Critical Angle Formulation of Nonuniform Plane Waves for Determining Correct Refraction Angles at Planar Interface

The expressions and properties of the critical angles of nonuniform plane waves for determining the correct refraction angle at the infinite planar interface of two linear, isotropic, and homogeneous media are presented. The two media could be lossless or lossy. For the case where the complex wave vector of Adler–Chu–Fano formulation and the normal vector to the interface are coplanar, a critical angle equation, which is simpler than the extant one, under the condition that one or two critical angles exist, is formulated. In addition, for the case where the complex wave vector and normal vector to the interface are noncoplanar, a critical angle equation is formulated, rendering the 3-D nonuniform plane wave refraction feasible for utilization in many areas of optics. The presented critical angle equations were validated for various nonuniform plane waves and media.