Huygens' principle in the transmission line matrix method (TLM). Local theory

Huygens' principle (HP) is a well-known fundamental principle of wave propagation. More generally, it can be understood as representing the principle of action-by-proximity (cf. Faraday's field theory etc.) and the superposition of secondary wavelets re-irradiated at each point of the wavefront (Huygens' construction). These wavelets are isotropic in free space and in isotropic materials. We will show, that HP is realized within the transmission line matrix method (TLM) for scalar fields in free space of any dimension, if one considers only the scattered fields to represent the secondary wavelets. This corrects and generalizes the previous result for the total field in 2D. This property of TLM provides another explanation for its wide range of applicability. Copyright (C) 2003 John Wiley Sons, Ltd.