Transient nonlinear wave mixing in collisional plasmas

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Abstract
The time dynamics of two-wave and four-wave mixing in a collisional plasma are explored. Maxwell's equations are coupled to the governing equations of a warm collisional plasma; this is followed by linearization based on a strong undepleted pump wave and simplification by the slowly varying envelope approximation. The resulting equations are solved via Laplace-transform techniques. We predict that in the presence of collisions between the plasma charged particles and background neutrals the two-wave-mixing geometry produces spatial amplification of an applied probe wave under transient (or nearly degenerate) conditions on the frequencies. The four-wave-mixing configuration produces a response that is governed by a ratio of characteristic time constants and the average number of collisions in a characteristic spatial scale. In both configurations enhancement of the plasma response occurs when transient or nearly degenerate conditions generate a moving intensity grating that propagates at a velocity of a natural mode of the plasma. The two-wave-mixing geometry has a single such resonance condition, and the four-wave-mixing geometry has two.