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Nonlinear diffraction in sub-critical femtosecond inscription

Material processing using high-intensity femtosecond (fs) laser pulses is a fast developing technology holding potential for direct writing of multi-dimensional optical structures in transparent media. In this work we re-examine nonlinear diffraction theory in context of fs laser processing of silica in sub-critical (input power less than the critical power of self-focusing) regime. We have applied well known theory, developed by Vlasov, Petrishev and Talanov, that gives analytical description of the evolution of a root-mean-square beam (not necessarily Gaussian) width RRMS(z) in medium with the Kerr nonlinearity.