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A generalized beam matrix method is used to investigate the mode structure of astigmatic misaligned optical systems with loss or gain. In these optical systems the usual real-argument polynomial-Gaussian beams are not eigenfunctions, and off-axis complex-argument polynomial beams must be used. New beam transformations for these complex-argument modes are reported. Stability criteria are developed, and mode selection in laser resonators that contain tilted, displaced, or curved complex optical elements is discussed.

Generalized beam matrices II Mode selection in lasers and periodic misaligned complex optical systems