Chirped Pulses in Laser Amplifiers

Abstract

This dissertation presents a theoretical investigation into the production, evolution, and asymptotic form of chirped pulses in homogeneously and inhomogeneously broadened laser amplifiers. Amplifier equations of motion are obtained in a form appropriate for dealing with such frequency-modulated pulses. The transient response of laser amplifiers to variously chirped Gaussian input pulses is studied parametrically using numerical solutions of the amplifier equations. The chirping mechanisms of the intensity dependence (Kerr effect) and the quadratic frequency dependence of the index of refraction are discussed briefly, as are the chirps produced by them and the amplification of Gaussian pulses in their presence. The amplifier whose host exhibits these dispersive effects is treated as a sequence of pairs of slices. One of each pair amplifies and exhibits the Kerr effect; the other has an index with a quadratic frequency dependence. This slice model is used to obtain steadystate pulses in both homogeneously and inhomogeneously broadened amplifiers whose host indexes have a quadratic frequency dependence. The steady-state pulse characteristics are determined as functions of amplifier parameters and the index curvature. The principal results are as follows: The homogeneously broadened amplifier responds predominately to the temporal character of a chirped input pulse whereas the inhomogeneously broadened amplifier response depends primarily upon the pulse spectrum. Of three important concepts (area theorem, echoes, and optical nutation) used to describe unchirped pulse amplification in inhomogeneously broadened media, only photon echo is useful when pulses are more than slightly chirped. The presence of the Kerr effect can produce significant chirps on large pulses. Amplification in the presence of the Kerr effect produces pulses strikingly similar to experimental results. Quadratic frequency dependence in the index has very little influence on most pulses in short amplifiers but has a cumulative effect in long amplifiers and laser oscillators. Chirped steady-state pulses exist in both homogeneously and inhomogeneously broadened amplifiers when the host index has such frequency dependence. In the homogeneously broadened case, they exist at relative gain levels dramatically below other theoretical predictions. They occur in the inhomogeneously broadened case only for the smaller index curvatures.