Exact image theory for the calculation of fields transmitted through a planar interface of two media
Abstract
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 a complex space for efficient computation. Expressions are derived for the transmission image of the most general threedimensional electric and magnetic sources and for media with both  epsilon and mu 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.
 Publication:

IEEE Transactions on Antennas and Propagation
 Pub Date:
 February 1986
 DOI:
 10.1109/TAP.1986.1143788
 Bibcode:
 1986ITAP...34..129L
 Keywords:

 Antenna Radiation Patterns;
 Electromagnetic Fields;
 Electromagnetic Wave Transmission;
 Loop Antennas;
 Sommerfeld Approximation;
 Asymptotic Methods;
 Electric Current;
 Interfaces;
 Magnetic Dipoles;
 Planar Structures;
 Communications and Radar