Abstract

In this Letter, we analyze the reflection of cylindrical waves (CWs) at planar interfaces. We consider the reflected CW proposed in the literature as a spectral integral. We present a Laurent series expansion of the Fresnel coefficient convergent on the whole real axis and we use it to solve analytically the reflected-wave integral. We found a solution that involves both Bessel functions and Anger–Weber functions, i.e., solutions of both the homogeneous and inhomogeneous Bessel differential equations. We compare the analytical solution with the numerical results obtained with a quadrature formula presented in the literature. Moreover, we present a physical interpretation that connects our solution to the image principle.

© 2014 Optical Society of America

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