Casperson’s Instability: Analytic Results
It has been recognized since the early days of the semiclassical laser theory that two thresholds occur in the study of the stationary field intensity as a function of the pump parameter: below the first threshold only the zero intensity is stable; between the two thresholds a pump-dependent finite intensity is stable and above the second threshold no stable stationary intensity exists. (See ref. 1 for a historical review and an extensive bibliography on this subject.) Much clarification was brought into the subject when Haken  showed the close analogy between a tuned single-mode ring laser and the Lorenz description of the Renard instability. However, the behavior of a laser beyond the second threshold (self-pulsing, subharmonic bifurcations, chaos,...) remained firmly in the realm of theoretical physics with only a remote chance of experimental connection since it was easily shown that the existence of a second threshold required a high intensity in a bad cavity. Hence the report by Casperson, and later by Abraham and his group, of the actual observation of the laser’s second threshold in the milliwatt range came as a surprise. The flaw in the usual derivation of the properties of the second threshold was quickly traced back to the complete neglect of inhomogeneous broadening. This point was advocated by Casperson, who showed that inhomogeneous broadening alters the properties of the second threshold to the extent that it becomes experimentally accessible. Henceforth, Casperson’s instability specifically refers to the laser’s second threshold in the presence of inhomogeneous broadening.
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