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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 18, Iss. 7 — Mar. 29, 2010
  • pp: 7288–7299

Exact iterative solution of second harmonic generation in quasi-phase-matched structures

Ming-Liang Ren and Zhi-Yuan Li  »View Author Affiliations

Optics Express, Vol. 18, Issue 7, pp. 7288-7299 (2010)

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A versatile and accurate approach that combines a numerical iteration technique and a transfer-matrix method (TMM) is developed to solve the general problem of second harmonic generation (SHG) with pump depletion in quasi-phase-matched (QPM) nonlinear optical structures. We derive the iterative formulae from the nonlinear coupled wave equations and obtain the intensity distribution of fundamental wave and second harmonic wave by TMM. The approach shows quick numerical convergence of iteration and maintains perfect conservation of total energy. The simulation results show that the model coincides with the one under undepleted pump approximation very well when the SHG efficiency is small (well below 15%) and agrees very well with the effective nonlinear susceptibility model in handling general SHG problems even when the conversion efficiency is high up to 100%. Our method is applicable to general nonlinear optical structures, such as periodic, quasi-periodic, and aperiodic QPM structures, photonic crystals, and micro-cavities that might involve complicated modulation on the linear and nonlinear susceptibility.

© 2010 OSA

OCIS Codes
(190.0190) Nonlinear optics : Nonlinear optics
(190.2620) Nonlinear optics : Harmonic generation and mixing
(230.4320) Optical devices : Nonlinear optical devices
(230.2035) Optical devices : Dispersion compensation devices

ToC Category:
Nonlinear Optics

Original Manuscript: January 13, 2010
Revised Manuscript: March 5, 2010
Manuscript Accepted: March 16, 2010
Published: March 24, 2010

Ming-Liang Ren and Zhi-Yuan Li, "Exact iterative solution of second harmonic generation in quasi-phase-matched structures," Opt. Express 18, 7288-7299 (2010)

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