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arXiv:nlin/0309040 · Optics Express

Weak-wave advancement in nearly collinear four-wave mixing

C. McCormick, R. Y. Chiao, Jandir Hickmann

Published Jul 1, 2002• 1 citation
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Abstract

We identify a new four-wave mixing process in which two nearly collinear pump beams produce phase-dependent gain into a weak bisector signal beam in a self-defocusing Kerr medium. Phase matching is achieved by weak-wave advancement caused by cross-phase modulation between the pump and signal beams. We relate this process to the inverse of spatial modulational instability and suggest a time-domain analog.

DOI
10.1364/oe.10.000581

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Weak-wave advancement in nearly collinear four-wave mixing: comment

Éric Lantz, Thibaut Sylvestre

The exponential gain predicted in "Weak-wave advancement in nearly collinear four-wave mixing" [Opt. Express 10, 581 (2002)], disappears when all interacting sidebands are properly taken into account. The demonstration closely follows well-established literature in the formally equivalent temporal domain.

Optics Express•Jan 1, 2004•0 citations
We identify a new four-wave mixing process in which two nearly collinear pump beams produce phase-dependent gain into a weak bisector signal beam in a self-defocusing Kerr medium. Phase matching is achieved by weak-wave advancement caused by cross-phase modulation between the pump and signal beams. We relate this process to the inverse of spatial modulational instability and suggest a time-domain analog.
The theory of collinear degenerate four-wave mixing in a lossless, isotropic Kerr medium is described and solved numerically. Multiple solutions to the equations governing the spatial evolution of the probe and signal fluxes are found when the input fluxes exceed a critical intensity determined by the electric susceptibility and the interaction length of the medium. This treatment includes all phase-matched contributions to the equations of motion of all fields, including the cross-coupled waves appearing in the collinear geometry.
The theory of probe beam amplification via degenerate optical wave mixing in a Kerr medium is presented. This theory includes consideration of the self-phase modulation, two-wave mixing, and multiwave mixing terms in the coupled-wave equations. Both analytical solutions, under the assumptions of a nondepleted pump beam and a transparent Kerr medium, and numerical solutions with these assumptions removed are presented. Our solutions show that under certain conditions, phase matching can be satisfied and a high probe beam gain is possible, even for a zero phase shift between the refractive index and the intensity gratings.
Two-wave mixing amplification of a weak probe beam interfering with a powerful pump beam of the same linear polarization is demonstrated when the probe beam enters the semiconductor sample before the pump pulse. This mixing of two beams of the same frequency is made possible by the difference between self-phase modulation and cross-phase modulation, which modify differently the instantaneous frequencies of both beams. Net gain coefficients up to 5.5 cm (-1) are obtained for experiments performed in CdTe. Theoretical calculations quantitatively confirm this interpretation and predict much higher gain for more resonant configurations or higher pump energies, making this process of potential interest for optical processing.
Mutually pumped phase conjugation, a process by which two incident laser beams can mutually pump each other to generate the phase-conjugate replica of the other beam, is studied in a transparent Kerr medium with an electrostrictive nonlinearity. The nonlinear medium acts as a phase-conjugating mirror to both of the incident beams and generates their Stokes-shifted phase-conjugated outputs by the nearly degenerate four-wave mixing process. Our results show that this process will occur only if the coupling strength, defined by the product of the Kerr amplitude gain coefficient, the total input intensity, and the interaction length, is above the threshold value of 2. If the intensity of one of the input beams exceeds the threshold value and the second input beam is weaker than the first, then the weak beam is phase conjugated with a large reflectivity that has a maximum value of the intensity ratio of the strong to the weak input beam. For negligible absorption in the medium, a complete transfer of energy of both the incident beams into the phase-conjugate beams can occur for finite interaction lengths that are only slightly larger than the threshold value. Seeding the oscillation beams tends to lower the phase-conjugate power reflectivities, probably because of increased contribution from the competing two-wave mixing process.