We consider the field that appears at the output of a first-order optical system when its input field is a Hermite-Gaussian mode. The generating function for the output modes is determined. The orthonormality property of the output modes is confirmed, and derivative and recurrence relations for these modes are derived. Mode converters that generate Laguerre-Gaussian and Hermite-Laguerre-Gaussian modes are considered as examples.
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Final publication in J. Phys. A: Math. Gen.