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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 15, Iss. 12 — Jun. 11, 2007
  • pp: 7303–7318

χ (2) and χ (3) harmonic generation at a critical power in inhomogeneous doubly resonant cavities

Alejandro Rodriguez, Marin Soljačić, J. D. Joannopoulos, and Steven G. Johnson  »View Author Affiliations

Optics Express, Vol. 15, Issue 12, pp. 7303-7318 (2007)

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We derive general conditions for 100% frequency conversion in any doubly resonant nonlinear cavity, for both second- and third-harmonic generation via χ(2) and χ(3) nonlinearities. We find that conversion efficiency is optimized for a certain “critical” power depending on the cavity parameters, and assuming reasonable parameters we predict 100% conversion using milliwatts of power or less. These results follow from a semi-analytical coupled-mode theory framework which is generalized from previous work to include both χ(2) and χ(3) media as well as inhomogeneous (fully vectorial) cavities, analyzed in the high-efficiency limit where down-conversion processes lead to a maximum efficiency at the critical power, and which is verified by direct finite-difference time-domain (FDTD) simulations of the nonlinear Maxwell equations. Explicit formulas for the nonlinear coupling coefficients are derived in terms of the linear cavity eigenmodes, which can be used to design and evaluate cavities in arbitrary geometries.

© 2007 Optical Society of America

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

ToC Category:
Nonlinear Optics

Original Manuscript: February 23, 2007
Revised Manuscript: May 22, 2007
Manuscript Accepted: May 23, 2007
Published: May 31, 2007

Alejandro Rodriguez, Marin Soljacic, J. D. Joannopoulos, and Steven G. Johnson, "Χ(2) and Χ(3) harmonic generation at a critical power in inhomogeneous doubly resonant cavities," Opt. Express 15, 7303-7318 (2007)

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