Space–time focusing: breakdown of the slowly varying envelope approximation in the self-focusing of femtosecond pulses

Abstract

Numerical analysis of the self-focusing of femtosecond optical pulses reveals that the usually invoked slowly varying envelope approximation breaks down long before the temporal structure reaches the time scale of an optical cycle. This breakdown leads to a dramatic departure from the recently predicted symmetric development of the self-focusing pulse. By properly including the linear space–time focusing properties of short pulses, it is found that the trailing half of the self-focusing pulse is greatly enhanced and culminates in the formation of a trailing shock edge.