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

Huygens' principle (HP) is understood as a universal principle governing no t only the propagation of light, but also of acoustic waves, heat and matte r diffusion, Schrodinger's matter waves, random walks, and many more. Accor ding to Hadamard's rigorous definition, HP comprehends the principle of act ion-by-proximity (cf. Faraday's field theory, etc.) and the superposition o f secondary wavelets (Huygens' construction). This definition is reformulat ed for discrete spaces. The global aspect concerns the propagation of field s (e.g. wavefronts). Within TLM, the appropriate field propagator (Green's function) is the Johns matrix. The compatibility with HP explains the succe ss of TLM in computing propagation, transport, and other evolution processe s from a different point of view. A possible practical application of these results for computing eigenmodes is mentioned. Copyright (C) 2001 John Wil ey & Sons, Ltd.