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Effect of particular nonlinear dispersion in photorefractive four-wave mixing on slow and fast light

P. Mathey, Konstantin Shcherbin, Dean R. Evans

Published Feb 22, 2018• 0 citations
Publisher

Abstract

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.

DOI
10.1117/12.2292709

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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.
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.
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.
We demonstrate slow and fast light at room temperature by dispersive phase-coupling in a photorefractive SBN:60 crystal. Non-degenerated wave-mixing is used to obtain delayed and amplified pulses with reduced or increased group velocity of vg = 0. 2c m s −1 and vg =− 1. 3c m s −1 , respectively. The gain spectrum is modulated by using multiple frequency shifted pumps simultaneously. The complete dispersion of the spectrum is determined via the phase modulation technique. We compare the experimental results to numerical simulations based on coupled-wave equations.
Using perturbation theory, an examination is made of the fidelity of the photorefractive degenerate four-wave mixing phase conjugator. The general case is considered in which the probe is spatially varying (a beam) and temporally varying (a pulse), and the pumps are allowed to deplete. The probe wave is expanded as a sum of monochromatic plane-wave components. Carrying out the perturbation procedure up to the third order, the authors found that the components of the probe interact in pairs, so that the reflectance of each component of the conjugate wave is a combination of a linear term, a self-nonlinear term, and a term representing crosstalk with all other components of the probe. The crosstalk effect as a function of the frequency difference exhibits resonance behavior.>