DIFFRACTION BY THE GRADIENT DIELECTRIC SPHERE (THE LUNEBERG LENS)

A plane wave is incident on a dielectric sphere with a permittivity ep silon = epsilon(R). The diffracted fields on the sphere surface and ne ar it should be determined. The sought-for fields are expanded into se ries in terms of associated Legendre functions. The analogy with the c lassical diffraction problem by a sphere with epsilon = const shows it self in the fact that, for angular field components, the coefficients of these series are represented by the coefficients in expressions for radial components; however, the Debye potentials are not introduced e xplicitly. The radial dependence of these coefficients is represented by two functions satisfying two independent ordinary linear second-ord er differential equations; for epsilon = const, these would be equatio ns for cylindrical functions of half-integer order multiplied by the s quare root of the argument. The numerical coefficients of these functi ons are obtained from a system of pairs of linear algebraic equations.