Exact image theory for the calculation of fields transmitted through a planar interface of two media

Exact image theory, recently developed for the calculation of fields reflected from a planar interface between two homogenous media, is extended for transmitted field calculation. The image of a point source is found to be a line source located in complex space for proper convergence. Unlike for the reflection image, the transmission image line is seen to be curved in complex space for efficient computation. Expressions are derived for the transmission image of the most general three-dimensional electric and magnetic sources and for media with both and discontinuous across the interface. The new theory is verified with several asymptotic tests and properties of the transmission image function are discussed. As an application, radiation from a resonant horizontal loop antenna into the ground is calculated and results are seen to agree with those given in the literature.