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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 18, Iss. 7 — Mar. 29, 2010
  • pp: 6831–6840

Investigation of phase matching for third-harmonic generation in silicon slow light photonic crystal waveguides using Fourier optics

Christelle Monat, Christian Grillet, Bill Corcoran, David J. Moss, Benjamin J. Eggleton, Thomas P. White, and Thomas F. Krauss  »View Author Affiliations

Optics Express, Vol. 18, Issue 7, pp. 6831-6840 (2010)

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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

OCIS Codes
(190.4160) Nonlinear optics : Multiharmonic generation
(190.4390) Nonlinear optics : Nonlinear optics, integrated optics
(130.5296) Integrated optics : Photonic crystal waveguides

ToC Category:
Nonlinear Optics

Original Manuscript: January 22, 2010
Revised Manuscript: February 19, 2010
Manuscript Accepted: February 21, 2010
Published: March 17, 2010

Christelle Monat, Christian Grillet, Bill Corcoran, David J. Moss, Benjamin J. Eggleton, Thomas P. White, and Thomas F. Krauss, "Investigation of phase matching for third-harmonic generation in silicon slow light photonic crystal waveguides using Fourier optics," Opt. Express 18, 6831-6840 (2010)

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  1. T. Baba, “Slow light in photonic crystals,” Nat. Photonics 2(8), 465–473 (2008). [CrossRef]
  2. M. Soljacić and J. D. Joannopoulos, “Enhancement of nonlinear effects using photonic crystals,” Nat. Mater. 3(4), 211–219 (2004). [CrossRef] [PubMed]
  3. 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]
  4. 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]
  5. 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]
  6. 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]
  7. 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]
  8. 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]
  9. 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]
  10. 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]
  11. 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]
  12. 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]
  13. 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]
  14. 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]
  15. 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]
  16. 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]
  17. 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]
  18. 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]
  19. 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]
  20. 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]
  21. 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]
  22. 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]
  23. 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]
  24. 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]
  25. 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]
  26. 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]
  27. 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]
  28. 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]
  29. 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]
  30. 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]
  31. 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]
  32. 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]
  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]
  34. 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)
  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.

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