Abstract

Using Fourier optics, we retrieve the wavevector dependence of the third-harmonic (green) light generated in a slow light silicon photonic crystal waveguide. We show that quasi-phase matching between the third-harmonic signal and the fundamental mode is provided in this geometry by coupling to the continuum of radiation modes above the light line. This process sustains third-harmonic generation with a relatively high efficiency and a substantial bandwidth limited only by the slow light window of the fundamental mode. The results give us insights into the physics of this nonlinear process in the presence of strong absorption and dispersion at visible wavelengths where bandstructure calculations are problematic. Since the characteristics (e.g. angular pattern) of the third-harmonic light primarily depend on the fundamental mode dispersion, they could be readily engineered.

© 2010 OSA

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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  33. G. Vecchi, J. Torres, D. Coquillat, M. L. d'Yerville, and A. M. Malvezzi, “Enhancement of visible second-harmonic generation in epitaxial GaN-based two-dimensional photonic crystal structures,” Appl. Phys. Lett. 84(8), 1245–1247 (2004).
    [CrossRef]
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  35. B. Corcoran, C. Monat, M.Pelusi, C. Grillet, T. P. White, L. O'Faolain, T. F. Krauss, B. J. Eggleton and D. J. Moss, “Optical signal processing on a silicon chip at 640Gb/s using slow-light,” submitted.

2010

C. Monat, B. Corcoran, D. Pudo, M. Ebnali-Heidari, C. Grillet, M. D. Pelusi, D. J. Moss, B. J. Eggleton, T. P. White, L. O’Faolain, and T. F. Krauss, “Slow light enhanced nonlinear optics in silicon photonic crystal waveguides,” J. Sel. Top. Quantum Electron 16, 344–356 (2010).
[CrossRef]

2009

B. Corcoran, C. Monat, C. Grillet, D. J. Moss, B. J. Eggleton, T. P. White, L. O'Faolain, and T. F. Krauss, “Green light emission in silicon through slow-light enhanced third-harmonic generation in photonic-crystal waveguides,” Nat. Photonics 3(4), 206–210 (2009).
[CrossRef]

A. Baron, A. Ryasnyanskiy, N. Dubreuil, P. Delaye, Q. Vy Tran, S. Combrié, A. de Rossi, R. Frey, and G. Roosen, “Light localization induced enhancement of third order nonlinearities in a GaAs photonic crystal waveguide,” Opt. Express 17(2), 552–557 (2009).
[CrossRef] [PubMed]

C. Monat, B. Corcoran, M. Ebnali-Heidari, C. Grillet, B. J. Eggleton, T. P. White, L. O’Faolain, and T. F. Krauss, “Slow light enhancement of nonlinear effects in silicon engineered photonic crystal waveguides,” Opt. Express 17(4), 2944–2953 (2009).
[CrossRef] [PubMed]

Y. Hamachi, S. Kubo, and T. Baba, “Slow light with low dispersion and nonlinear enhancement in a lattice-shifted photonic crystal waveguide,” Opt. Lett. 34(7), 1072–1074 (2009).
[CrossRef] [PubMed]

K. Inoue, H. Oda, N. Ikeda, and K. Asakawa, “Enhanced third-order nonlinear effects in slow-light photonic-crystal slab waveguides of line-defect,” Opt. Express 17(9), 7206–7216 (2009).
[CrossRef] [PubMed]

M. Ebnali-Heidari, C. Monat, C. Grillet, and M. K. Moravvej-Farshi, “A proposal for enhancing four-wave mixing in slow light engineered photonic crystal waveguides and its application to optical regeneration,” Opt. Express 17(20), 18340–18353 (2009).
[CrossRef] [PubMed]

C. Husko, S. Combrié, Q. V. Tran, F. Raineri, C. W. Wong, and A. De Rossi, “Non-trivial scaling of self-phase modulation and three-photon absorption in III-V photonic crystal waveguides,” Opt. Express 17(25), 22442–22451 (2009).
[CrossRef]

2008

2007

H. Oda, K. Inoue, Y. Tanaka, N. Ikeda, Y. Sugimoto, H. Ishikawa, and K. Asakawa, “Self-phase modulation in photonic-crystal-slab line-defect waveguides,” Appl. Phys. Lett. 90(23), 231102 (2007).
[CrossRef]

A. Gomez-Iglesias, D. O'Brien, L. O'Faolain, A. Miller, and T. F. Krauss, “Direct measurement of the group index of photonic crystal waveguides via Fourier transform spectral interferometry,” Appl. Phys. Lett. 90(26), 261107 (2007).
[CrossRef]

N. Le Thomas, R. Houdre, L. H. Frandsen, J. Fage-Pedersen, A. V. Lavrinenko, and P. I. Borel, “Grating-assisted superresolution of slow waves in Fourier space,” Phys. Rev. B 76(3), 035103 (2007).
[CrossRef]

N. Le Thomas, R. Houdre, M. V. Kotlyar, D. O'Brien, and T. E. Krauss, “Exploring light propagating in photonic crystals with Fourier optics,” J. Opt. Soc. Am. B 24(12), 2964–2971 (2007).
[CrossRef]

2006

J. F. McMillan, X. D. Yang, N. C. Panoiu, R. M. Osgood, and C. W. Wong, “Enhanced stimulated Raman scattering in slow-light photonic crystal waveguides,” Opt. Lett. 31(9), 1235–1237 (2006).
[CrossRef] [PubMed]

L. O'Faolain, X. Yuan, D. McIntyre, S. Thoms, H. Chong, R. M. De la Rue, and T. F. Krauss, “Low-loss propagation in photonic crystal waveguides,” Electron. Lett. 42(25), 1454–1455 (2006).
[CrossRef]

2005

C. Comaschi, G. Vecchi, A. M. Malvezzi, M. Patrini, G. Guizzetti, M. Liscidini, L. C. Andreani, D. Peyrade, and Y. Chen, “Enhanced third harmonic reflection and diffraction in Silicon on Insulator photonic waveguides,” Appl. Phys. B 81(2-3), 305–311 (2005).
[CrossRef]

A. R. Cowan and J. F. Young, “Nonlinear optics in high refractive index contrast periodic structures,” Semicond. Sci. Technol. 20(9), R41–R56 (2005).
[CrossRef]

D. Coquillat, G. Vecchi, C. Comaschi, A. M. Malvezzi, J. Torres, and M. L. d'Yerville, “Enhanced second- and third-harmonic generation and induced photoluminescence in a two-dimensional GaN photonic crystal,” Appl. Phys. Lett. 87(10), 101106 (2005).
[CrossRef]

2004

G. Vecchi, J. Torres, D. Coquillat, M. L. d'Yerville, and A. M. Malvezzi, “Enhancement of visible second-harmonic generation in epitaxial GaN-based two-dimensional photonic crystal structures,” Appl. Phys. Lett. 84(8), 1245–1247 (2004).
[CrossRef]

D. Coquillat, J. Torres, D. Peyrade, R. Legros, J. P. Lascaray, M. Le Vassor d’Yerville, E. Centeno, D. Cassagne, J. P. Albert, Y. Chen, and R. M. De La Rue, “Equifrequency surfaces in a two-dimensional GaN-based photonic crystal,” Opt. Express 12(6), 1097–1108 (2004).
[CrossRef] [PubMed]

J. Torres, D. Coquillat, R. Legros, J. P. Lascaray, F. Teppe, D. Scalbert, D. Peyrade, Y. Chen, O. Briot, M. L. d'Yerville, E. Centeno, D. Cassagne, and J. P. Albert, “Giant second-harmonic generation in a one-dimensional GaN photonic crystal,” Phys. Rev. B 69(8), 085105 (2004).
[CrossRef]

P. P. Markowicz, H. Tiryaki, H. Pudavar, P. N. Prasad, N. N. Lepeshkin, and R. W. Boyd, “Dramatic enhancement of third-harmonic generation in three-dimensional photonic crystals,” Phys. Rev. Lett. 92(8), 083903 (2004).
[CrossRef] [PubMed]

M. Soljacić and J. D. Joannopoulos, “Enhancement of nonlinear effects using photonic crystals,” Nat. Mater. 3(4), 211–219 (2004).
[CrossRef] [PubMed]

2003

2002

Y. Desieres, T. Benyattou, R. Orobtchouk, A. Morand, P. Benech, C. Grillet, C. Seassal, X. Letartre, P. Rojo-Romeo, and P. Viktorovitch, “Propagation losses of the fundamental mode in a single line-defect photonic crystal waveguide on an InP membrane,” J. Appl. Phys. 92(5), 2227 (2002).
[CrossRef]

A. R. Cowan and J. F. Young, “Mode matching for second-harmonic generation in photonic crystal waveguides,” Phys. Rev. B 65(8), 085106 (2002).
[CrossRef]

2001

N. A. R. Bhat and J. E. Sipe, “Optical pulse propagation in nonlinear photonic crystals,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 64(5), 056604 (2001).
[CrossRef] [PubMed]

