Closed or stable optical cavities, used frequently to determine the efficiency of high performance chemical laser nozzles, are designed primarily for maximum multimode power extraction from the medium. The very large (>500) Fresnel numbers associated with such cavities have in the past necessitated their analytical modeling by representing them as plane-parallel Fabry-Perot or rooftop cavities. In this paper, a rigorous 2-D scalar diffraction formalism of the closed cavity is presented in which quasi-monochromatic partially coherent fields in the space-frequency domain are used to obtain quasi-steady state but stable solutions using a simplified gain model. Small power fluctuations in the numerical iterative solution history that displays no monotonic increasing or decreasing trends are interpreted as the redistribution of energy from one degenerate set of high-order transverse modes into another. The degree of coherence in the second-order spatial correlation function (or the mutual coherence function) required of the input fields which permit such solutions is presented. Further, it is shown that the upstream/downstream coupling in this closed cavity occurs as a natural consequence of the physical model itself rather than through some artificial geometrical means, such as that introduced in the rooftop model. The axial variation in the resulting mode width is in excellent agreement with the Hermite-Gaussian distribution predicted for the particular geometry of interest. The computed closed-cavity power variation with mode width using a simplified gain model shows qualitative agreement with experimentally observed trends; quantitative agreement is poor and is ascribed to the rudimentary nature of the gain model. In the limiting case of small Fresnel numbers (NF ∼ 1) this procedure yields, in the bare cavity, the well-known fundamental mode of the cavity when appropriate symmetry constraints are applied.
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