Asymptotics of evanescence

The wave from an isotropic point source in two and three dimensions is sepa rated into its homogeneous (H) and evanescent (E) parts, with respect to a a distinguished direction z, and the far field r --> infinity evaluated asy mptotically as a function of polar angle theta. Only in the 'forward needle ' theta =0 (three dimensions) and the transversed directions theta-pi /2 (t wo and three dimensions) is the E wave of comparable strength to the H wave . Uniform asymptotic approximations (in terms of Bessel functions and Fresn el integrals) accurately interpolate between these directions of significan t evanescence and all other angles (where the amplitude of E relative to H decays as 1/r(1/2)). The forward needle in three dimensions is analogous to glory scattering.