X. Letartre, C. Seassal, C. Grillet, P. Rojo-Romeo, P. Viktorovitch, M. L. d'Yerville, D. Cassagne, and C. Jouanin, “Group velocity and propagation losses measurement in a single-line photonic-crystal waveguide on InP membranes,” Appl. Phys. Lett. 79(15), 2312–2314 (2001).
[CrossRef]

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, “Extremely large group-velocity dispersion of line-defect waveguides in photonic crystal slabs,” Phys. Rev. Lett. 87(25), 253902 (2001).
[CrossRef] [PubMed]

Y. Dumeige, P. Vidakovic, S. Sauvage, I. Sagnes, J. A. Levenson, C. Sibilia, M. Centini, G. D'Aguanno, and M. Scalora, “Enhancement of second-harmonic generation in a one-dimensional semiconductor photonic band gap,” Appl. Phys. Lett. 78(20), 3021–3023 (2001).
[CrossRef]

1999

M. Centini, C. Sibilia, M. Scalora, G. D’Aguanno, M. Bertolotti, M. J. Bloemer, C. M. Bowden, and I. Nefedov, “Dispersive properties of finite, one-dimensional photonic band gap structures: applications to nonlinear quadratic interactions,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 60(44 Pt B), 4891–4898 (1999).
[CrossRef]

S. G. Johnson, S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and L. A. Kolodziejski, “Guided modes in photonic crystal slabs,” Phys. Rev. B 60(8), 5751–5758 (1999).
[CrossRef]

Albert, J. P.

D. Coquillat, J. Torres, D. Peyrade, R. Legros, J. P. Lascaray, M. Le Vassor d’Yerville, E. Centeno, D. Cassagne, J. P. Albert, Y. Chen, and R. M. De La Rue, “Equifrequency surfaces in a two-dimensional GaN-based photonic crystal,” Opt. Express 12(6), 1097–1108 (2004).
[CrossRef] [PubMed]

J. Torres, D. Coquillat, R. Legros, J. P. Lascaray, F. Teppe, D. Scalbert, D. Peyrade, Y. Chen, O. Briot, M. L. d'Yerville, E. Centeno, D. Cassagne, and J. P. Albert, “Giant second-harmonic generation in a one-dimensional GaN photonic crystal,” Phys. Rev. B 69(8), 085105 (2004).
[CrossRef]

Andreani, L. C.

C. Comaschi, G. Vecchi, A. M. Malvezzi, M. Patrini, G. Guizzetti, M. Liscidini, L. C. Andreani, D. Peyrade, and Y. Chen, “Enhanced third harmonic reflection and diffraction in Silicon on Insulator photonic waveguides,” Appl. Phys. B 81(2-3), 305–311 (2005).
[CrossRef]

Asakawa, K.

K. Inoue, H. Oda, N. Ikeda, and K. Asakawa, “Enhanced third-order nonlinear effects in slow-light photonic-crystal slab waveguides of line-defect,” Opt. Express 17(9), 7206–7216 (2009).
[CrossRef] [PubMed]

H. Oda, K. Inoue, Y. Tanaka, N. Ikeda, Y. Sugimoto, H. Ishikawa, and K. Asakawa, “Self-phase modulation in photonic-crystal-slab line-defect waveguides,” Appl. Phys. Lett. 90(23), 231102 (2007).
[CrossRef]

Baba, T.

Baron, A.

Benech, P.

Y. Desieres, T. Benyattou, R. Orobtchouk, A. Morand, P. Benech, C. Grillet, C. Seassal, X. Letartre, P. Rojo-Romeo, and P. Viktorovitch, “Propagation losses of the fundamental mode in a single line-defect photonic crystal waveguide on an InP membrane,” J. Appl. Phys. 92(5), 2227 (2002).
[CrossRef]

Benyattou, T.

Y. Desieres, T. Benyattou, R. Orobtchouk, A. Morand, P. Benech, C. Grillet, C. Seassal, X. Letartre, P. Rojo-Romeo, and P. Viktorovitch, “Propagation losses of the fundamental mode in a single line-defect photonic crystal waveguide on an InP membrane,” J. Appl. Phys. 92(5), 2227 (2002).
[CrossRef]

Bertolotti, M.

M. Centini, C. Sibilia, M. Scalora, G. D’Aguanno, M. Bertolotti, M. J. Bloemer, C. M. Bowden, and I. Nefedov, “Dispersive properties of finite, one-dimensional photonic band gap structures: applications to nonlinear quadratic interactions,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 60(44 Pt B), 4891–4898 (1999).
[CrossRef]

Bhat, N. A. R.

N. A. R. Bhat and J. E. Sipe, “Optical pulse propagation in nonlinear photonic crystals,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 64(5), 056604 (2001).
[CrossRef] [PubMed]

Bloemer, M. J.

M. Centini, C. Sibilia, M. Scalora, G. D’Aguanno, M. Bertolotti, M. J. Bloemer, C. M. Bowden, and I. Nefedov, “Dispersive properties of finite, one-dimensional photonic band gap structures: applications to nonlinear quadratic interactions,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 60(44 Pt B), 4891–4898 (1999).
[CrossRef]

Borel, P. I.

N. Le Thomas, R. Houdre, L. H. Frandsen, J. Fage-Pedersen, A. V. Lavrinenko, and P. I. Borel, “Grating-assisted superresolution of slow waves in Fourier space,” Phys. Rev. B 76(3), 035103 (2007).
[CrossRef]

Bowden, C. M.

M. Centini, C. Sibilia, M. Scalora, G. D’Aguanno, M. Bertolotti, M. J. Bloemer, C. M. Bowden, and I. Nefedov, “Dispersive properties of finite, one-dimensional photonic band gap structures: applications to nonlinear quadratic interactions,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 60(44 Pt B), 4891–4898 (1999).
[CrossRef]

Boyd, R. W.

P. P. Markowicz, H. Tiryaki, H. Pudavar, P. N. Prasad, N. N. Lepeshkin, and R. W. Boyd, “Dramatic enhancement of third-harmonic generation in three-dimensional photonic crystals,” Phys. Rev. Lett. 92(8), 083903 (2004).
[CrossRef] [PubMed]

Briot, O.

J. Torres, D. Coquillat, R. Legros, J. P. Lascaray, F. Teppe, D. Scalbert, D. Peyrade, Y. Chen, O. Briot, M. L. d'Yerville, E. Centeno, D. Cassagne, and J. P. Albert, “Giant second-harmonic generation in a one-dimensional GaN photonic crystal,” Phys. Rev. B 69(8), 085105 (2004).
[CrossRef]

Cassagne, D.

J. Torres, D. Coquillat, R. Legros, J. P. Lascaray, F. Teppe, D. Scalbert, D. Peyrade, Y. Chen, O. Briot, M. L. d'Yerville, E. Centeno, D. Cassagne, and J. P. Albert, “Giant second-harmonic generation in a one-dimensional GaN photonic crystal,” Phys. Rev. B 69(8), 085105 (2004).
[CrossRef]

D. Coquillat, J. Torres, D. Peyrade, R. Legros, J. P. Lascaray, M. Le Vassor d’Yerville, E. Centeno, D. Cassagne, J. P. Albert, Y. Chen, and R. M. De La Rue, “Equifrequency surfaces in a two-dimensional GaN-based photonic crystal,” Opt. Express 12(6), 1097–1108 (2004).
[CrossRef] [PubMed]

X. Letartre, C. Seassal, C. Grillet, P. Rojo-Romeo, P. Viktorovitch, M. L. d'Yerville, D. Cassagne, and C. Jouanin, “Group velocity and propagation losses measurement in a single-line photonic-crystal waveguide on InP membranes,” Appl. Phys. Lett. 79(15), 2312–2314 (2001).
[CrossRef]

Centeno, E.

J. Torres, D. Coquillat, R. Legros, J. P. Lascaray, F. Teppe, D. Scalbert, D. Peyrade, Y. Chen, O. Briot, M. L. d'Yerville, E. Centeno, D. Cassagne, and J. P. Albert, “Giant second-harmonic generation in a one-dimensional GaN photonic crystal,” Phys. Rev. B 69(8), 085105 (2004).
[CrossRef]

D. Coquillat, J. Torres, D. Peyrade, R. Legros, J. P. Lascaray, M. Le Vassor d’Yerville, E. Centeno, D. Cassagne, J. P. Albert, Y. Chen, and R. M. De La Rue, “Equifrequency surfaces in a two-dimensional GaN-based photonic crystal,” Opt. Express 12(6), 1097–1108 (2004).
[CrossRef] [PubMed]

Centini, 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(20), 3021–3023 (2001).
[CrossRef]

M. Centini, C. Sibilia, M. Scalora, G. D’Aguanno, M. Bertolotti, M. J. Bloemer, C. M. Bowden, and I. Nefedov, “Dispersive properties of finite, one-dimensional photonic band gap structures: applications to nonlinear quadratic interactions,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 60(44 Pt B), 4891–4898 (1999).
[CrossRef]

Chen, Y.

