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Computer Optics

Transient four-wave mixing in a transparent two-component medium

Valery V. Ivakhnik, M. Savelyev

Published Jan 1, 2018• 4 citations
Publisher

Abstract

We analyze changes in the spatial structure of an object wave under four-wave mixing in a transparent two-component medium in schemes with opposing and concurrent pump waves. It is shown that in the spatial spectrum of the object wave there is a dip, whose position is determined by the propagation direction of the second pump wave. Angular rotation and frequency shift of the pump waves lead to a decrease in the conversion efficiency of high spatial frequencies. The bandwidth of the spatial frequencies cut out by the four-wave radiation converter decreases monotonically over time, whereas the bandwidth of the most efficiently converted spatial frequencies increases.

DOI
10.18287/2412-6179-2018-42-2-227-235

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We analyze changes in the spatial structure of an object wave under four-wave mixing in a transparent two-component medium in schemes with opposing and concurrent pump waves. It is shown that in the spatial spectrum of the object wave there is a dip, whose position is determined by the propagation direction of the second pump wave. Angular rotation and frequency shift of the pump waves lead to a decrease in the conversion efficiency of high spatial frequencies. The bandwidth of the spatial frequencies cut out by the four-wave radiation converter decreases monotonically over time, whereas the bandwidth of the most efficiently converted spatial frequencies increases.
We analyze changes in the spatial structure of an object wave under four-wave mixing in a transparent two-component medium in schemes with opposing and concurrent pump waves.It is shown that in the spatial spectrum of the object wave there is a dip, whose position is determined by the propagation direction of the second pump wave.Angular rotation and frequency shift of the pump waves lead to a decrease in the conversion efficiency of high spatial frequencies.The bandwidth of the spatial frequencies cut out by the four-wave radiation converter decreases monotonically over time, whereas the bandwidth of the most efficiently converted spatial frequencies increases.
Spatial characteristics of the degenerate four-wave radiation converter in a liquid containing nanoparticles were studied using a scheme with concurrent pump waves. The phase matching condition was shown to determine the general form of the spatial spectrum amplitude of the object wave, with the electrostriction phenomenon and Dufour effect shown to cause the emergence of dips in the spatial spectrum amplitude, with the dip positions corresponding to the propagation directions of the pump waves. The relationship between characteristics of the dips and the pump wave parameters were obtained.
The coincidence of the amplitude reflection coefficients, half-widths of the spatial frequencies bands of a four-wave radiation converter on thermal nonlinearity with feedback for signal or object waves has been shown at equal pump waves intensity. The dependence of the amplitude reflection coefficient, spatial selectivity of the four-wave radiation converter on thermal nonlinearity on the pump waves intensity has been analyzed. An increase in the half-width of the spatial frequency band is observed with an increase in the pump waves intensity at the compensation for the phase shift arising as a result of the propagation of the pump waves in the medium. There is a threshold value of the pump waves intensity, above which the value of the amplitude reflection coefficient of the four-wave converter with feedback for signal or object waves, is less than in the absence of feedback.
Spatial and temporal characteristics of a degenerate four-wave converter in a multimode waveguide with resonant nonlinearity in a scheme with counter-pumping waves are analyzed using the time response function and the point spread function. For single-mode pump waves with equal mode numbers, the dependences of the time response width on the waveguide length, the intensity of the first pump waves, and the mode number in the mode expansion of the object wave amplitude are obtained for the four-wave converter. The greatest contribution to the object wave amplitude is shown to be from the waveguide mode whose number coincides with the mode number of single-mode pump waves. For the stationary model, taking into account the spatial structure of the Gaussian pump wave leads to a monotonous decrease with a decrease in the pump beam width, followed by a constant value of the PSF module width. With single-mode pump waves with equal mode numbers, An increase in the mode number of the pump waves leads to a redistribution of energy concentrated in the side maxima of the point signal image and improvement in the quality of the wavefront reversal for a model with single-mode pump waves with equal mode numbers.
Quasi-degenerate four-wave mixing (FWM) of low-intensity radiation (with an intensity less than 1 mW cm -2 ) was observed for the 5 S 1/2 ( F =2)—5 P 3/2 ( F '=3) transition in an optically transparent 87 Rb vapour under conditions of electromagnetically induced absorption. The efficiency of frequency conversion was no less than 1% with respect to the intensity of pump waves. Nonlinear FWM is highly selective relative to the frequency detuning of pump waves (the FWM full width at half maximum was less than 50 kHz).
We propose a new scheme of the resonant four-wave mixing (FWM) for the frequency up or down conversion, which is more efficient than the commonly-used scheme of the non-resonant FWM. In this new scheme, two control fields are spatially varied such that a probe field at the input can be converted to a signal field at the output. The efficiency of probe-to-signal energy conversion can be 90% at medium's optical depth of about 100. Our proposed scheme works for both the continuous-wave and pulse cases, and is flexible in choosing the control field intensity. This work provides a very useful tool in the nonlinear frequency conversion.