On the theory of diffraction by a composite cylinder

Formulas are developed fo r t he diffracted fi eld a round a perfectly co ndu d ing cylinder with a dielectr ic sleeve of a rbi trary t hickn ess . These formu las r eprese nt t he ficld du e to a unit electri c line so urce p aralle l to t he cylinder (eit her inside or o u tside t h e dielect ric sleeve) as a sp ectrum of r a di a l eige nfun ctio ns. It is sh own that in each case t he fi eld in t he regio n co ntaining t he sour ce can be exp r essed a s t h e sum of two terms, t he fir st of which is a s pectre,l represen tation of t he fi eld n t he outer as weU as t he inne r surface of t he die lectri c is a perfectly condu ctin g b ounda ry. The seco nd t e rm of t h e su m, whi ch a loll e i n vo lves t he proper t ies of t he dielectr ic, is a n integral t hat converges r apidly at hi g h fr equ encies. Us ing t h ese gener a l r es ults, p ert urbat io n calculations a rc carried ou t fo r t hree lim it ing examp les of plane wave scatterin g: (1 ) Thin d ie lectric ; (2) low-refract ive index; (3) very s ma ll sUt"face curvature. In t h e latter approximat ion t he eorresponcle nce w ith op t ical r es u lts is shown .