Abstract

A family of analytical solutions of the time-dependent wave equation, the ultrashort pulsed sinc-Gaussian light beams (UPSGLB’s), are presented in the paraxial approximation. Each of them has the product form of the monochromatic Gaussian light beam with the central frequency νc times the sinc function of the complex temporal–spatial beam parameter Pn. The complex temporal–spatial beam parameter Pn, which corresponds to the order n, is directly related to the temporal–spatial coupling properties of the nth-order UPSGLB. The UPSGLB’s are used, for the first time to our knowledge, as an analytical expansion set for bandwidth-limited ultrashort light pulses emitted from mode-locked lasers with stable resonators (ULPEMLLSR’s). Two special examples of bandwidth-limited ULPEMLLSR’s, a single zeroth-order UPSGLB and a novel model of a nearly temporal–spatial Gaussian beam, are analytically investigated and compared with experimental results.

© 2000 Optical Society of America

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