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Journal of the Optical Society of America B

Journal of the Optical Society of America B

| OPTICAL PHYSICS

  • Editor: Henry van Driel
  • Vol. 28, Iss. 12 — Dec. 1, 2011
  • pp: 2879–2887

Enhancement of second-harmonic generation in an air-bridge photonic crystal slab: simulation by spectral element method

Ma Luo and Qing Huo Liu  »View Author Affiliations


JOSA B, Vol. 28, Issue 12, pp. 2879-2887 (2011)
http://dx.doi.org/10.1364/JOSAB.28.002879


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Abstract

The enhancement of second-harmonic generation (SHG) across a 2D photonic crystal (PC) slab consisting of GaP is investigated in this study with the three-dimensional spectral element method (SEM). The in-plane band structure is calculated, and it is compared with the peaks of the SHG to reveal the mechanisms behind the enhancement. The numerical result from the SEM shows that, under normal incidence, the scattered power of the SHG is enhanced for the eigenstates with large decay rates, while the stored energy of the SHG is enhanced for the eigenstates with a zero decay rate. The SHG is enhanced under two conditions: (i) phase matching between the fundamental and second-harmonic (SH) fields and (ii) symmetry matching between the field pattern of the resonant eigenstate and the generated SH polarization field. Compared with a homogeneous dielectric slab, the air-bridge PC slab can enhance the SHG by 4 orders of magnitude.

© 2011 Optical Society of America

OCIS Codes
(000.4430) General : Numerical approximation and analysis
(160.5298) Materials : Photonic crystals

ToC Category:
Photonic Crystals

History
Original Manuscript: May 9, 2011
Revised Manuscript: September 29, 2011
Manuscript Accepted: September 30, 2011
Published: November 11, 2011

Citation
Ma Luo and Qing Huo Liu, "Enhancement of second-harmonic generation in an air-bridge photonic crystal slab: simulation by spectral element method," J. Opt. Soc. Am. B 28, 2879-2887 (2011)
http://www.opticsinfobase.org/josab/abstract.cfm?URI=josab-28-12-2879


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References

  1. P. A. Franken, A. E. Hill, C. W. Peters, and G. Weinreich, “Generation of optical harmonics,” Phys. Rev. Lett. 7, 118-119(1961). [CrossRef]
  2. R. L. Sutherland, Handbook of Nonlinear Optics, 2nd ed.(Marcel Dekker, 2003). [CrossRef]
  3. M. Soljacic and J. D. Joannopoulos, “Enhancement of nonlinear effects using photonic crystals,” Nat. Mater. 3, 211-219 (2004). [CrossRef] [PubMed]
  4. M. Liscidini and L. C. Andreani, “Second-harmonic generation in doubly resonant microcavities with periodic dielectric mirrors,” Phys. Rev. E 73, 016613 (2006). [CrossRef]
  5. J. Bravo-Abad, A. Rodriguez, P. Bermel, S. G. Johnson, J. D. Joannopoulos, and M. Soljacic, “Enhanced nonlinear optics in photonic-crystal microcavities,” Opt. Express 15, 16161-16176(2007). [CrossRef] [PubMed]
  6. 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 60, 4891-4898 (1999). [CrossRef]
  7. Y. Dumeige, I. Sagnes, P. Monnier, P. Vidakovic, I. Abram, C. Mriadec, and A. Levenson, “Phase-matched frequency doubling at photonic band edges: efficiency scaling as the fifth power of the length,” Phys. Rev. Lett. 89, 043901 (2002). [CrossRef] [PubMed]
  8. Y. Dumeige, F. Raineri, A. Levenson, and X. Letartre, “Second-harmonic generation in one-dimensional photonic edge waveguides,” Phys. Rev. B 68, 066617 (2003). [CrossRef]
  9. R. Iliew, C. Etrich, T. Pertsch, F. Lederer, and Y. S. Kivshar, “Huge enhancement of backward second-harmonic generation with slow light in photonic crystals,” Phys. Rev. A 81, 023820(2010). [CrossRef]
  10. S. E. Harris, “Proposed backward wave oscillation in the infrared,” Appl. Phys. Lett. 9, 114 (1966). [CrossRef]
  11. J. Torres, D. Coquillat, R. Legros, J. P. Lascaray, F. Teppe, D. Scalbert, D. Peyrade, Y. Chen, O. Briot, M. Le Vassor 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, 085105 (2004). [CrossRef]
  12. D. C. Marinica, A. G. Borisov, and S. V. Shabanov, “Second harmonic generation from arrays of subwavelength cylinders,” Phys. Rev. B 76, 085311 (2007). [CrossRef]
  13. B. Maes, P. Bienstman, R. Baets, B. Hu, P. Sewell, and T. Benson, “Modeling comparison of second-harmonic generation in high-index-contrast devices,” Opt. Quantum Electron. 40, 13-22(2008). [CrossRef]
  14. A. R. Cowan and J. F. Young, “Mode matching for second-harmonic generation in photonic crystal waveguides,” Phys. Rev. B 65, 085106 (2002). [CrossRef]
  15. A. M. Malvezzi, G. Vecchi, M. Patrini, G. Guizzetti, L. C. Andreani, F. Romanato, L. Businaro, E. Di Fabrizio, A. Passaseo, and M. D. Vittorio, “Resonant second-harmonic generation in a GaAs photonic crystal waveguide,” Phys. Rev. B 68, 161306(R) (2003). [CrossRef]
  16. J. S. Savage and A. F. Peterson, “Higher-order vector finite elements for tetrahedral cells,” IEEE Trans. Microw. Theory Technol. 44, 874-879 (1996). [CrossRef]
  17. M. Luo and Q. H. Liu, “Spectral element method for band structures of three-dimensional anisotropic photonic crystals,” Phys. Rev. E 80, 056702 (2009). [CrossRef]
  18. M. Luo and Q. H. Liu, “Extraordinary transmission of a thick film with a periodic structure consisting of strongly dispersive materials,” J. Opt. Soc. Am. B 28, 629-636 (2011). [CrossRef]
  19. K. B. Crozier, V. Lousse, O. Kilic, S. Kim, S. Fan, and O. Solgaard, “Air-bridged photonic crystal slabs at visible and near-infrared wavelengths,” Phys. Rev. B 73, 115126 (2006). [CrossRef]
  20. D. E. Aspnes and A. A. Studna, “Dielectric functions and optical parameters of Si, Ge, GaP, GaAs, GaSb, InP, InAs, and InSb from 1.5 to 6.0 eV,” Phys. Rev. B 27, 985-1009 (1983). [CrossRef]
  21. I. Shoji, T. Kondo, A. Kitamoto, M. Shirane, and R. Ito, “Absolute scale of second-order nonlinear-optical coefficients,” J. Opt. Soc. Am. B 14, 2268-2294 (1997). [CrossRef]

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