Choice of maximum number of internal reflections for transmission through a lossless dielectric slab
Résumé
Most of the time, when an electromagnetic wave undergoes a transmission in indoor environments, the interacting material thickness is taken into account to model the wave propagation in an accurate way. Therefore, the wave is considered to undergo multiple reflections inside the material and these internal reflections have to be modelled if a deterministic propagation tool is used. But we can wonder how many internal reflections are necessary to correctly describe the transmission phenomenon. In the literature, transmission coefficients are only used with simplifying hypothesis, assuming automatically an infinity of reflections and a Receiver (Rx) far from the interacting material. But the authors have developed their own transmission coefficient, extracted from a correction method presented, which finds the exact rays that undergo multiple reflections inside lossless slabs with no simplifying hypothesis. This new coefficient depends on the internal reflections number and on the receiver position. This paper focuses on the behavior of this last coefficient in terms of internal reflections number. It gives rules for the choice of the maximum number of internal reflections depending on propagation transmission scenario parameters, i.e. polarization, frequency, Transmitter (Tx) and Rx positions, and interacting material characteristics. Indeed, if we can find rules to fix this maximum number for a given transmission scenario, we can decrease the computation time of the presented coefficient but, also, re strict the length of time windows necessary to display received Ultra Wide Band (UWB) pulses in an indoor environment.