Time‐dependent phase conjugation and four‐wave mixing in plasmas

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Abstract
Time‐dependent four‐wave mixing and phase conjugation in plasmas are treated, taking into account resonant longitudinal plasma modes and effects of spatial nonuniformity. A space‐time formulation of four‐wave processes in the ponderomotive force regime yields linearized equations, which are solved analytically as a combined initial/boundary‐value problem in slab and inhomogeneous geometries. The plasma response is incorporated in a ‘‘grating’’ Green’s function, expressed in terms of linear quasilongitudinal susceptibilities. Response times, decay times, and absolute instabilities are treated analytically. Plasma nonuniformity can speed up the response of the conjugate wave and modify resonant absolute instability thresholds. A new class of resonant absolute instabilities occurs when the counterpropagating pump waves have unequal intensities. The thresholds can be rather low for pump waves of modest intensity, provided the resonant grating has a long lifetime. Below these thresholds, regimes of stable amplification of the phase‐conjugate wave relative to the incident signal are possible with pumps of unequal intensity.