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Partial differential rate equations for a bilevel absorber.

The interaction of a directed beam of radiation with an absorber is described using a two-level model. Transmitted light intensities and level populations are treated as functions of temporal and spatial independent variables. The general rate equations are given as partial differential equations. Combinations of material constants are identified as scale parameters and used to express the rate equations in nondimensional form as a hyperbolic partial differential equation in canonical form. One integration yields a time-independent relationship between two transmitted beam intensities at different wavelengths. Several calibration experiments are described to evaluate material parameters.