Abstract
This paper shows under what condition the well-knownABCD law — which can be applied to describe the propagation of one-dimensional Gaussian light through first-order optical systems (orABCD systems) — can be extended to more than one dimension. It is shown that in the two-dimensional (or higher-dimensional) case anABCD law only holds for partially coherent Gaussian light for which the matrix of second-order moments of the Wigner distribution function is proportional to a symplectic matrix. Moreover, it is shown that this is the case if we are dealing with a special kind of Gaussian Schell model light, for which the real parts of the quadratic forms that arise in the exponents of the Gaussians are described by the same real, positive-definite symmetric matrix.
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