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 di!usion, SchroK dinger's matter waves, random walks, and many more. According to Hadamard's rigorous de"nition, HP comprehends the principle of action-by-proximity (cf. Faraday's "eld theory, etc.) and the superposition of secondary wavelets (Huygens' construction). This de"nition is reformulated for discrete spaces. The global aspect concerns the propagation of "elds (e.g. wavefronts). Within TLM, the appropriate "eld 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 di!erent point of view. A possible practical application of these results for computing eigenmodes is mentioned. Copyright 2001 John Wiley & Sons, Ltd.