C. Comaschi, G. Vecchi, A. M. Malvezzi, M. Patrini, G. Guizzetti, M. Liscidini, L. C. Andreani, D. Peyrade, and Y. Chen, “Enhanced third harmonic reflection and diffraction in Silicon on Insulator photonic waveguides,” Appl. Phys. B 81(2-3), 305–311 (2005).
[CrossRef]

J. Torres, D. Coquillat, R. Legros, J. P. Lascaray, F. Teppe, D. Scalbert, D. Peyrade, Y. Chen, O. Briot, M. L. d'Yerville, E. Centeno, D. Cassagne, and J. P. Albert, “Giant second-harmonic generation in a one-dimensional GaN photonic crystal,” Phys. Rev. B 69(8), 085105 (2004).
[CrossRef]

D. Coquillat, J. Torres, D. Peyrade, R. Legros, J. P. Lascaray, M. Le Vassor d’Yerville, E. Centeno, D. Cassagne, J. P. Albert, Y. Chen, and R. M. De La Rue, “Equifrequency surfaces in a two-dimensional GaN-based photonic crystal,” Opt. Express 12(6), 1097–1108 (2004).
[CrossRef] [PubMed]

Chong, H.

L. O'Faolain, X. Yuan, D. McIntyre, S. Thoms, H. Chong, R. M. De la Rue, and T. F. Krauss, “Low-loss propagation in photonic crystal waveguides,” Electron. Lett. 42(25), 1454–1455 (2006).
[CrossRef]

Comaschi, C.

C. Comaschi, G. Vecchi, A. M. Malvezzi, M. Patrini, G. Guizzetti, M. Liscidini, L. C. Andreani, D. Peyrade, and Y. Chen, “Enhanced third harmonic reflection and diffraction in Silicon on Insulator photonic waveguides,” Appl. Phys. B 81(2-3), 305–311 (2005).
[CrossRef]

D. Coquillat, G. Vecchi, C. Comaschi, A. M. Malvezzi, J. Torres, and M. L. d'Yerville, “Enhanced second- and third-harmonic generation and induced photoluminescence in a two-dimensional GaN photonic crystal,” Appl. Phys. Lett. 87(10), 101106 (2005).
[CrossRef]

Combrié, S.

Coquillat, D.

D. Coquillat, G. Vecchi, C. Comaschi, A. M. Malvezzi, J. Torres, and M. L. d'Yerville, “Enhanced second- and third-harmonic generation and induced photoluminescence in a two-dimensional GaN photonic crystal,” Appl. Phys. Lett. 87(10), 101106 (2005).
[CrossRef]

J. Torres, D. Coquillat, R. Legros, J. P. Lascaray, F. Teppe, D. Scalbert, D. Peyrade, Y. Chen, O. Briot, M. L. d'Yerville, E. Centeno, D. Cassagne, and J. P. Albert, “Giant second-harmonic generation in a one-dimensional GaN photonic crystal,” Phys. Rev. B 69(8), 085105 (2004).
[CrossRef]

D. Coquillat, J. Torres, D. Peyrade, R. Legros, J. P. Lascaray, M. Le Vassor d’Yerville, E. Centeno, D. Cassagne, J. P. Albert, Y. Chen, and R. M. De La Rue, “Equifrequency surfaces in a two-dimensional GaN-based photonic crystal,” Opt. Express 12(6), 1097–1108 (2004).
[CrossRef] [PubMed]

G. Vecchi, J. Torres, D. Coquillat, M. L. d'Yerville, and A. M. Malvezzi, “Enhancement of visible second-harmonic generation in epitaxial GaN-based two-dimensional photonic crystal structures,” Appl. Phys. Lett. 84(8), 1245–1247 (2004).
[CrossRef]

Corcoran, B.

C. Monat, B. Corcoran, D. Pudo, M. Ebnali-Heidari, C. Grillet, M. D. Pelusi, D. J. Moss, B. J. Eggleton, T. P. White, L. O’Faolain, and T. F. Krauss, “Slow light enhanced nonlinear optics in silicon photonic crystal waveguides,” J. Sel. Top. Quantum Electron 16, 344–356 (2010).
[CrossRef]

B. Corcoran, C. Monat, C. Grillet, D. J. Moss, B. J. Eggleton, T. P. White, L. O'Faolain, and T. F. Krauss, “Green light emission in silicon through slow-light enhanced third-harmonic generation in photonic-crystal waveguides,” Nat. Photonics 3(4), 206–210 (2009).
[CrossRef]

C. Monat, B. Corcoran, M. Ebnali-Heidari, C. Grillet, B. J. Eggleton, T. P. White, L. O’Faolain, and T. F. Krauss, “Slow light enhancement of nonlinear effects in silicon engineered photonic crystal waveguides,” Opt. Express 17(4), 2944–2953 (2009).
[CrossRef] [PubMed]

Cowan, A. R.

A. R. Cowan and J. F. Young, “Nonlinear optics in high refractive index contrast periodic structures,” Semicond. Sci. Technol. 20(9), R41–R56 (2005).
[CrossRef]

J. P. Mondia, H. M. van Driel, W. Jiang, A. R. Cowan, and J. F. Young, “Enhanced second-harmonic generation from planar photonic crystals,” Opt. Lett. 28(24), 2500–2502 (2003).
[CrossRef] [PubMed]

A. R. Cowan and J. F. Young, “Mode matching for second-harmonic generation in photonic crystal waveguides,” Phys. Rev. B 65(8), 085106 (2002).
[CrossRef]

D’Aguanno, G.

M. Centini, C. Sibilia, M. Scalora, G. D’Aguanno, M. Bertolotti, M. J. Bloemer, C. M. Bowden, and I. Nefedov, “Dispersive properties of finite, one-dimensional photonic band gap structures: applications to nonlinear quadratic interactions,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 60(44 Pt B), 4891–4898 (1999).
[CrossRef]

D'Aguanno, G.

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(20), 3021–3023 (2001).
[CrossRef]

De la Rue, R. M.

De Rossi, A.

Delaye, P.

Desieres, Y.

Y. Desieres, T. Benyattou, R. Orobtchouk, A. Morand, P. Benech, C. Grillet, C. Seassal, X. Letartre, P. Rojo-Romeo, and P. Viktorovitch, “Propagation losses of the fundamental mode in a single line-defect photonic crystal waveguide on an InP membrane,” J. Appl. Phys. 92(5), 2227 (2002).
[CrossRef]

Dubreuil, N.

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(20), 3021–3023 (2001).
[CrossRef]

d'Yerville, M. L.

D. Coquillat, G. Vecchi, C. Comaschi, A. M. Malvezzi, J. Torres, and M. L. d'Yerville, “Enhanced second- and third-harmonic generation and induced photoluminescence in a two-dimensional GaN photonic crystal,” Appl. Phys. Lett. 87(10), 101106 (2005).
[CrossRef]

J. Torres, D. Coquillat, R. Legros, J. P. Lascaray, F. Teppe, D. Scalbert, D. Peyrade, Y. Chen, O. Briot, M. L. d'Yerville, E. Centeno, D. Cassagne, and J. P. Albert, “Giant second-harmonic generation in a one-dimensional GaN photonic crystal,” Phys. Rev. B 69(8), 085105 (2004).
[CrossRef]

G. Vecchi, J. Torres, D. Coquillat, M. L. d'Yerville, and A. M. Malvezzi, “Enhancement of visible second-harmonic generation in epitaxial GaN-based two-dimensional photonic crystal structures,” Appl. Phys. Lett. 84(8), 1245–1247 (2004).
[CrossRef]

X. Letartre, C. Seassal, C. Grillet, P. Rojo-Romeo, P. Viktorovitch, M. L. d'Yerville, D. Cassagne, and C. Jouanin, “Group velocity and propagation losses measurement in a single-line photonic-crystal waveguide on InP membranes,” Appl. Phys. Lett. 79(15), 2312–2314 (2001).
[CrossRef]

Ebnali-Heidari, M.

Eggleton, B. J.

C. Monat, B. Corcoran, D. Pudo, M. Ebnali-Heidari, C. Grillet, M. D. Pelusi, D. J. Moss, B. J. Eggleton, T. P. White, L. O’Faolain, and T. F. Krauss, “Slow light enhanced nonlinear optics in silicon photonic crystal waveguides,” J. Sel. Top. Quantum Electron 16, 344–356 (2010).
[CrossRef]

C. Monat, B. Corcoran, M. Ebnali-Heidari, C. Grillet, B. J. Eggleton, T. P. White, L. O’Faolain, and T. F. Krauss, “Slow light enhancement of nonlinear effects in silicon engineered photonic crystal waveguides,” Opt. Express 17(4), 2944–2953 (2009).
[CrossRef] [PubMed]

B. Corcoran, C. Monat, C. Grillet, D. J. Moss, B. J. Eggleton, T. P. White, L. O'Faolain, and T. F. Krauss, “Green light emission in silicon through slow-light enhanced third-harmonic generation in photonic-crystal waveguides,” Nat. Photonics 3(4), 206–210 (2009).
[CrossRef]

Fage-Pedersen, J.

