COMPLEX RAYS AND APPLICATIONS

COMPLEX RAYS AND APPLICATIONS

E.Hasanoglu

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Abstract

Complex rays are a fascinating aspect of modern diffraction theory, typically sought as complex solutions to the eikonal equation. Traditionally, these solutions are obtained by analytically continuing real rays into the complex domain. However, this approach demands the analyticity of initial data, significantly limiting its applicability to many practical problems. Additionally, unlike real rays, complex rays cannot be visualized in space, presenting another drawback. In this paper, we present an alternative interpretation of complex rays, as introduced in [1], and describe a novel approach to two model diffraction problems and Gaussian beams.

Keywords

wave equation, eikonal equation, complex rays, Minkowski space, Gaussian beams.