Numerical and asymptotic results for focusing of two-dimensional waves in uniaxial crystals

Recently exact integral representations were presented for focusing of two-dimensional (2D) waves through a plane interface into a uniaxial crystal. These exact results were given for the special case in which (i) the incident field is a 2D transverse magnetic (TM) wave and (ii) the optical axis of the crystal lies in the plane of incidence, implying that we have a 2D vectorial problem with no coupling between transverse electric (TE) plane waves and TM plane waves upon reflection and refraction at the interface of the crystal. Here we apply these integral representations to obtain numerical results for focused TM fields inside positive and negative uniaxial crystals with several different orientations of the optical axis in the plane of incidence. Our numerical results show that the co-polarized intensity is symmetric about the direction of the Poynting vector of the transmitted axial ray, while the longitudinally-polarized intensity does not have this symmetry. Further it is shown that when the optical axis in the crystal makes a large angle with the interface normal, the longitudinally-polarized component of the electric field can be significant even for paraxial focusing geometries. (C) 1999 Published by Elsevier Science B.V. All rights reserved.