N. Le Thomas, R. Houdre, L. H. Frandsen, J. Fage-Pedersen, A. V. Lavrinenko, and P. I. Borel, “Grating-assisted superresolution of slow waves in Fourier space,” Phys. Rev. B 76(3), 035103 (2007).
[CrossRef]

Fan, S.

S. G. Johnson, S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and L. A. Kolodziejski, “Guided modes in photonic crystal slabs,” Phys. Rev. B 60(8), 5751–5758 (1999).
[CrossRef]

Frandsen, L. H.

N. Le Thomas, R. Houdre, L. H. Frandsen, J. Fage-Pedersen, A. V. Lavrinenko, and P. I. Borel, “Grating-assisted superresolution of slow waves in Fourier space,” Phys. Rev. B 76(3), 035103 (2007).
[CrossRef]

Frey, R.

Gomez-Iglesias, A.

J. Li, T. P. White, L. O’Faolain, A. Gomez-Iglesias, and T. F. Krauss, “Systematic design of flat band slow light in photonic crystal waveguides,” Opt. Express 16(9), 6227–6232 (2008).
[CrossRef] [PubMed]

A. Gomez-Iglesias, D. O'Brien, L. O'Faolain, A. Miller, and T. F. Krauss, “Direct measurement of the group index of photonic crystal waveguides via Fourier transform spectral interferometry,” Appl. Phys. Lett. 90(26), 261107 (2007).
[CrossRef]

Grillet, C.

C. Monat, B. Corcoran, D. Pudo, M. Ebnali-Heidari, C. Grillet, M. D. Pelusi, D. J. Moss, B. J. Eggleton, T. P. White, L. O’Faolain, and T. F. Krauss, “Slow light enhanced nonlinear optics in silicon photonic crystal waveguides,” J. Sel. Top. Quantum Electron 16, 344–356 (2010).
[CrossRef]

M. Ebnali-Heidari, C. Monat, C. Grillet, and M. K. Moravvej-Farshi, “A proposal for enhancing four-wave mixing in slow light engineered photonic crystal waveguides and its application to optical regeneration,” Opt. Express 17(20), 18340–18353 (2009).
[CrossRef] [PubMed]

C. Monat, B. Corcoran, M. Ebnali-Heidari, C. Grillet, B. J. Eggleton, T. P. White, L. O’Faolain, and T. F. Krauss, “Slow light enhancement of nonlinear effects in silicon engineered photonic crystal waveguides,” Opt. Express 17(4), 2944–2953 (2009).
[CrossRef] [PubMed]

B. Corcoran, C. Monat, C. Grillet, D. J. Moss, B. J. Eggleton, T. P. White, L. O'Faolain, and T. F. Krauss, “Green light emission in silicon through slow-light enhanced third-harmonic generation in photonic-crystal waveguides,” Nat. Photonics 3(4), 206–210 (2009).
[CrossRef]

Y. Desieres, T. Benyattou, R. Orobtchouk, A. Morand, P. Benech, C. Grillet, C. Seassal, X. Letartre, P. Rojo-Romeo, and P. Viktorovitch, “Propagation losses of the fundamental mode in a single line-defect photonic crystal waveguide on an InP membrane,” J. Appl. Phys. 92(5), 2227 (2002).
[CrossRef]

X. Letartre, C. Seassal, C. Grillet, P. Rojo-Romeo, P. Viktorovitch, M. L. d'Yerville, D. Cassagne, and C. Jouanin, “Group velocity and propagation losses measurement in a single-line photonic-crystal waveguide on InP membranes,” Appl. Phys. Lett. 79(15), 2312–2314 (2001).
[CrossRef]

Guizzetti, G.

C. Comaschi, G. Vecchi, A. M. Malvezzi, M. Patrini, G. Guizzetti, M. Liscidini, L. C. Andreani, D. Peyrade, and Y. Chen, “Enhanced third harmonic reflection and diffraction in Silicon on Insulator photonic waveguides,” Appl. Phys. B 81(2-3), 305–311 (2005).
[CrossRef]

Hamachi, Y.

Houdre, R.

N. Le Thomas, R. Houdre, M. V. Kotlyar, D. O'Brien, and T. E. Krauss, “Exploring light propagating in photonic crystals with Fourier optics,” J. Opt. Soc. Am. B 24(12), 2964–2971 (2007).
[CrossRef]

N. Le Thomas, R. Houdre, L. H. Frandsen, J. Fage-Pedersen, A. V. Lavrinenko, and P. I. Borel, “Grating-assisted superresolution of slow waves in Fourier space,” Phys. Rev. B 76(3), 035103 (2007).
[CrossRef]

Husko, C.

Ikeda, N.

K. Inoue, H. Oda, N. Ikeda, and K. Asakawa, “Enhanced third-order nonlinear effects in slow-light photonic-crystal slab waveguides of line-defect,” Opt. Express 17(9), 7206–7216 (2009).
[CrossRef] [PubMed]

H. Oda, K. Inoue, Y. Tanaka, N. Ikeda, Y. Sugimoto, H. Ishikawa, and K. Asakawa, “Self-phase modulation in photonic-crystal-slab line-defect waveguides,” Appl. Phys. Lett. 90(23), 231102 (2007).
[CrossRef]

Inoue, K.

K. Inoue, H. Oda, N. Ikeda, and K. Asakawa, “Enhanced third-order nonlinear effects in slow-light photonic-crystal slab waveguides of line-defect,” Opt. Express 17(9), 7206–7216 (2009).
[CrossRef] [PubMed]

H. Oda, K. Inoue, Y. Tanaka, N. Ikeda, Y. Sugimoto, H. Ishikawa, and K. Asakawa, “Self-phase modulation in photonic-crystal-slab line-defect waveguides,” Appl. Phys. Lett. 90(23), 231102 (2007).
[CrossRef]

Ishikawa, H.

H. Oda, K. Inoue, Y. Tanaka, N. Ikeda, Y. Sugimoto, H. Ishikawa, and K. Asakawa, “Self-phase modulation in photonic-crystal-slab line-defect waveguides,” Appl. Phys. Lett. 90(23), 231102 (2007).
[CrossRef]

Jiang, W.

Joannopoulos, J. D.

M. Soljacić and J. D. Joannopoulos, “Enhancement of nonlinear effects using photonic crystals,” Nat. Mater. 3(4), 211–219 (2004).
[CrossRef] [PubMed]

S. G. Johnson, S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and L. A. Kolodziejski, “Guided modes in photonic crystal slabs,” Phys. Rev. B 60(8), 5751–5758 (1999).
[CrossRef]

Johnson, S. G.

S. G. Johnson, S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and L. A. Kolodziejski, “Guided modes in photonic crystal slabs,” Phys. Rev. B 60(8), 5751–5758 (1999).
[CrossRef]

Jouanin, C.

X. Letartre, C. Seassal, C. Grillet, P. Rojo-Romeo, P. Viktorovitch, M. L. d'Yerville, D. Cassagne, and C. Jouanin, “Group velocity and propagation losses measurement in a single-line photonic-crystal waveguide on InP membranes,” Appl. Phys. Lett. 79(15), 2312–2314 (2001).
[CrossRef]

Kolodziejski, L. A.

S. G. Johnson, S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and L. A. Kolodziejski, “Guided modes in photonic crystal slabs,” Phys. Rev. B 60(8), 5751–5758 (1999).
[CrossRef]

Kotlyar, M. V.

Krauss, T. E.

Krauss, T. F.

C. Monat, B. Corcoran, D. Pudo, M. Ebnali-Heidari, C. Grillet, M. D. Pelusi, D. J. Moss, B. J. Eggleton, T. P. White, L. O’Faolain, and T. F. Krauss, “Slow light enhanced nonlinear optics in silicon photonic crystal waveguides,” J. Sel. Top. Quantum Electron 16, 344–356 (2010).
[CrossRef]

C. Monat, B. Corcoran, M. Ebnali-Heidari, C. Grillet, B. J. Eggleton, T. P. White, L. O’Faolain, and T. F. Krauss, “Slow light enhancement of nonlinear effects in silicon engineered photonic crystal waveguides,” Opt. Express 17(4), 2944–2953 (2009).
[CrossRef] [PubMed]

B. Corcoran, C. Monat, C. Grillet, D. J. Moss, B. J. Eggleton, T. P. White, L. O'Faolain, and T. F. Krauss, “Green light emission in silicon through slow-light enhanced third-harmonic generation in photonic-crystal waveguides,” Nat. Photonics 3(4), 206–210 (2009).
[CrossRef]

J. Li, T. P. White, L. O’Faolain, A. Gomez-Iglesias, and T. F. Krauss, “Systematic design of flat band slow light in photonic crystal waveguides,” Opt. Express 16(9), 6227–6232 (2008).
[CrossRef] [PubMed]

A. Gomez-Iglesias, D. O'Brien, L. O'Faolain, A. Miller, and T. F. Krauss, “Direct measurement of the group index of photonic crystal waveguides via Fourier transform spectral interferometry,” Appl. Phys. Lett. 90(26), 261107 (2007).
[CrossRef]

L. O'Faolain, X. Yuan, D. McIntyre, S. Thoms, H. Chong, R. M. De la Rue, and T. F. Krauss, “Low-loss propagation in photonic crystal waveguides,” Electron. Lett. 42(25), 1454–1455 (2006).
[CrossRef]

Kubo, S.

