Abstract
We present a theoretical analysis for the lossless beam shaping of ultra-short laser pulses based on geometrical optics calculations by considering a phase element in conjunction with a Fourier transform lens. The theory developed for continuous waves (JOSA A vol. 13, p. 751, 1996) is extended to include a Gaussian frequency distribution for the laser pulse. We compare two numerical methods for solving this two-dimensional problem, an extended Gaussian numerical integral method and a Monte Carlo approach. We show that the Monte Carlo method is superior to the extended Gaussian method.
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