Theory of transient self-focusing

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Abstract
By using the hydrodynamic symmetric description, the quasi-static model of self-focusing processes has been extended to include the transient effect of nonlinear medium response. This paper presents a new operator method to study the transient nonlinear refractive index and two-photon absorption processes in which the laser pulse-width is assumed to be much shorter than or comparable to the response time of the nonlinear medium. The numerical computation uses a finite-difference implementation of a characteristic method. The asymmetrical focusing structure in full spatial and temporal coordinates are obtained. The pulse-width self- compression and the peak shifting of the wave field envelope, corresponding to the asymmetrical and anomalous broadening of the spectrum, are verified in the transient case. The influence on the self-focusing process of various parameters, including the saturation effect, is discussed.

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