Some Aspects of the Inverse Problem of Determination of Cr^(4+) :YAG Absorption Cross Sections Using Experimental Data of Transmission - Dement’ev, A.; Navakas, R. (Nonlinear Analysis: Modelling and Control, 2001)
Mathematical modelling of nonlinear transmission of Cr4+:YAG crystals excited by Nd:YAG laser pulses of different duration are reported. Numerical simulation of transmission using a five-level scheme which included finite excitation lifetimes in Cr4+:YAG, focusing and diffraction of transversely nonhomogeneous pump radiation allowed to specify more precisely the limits of applicability of the four-level model. Critical analysis of typical simplifications commonly used for solving an inverse problem of determination of absorption cross sections is undertaken. It is shown that some of these assumptions that seem plausible enough might lead to considerable deviations of the determined absorption cross sections from their “true” values. A technique for determination of confidence intervals in case of the nonlinear regression is emphasized.
Keywords: transmission saturation; inverse problem; absorption cross sections