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Journal of the Optical Society of America B

Journal of the Optical Society of America B


  • Editor: Henry van Driel
  • Vol. 28, Iss. 9 — Sep. 1, 2011
  • pp: 2207–2215

Dynamic mode theory of optical resonators undergoing refractive index changes

Brian A. Daniel, Drew N. Maywar, and Govind P. Agrawal  »View Author Affiliations

JOSA B, Vol. 28, Issue 9, pp. 2207-2215 (2011)

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We present a theoretical model describing the dynamics of the electromagnetic field in an optical resonator undergoing refractive index changes. We use an operator formulation of Maxwell’s equations with a standard time- dependent perturbation theory to derive the dynamic mode-amplitude equations that govern the response of a resonator to a perturbing dipole-moment density. We show that in the case of time-dependent changes in the refractive index, a coupling matrix Γ k m ( t ) that appears in the equations accounts for all novel physical processes that can be expected to occur. In particular, the phenomenon of adiabatic wavelength conversion is governed by the diagonal elements of this matrix, and the off-diagonal elements are responsible for the transfer of energy from an excited resonator mode into its neighboring modes. Our model clearly shows that the latter process can occur only when the index changes are spatially nonuniform. We discuss the spatially uniform and nonuniform cases separately and compare the predictions of our model with experimental data available in the literature. The overall good agreement suggests that this model should be useful in the study of dynamic optical resonators. Moreover, since we do not make any assumptions about the type of dielectric cavity used, the width of input pulses, or the speed with which the refractive index is changed, this model should be applicable under most experimental situations.

© 2011 Optical Society of America

OCIS Codes
(130.0130) Integrated optics : Integrated optics
(230.0230) Optical devices : Optical devices
(070.5753) Fourier optics and signal processing : Resonators
(130.7405) Integrated optics : Wavelength conversion devices

ToC Category:
Integrated Optics

Original Manuscript: July 5, 2011
Manuscript Accepted: July 27, 2011
Published: August 23, 2011

Brian A. Daniel, Drew N. Maywar, and Govind P. Agrawal, "Dynamic mode theory of optical resonators undergoing refractive index changes," J. Opt. Soc. Am. B 28, 2207-2215 (2011)

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