Novel asymptotic solution in the transition region for transmitted wave through a plane dielectric interface

When the cylindrical wave or the spherical wave is incident on a plane dielectric interface from a denser (1st) medium to a rarer (2nd) one, the observer placed in the 2nd medium may receive only the transmitted geometrical ray in the short distance and both the transmitted geometrical ray and evanescent wave in the long distance. Therefore, it is necessary to find the solution which can connect the transmitted ray solution in the short distance to the transmitted ray and evanescent wave solutions in the long distance. In this work, we shall derive a novel asymptotic solution for the transmitted and scattered waves observed in the 2nd medium when the cylindrical wave is incident on a plane dielectric interface from the 1st medium. We will confirm the validity of the novel asymptotic solution proposed in the present study by comparing with the reference solution calculated by the numerical integration of the integral representing the transmitted and scattered fields.