In this paper we show that numerical and kernel expansion procedures for solving the laser mode problem do not differ in essence; both convert the integral equation into a matrix equation. Furthermore, the Fox and Li iterative method is shown to be a matrix diagonalization technique. A particular kernel expansion using Gaussian-Hermite functions is discussed, as are matrix diagonalization techniques. Numerical results are compared with other published values. We conclude that the optimum procedure is to use gaussian quadrature numerical integration to convert to a matrix equation and diagonalize the matrix with the computer program ALLMAT. This method is computationally simple and simultaneously determines many modes. Also, it is applicable to unstable and/or tilted mirror resonators with selectively coated reflectors.
© 1969 Optical Society of America
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