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

Huygens' principle (HP) is understood as a universal principle governing not only the propagation of light, but also of acoustic waves, heat and matter diffusion, Schrodinger's matter waves, random walks, and many more. According to Hadamard's rigorous definition, HP comprehends the principle of action-by-proximity (cf. Faraday's field theory, etc.) and the superposition of secondary wavelets (Huygens' construction). This definition is reformulated for discrete spaces. The global aspect concerns the propagation of fields (e.g. wavefronts). Within TLM, the appropriate field propagator (Green's function) is the Johns matrix. The compatibility with HP explains the success of TLM in computing propagation, transport, and other evolution processes from a different point of view. A possible practical application of these results for computing eigenmodes is mentioned. Copyright (C) 2001 John Wiley & Sons, Ltd.