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Radiophysics and Quantum Electronics

Propagation of a wave beam in an active medium with resonant and Kerr nonlinearities

N. D. Milovskiĭ, N. Yu. Rusov, T. V. Yastrebova

Published Feb 1, 1982• 0 citations
Publisher
DOI
10.1007/bf01034258

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We have shown previously that two strong laser beams (with the same frequency) counterpropagating in a Kerr nonlinear medium with linear dispersion become un stable when their intensities exceed a certain threshold.1 We demonstrate here that the system exhibits large (theoretically unlimited) amplification of a probe beam when the two pumping beams have their intensities slightly below the threshold. This is in contrast to the conventional phase conjugation due to four-wave mixing in a nondispersive Kerr nonlinear medium. The mechanism of amplification in our system can be explained in terms of positive distributed feedback from the Kerr nonlinear index grating formed by two strong pumping laser beams in the presence of dispersion giving rise to a light-induced distributed-feedback resonator. This feedback is attributed to the fact that the weak beams with both signal frequency, ω + δ, and conjugate frequency, ω − δ, propagate with phase speed different (due to dispersion) from that of a pumping wave with frequency ω, which triggers the exponentially increasing energy exchange between weak and strong beams at the nonlinear index grating (this energy exchange is prohibited in nondispersive media). When the probe frequency approaches a frequency of one of the longitudinal modes of the light-induced distributed resonator, and the pumping intensity approaches the threshold of instability, the resonant amplification increases infinitely; for presently available laser intensity stabilities, amplification as large as 104 is feasible.
We investigate the focusing characteristics of scalar and vector beams within an atomic medium. An active-Raman-gain configuration is employed to achieve significant Kerr nonlinearity in a four-state atomic system. The probe beams can attain focusing within the medium through careful selection of input beam intensities and the spatial profile of the control field. We analytically derive the linear and third-order nonlinear susceptibilities for both scalar and vector probe beams. Our observations indicate that, in addition to the energy transfer from the control beam to the probe beam, the giant cross-Kerr nonlinearity facilitates the focusing of the scalar probe beam into a significantly smaller spot size. Conversely, the vector probe beams exhibit gain-induced narrowing. Furthermore, we evaluate the state of polarization for the vector beam at the minimum beam waist, observing a polarization rotation and a change in ellipticity during propagation. Through the mechanism of focusing, we achieve a reduced spot size for the probe beam, which may have substantial implications for resolution enhancement in microscopy applications.
In our recent research1, it was suggested that counter-propagating laser beams in a Kerr-nonlinear medium can induce intensity-dependent nonreciprocity which consists in different changes of refractive indecies for both of the waves. Under some conditions, this can result in such directionally asymmetrical effects as (i) directional bistability in a nonlinear ring resonator which allows one to switch the direction of propagation of a dominant mode and (ii) enhancement of the Sagnac effect in a rotating ring resonator.