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Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Vol. 19, Iss. 9 — Sep. 1, 2002
  • pp: 1919–1928

Analysis of enhanced second-harmonic generation in periodic nanostructures using modified rigorous coupled-wave analysis in the undepleted-pump approximation

Wataru Nakagawa, Rong-Chung Tyan, and Yeshaiahu Fainman  »View Author Affiliations

JOSA A, Vol. 19, Issue 9, pp. 1919-1928 (2002)

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We present an extension of the rigorous coupled-wave analysis technique to analyze second-harmonic generation (SHG) in periodic optical nanostructures in the undepleted-pump approximation. We apply this method to analyze SHG in two example nanostructures for which we predict enhanced nonlinearity due to transverse near-field localization of the fundamental optical field in the nonlinear material. First, we examine a periodic nanostructure that yields up to twice the transmitted SHG intensity output compared with the bulk nonlinear material but only for small nanostructure depths because of mismatch of the fundamental and second-harmonic mode phase velocities. Second, we develop and analyze a modified nanostructure and find that this nanostructure concurrently achieves transverse localization and phase matching for SHG. In principle, this permits an arbitrary coherent interaction length, and for several specific nanostructure depths we predict a transmitted SHG intensity output more than two orders of magnitude greater than that of the bulk material.

© 2002 Optical Society of America

OCIS Codes
(000.4430) General : Numerical approximation and analysis
(190.2620) Nonlinear optics : Harmonic generation and mixing
(190.4420) Nonlinear optics : Nonlinear optics, transverse effects in
(230.4320) Optical devices : Nonlinear optical devices

Original Manuscript: December 21, 2001
Revised Manuscript: April 10, 2002
Manuscript Accepted: April 16, 2002
Published: September 1, 2002

Wataru Nakagawa, Rong-Chung Tyan, and Yeshaiahu 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)