Lascaray, J. P.

J. Torres, D. Coquillat, R. Legros, J. P. Lascaray, F. Teppe, D. Scalbert, D. Peyrade, Y. Chen, O. Briot, M. L. d'Yerville, E. Centeno, D. Cassagne, and J. P. Albert, “Giant second-harmonic generation in a one-dimensional GaN photonic crystal,” Phys. Rev. B 69(8), 085105 (2004).
[CrossRef]

D. Coquillat, J. Torres, D. Peyrade, R. Legros, J. P. Lascaray, M. Le Vassor d’Yerville, E. Centeno, D. Cassagne, J. P. Albert, Y. Chen, and R. M. De La Rue, “Equifrequency surfaces in a two-dimensional GaN-based photonic crystal,” Opt. Express 12(6), 1097–1108 (2004).
[CrossRef] [PubMed]

Lavrinenko, A. V.

N. Le Thomas, R. Houdre, L. H. Frandsen, J. Fage-Pedersen, A. V. Lavrinenko, and P. I. Borel, “Grating-assisted superresolution of slow waves in Fourier space,” Phys. Rev. B 76(3), 035103 (2007).
[CrossRef]

Le Thomas, N.

N. Le Thomas, R. Houdre, L. H. Frandsen, J. Fage-Pedersen, A. V. Lavrinenko, and P. I. Borel, “Grating-assisted superresolution of slow waves in Fourier space,” Phys. Rev. B 76(3), 035103 (2007).
[CrossRef]

N. Le Thomas, R. Houdre, M. V. Kotlyar, D. O'Brien, and T. E. Krauss, “Exploring light propagating in photonic crystals with Fourier optics,” J. Opt. Soc. Am. B 24(12), 2964–2971 (2007).
[CrossRef]

Le Vassor d’Yerville, M.

Legros, R.

D. Coquillat, J. Torres, D. Peyrade, R. Legros, J. P. Lascaray, M. Le Vassor d’Yerville, E. Centeno, D. Cassagne, J. P. Albert, Y. Chen, and R. M. De La Rue, “Equifrequency surfaces in a two-dimensional GaN-based photonic crystal,” Opt. Express 12(6), 1097–1108 (2004).
[CrossRef] [PubMed]

J. Torres, D. Coquillat, R. Legros, J. P. Lascaray, F. Teppe, D. Scalbert, D. Peyrade, Y. Chen, O. Briot, M. L. d'Yerville, E. Centeno, D. Cassagne, and J. P. Albert, “Giant second-harmonic generation in a one-dimensional GaN photonic crystal,” Phys. Rev. B 69(8), 085105 (2004).
[CrossRef]

Lepeshkin, N. N.

P. P. Markowicz, H. Tiryaki, H. Pudavar, P. N. Prasad, N. N. Lepeshkin, and R. W. Boyd, “Dramatic enhancement of third-harmonic generation in three-dimensional photonic crystals,” Phys. Rev. Lett. 92(8), 083903 (2004).
[CrossRef] [PubMed]

Letartre, X.

Y. Desieres, T. Benyattou, R. Orobtchouk, A. Morand, P. Benech, C. Grillet, C. Seassal, X. Letartre, P. Rojo-Romeo, and P. Viktorovitch, “Propagation losses of the fundamental mode in a single line-defect photonic crystal waveguide on an InP membrane,” J. Appl. Phys. 92(5), 2227 (2002).
[CrossRef]

X. Letartre, C. Seassal, C. Grillet, P. Rojo-Romeo, P. Viktorovitch, M. L. d'Yerville, D. Cassagne, and C. Jouanin, “Group velocity and propagation losses measurement in a single-line photonic-crystal waveguide on InP membranes,” Appl. Phys. Lett. 79(15), 2312–2314 (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(20), 3021–3023 (2001).
[CrossRef]

Li, J.

Liscidini, M.

C. Comaschi, G. Vecchi, A. M. Malvezzi, M. Patrini, G. Guizzetti, M. Liscidini, L. C. Andreani, D. Peyrade, and Y. Chen, “Enhanced third harmonic reflection and diffraction in Silicon on Insulator photonic waveguides,” Appl. Phys. B 81(2-3), 305–311 (2005).
[CrossRef]

Malvezzi, A. M.

C. Comaschi, G. Vecchi, A. M. Malvezzi, M. Patrini, G. Guizzetti, M. Liscidini, L. C. Andreani, D. Peyrade, and Y. Chen, “Enhanced third harmonic reflection and diffraction in Silicon on Insulator photonic waveguides,” Appl. Phys. B 81(2-3), 305–311 (2005).
[CrossRef]

D. Coquillat, G. Vecchi, C. Comaschi, A. M. Malvezzi, J. Torres, and M. L. d'Yerville, “Enhanced second- and third-harmonic generation and induced photoluminescence in a two-dimensional GaN photonic crystal,” Appl. Phys. Lett. 87(10), 101106 (2005).
[CrossRef]

G. Vecchi, J. Torres, D. Coquillat, M. L. d'Yerville, and A. M. Malvezzi, “Enhancement of visible second-harmonic generation in epitaxial GaN-based two-dimensional photonic crystal structures,” Appl. Phys. Lett. 84(8), 1245–1247 (2004).
[CrossRef]

Markowicz, P. P.

P. P. Markowicz, H. Tiryaki, H. Pudavar, P. N. Prasad, N. N. Lepeshkin, and R. W. Boyd, “Dramatic enhancement of third-harmonic generation in three-dimensional photonic crystals,” Phys. Rev. Lett. 92(8), 083903 (2004).
[CrossRef] [PubMed]

McIntyre, D.

L. O'Faolain, X. Yuan, D. McIntyre, S. Thoms, H. Chong, R. M. De la Rue, and T. F. Krauss, “Low-loss propagation in photonic crystal waveguides,” Electron. Lett. 42(25), 1454–1455 (2006).
[CrossRef]

McMillan, J. F.

Miller, A.

A. Gomez-Iglesias, D. O'Brien, L. O'Faolain, A. Miller, and T. F. Krauss, “Direct measurement of the group index of photonic crystal waveguides via Fourier transform spectral interferometry,” Appl. Phys. Lett. 90(26), 261107 (2007).
[CrossRef]

Monat, C.

C. Monat, B. Corcoran, D. Pudo, M. Ebnali-Heidari, C. Grillet, M. D. Pelusi, D. J. Moss, B. J. Eggleton, T. P. White, L. O’Faolain, and T. F. Krauss, “Slow light enhanced nonlinear optics in silicon photonic crystal waveguides,” J. Sel. Top. Quantum Electron 16, 344–356 (2010).
[CrossRef]

M. Ebnali-Heidari, C. Monat, C. Grillet, and M. K. Moravvej-Farshi, “A proposal for enhancing four-wave mixing in slow light engineered photonic crystal waveguides and its application to optical regeneration,” Opt. Express 17(20), 18340–18353 (2009).
[CrossRef] [PubMed]

B. Corcoran, C. Monat, C. Grillet, D. J. Moss, B. J. Eggleton, T. P. White, L. O'Faolain, and T. F. Krauss, “Green light emission in silicon through slow-light enhanced third-harmonic generation in photonic-crystal waveguides,” Nat. Photonics 3(4), 206–210 (2009).
[CrossRef]

C. Monat, B. Corcoran, M. Ebnali-Heidari, C. Grillet, B. J. Eggleton, T. P. White, L. O’Faolain, and T. F. Krauss, “Slow light enhancement of nonlinear effects in silicon engineered photonic crystal waveguides,” Opt. Express 17(4), 2944–2953 (2009).
[CrossRef] [PubMed]

Mondia, J. P.

Morand, A.

Y. Desieres, T. Benyattou, R. Orobtchouk, A. Morand, P. Benech, C. Grillet, C. Seassal, X. Letartre, P. Rojo-Romeo, and P. Viktorovitch, “Propagation losses of the fundamental mode in a single line-defect photonic crystal waveguide on an InP membrane,” J. Appl. Phys. 92(5), 2227 (2002).
[CrossRef]

Moravvej-Farshi, M. K.

Moss, D. J.

C. Monat, B. Corcoran, D. Pudo, M. Ebnali-Heidari, C. Grillet, M. D. Pelusi, D. J. Moss, B. J. Eggleton, T. P. White, L. O’Faolain, and T. F. Krauss, “Slow light enhanced nonlinear optics in silicon photonic crystal waveguides,” J. Sel. Top. Quantum Electron 16, 344–356 (2010).
[CrossRef]

B. Corcoran, C. Monat, C. Grillet, D. J. Moss, B. J. Eggleton, T. P. White, L. O'Faolain, and T. F. Krauss, “Green light emission in silicon through slow-light enhanced third-harmonic generation in photonic-crystal waveguides,” Nat. Photonics 3(4), 206–210 (2009).
[CrossRef]

Nefedov, I.

