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Journal of the Optical Society of America B

Journal of the Optical Society of America B

| OPTICAL PHYSICS

  • Editor: Henry M. Van Driel
  • Vol. 24, Iss. 5 — May. 1, 2007
  • pp: 1105–1112

Fourier modal method for the analysis of second-harmonic generation in two-dimensionally periodic structures containing anisotropic materials

Benfeng Bai and Jari Turunen  »View Author Affiliations


JOSA B, Vol. 24, Issue 5, pp. 1105-1112 (2007)
http://dx.doi.org/10.1364/JOSAB.24.001105


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Abstract

The rigorous Fourier modal method for crossed anisotropic gratings is extended to the analysis of second-harmonic generation in two-dimensionally periodic structures. The method takes the undepleted-pump approximation that uncouples the calculations of the fundamental and the second-harmonic fields. The effectiveness of the method is verified by solving a one-dimensional problem, which has been analyzed by two previously developed methods, and by comparing the simulation results of the L-shaped gold nanoparticle arrays with the previous experimental measurements.

© 2007 Optical Society of America

OCIS Codes
(000.3860) General : Mathematical methods in physics
(050.1950) Diffraction and gratings : Diffraction gratings
(190.3970) Nonlinear optics : Microparticle nonlinear optics
(190.4160) Nonlinear optics : Multiharmonic generation

ToC Category:
Nonlinear Optics

History
Original Manuscript: October 17, 2006
Manuscript Accepted: December 26, 2006
Published: April 17, 2007

Citation
Benfeng Bai and Jari Turunen, "Fourier modal method for the analysis of second-harmonic generation in two-dimensionally periodic structures containing anisotropic materials," J. Opt. Soc. Am. B 24, 1105-1112 (2007)
http://www.opticsinfobase.org/josab/abstract.cfm?URI=josab-24-5-1105


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References

  1. G. Purvinis, P. S. Priambodo, M. Pomerantz, M. Zhou, T. A. Maldonado, and R. Magnusson, 'Second-harmonic generation in resonant waveguide gratings incorporating ionic self-assembled monolayer polymer films,' Opt. Lett. 29, 1108-1110 (2004). [CrossRef] [PubMed]
  2. W. Nakagawa, R.-C. Tyan, P.-C. Sun, and Y. Fainman, 'Near-field localization of ultrashort optical pulses in transverse 1-D periodic nanostructures,' Opt. Express 7, 123-128 (2000). [CrossRef] [PubMed]
  3. C. De Angelis, F. Gringoli, M. Midrio, D. Modotto, J. S. Aitchison, and G. G. Nalesso, 'Conversion efficiency for second-harmonic generation in photonic crystals,' J. Opt. Soc. Am. B 18, 348-351 (2001). [CrossRef]
  4. 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, 2500-2502 (2003). [CrossRef] [PubMed]
  5. H. Tuovinen, M. Kauranen, K. Jefimovs, P. Vahimaa, T. Vallius, J. Turunen, N. V. Tkachenko, and H. Lemmetyinen, 'Linear and second-order nonlinear optical properties of arrays of noncentrosymmetric gold nanoparticles,' J. Nonlinear Opt. Phys. Mater. 11, 421-432 (2002). [CrossRef]
  6. B. K. Canfield, S. Kujala, K. Jefimovs, J. Turunen, and M. Kauranen, 'Linear and nonlinear optical responses influenced by broken symmetry in an array of gold nanoparticles,' Opt. Express 12, 5418-5423 (2004). [CrossRef] [PubMed]
  7. B. K. Canfield, S. Kujala, K. Jefimovs, T. Vallius, J. Turunen, and M. Kauranen, 'Polarization effects in the linear and nonlinear optical responses of gold nanoparticle arrays,' J. Opt. A, Pure Appl. Opt. 7, S110-S117 (2005). [CrossRef]
  8. B. K. Canfield, S. Kujala, K. Jefimovs, Y. Svirko, J. Turunen, and M. Kauranen, 'A macroscopic formalism to describe the second-order nonlinear optical response of nanostructures,' J. Opt. A, Pure Appl. Opt. 8, S278-S284 (2006). [CrossRef]
  9. 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]
  10. M. Nevière, P. Vincent, D. Maystre, R. Reinisch, and J. L. Coutaz, 'Differential theory for metallic gratings in nonlinear optics: second-harmonic generation,' J. Opt. Soc. Am. B 5, 330-337 (1988). [CrossRef]
  11. D. Maystre, M. Nevière, R. Reinisch, and J. L. Coutaz, 'Integral theory for metallic gratings in nonlinear optics and comparison with experimental results on second-harmonic generation,' J. Opt. Soc. Am. B 5, 338-346 (1988). [CrossRef]
  12. E. Popov and M. Nevière, 'Surface-enhanced second-harmonic generation in nonlinear corrugated dielectrics: new theoretical approaches,' J. Opt. Soc. Am. B 11, 1555-1564 (1994). [CrossRef]
  13. W. Nakagawa, R.-C. Tyan, and Y. Fainman, 'Analysis of enhanced second-harmonic generation in periodic nanostructures using modified rigorous coupled-wave analysis in the undepleted-pump approximation,' J. Opt. Soc. Am. A 19, 1919-1928 (2002). [CrossRef]
  14. A. Locatelli, D. Modotto, C. De Angelis, F. M. Pigozzo, and A.-D. Capobianco, 'Nonlinear bidirectional beam propagation method based on scattering operators for periodic microstructured waveguides,' J. Opt. Soc. Am. B 20, 1724-1731 (2003). [CrossRef]
  15. C. De Angelis, G. Nalesso, D. Modotto, M. Midrio, A. Locatelli, and J. S. Aitchison, 'Multiple-scale coupled-mode theory for second-harmonic generation in one-dimensional periodic structures,' J. Opt. Soc. Am. B 20, 1853-1865 (2003). [CrossRef]
  16. F. Raineri, Y. Dumeige, A. Levenson, and X. Letartre, 'Nonlinear decoupled FDTD code: phase-matching in 2D defective photonic crystal,' Electron. Lett. 38, 1704-1706 (2002). [CrossRef]
  17. B. Maes, P. Bienstman, and R. Baets, 'Modeling second-harmonic generation by use of mode expansion,' J. Opt. Soc. Am. B 22, 1378-1383 (2005). [CrossRef]
  18. L. Li, 'Fourier modal method for crossed anisotropic gratings with arbitrary permittivity and permeability tensors,' J. Opt. A, Pure Appl. Opt. 5, 345-355 (2003). [CrossRef]
  19. L. Li, 'Use of Fourier series in the analysis of discontinuous periodic structures,' J. Opt. Soc. Am. A 13, 1870-1876 (1996). [CrossRef]
  20. L. Li, 'Formulation and comparison of two recursive matrix algorithms for modeling layered diffraction gratings,' J. Opt. Soc. Am. A 13, 1024-1035 (1996). [CrossRef]
  21. L. Li, 'Note on the S-matrix propagation algorithm,' J. Opt. Soc. Am. A 20, 655-660 (2003). [CrossRef]

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