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  1. P. Lalanne, J.-P. Hugonin, “High-order effective-medium theory of subwavelength gratings in classical mounting: application to volume holograms,” J. Opt. Soc. Am. A 15, 1843–1851 (1998). [CrossRef]
  2. J. N. Mait, D. W. Prather, M. S. Mirotznik, “Design of binary subwavelength diffractive lenses by use of zeroth-order effective-medium theory,” J. Opt. Soc. Am. A 16, 1157–1167 (1999). [CrossRef]
  3. F. Xu, R.-C. Tyan, P.-C. Sun, Y. Fainman, C.-C. Cheng, A. Scherer, “Form-birefringent computer-generated holograms,” Opt. Lett. 21, 1513–1515 (1996). [CrossRef] [PubMed]
  4. R.-C. Tyan, A. A. Salvekar, H.-P. Chou, C.-C. Cheng, A. Scherer, P.-C. Sun, F. Xu, Y. Fainman, “Design, fabrication and characterization of form-birefringent multilayer polarizing beam splitter,” J. Opt. Soc. Am. A 14, 1627–1636 (1997). [CrossRef]
  5. E. Yablonovitch, “Photonic band-gap structures,” J. Opt. Soc. Am. B 10, 283–295 (1993). [CrossRef]
  6. R.-C. Tyan, P.-C. Sun, A. A. Salvekar, H.-P. Chou, C.-C. Cheng, F. Xu, A. Scherer, Y. Fainman, “Subwavelength multilayer binary grating design for implementing photonic crystals,” in Quantum Optoelectronics, Vol. 9 of 1997 OSA Technical Digest Series (Optical Society of America, Washington D.C.,1997), pp. 35–37.
  7. W. Nakagawa, P.-C. Sun, C.-H. Chen, Y. Fainman, “Wide-field-of-view narrow-band spectral filters based on photonic crystal nanocavities,” Opt. Lett. 27, 191–193 (2002). [CrossRef]
  8. W. Nakagawa, R.-C. Tyan, P.-C. Sun, Y. Fainman, “Near-field localization of ultrashort optical pulses in transverse 1-D periodic nanostructures,” Opt. Express 7, 123–128 (2000), http://www.opticsexpress.org . [CrossRef] [PubMed]
  9. J. E. Sipe, R. W. Boyd, “Nonlinear susceptibility of composite optical materials in the Maxwell Garnett model,” Phys. Rev. A 46, 1614–1629 (1992). [CrossRef] [PubMed]
  10. R. W. Boyd, J. E. Sipe, “Nonlinear optical susceptibilities of layered composite materials,” J. Opt. Soc. Am. B 11, 297–303 (1994). [CrossRef]
  11. G. L. Fischer, R. W. Boyd, R. J. Gehr, S. A. Jenekhe, J. A. Osaheni, J. E. Sipe, L. A. Weller-Brophy, “Enhanced nonlinear optical response of composite materials,” Phys. Rev. Lett. 74, 1871–1874 (1995). [CrossRef] [PubMed]
  12. K. P. Yuen, M. F. Law, K. W. Yu, P. Sheng, “Enhancement of optical nonlinearity through anisotropic microstructures,” Opt. Commun. 148, 197–207 (1998). [CrossRef]
  13. H. Ma, R. Xiao, P. Sheng, “Third-order optical nonlinearity enhancement through composite microstructures,” J. Opt. Soc. Am. B 15, 1022–1029 (1998). [CrossRef]
  14. A. Fiore, S. Janz, L. Delobel, P. van der Meer, P. Bravetti, V. Berger, E. Rosencher, J. Nagle, “Second-harmonic generation at λ=1.6 µm in AlGaAs/Al2O3 waveguides using birefringence phase matching,” Appl. Phys. Lett. 72, 2942–2944 (1998). [CrossRef]
  15. A. Fiore, V. Berger, E. Rosencher, P. Bravetti, J. Nagle, “Phase matching using an isotropic nonlinear optical material,” Nature (London) 391, 463–466 (1998). [CrossRef]
  16. A. Saher Helmy, D. C. Hutchings, T. C. Kleckner, J. H. Marsh, A. C. Bryce, J. M. Arnold, C. R. Stanley, J. S. Aitchison, C. T. A. Brown, K. Moutzouris, M. Ebrahimzadeh, “Quasi phase matching in GaAs-AlAs superlattice waveguides through bandgap tuning by use of quantum-well intermixing,” Opt. Lett. 25, 1370–1372 (2000). [CrossRef]
  17. L. A. Eyres, P. J. Tourreau, T. J. Pinguet, C. B. Ebert, J. S. Harris, M. M. Fejer, L. Becouarn, B. Gerard, E. Lallier, “All-epitaxial fabrication of thick, orientation-patterned GaAs films for nonlinear optical frequency conversion,” Appl. Phys. Lett. 79, 904–906 (2001). [CrossRef]
  18. K. Moutzouris, S. Venugopal Rao, M. Ebrahimzadeh, A. De Rossi, V. Berger, M. Calligaro, V. Ortiz, “Efficient second-harmonic generation in birefringently phase-matched GaAs/Al2O3 waveguides,” Opt. Lett. 26, 1785–1787 (2001). [CrossRef]
  19. E. U. Rafailov, P. Loza-Alvarez, C. T. A. Brown, W. Sibbett, R. M. De La Rue, P. Millar, D. A. Yanson, J. S. Roberts, P. A. Houston, “Second-harmonic generation from a first-order quasi-phase-matched GaAs/AlGaAs waveguide crystal,” Opt. Lett. 26, 1984–1986 (2001). [CrossRef]
  20. M. G. Moharam, T. K. Gaylord, “Diffraction analysis of dielectric surface-relief gratings,” J. Opt. Soc. Am. 72, 1385–1392 (1982). [CrossRef]
  21. M. G. Moharam, E. B. Grann, D. A. Pommet, T. K. Gaylord, “Formulation for stable and efficient implementation of the rigorous coupled-wave analysis of binary gratings,” J. Opt. Soc. Am. A 12, 1068–1076 (1995). [CrossRef]
  22. E. N. Glytsis, T. K. Gaylord, “Rigorous three-dimensional coupled-wave diffraction analysis of single and cascaded anisotropic gratings,” J. Opt. Soc. Am. A 4, 2061–2080 (1987). [CrossRef]
  23. L. Li, “Use of Fourier series in the analysis of discontinuous periodic structures,” J. Opt. Soc. Am. A 13, 1870–1876 (1996). [CrossRef]
  24. L. Li, “Reformulation of the Fourier modal method for surface-relief gratings made with anisotropic materials,” J. Mod. Opt. 45, 1313–1334 (1998). [CrossRef]

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