Novel uniform asymptotic solutions for high-frequency scattered electromagnetic fields by a dielectric cylinder

We derive a novel uniform asymptotic solution (extended UTD solution) for the field scattered by a dielectric circular cylinder. The extended UTD solution, derived by applying higher-order asymptotic formulas for the cylindrical functions, can be applied in the wide area extending from the illuminated region to the deep shadow region where the current UTD becomes increasingly inaccurate with the increasing frequency and azimuthal distance. We also derive the modified UTD solution from the new extended Pekeris carot function by applying the residue theorem. The modified UTD solution is the improved version of the current GTD and the UTD, and can be applied uniformly from the transition region in the illuminated region to the deep shadow region, including the region near the cylinder where the UTD deviates substantially from the eigenfunction solution. Comparisons with the exact solution calculated from the eigenfunction expansion confirm the validity and the utility of the extended UTD solution and the modified UTD solution.