Abstract
Scalar wave fields satisfying the Helmholtz equation in two dimensions are represented by means of a complex variable associated with the two-dimensional physical plane. This characterizes the wave functions as generalizations of analytic functions, which allows the existence of a generalized Cauchy integral formula constituting the nucleus of well-known theorems of optics such as the theorem of Helmholtz and Kirchhoff and the Ewald–Oseen extinction theorem. It also seems useful in the interpretation of inverse diffraction and scattering problems.
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