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Soviet Journal of Quantum Electronics

Polarization characteristics of a noncoplanar concurrent four-wave interaction in resonant media

Anatolii A Afanas'ev, M V Dotsenko

Published Oct 31, 1990• 0 citations
Publisher

Abstract

An analysis is made of a noncoplanar concurrent four-wave interaction in the field of linearly polarized pump waves in resonant media modeled by linear (or circular) dipoles. The parametric gain increments and the polarization of weak radiation are determined, in the cubic approximation, as a function of the polarization characteristics of the waves being mixed and of the properties of the resonant medium. In the case of orthogonally polarized pump waves the polarization of the signal is conserved irrespective of the model adopted for a resonant medium and the polarization of a diffracted wave is reversed relative to the signal. In the case of parallel orientation of the pump wave vectors the polarization of a linearly polarized signal is retained if the vector of its amplitude is oriented parallel or orthogonal to the pump waves. In a medium modeled by an ensemble of randomly oriented dipoles when the angle between the pump wave vectors is 2π/3 or π/3 the radiation is linearly polarized irrespective of the polarization structure of the input signal.

DOI
10.1070/qe1990v020n10abeh007459

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Soviet Journal of Quantum Electronics•Apr 30, 1985•1 citation
An analysis is made of a noncoplanar concurrent four-wave interaction in the field of linearly polarized pump waves in resonant media modeled by linear (or circular) dipoles. The parametric gain increments and the polarization of weak radiation are determined, in the cubic approximation, as a function of the polarization characteristics of the waves being mixed and of the properties of the resonant medium. In the case of orthogonally polarized pump waves the polarization of the signal is conserved irrespective of the model adopted for a resonant medium and the polarization of a diffracted wave is reversed relative to the signal. In the case of parallel orientation of the pump wave vectors the polarization of a linearly polarized signal is retained if the vector of its amplitude is oriented parallel or orthogonal to the pump waves. In a medium modeled by an ensemble of randomly oriented dipoles when the angle between the pump wave vectors is 2π/3 or π/3 the radiation is linearly polarized irrespective of the polarization structure of the input signal.
The optical-pumping theory of the passage of polarised radiation through a resonant medium was developed in the irreducible tensorial formalism. Transitions with arbitrary momenta J 1.2 are considered in the cubic approximation. For transitions with small values of momenta (J 1 =1 to J 2 =0; J 1 = 1 / 2 to J 2 = 1 / 2 ) the vector form of the equation system in density-matrix notation allows the problem to be solved exactly for light intensity. In the general case of an elliptically polarised wave, the equation systems for the interaction between circular components of polarisation of light in a resonant medium are obtained. Numerical calculations for deformation and rotation of the polarisation ellipse in a medium subject to saturation effects are also carried out. Irrespective of the initial state the polarisation tends either to a linear or to a circular form as it propagates, depending on times of collisional relaxation of orientation and alignment. The polarisation of linearly and circularly polarised waves does not change as the waves propagate, but the values of the saturation power for these polarisations differ considerably.
Equations describing a transient degenerate four-wave interaction in a resonant medium are derived and solved numerically. The approximation of a "following" nonlinear polarization state is used to determine the range of values of the parameters of the medium and the radiation field in which the efficiency of a transient four-wave interaction is higher than that of the steady-state process. It is found that amplification of weak radiation as a result of transient energy exchange can only be achieved in the four-wave interaction for different pump wave intensities.
An investigation is made of wavefront reversal of optical radiation in a nondegenerate four-wave interaction in a resonant medium. It is shown that for a pump intensity comparable with the saturation intensity of the absorption line of the resonant medium, the reversed wave spectrum has two side peaks positioned symmetrically relative to the central peak which corresponds to a degenerate interaction. These side peaks are attributable to regions of negative absorption (amplification) of weak radiation by the resonant medium situated in a high-power field of opposite pump waves. The dependences of the magnitudes and positions of these peaks on the pump intensity can be used to control the spectral and energy characteristics of the reflected radiation. The conditions for self-excitation of a reversing system based on resonant four-wave interaction are determined. In particular, the ranges of the pump intensity and the optical density of the resonant medium in which self-excitation of the reversing system may occur, are determined for a degenerate interaction.
An analysis is made of nondegenerate four-wave interaction (FWI) in a resonant medium (two-level model) with Doppler line broadening allowing for nonlinear absorption of the weak radiation. The cubic approximation with respect to the field is used to derive expressions for the coefficients of parametric coupling and absorption of the mixed waves. The angular dependences of the reflection coefficient are studied for quasicollinear and orthogonal FWI geometries. It is shown that, as a result of the thermal motion of the particles, the dependence of the reflection coefficient on the angle θ between the interacting waves results in considerable limitation of the angular width of the reversed beams. This limitation is greater for degenerate FWI. In the case of nondegenerate FWI, as a result of the selective action of waves on groups of atoms having a specific velocity projection, the reversal efficiency may increase on increase in θ.
The functional relations have been presented between the complex amplitude (including polarization) of reflected wave on the one hand and amplitudes, polarizations of pump and probe waves, the third-order nonlinear susceptibility on the other hand, for degenerate four-wave mixing (DFWM) in isotropic medium, in which the polarizations are linear and/or circular, and the geometry is collinear or non-collinear. In the non-collinear geometry, when the polarizations of pump waves are parallel to each other, one can determine the ratio x1111/x1221 from the angles between polarization directions of probe and reflected waves; when the polarizations of pump are circular polarizations of the same handedness, one can get the ideal complex conjugate wave in this geometry. In the collinear geometry, there are always some non-conjugate component in the reflected wave, and the functional relation between reflection coefficient of amplitude and the thickness of sample can have the form of tangent function, hyperbolic tangent function and linear function; when the polarizations of pump waves are parallel to each other and |x1221|> |x1122|, this geometry is capable of generating self-oscillation; when polarizations of pump are circular ones of different handedness, DFWM acts as an ideal plane-mirror for probe wave with circular polarization, etc. The results can be used to explain some well-known experimental results and provide some theoretical guidance for designing new experiments.
A theoretical analysis is made of a four-wave parametric interaction accompanied by reversal of the signal wavefront in a thin layer of a two-level medium as a result of a two-photon resonance of opposite waves of randomly modulated pumping. An allowance is made for the inertia of the interaction, saturation of the transition involved in the interaction, Stark shift of the levels, and width of the pump spectrum. A study is made of the influence of random modulation of the pump waves on the average value and relative variance of the intensity of the reversed wave. It is shown that the relative amplitude of the intensity fluctuations of the reversed wave is minimal when the maximum average intensity is reached.