M. Centini, C. Sibilia, M. Scalora, G. D’Aguanno, M. Bertolotti, M. J. Bloemer, C. M. Bowden, and I. Nefedov, “Dispersive properties of finite, one-dimensional photonic band gap structures: applications to nonlinear quadratic interactions,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 60(44 Pt B), 4891–4898 (1999).
[CrossRef]

Notomi, M.

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, “Extremely large group-velocity dispersion of line-defect waveguides in photonic crystal slabs,” Phys. Rev. Lett. 87(25), 253902 (2001).
[CrossRef] [PubMed]

O’Faolain, L.

O'Brien, D.

N. Le Thomas, R. Houdre, M. V. Kotlyar, D. O'Brien, and T. E. Krauss, “Exploring light propagating in photonic crystals with Fourier optics,” J. Opt. Soc. Am. B 24(12), 2964–2971 (2007).
[CrossRef]

A. Gomez-Iglesias, D. O'Brien, L. O'Faolain, A. Miller, and T. F. Krauss, “Direct measurement of the group index of photonic crystal waveguides via Fourier transform spectral interferometry,” Appl. Phys. Lett. 90(26), 261107 (2007).
[CrossRef]

Oda, H.

K. Inoue, H. Oda, N. Ikeda, and K. Asakawa, “Enhanced third-order nonlinear effects in slow-light photonic-crystal slab waveguides of line-defect,” Opt. Express 17(9), 7206–7216 (2009).
[CrossRef] [PubMed]

H. Oda, K. Inoue, Y. Tanaka, N. Ikeda, Y. Sugimoto, H. Ishikawa, and K. Asakawa, “Self-phase modulation in photonic-crystal-slab line-defect waveguides,” Appl. Phys. Lett. 90(23), 231102 (2007).
[CrossRef]

O'Faolain, L.

B. Corcoran, C. Monat, C. Grillet, D. J. Moss, B. J. Eggleton, T. P. White, L. O'Faolain, and T. F. Krauss, “Green light emission in silicon through slow-light enhanced third-harmonic generation in photonic-crystal waveguides,” Nat. Photonics 3(4), 206–210 (2009).
[CrossRef]

A. Gomez-Iglesias, D. O'Brien, L. O'Faolain, A. Miller, and T. F. Krauss, “Direct measurement of the group index of photonic crystal waveguides via Fourier transform spectral interferometry,” Appl. Phys. Lett. 90(26), 261107 (2007).
[CrossRef]

L. O'Faolain, X. Yuan, D. McIntyre, S. Thoms, H. Chong, R. M. De la Rue, and T. F. Krauss, “Low-loss propagation in photonic crystal waveguides,” Electron. Lett. 42(25), 1454–1455 (2006).
[CrossRef]

Orobtchouk, R.

Y. Desieres, T. Benyattou, R. Orobtchouk, A. Morand, P. Benech, C. Grillet, C. Seassal, X. Letartre, P. Rojo-Romeo, and P. Viktorovitch, “Propagation losses of the fundamental mode in a single line-defect photonic crystal waveguide on an InP membrane,” J. Appl. Phys. 92(5), 2227 (2002).
[CrossRef]

Osgood, R. M.

Panoiu, N. C.

Patrini, M.

C. Comaschi, G. Vecchi, A. M. Malvezzi, M. Patrini, G. Guizzetti, M. Liscidini, L. C. Andreani, D. Peyrade, and Y. Chen, “Enhanced third harmonic reflection and diffraction in Silicon on Insulator photonic waveguides,” Appl. Phys. B 81(2-3), 305–311 (2005).
[CrossRef]

Pelusi, M. D.

C. Monat, B. Corcoran, D. Pudo, M. Ebnali-Heidari, C. Grillet, M. D. Pelusi, D. J. Moss, B. J. Eggleton, T. P. White, L. O’Faolain, and T. F. Krauss, “Slow light enhanced nonlinear optics in silicon photonic crystal waveguides,” J. Sel. Top. Quantum Electron 16, 344–356 (2010).
[CrossRef]

Peyrade, D.

C. Comaschi, G. Vecchi, A. M. Malvezzi, M. Patrini, G. Guizzetti, M. Liscidini, L. C. Andreani, D. Peyrade, and Y. Chen, “Enhanced third harmonic reflection and diffraction in Silicon on Insulator photonic waveguides,” Appl. Phys. B 81(2-3), 305–311 (2005).
[CrossRef]

J. Torres, D. Coquillat, R. Legros, J. P. Lascaray, F. Teppe, D. Scalbert, D. Peyrade, Y. Chen, O. Briot, M. L. d'Yerville, E. Centeno, D. Cassagne, and J. P. Albert, “Giant second-harmonic generation in a one-dimensional GaN photonic crystal,” Phys. Rev. B 69(8), 085105 (2004).
[CrossRef]

D. Coquillat, J. Torres, D. Peyrade, R. Legros, J. P. Lascaray, M. Le Vassor d’Yerville, E. Centeno, D. Cassagne, J. P. Albert, Y. Chen, and R. M. De La Rue, “Equifrequency surfaces in a two-dimensional GaN-based photonic crystal,” Opt. Express 12(6), 1097–1108 (2004).
[CrossRef] [PubMed]

Prasad, P. N.

P. P. Markowicz, H. Tiryaki, H. Pudavar, P. N. Prasad, N. N. Lepeshkin, and R. W. Boyd, “Dramatic enhancement of third-harmonic generation in three-dimensional photonic crystals,” Phys. Rev. Lett. 92(8), 083903 (2004).
[CrossRef] [PubMed]

Pudavar, H.

P. P. Markowicz, H. Tiryaki, H. Pudavar, P. N. Prasad, N. N. Lepeshkin, and R. W. Boyd, “Dramatic enhancement of third-harmonic generation in three-dimensional photonic crystals,” Phys. Rev. Lett. 92(8), 083903 (2004).
[CrossRef] [PubMed]

Pudo, D.

C. Monat, B. Corcoran, D. Pudo, M. Ebnali-Heidari, C. Grillet, M. D. Pelusi, D. J. Moss, B. J. Eggleton, T. P. White, L. O’Faolain, and T. F. Krauss, “Slow light enhanced nonlinear optics in silicon photonic crystal waveguides,” J. Sel. Top. Quantum Electron 16, 344–356 (2010).
[CrossRef]

Raineri, F.

Rojo-Romeo, P.

Y. Desieres, T. Benyattou, R. Orobtchouk, A. Morand, P. Benech, C. Grillet, C. Seassal, X. Letartre, P. Rojo-Romeo, and P. Viktorovitch, “Propagation losses of the fundamental mode in a single line-defect photonic crystal waveguide on an InP membrane,” J. Appl. Phys. 92(5), 2227 (2002).
[CrossRef]

X. Letartre, C. Seassal, C. Grillet, P. Rojo-Romeo, P. Viktorovitch, M. L. d'Yerville, D. Cassagne, and C. Jouanin, “Group velocity and propagation losses measurement in a single-line photonic-crystal waveguide on InP membranes,” Appl. Phys. Lett. 79(15), 2312–2314 (2001).
[CrossRef]

Roosen, G.

Ryasnyanskiy, A.

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(20), 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(20), 3021–3023 (2001).
[CrossRef]

Scalbert, D.

J. Torres, D. Coquillat, R. Legros, J. P. Lascaray, F. Teppe, D. Scalbert, D. Peyrade, Y. Chen, O. Briot, M. L. d'Yerville, E. Centeno, D. Cassagne, and J. P. Albert, “Giant second-harmonic generation in a one-dimensional GaN photonic crystal,” Phys. Rev. B 69(8), 085105 (2004).
[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(20), 3021–3023 (2001).
[CrossRef]

M. Centini, C. Sibilia, M. Scalora, G. D’Aguanno, M. Bertolotti, M. J. Bloemer, C. M. Bowden, and I. Nefedov, “Dispersive properties of finite, one-dimensional photonic band gap structures: applications to nonlinear quadratic interactions,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 60(44 Pt B), 4891–4898 (1999).
[CrossRef]

Seassal, C.

Y. Desieres, T. Benyattou, R. Orobtchouk, A. Morand, P. Benech, C. Grillet, C. Seassal, X. Letartre, P. Rojo-Romeo, and P. Viktorovitch, “Propagation losses of the fundamental mode in a single line-defect photonic crystal waveguide on an InP membrane,” J. Appl. Phys. 92(5), 2227 (2002).
[CrossRef]

X. Letartre, C. Seassal, C. Grillet, P. Rojo-Romeo, P. Viktorovitch, M. L. d'Yerville, D. Cassagne, and C. Jouanin, “Group velocity and propagation losses measurement in a single-line photonic-crystal waveguide on InP membranes,” Appl. Phys. Lett. 79(15), 2312–2314 (2001).
[CrossRef]

Shinya, A.

