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Analytic solution for the reflection of cylindrical wave at planar interfaces

In this paper, we present an analytical solution for the spectral integral representing the reflected cylindrical wave at a plane interface. The analytical solution involves the Bessel and Anger-Weber functions. We compare the analytical expression with the results obtained with a quadrature method previously proposed in the literature, finding very good agreement. Moreover, we find that the quadrature method is affected by some numerical errors in the near field, due to the highly oscillating integral's kernel. We try a physical interpretation of the result obtained connecting it to the well known Image Principle.