. 17, 2063–2077 (1999).
[CrossRef]

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

Whittaker, D. M.

V. N. Astratov, D. M. Whittaker, I. S. Culshaw, R. M. Stevenson, M. S. Skolnick, T. F. Krauss, and R. M. De La Rue, “Photonic band-structure effects in the reflectivity of periodically patterned waveguides,” Phys. Rev. B 60, R16255–R16258 (1999).
[CrossRef]

Xiao, X.

X. Xiao, X. D. Zhu, W. Daum, and Y. R. Shen, “Optical second-harmonic diffraction study of anisotropic surface diffusion: CO on Ni(110),” Phys. Rev. B 46, 9732–9743 (1992).
[CrossRef]

Zhu, X. D.

X. Xiao, X. D. Zhu, W. Daum, and Y. R. Shen, “Optical second-harmonic diffraction study of anisotropic surface diffusion: CO on Ni(110),” Phys. Rev. B 46, 9732–9743 (1992).
[CrossRef]

X. D. Zhu, Th. Rasing, and Y. R. Shen, “Surface diffusion of CO on Ni(111) studied by diffraction of optical second-harmonic generation off a monolayer grating,” Phys. Rev. Lett. 61, 2883–2885 (1988).
[CrossRef] [PubMed]

Eur. Phys. J. B

M. Galli, M. Agio, L. C. Andreani, L. Atzeni, D. Bajoni, G. Guizzeti, L. Businaro, E. D. Fabrizio, F. Romanato, and A. Passaseo, “Optical properties and photonic bands of GaAs photonic crystal waveguides with a tilted square lattice,” Eur. Phys. J. B 27, 79–87 (2002).
[CrossRef]

J. Lightwave Technol.

J. Opt. Soc. Am. A

J. Opt. Soc. Am. B

Nature

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

Opt. Commun.

G. A. Reider, M. Huemer, and A. J. Schmidt, “Surface second harmonic generation spectroscopy without interference of substrate contributions,” Opt. Commun. 68, 149–152 (1988).
[CrossRef]

R. W. J. Hollering, Q. H. F. Vrehen, and G. Marowsky, “Angular dependence of optical second-harmonic generation from a monolayer grating,” Opt. Commun. 78, 387–392 (1990).
[CrossRef]

Opt. Lett.

Phys. Rev.

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

Phys. Rev. B

V. N. Astratov, D. M. Whittaker, I. S. Culshaw, R. M. Stevenson, M. S. Skolnick, T. F. Krauss, and R. M. De La Rue, “Photonic band-structure effects in the reflectivity of periodically patterned waveguides,” Phys. Rev. B 60, R16255–R16258 (1999).
[CrossRef]

R. Reinisch and M. Nevière, “Electromagnetic theory of diffraction in nonlinear optics and surface-enhanced nonlinear optical effects,” Phys. Rev. B 28, 1870–1885 (1983).
[CrossRef]

J. L. Coutaz, M. Nevière, E. Pic, and R. Reinisch, “Experi-mental study of surface-enhanced second-harmonic generation on silver gratings,” Phys. Rev. B 32, 2227–2232 (1985).
[CrossRef]

M. Nevière, R. Reinisch, and D. Maystre, “Surface-enhanced second-harmonic generation at a silver grating: a numerical study,” Phys. Rev. B 32, 3634–3641 (1985).
[CrossRef]

H. J. Simon and Z. Chen, “Optical second-harmonic generation with grating-coupled surface plasmons from a quartz–silver–quartz grating structure,” Phys. Rev. B 39, 3077–3085 (1989).
[CrossRef]

X. Xiao, X. D. Zhu, W. Daum, and Y. R. Shen, “Optical second-harmonic diffraction study of anisotropic surface diffusion: CO on Ni(110),” Phys. Rev. B 46, 9732–9743 (1992).
[CrossRef]

A. C. R. Pipino, G. R. Schatz, and R. P. Van Duyne, “Surface-enhanced second-harmonic diffraction: selective enhancement by spatial harmonics,” Phys. Rev. B 49, 8320–8330 (1994).
[CrossRef]

A. C. R. Pipino, R. P. Van Duyne, and G. C. Schatz, “Surface-enhanced second-harmonic diffraction: experimental investigation of selective enhancement,” Phys. Rev. B 53, 4162–4169 (1996).
[CrossRef]

Phys. Rev. Lett.

