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The method of modal expansion is used to develop a theory for the analysis of frustrated total reflection (FTR) filters or similar layered systems of finite lateral extent. The theory is applied to determine the (spectral) transmission properties of the FTR filter of finite lateral extent (for an incident plane wave propagating in direction of maximum transmission). It is found that the finiteness of the lateral dimensions of the filter has a great effect on the transmission properties of the filter. The results are in agreement with available experimental data and clearly show that the unbounded wave theory (i.e., an analysis which assumes that both the incident electromagnetic radiation and the filter are of infinite lateral extent) cannot be applied to FTR filters even when the lateral filter dimensions are several orders of magnitude larger than the wavelength of the incident radiation.
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Bergstein et al. (1966) studied this question.
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