ANALYSIS OF HIGH FREQUENCY FIELD IN FOCAL REGION USING MASLOV’S METHOD

Abstract

Maslov’s method has been used to derive high frequency field expression for differ- ent focusing systems. Derived high frequency field expression is valid around the focal region of focusing systems. Both reflection and transmission based focusing geometries are considered for discussion. Three dimensional Cassegrain and Gregorian systems are considered reflection problems. Hyperbolic lens, hyperboliodal lens, plano-convex lens, inhomogeneous slab and its three dimensional version, that is Wood lens are con- sidered as transmission problems. It is assumed that each focusing system is placed in isotropic, homogeneous medium and observed their focused field around the focal region. Next it is consider that transmitted fields from inhomogeneous slab, Wood lens and plano-convex lens are focused into negative uniaxial crystal. The numerical results for focused fields inside negative uniaxial crystal with several different orientations of the optical axis in the plane of incidence are obtained. Maslov’s method is a systematic procedure for predicting the field in the caus- tic region. It combines the simplicity of ray theory and generality of the transform method and provides remedy of geometrical optics which fails at caustic. Geomet- rical optics field may be recovered from the high frequency field expression, derived using Maslov’s method, for observation points away from the caustic. Field patterns obtained using Malov’s method are compared with those obtained using equivalent current distribution method, Huygens Krichhoff’s integral, and Debye Wolf focusing integral and comparisons are found to be in good agreement.