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

X. D. Zhu, Th. Rasing, and Y. R. Shen, “Surface diffusion of CO on Ni(111) studied by diffraction of optical second-harmonic generation off a monolayer grating,” Phys. Rev. Lett. 61, 2883–2885 (1988).
[CrossRef] [PubMed]

I. Freund, “Nonlinear diffraction,” Phys. Rev. Lett. 21, 1404–1406 (1968).
[CrossRef]

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

G. A. Reider, U. Höfer, and T. F. Heinz, “Surface diffusion of hydrogen on Si(111)7×7,” Phys. Rev. Lett. 66, 1994–1997 (1991).
[CrossRef] [PubMed]

J. Ducuing and N. Bloembergen, “Observation of reflected light harmonics at the boundary of piezoelectric crystals,” Phys. Rev. Lett. 10, 474–476 (1963).
[CrossRef]

R. K. Chang, J. Ducuing, and N. Bloembergen, “Dispersion of the optical nonlinearity in semiconductors,” Phys. Rev. Lett. 15, 415–418 (1965).
[CrossRef]

Other

For recent reviews see, e.g., C. M. Soukoulis, ed., Photonic Crystals and Light Localization in the 21st Century, Vol. 563 of NATO Science Series C: Mathematical and Physical Sciences (Kluwer, Dordrecht, The Netherlands, 2001).

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Figures (8)

Fig. 1
Fig. 1

Scanning electron micrographs of the sample studied in the research reported here. (a) Front view, (b) cross section showing vertical air structures. The lattice constant of the square Bravais lattice is a=500 nm.

Fig. 2
Fig. 2

Linear variable-angle reflectance for s-polarized light (s-pol) incident in the ΓM direction. The angle of incidence varies from 5° to 60°, in steps of 5°. The curves are shifted vertically for clarity. The vertical bars denote the energy positions of the photonic resonances for θ=5° and θ=60°.

Fig. 3
Fig. 3

Experimental geometry for SHG at the sample. The incident (i), reflected (r), and diffracted (d) wave directions are represented by thick lines. n is the normal to the sample surface, and the relevant angles are indicated.

Fig. 4
Fig. 4

Nonlinear diffraction angles for light incident along the ΓX orientation of the photonic crystal, assuming that λ=800 nm and a=500 nm: (a) polar angle θ, (b) azimuthal angle ϕ. Solid (dotted) curves, diffraction in the plane (out of the plane) of incidence. The integer numbers (n1 and n2) that label the diffraction order [Eqs. (2)] are indicated on each curve.

Fig. 5
Fig. 5

Nonlinear diffraction angles for light incident along the ΓM orientation of the photonic crystal, assuming that λ=800 nm and a=500 nm: (a) polar angle θ, (b) azimuthal angle ϕ. Solid (dotted) curves, diffraction in the plane (out of the plane) of incidence. The integer numbers (n1 and n2) that label the diffraction order [Eqs. (2)] are indicated on each curve.

Fig. 6
Fig. 6

Measured and calculated diffraction angles for light incident along the ΓX and the ΓM crystal orientations and for the two polarizations (s-pol and p-pol) of the pump beam as a function of the angle of incidence θ. The pump wavelength is 814 nm, and this value is also used for the theoretical curves.

Fig. 7
Fig. 7

Nonlinear (a) reflection and (b) diffraction coefficients as a function of angle of incidence for a pump wavelength of λ=814 nm, for the crystal orientations and input polarizations (p-pol and s-pol) considered. Note the break in the vertical scale in (a). Insets, results of an approximate theoretical model (see text).

Fig. 8
Fig. 8

Nonlinear reflection and diffraction coefficients as a function of pump wavelength for the ΓX sample orientation, angle of incidence θ=45°, and s polarization (s-pol).

Equations (3)

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

k=2k+G,
sin θ cos(ϕ+ϕ)=sin θ cos ϕ+n1 λ2a,
sin θ sin(ϕ+ϕ)=sin θ sin ϕ+n2 λ2a,

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