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Journal of Nonlinear Optical Physics & Materials

NON-LAGRANGIAN NONLINEARITY AND COHERENT OPTICAL WAVE MIXING PROCESSES

A.L. MURAZYAN, Nelson V. Tabiryan, B. YA. ZEL’DOVICH, I. C. Khoo

Published Jan 1, 1994• 0 citations
Publisher

Abstract

Interaction of optical beams in media with diagonal-bipolar nonlinearity is theoretically investigated. It is shown that the nonlinearity is not Lagrangian and allows processes violating energy flux conservation law. Conditions for energy exchange to take place are found. Probe beam amplification in the field of counterpropagating pumps and wavefront conjugation are investigated to exhibit some remarkable features. Coherent interaction of waves of different frequencies through recording static gratings is shown to lead also to energy exchange processes owing to non-Lagrangian character of nonlinearity.

DOI
10.1142/s0218199194000043

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Interaction of optical beams in media with diagonal-bipolar nonlinearity is theoretically investigated. It is shown that the nonlinearity is not Lagrangian and allows processes violating energy flux conservation law. Conditions for energy exchange to take place are found. Probe beam amplification in the field of counterpropagating pumps and wavefront conjugation are investigated to exhibit some remarkable features. Coherent interaction of waves of different frequencies through recording static gratings is shown to lead also to energy exchange processes owing to non-Lagrangian character of nonlinearity.
Energy exchange between counter propagating light waves of equal frequency is possible in media with instantaneous and local nonlinear optical response which, however, provides a special form of nonlinearity tensor. The major requirement is that there has to be no Lagrangian describing the light-medium interaction. There is a limited region of the pump wave intensity where the signal wave amplification takes place. The thermal mechanisms of interaction between light waves and liquid crystals provide examples of "non-Lagrangian" nonlinearity.
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.
This paper presents the results of theoretical and experimental studies into the processes of light field transformations upon multiwave mixing. The principal aim is to develop a theory of multiwave mixing in complex molecular media in conditions of exhibited internal (scattering from dynamic gratings) and external (resonator) feedback, to determine a mechanism of light field transformations at the dynamic holograms and by nonlinear interferometers, to work out and introduce into practice novel nonlinear-optical methods for the control over the energy and spatial-temporal characteristics of light beams. The possibilities for phase conjugation with simultaneous frequency conversion of a signal wave are analyzed. The methods aimed at the realization of various types of optical bistability, spatial hysteresis, regular and chaotic intensity oscillations are proposed and investigated
In the case of disordered nonlinear media, it is shown that in four-wave mixing a phenomena analogous to phase conjugation may occur. In contrast to the case of transparent media in which two counterpropagating pump waves (with frequency ${\ensuremath{\omega}}_{p}$) are required, phase conjugation may occur in the presence of a single pump wave injected into the disordered nonlinear material. We find that in the angular distribution of radiation of frequency ${\ensuremath{\omega}}_{s}$ (${\ensuremath{\omega}}_{s}$=2${\ensuremath{\omega}}_{p}$-${\ensuremath{\omega}}_{i}$, where ${\ensuremath{\omega}}_{i}$ is the frequency of probe wave) there is a narrow peak in the backscattered direction associated with the probe wave. The intensity of this peak may be some orders of magnitude larger than the diffuse background at the frequency ${\ensuremath{\omega}}_{s}$.