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Optical pulse propagation in media exhibiting a third order nonlinear polarization

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A theoretical investigation is made of two types of distortions, self phase modulation and self-focusing, produced when an intense optical pulse propagates in a medium whose induced polarization contains terms cubic in the field strength. The first analysis indicates that the insertion of such a medium into a laser cavity can result in the generation of a train of very stable, reproducible, bandwidth-limited pulses. By using a "circulating pulse" model, the physical processes involved are clarified, particularly in the case of high gain in the amplifying medium. Examples are given of the Q-switched operation of such a laser, for which the pulse train differs considerably from that of conventional mode-locked systems. A second analysis deals with the steady-state self-focusing of non-axisymmetrical beams; several approaches are used to derive the increase in the threshold power for elliptical-Gaussian beam shapes. As an alternative to a fully numerical solution, a series of increasingly accurate approximate results are obtained in the form of parameterized beam functions. When an Action-Integral minimization technique is employed to optimize these parameters, the method is capable of describing the self-focusing process in some detail.

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