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Abstract Methods are presented of using rays to calculate the properties of a propagating generally astigmatic Gaussian beam at any point in an optical system, and to optimize a generally astigmatic optical system to obtain the desired Gaussian beam focus and minimize aberrations. The optimization method requires very little computation beyond that of a conventional ray optimization, and requires no explicit calculation of the properties of the propagating Gaussian beam. Unlike previous methods, the calculation of beam parameters does not require matrix calculations or the introduction of non-physical concepts such as imaginary rays. A ray set can be generated which has a ray density proportional to the Gaussian field amplitude or intensity at all points in space, which can be used for Monte Carlo analyses of stray light. Such a ray set can also be used to compute the output field amplitude and the coupling efficiency into a fiber or waveguide mode. A simplified method is presented for computing the coupling efficiency when the output mode has a Gaussian profile.
Keywords: Gaussian beam, ray, optics, optimization, general astigmatism
1. Introduction
Although several authors have shown that propagating rays can represent propagating Gaussian beams [1-8], these techniques are not well known among optical designers. Steier [1] showed that a ray packet consisting of a family of an infinite number of rays propagates in a manner equivalent to the propagation of a Gaussian beam. Arnaud [2] showed that Gaussian beam propagation can be described by the propagation of "complex rays" (a complex ray consisting of a "real" ray and an "imaginary" ray, essentially two rays), and he also showed that skew rays follow the envelope of a propagating circular Gaussian beam. Herloski et al. [3] have shown that by propagating two carefully selected rays through a simply astigmatic optical system (separable into x and y components), simple calculations allow the determination of the properties of a propagating Gaussian beam. Because of their simplicity, the techniques of Herloski et al. are commonly used by optical design software to compute Gaussian beam parameters, but the results are not correct for the case of general astigmatism, where the optics need not be aligned with the x-y axes. Greynolds [4], Arnaud [5], and Lü et al. [6] have shown that...