The use of piecewise-exponential functions in transfer theory

A method for the numerical integration of one-dimensional equations of radiative transfer in lasers is proposed which is based on the search for approximate solutions in the form of continuous piecewise-exponential functions. It is shown that the proposed method, using a two-level laser model, makes possible the numerical determination of the power characteristics of various types of lasers with an accuracy acceptable for practical purposes; only a small number (2-3) spatial points are required. This method is especially applicable to lasers in which the pumping does not depend on the spatial variable and is a function of time alone.