Stability and transient effects in ultraviolet filaments

Abstract

Short, high intensity laser pulses induce nonlinear optical effects in the atmosphere that have the potential to make them propagate for long distances. Applications for long distance propagation of short pulses include active spectral remote sensing and laser lightning control. Much of the work in this field has been done with infrared pulses; however, it has been proposed that ultraviolet pulses have the advantage that longer pulse lengths can be used, thereby delivering more energy. Long pulse lengths lead to a simplified instantaneous model for the plasma response, which has been shown by Schwarz and Diels to admit steady state or oscillatory solutions corresponding to beam propagation. We have verified this model and have adjusted it to achieve closer agreement with numerical results. In this work we investigate the effects of transient behavior, and the stability of these solutions. Analysis of the modulational instability is done from the plane wave level to a full three dimensional model of the propagation. It is shown that both the transient behavior arising from the finite pulse length, and the modulational instability cause pulses to fragment over lengths on the scale of meters. We present results showing the growth of unstable modes in various propagation regimes. We discuss the pertinent length scales for ultraviolet pulses, as well as the impact of the instability and transient effects on theory and experiment. The results imply that continuous-wave models are very limited when used to predict dynamical properties of pulse propagation.