FOCUSING OF ELECTROMAGNETIC-WAVES INTO A UNIAXIAL CRYSTAL

We derive integral representations suitable for studying the focusing of electromagnetic waves through a plane interface into a uniaxial cry stal. To that end we start from existing exact solutions for the trans mitted fields due to an arbitrary three-dimensional (3D) wave that is incident upon a plane interface separating two uniaxial crystals with arbitrary orientation of the optical axis in each medium. Then we spec ialize to the case in which the medium of the incident wave is isotrop ic and derive explicit expressions for the dyadic Green's functions as sociated with the transmitted fields as well as integral representatio ns suitable for asymptotic analysis and efficient numerical evaluation . Relevant integral representations for focused 3D electromagnetic wav es are also given. Next we consider the special case in which (i) the incident field is a two-dimensional (2D) TM wave and (ii) the optical axis in the crystal lies in the plane of incidence, implying that we h ave a 2D vectorial problem, and derive dyadic Green's:Functions, integ ral representations suitable for asymptotic and numerical treatment, a nd integral representations for focused TM fields. Numerical results f or focused 2D TM fields based on these integral representations as wel l as corresponding experimental results will be presented in forthcomi ng papers. (C) 1998 Elsevier Science B.V. All rights reserved.