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Journal of the Optical Society of America B

Nonlinear dispersion of backward-wave four-wave mixing in a photorefractive semiconductor and its effect on group velocity

Konstantin Shcherbin, P. Mathey, Alexander N. Shumelyuk, Dean R. Evans

Published Sep 24, 2024• 0 citations
Publisher

Abstract

Photorefractive backward-wave four-wave mixing may be configured for the amplification of the phase conjugate output and the attenuation of the transmitted output. The nondegenerate-in-frequency interaction is studied in such a configuration, realized in a semiconductor CdTe crystal. The spectra measured at different outputs show the gain and attenuation resonances. The preliminary study of optical pulse propagation demonstrates that, due to different nonlinear dispersions at different outputs of the selected wave mixing configuration, a slowing down of light is observed at the phase conjugate output, while an acceleration of light is detected at the transmitted output for the same input pulse at the same interaction.

DOI
10.1364/josab.534061

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Photorefractive backward-wave four-wave mixing may be configured for the amplification of the phase conjugate output and the attenuation of the transmitted output. The nondegenerate-in-frequency interaction is studied in such a configuration, realized in a semiconductor CdTe crystal. The spectra measured at different outputs show the gain and attenuation resonances. The preliminary study of optical pulse propagation demonstrates that, due to different nonlinear dispersions at different outputs of the selected wave mixing configuration, a slowing down of light is observed at the phase conjugate output, while an acceleration of light is detected at the transmitted output for the same input pulse at the same interaction.
A slowing down of light pulses using backward-wave four-wave mixing is achieved in photorefractive crystals with different coupling strength. The delay and width of the output pulse are studied as a function of the input pulse width and pump intensity ratio for the amplified transmitted beam and for the phase-conjugated beam. The delay characteristics are compared with those of the two-beam coupling. It is demonstrated that the four-wave mixing process ensures a larger slowing down of short pulses (pulses with width shorter than the photorefractive response time) as compared to the photorefractive two-beam coupling scheme and guarantees the elimination of forerunners. The delay of long pulses in the four-wave mixing configuration is almost the same as the one that can be reached with two-beam coupling. The effect of absorption on the nonlinear shape transformation of the output pulses is discussed qualitatively.
The nonlinear phase shift per unit length acquired by the transmitted and phase conjugate waves in backward-wave four-wave mixing may be considered as an effective refractive index. Consequently, a narrow spectrum of the nonlinear phase shift in non-degenerate frequency interaction corresponds to natural dispersion and such interaction may be used for temporal manipulation of light pulses. Analysis of the narrow spectra of the nonlinear phase shift shows high potential of the backward-wave four-wave for slowing down of light pulses. The slowing down is achieved using backward-wave four-wave mixing in media with local and nonlocal response. The delay and shape transformation of output pulses are studied and compared for the transmitted and phase conjugate channels. It is shown that the phase conjugate pulse achieves a longer delay under typical experimental conditions.
The phase shift occurred by optical waves in nonlinear interaction may be considered as phase shift resulted from a nonlinear refractive index. Consequently, a spectrum of the nonlinear phase shift in non-degenerate in frequency interactions represents nonlinear dispersion. Thus the nonlinear interaction with such dispersion may be used to achieve slow and fast light. The phase-conjugate reflectivity in photorefractive four-wave mixing may reveal spectrum with two maxima, which are located symmetrically with respect to zero frequency detuning. A complicated nonlinear dispersion corresponds to such reflectivity spectrum. Qualitative analysis of the nonlinear dispersion suggests unusual behavior when the nonlinear effect, i.e., delay of the light pulse, may decrease with increase of nonlinear coupling strength. The numerical calculations confirm such a nontrivial behavior. The experimental conditions are found, for which the delay of the phase-conjugate pulse decreases when the coupling strength increases. The conclusions of the theoretical analysis are confirmed experimentally for photorefractive four-wave mixing in barium titanate.
The slowing down of light pulses with backward-wave four-wave mixing is analyzed for photorefractive crystals with different coupling strengths. The conditions are found for which the delay of a phase-conjugate pulse decreases when the coupling strength increases and can even become negative, switching the pulse deceleration to acceleration. It is shown that for relatively low coupling strength the backward-wave four-wave mixing ensures a longer delay as compared to the two-beam-coupling technique. For coupling strengths tending to zero, the delay of long pulses approaches the response time of the medium. The conclusions of the theoretical analysis are confirmed experimentally with backward-wave four-wave mixing in barium titanate.
Nondegenerate four-wave mixing (FWM) of picosecond optical pulses in semiconductor optical amplifiers is investigated theoretically, taking into account various carrier processes, probe depletion, and cross-gain modulation effects. Analytical solutions for greatly simplified coupled-wave mixing equations are obtained from which conditions where probe depletion and cross-gain modulation effects cannot be neglected are found. On the other hand, the frequency detuning dependence of optimum input pump pulse energy and shaping of output conjugate pulses are observed from numerical simulations. In particular, calculations show that the frequency symmetry of conjugate and probe pulses with respect to the pump pulse does not hold for optical pulse FWM. Two-photon absorption and ultrafast nonlinear refraction effects are shown to decrease the FWM conversion efficiency.
Slow and fast light are achieved in two experiments using SPS photorefractive crystal at room temperature. We report that the photorefractive gain achieved by the two wave mixing (TWM) method can control the group velocity of the transmitted light pulses at visible wavelength. It is shown theoretically and experimentally that the time delay and the shape of the output pulse change as a function of the photorefractive gain. The beam fanning has also been used to control the velocity propagation of a single light pulse in the same crystal at λ = 1064 nm. Depending on the orientation of the polar axis, it is possible to accelerate or decelerate a short pulse with duration of order of μs in the crystal.