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General sets of higher-order beam modes are derived for light propagation in media having spatial variations of the gain or loss. The resulting expressions are also valid for propagation through conventional optical elements and graded transmission filters. The four basic mode sets obtained include off-axis Hermite-Gaussian and Laguerre-Gaussian modes of both real and complex argument. A procedure is developed for finding the resonant modes of laser oscillators containing arbitrary complex lens elements, and the mode stability properties of lasers can be interpreted physically by means of these formulas.
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Lee W. Casperson (1976) studied this question.
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