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Journal of the Optical Society of America B

Cascaded nonlinear phase shift in a novel anharmonic phase-mismatch configuration

G. Baldenberger, Sophie LaRochelle, A. Villeneuve

Published Nov 1, 1999• 2 citations
Publisher

Abstract

We theoretically analyze a new class of aperiodic phase mismatch. The phase-matching function that is chosen depends on the calculated second-harmonic amplitude generated in the device during the propagation of the fundamental beam at given input intensity and wavelength. We show that, in such a configuration, the fields evolve toward the eigenmodes of a χ(2) two-wave mixing process. Hence a constant pump and an enhanced nonlinear phase shift that grows linearly with propagation length are obtained. We also discuss the feasibility of this scheme that provides an alternative approach for the realization of optical switching devices or Kerr-effect compensators.

DOI
10.1364/josab.16.001894

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We theoretically analyze a new class of aperiodic phase mismatch. The phase-matching function that is chosen depends on the calculated second-harmonic amplitude generated in the device during the propagation of the fundamental beam at given input intensity and wavelength. We show that, in such a configuration, the fields evolve toward the eigenmodes of a χ(2) two-wave mixing process. Hence a constant pump and an enhanced nonlinear phase shift that grows linearly with propagation length are obtained. We also discuss the feasibility of this scheme that provides an alternative approach for the realization of optical switching devices or Kerr-effect compensators.
Cascaded nonlinear phase shifts via second-harmonic generation are theoretically studied for quasi-phase-matched (QPM) structures. Both the effective phase mismatch and the structure itself contribute to the resultant nonlinear phase shift. Depending on the sign of the effective phase mismatch, structural contribution may enhance or depress the nonlinear phase shift. The fundamental wave will experience a nonlinear phase shift even if the effective phase matching is satisfied. By properly designing the effective phase mismatch, QPM structures with large material-based phase mismatch may provide large nonlinear phase shifts before saturation.
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The resurgence of interest in cascaded second order nonlinearities[1,2] has resulted in several schemes for applying cascading in second-harmonic generating (SHG) crystals to optical transistor-like devices [3-7], Such devices allow a weak signal beam to impose a large amplitude modulation on a strong “pump” beam, through mixing in a χ(2) crystal. However, all of the devices reported to date require the pump and signal beams to be temporally coherent, as the process is strongly dependent on the phase between these two beams. There have been some suggestions[6,7] that type II phasematched SHG may remove phase sensitivity, but the devices proposed still require that the signal must be in phase with approximately half of the pump intensity. In this letter, we describe how one may properly exploit type II phase matching to produce a truly phase-insensitive all-optical transistor (AOT) based on second order nonlinearities.
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Recently there has been increasing interest in obtaining large nonlinear phase shifts by an effective intensity dependent refractive index n2 based on second-order nonlinearities. These phase shifts arise as down-conversion of the second harmonic, away from perfect phase-matching, to the fundamental, which in general is out of phase with the fundamental source field. This process has been termed cascaded,1,2 as it involves the consecutive application of second-order nonlinearities χ(2)(ω,ω):χ(2)(—ω,2ω).
We have analyzed squeezing of the fundamental field by means of traveling-wave, type-II phase-matched, secondharmonic generation, taking into account depletion of the fundamental field and phase mismatch between the fundamental and the harmonic fields. For the phase-matched case we show that the generated squeezing is S = 1 - gamma, where gamma is the harmonic conversion efficiency. In the case of a large phase-mismatch we have identified a new mechanism that generates squeezing. It is the nonlinear phase shift of the fundamental field that is due to the cascaded chi((2)) nonlinearity.