Threshold and Stability of a Simplified Model Optical Maser

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Abstract
The population behavior of three level optical masers can be described by a set of four nonlinear differential equations. For practical purposes, a satisfactory analytical discussion of the stability of such a set of equations does not seem to be available in the mathematical literature. The similarity with solvable cases of the Volterra fish problem is emphasized. The equations yield the standard threshold conditions obtained by more direct physical methods when one assumes that steady state solutions exist. Instability may now occur if there is a discrepancy between the threshold power and the power needed to maintain the steady state. An extreme case, requiring infinite steady state power, is discussed.
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