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, “Extremely large group-velocity dispersion of line-defect waveguides in photonic crystal slabs,” Phys. Rev. Lett. 87(25), 253902 (2001).
[CrossRef] [PubMed]

Sibilia, C.

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(20), 3021–3023 (2001).
[CrossRef]

M. Centini, C. Sibilia, M. Scalora, G. D’Aguanno, M. Bertolotti, M. J. Bloemer, C. M. Bowden, and I. Nefedov, “Dispersive properties of finite, one-dimensional photonic band gap structures: applications to nonlinear quadratic interactions,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 60(44 Pt B), 4891–4898 (1999).
[CrossRef]

Sipe, J. E.

N. A. R. Bhat and J. E. Sipe, “Optical pulse propagation in nonlinear photonic crystals,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 64(5), 056604 (2001).
[CrossRef] [PubMed]

Soljacic, M.

M. Soljacić and J. D. Joannopoulos, “Enhancement of nonlinear effects using photonic crystals,” Nat. Mater. 3(4), 211–219 (2004).
[CrossRef] [PubMed]

Sugimoto, Y.

H. Oda, K. Inoue, Y. Tanaka, N. Ikeda, Y. Sugimoto, H. Ishikawa, and K. Asakawa, “Self-phase modulation in photonic-crystal-slab line-defect waveguides,” Appl. Phys. Lett. 90(23), 231102 (2007).
[CrossRef]

Takahashi, C.

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, “Extremely large group-velocity dispersion of line-defect waveguides in photonic crystal slabs,” Phys. Rev. Lett. 87(25), 253902 (2001).
[CrossRef] [PubMed]

Takahashi, J.

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, “Extremely large group-velocity dispersion of line-defect waveguides in photonic crystal slabs,” Phys. Rev. Lett. 87(25), 253902 (2001).
[CrossRef] [PubMed]

Tanaka, Y.

H. Oda, K. Inoue, Y. Tanaka, N. Ikeda, Y. Sugimoto, H. Ishikawa, and K. Asakawa, “Self-phase modulation in photonic-crystal-slab line-defect waveguides,” Appl. Phys. Lett. 90(23), 231102 (2007).
[CrossRef]

Teppe, F.

J. Torres, D. Coquillat, R. Legros, J. P. Lascaray, F. Teppe, D. Scalbert, D. Peyrade, Y. Chen, O. Briot, M. L. d'Yerville, E. Centeno, D. Cassagne, and J. P. Albert, “Giant second-harmonic generation in a one-dimensional GaN photonic crystal,” Phys. Rev. B 69(8), 085105 (2004).
[CrossRef]

Thoms, S.

L. O'Faolain, X. Yuan, D. McIntyre, S. Thoms, H. Chong, R. M. De la Rue, and T. F. Krauss, “Low-loss propagation in photonic crystal waveguides,” Electron. Lett. 42(25), 1454–1455 (2006).
[CrossRef]

Tiryaki, H.

P. P. Markowicz, H. Tiryaki, H. Pudavar, P. N. Prasad, N. N. Lepeshkin, and R. W. Boyd, “Dramatic enhancement of third-harmonic generation in three-dimensional photonic crystals,” Phys. Rev. Lett. 92(8), 083903 (2004).
[CrossRef] [PubMed]

Torres, J.

D. Coquillat, G. Vecchi, C. Comaschi, A. M. Malvezzi, J. Torres, and M. L. d'Yerville, “Enhanced second- and third-harmonic generation and induced photoluminescence in a two-dimensional GaN photonic crystal,” Appl. Phys. Lett. 87(10), 101106 (2005).
[CrossRef]

J. Torres, D. Coquillat, R. Legros, J. P. Lascaray, F. Teppe, D. Scalbert, D. Peyrade, Y. Chen, O. Briot, M. L. d'Yerville, E. Centeno, D. Cassagne, and J. P. Albert, “Giant second-harmonic generation in a one-dimensional GaN photonic crystal,” Phys. Rev. B 69(8), 085105 (2004).
[CrossRef]

D. Coquillat, J. Torres, D. Peyrade, R. Legros, J. P. Lascaray, M. Le Vassor d’Yerville, E. Centeno, D. Cassagne, J. P. Albert, Y. Chen, and R. M. De La Rue, “Equifrequency surfaces in a two-dimensional GaN-based photonic crystal,” Opt. Express 12(6), 1097–1108 (2004).
[CrossRef] [PubMed]

G. Vecchi, J. Torres, D. Coquillat, M. L. d'Yerville, and A. M. Malvezzi, “Enhancement of visible second-harmonic generation in epitaxial GaN-based two-dimensional photonic crystal structures,” Appl. Phys. Lett. 84(8), 1245–1247 (2004).
[CrossRef]

Tran, Q. V.

van Driel, H. M.

Vecchi, G.

C. Comaschi, G. Vecchi, A. M. Malvezzi, M. Patrini, G. Guizzetti, M. Liscidini, L. C. Andreani, D. Peyrade, and Y. Chen, “Enhanced third harmonic reflection and diffraction in Silicon on Insulator photonic waveguides,” Appl. Phys. B 81(2-3), 305–311 (2005).
[CrossRef]

D. Coquillat, G. Vecchi, C. Comaschi, A. M. Malvezzi, J. Torres, and M. L. d'Yerville, “Enhanced second- and third-harmonic generation and induced photoluminescence in a two-dimensional GaN photonic crystal,” Appl. Phys. Lett. 87(10), 101106 (2005).
[CrossRef]

G. Vecchi, J. Torres, D. Coquillat, M. L. d'Yerville, and A. M. Malvezzi, “Enhancement of visible second-harmonic generation in epitaxial GaN-based two-dimensional photonic crystal structures,” Appl. Phys. Lett. 84(8), 1245–1247 (2004).
[CrossRef]

Vidakovic, P.

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(20), 3021–3023 (2001).
[CrossRef]

Viktorovitch, P.

Y. Desieres, T. Benyattou, R. Orobtchouk, A. Morand, P. Benech, C. Grillet, C. Seassal, X. Letartre, P. Rojo-Romeo, and P. Viktorovitch, “Propagation losses of the fundamental mode in a single line-defect photonic crystal waveguide on an InP membrane,” J. Appl. Phys. 92(5), 2227 (2002).
[CrossRef]

X. Letartre, C. Seassal, C. Grillet, P. Rojo-Romeo, P. Viktorovitch, M. L. d'Yerville, D. Cassagne, and C. Jouanin, “Group velocity and propagation losses measurement in a single-line photonic-crystal waveguide on InP membranes,” Appl. Phys. Lett. 79(15), 2312–2314 (2001).
[CrossRef]

Villeneuve, P. R.

S. G. Johnson, S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and L. A. Kolodziejski, “Guided modes in photonic crystal slabs,” Phys. Rev. B 60(8), 5751–5758 (1999).
[CrossRef]

Vy Tran, Q.

White, T. P.

C. Monat, B. Corcoran, D. Pudo, M. Ebnali-Heidari, C. Grillet, M. D. Pelusi, D. J. Moss, B. J. Eggleton, T. P. White, L. O’Faolain, and T. F. Krauss, “Slow light enhanced nonlinear optics in silicon photonic crystal waveguides,” J. Sel. Top. Quantum Electron 16, 344–356 (2010).
[CrossRef]

C. Monat, B. Corcoran, M. Ebnali-Heidari, C. Grillet, B. J. Eggleton, T. P. White, L. O’Faolain, and T. F. Krauss, “Slow light enhancement of nonlinear effects in silicon engineered photonic crystal waveguides,” Opt. Express 17(4), 2944–2953 (2009).
[CrossRef] [PubMed]

B. Corcoran, C. Monat, C. Grillet, D. J. Moss, B. J. Eggleton, T. P. White, L. O'Faolain, and T. F. Krauss, “Green light emission in silicon through slow-light enhanced third-harmonic generation in photonic-crystal waveguides,” Nat. Photonics 3(4), 206–210 (2009).
[CrossRef]

J. Li, T. P. White, L. O’Faolain, A. Gomez-Iglesias, and T. F. Krauss, “Systematic design of flat band slow light in photonic crystal waveguides,” Opt. Express 16(9), 6227–6232 (2008).
[CrossRef] [PubMed]

Wong, C. W.

Yamada, K.

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, “Extremely large group-velocity dispersion of line-defect waveguides in photonic crystal slabs,” Phys. Rev. Lett. 87(25), 253902 (2001).
[CrossRef] [PubMed]

Yang, X. D.

Yokohama, I.

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, “Extremely large group-velocity dispersion of line-defect waveguides in photonic crystal slabs,” Phys. Rev. Lett. 87(25), 253902 (2001).
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Young, J. F.

A. R. Cowan and J. F. Young, “Nonlinear optics in high refractive index contrast periodic structures,” Semicond. Sci. Technol. 20(9), R41–R56 (2005).
[CrossRef]

J. P. Mondia, H. M. van Driel, W. Jiang, A. R. Cowan, and J. F. Young, “Enhanced second-harmonic generation from planar photonic crystals,” Opt. Lett. 28(24), 2500–2502 (2003).
[CrossRef] [PubMed]

A. R. Cowan and J. F. Young, “Mode matching for second-harmonic generation in photonic crystal waveguides,” Phys. Rev. B 65(8), 085106 (2002).
[CrossRef]

Yuan, X.

