The propagation of Gaussian light through first-order optical systems is studied; in particular, the twist in the output (or input) plane is expressed in terms of the characteristics of the light in the other plane. Conditions are derived for which zero twist in the input plane corresponds to zero twist in the output plane, and vice versa. Three special cases for which zero twist is preserved, are described: (i) propagation between conjugated planes, (ii) adaptation of the signal to the system, and (iii) the case of symplectic Gaussian light.
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