The self-trapping of light waves by beat-wave excitation.

Self-fosusing thresholds are derived for multiple laser beams in the presence of a beat-excited plasma wave. The effects of relativistic electron ‘‘quiver’’ motion and the interaction of the beams with the plasma wave are included self-consistently. When the plasma wave is driven resonantly to large amplitude, transfer of the pump energy into sidebands causes the beams to defocus more rapidly. Consequently, relativistic focusing occurs above an irradiance threshold of Iλ2≊2×1017 W cm−2 μm2, instead of the usual power threshold for double-frequency illumination P≊4√2×109(ω0/ωp)2 W. Numerical solusions show that self-trapping of the laser energy is possible only for relatively small amplitude plasma waves. Comparisons are made with ‘‘cascade focusing,’’ which occurs when the plasma wave is driven below the plasma frequency. The threshold for the latter is up to ten times lower than for relativistic focusing. Numerical studies in this case indicate that self-trapped solutions do not exist, but the rate of beam collapse can be controlled by choosing an appropriate density mismatch.