L. O'Faolain, X. Yuan, D. McIntyre, S. Thoms, H. Chong, R. M. De la Rue, and T. F. Krauss, “Low-loss propagation in photonic crystal waveguides,” Electron. Lett. 42(25), 1454–1455 (2006).
[CrossRef]

Appl. Phys. B

C. Comaschi, G. Vecchi, A. M. Malvezzi, M. Patrini, G. Guizzetti, M. Liscidini, L. C. Andreani, D. Peyrade, and Y. Chen, “Enhanced third harmonic reflection and diffraction in Silicon on Insulator photonic waveguides,” Appl. Phys. B 81(2-3), 305–311 (2005).
[CrossRef]

Appl. Phys. Lett.

H. Oda, K. Inoue, Y. Tanaka, N. Ikeda, Y. Sugimoto, H. Ishikawa, and K. Asakawa, “Self-phase modulation in photonic-crystal-slab line-defect waveguides,” Appl. Phys. Lett. 90(23), 231102 (2007).
[CrossRef]

A. Gomez-Iglesias, D. O'Brien, L. O'Faolain, A. Miller, and T. F. Krauss, “Direct measurement of the group index of photonic crystal waveguides via Fourier transform spectral interferometry,” Appl. Phys. Lett. 90(26), 261107 (2007).
[CrossRef]

X. Letartre, C. Seassal, C. Grillet, P. Rojo-Romeo, P. Viktorovitch, M. L. d'Yerville, D. Cassagne, and C. Jouanin, “Group velocity and propagation losses measurement in a single-line photonic-crystal waveguide on InP membranes,” Appl. Phys. Lett. 79(15), 2312–2314 (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(20), 3021–3023 (2001).
[CrossRef]

D. Coquillat, G. Vecchi, C. Comaschi, A. M. Malvezzi, J. Torres, and M. L. d'Yerville, “Enhanced second- and third-harmonic generation and induced photoluminescence in a two-dimensional GaN photonic crystal,” Appl. Phys. Lett. 87(10), 101106 (2005).
[CrossRef]

G. Vecchi, J. Torres, D. Coquillat, M. L. d'Yerville, and A. M. Malvezzi, “Enhancement of visible second-harmonic generation in epitaxial GaN-based two-dimensional photonic crystal structures,” Appl. Phys. Lett. 84(8), 1245–1247 (2004).
[CrossRef]

Electron. Lett.

L. O'Faolain, X. Yuan, D. McIntyre, S. Thoms, H. Chong, R. M. De la Rue, and T. F. Krauss, “Low-loss propagation in photonic crystal waveguides,” Electron. Lett. 42(25), 1454–1455 (2006).
[CrossRef]

J. Appl. Phys.

Y. Desieres, T. Benyattou, R. Orobtchouk, A. Morand, P. Benech, C. Grillet, C. Seassal, X. Letartre, P. Rojo-Romeo, and P. Viktorovitch, “Propagation losses of the fundamental mode in a single line-defect photonic crystal waveguide on an InP membrane,” J. Appl. Phys. 92(5), 2227 (2002).
[CrossRef]

J. Opt. Soc. Am. B

J. Sel. Top. Quantum Electron

C. Monat, B. Corcoran, D. Pudo, M. Ebnali-Heidari, C. Grillet, M. D. Pelusi, D. J. Moss, B. J. Eggleton, T. P. White, L. O’Faolain, and T. F. Krauss, “Slow light enhanced nonlinear optics in silicon photonic crystal waveguides,” J. Sel. Top. Quantum Electron 16, 344–356 (2010).
[CrossRef]

Nat. Mater.

M. Soljacić and J. D. Joannopoulos, “Enhancement of nonlinear effects using photonic crystals,” Nat. Mater. 3(4), 211–219 (2004).
[CrossRef] [PubMed]

Nat. Photonics

T. Baba, “Slow light in photonic crystals,” Nat. Photonics 2(8), 465–473 (2008).
[CrossRef]

B. Corcoran, C. Monat, C. Grillet, D. J. Moss, B. J. Eggleton, T. P. White, L. O'Faolain, and T. F. Krauss, “Green light emission in silicon through slow-light enhanced third-harmonic generation in photonic-crystal waveguides,” Nat. Photonics 3(4), 206–210 (2009).
[CrossRef]

Opt. Express

J. Li, T. P. White, L. O’Faolain, A. Gomez-Iglesias, and T. F. Krauss, “Systematic design of flat band slow light in photonic crystal waveguides,” Opt. Express 16(9), 6227–6232 (2008).
[CrossRef] [PubMed]

A. Baron, A. Ryasnyanskiy, N. Dubreuil, P. Delaye, Q. Vy Tran, S. Combrié, A. de Rossi, R. Frey, and G. Roosen, “Light localization induced enhancement of third order nonlinearities in a GaAs photonic crystal waveguide,” Opt. Express 17(2), 552–557 (2009).
[CrossRef] [PubMed]

C. Monat, B. Corcoran, M. Ebnali-Heidari, C. Grillet, B. J. Eggleton, T. P. White, L. O’Faolain, and T. F. Krauss, “Slow light enhancement of nonlinear effects in silicon engineered photonic crystal waveguides,” Opt. Express 17(4), 2944–2953 (2009).
[CrossRef] [PubMed]

K. Inoue, H. Oda, N. Ikeda, and K. Asakawa, “Enhanced third-order nonlinear effects in slow-light photonic-crystal slab waveguides of line-defect,” Opt. Express 17(9), 7206–7216 (2009).
[CrossRef] [PubMed]

M. Ebnali-Heidari, C. Monat, C. Grillet, and M. K. Moravvej-Farshi, “A proposal for enhancing four-wave mixing in slow light engineered photonic crystal waveguides and its application to optical regeneration,” Opt. Express 17(20), 18340–18353 (2009).
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[CrossRef]

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[CrossRef]

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B. Corcoran, C. Monat, M. Pelusi, C. Grillet, T. P. White, L. O’Faolain, T. F. Krauss, B. J. Eggleton, D. J. Moss, “Optical performance monitoring via slow light enhanced third harmonic generation in silicon photonic crystal waveguides,” IEEE / OSA OFC, Postdeadline paper PDPA5 (2009)

B. Corcoran, C. Monat, M.Pelusi, C. Grillet, T. P. White, L. O'Faolain, T. F. Krauss, B. J. Eggleton and D. J. Moss, “Optical signal processing on a silicon chip at 640Gb/s using slow-light,” submitted.

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Figures (6)

Fig. 1
Fig. 1

Schematic of our experiment of THG in a PhC waveguide. The near-infrared pump signal (frequency ω, wavevector kz(ω)) is butt-coupled into the waveguide, while the TH light (3ω, kz(3ω)) is generated with an outgoing angle of emission that is directly related to the TH wavevector kz(3ω).

Fig. 2
Fig. 2

(a) Calculated dispersion of the fundamental mode of a slow light engineered silicon PhC waveguide (inset: SEM image). (b) Average TH power (black circles) when tuning the wavelength of the pump with a fixed power, and measured group index (red stars) dispersion of the fundamental mode. The grey area denotes the spectral region where vg is almost constant and equal to ~c/40.

Fig. 3
Fig. 3

Set-up used to measure the angle, and in turn, the wavevector of the TH light, generated out of the plane from the conversion of a near-infrared pump signal butt-coupled into the silicon PhC waveguide. A real image of the sample is produced onto CCD1 (inset a,b), while the associated image in the Fourier space (i.e. k-space) is produced onto the CCD2 at ~520nm (inset c).

Fig. 4
Fig. 4

(a) Fourier space images of the slow light silicon PhC waveguide W14816 at the TH frequency, when tuning the wavelength of the pump between 1542nm and 1557nm. (b) 2D map of the TH light dispersion (kzTH), ωTH = 3ω) inferred from these images (colorbar increases with the green light intensity). The quasi-phase matching condition (3kz(ω)-2π/a, 3ω) predicted from the calculated fundamental mode dispersion (kz(ω), ω) is superimposed (red dots).

Fig. 5
Fig. 5

(a,b) Dispersion (kzTH),ωTH = 3ω) of the TH, inferred from the CCD2 images for two slow PhC waveguides ((a) W15200, (b) W15010) with different dispersion. (c) Comparison between the measured TH dispersion extracted from the brightest features of Fig. 4(b) and Figs. 5(a,b) (dots), and the quasi-phase matching condition (3kz(ω)-2π/a, 3ω) predicted from the calculated fundamental mode dispersion (kz(ω), ω) for each waveguide (solid lines). All experimental TH dispersion in (c) have been shifted by a constant Δkz = + 0.03 [2π/a] offset.

Fig. 6
Fig. 6

(a,b) Fourier space images of the THG induced green light emitted from two different slow light PhC waveguides pumped at 1554nm.

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