Further comments on the theory of the frustrated total reflection filter.
In view of the comments made by Iogansen it would be worthwhile to compare first the two methods of analysis. The method developed by Iogansen is based on an approximate solution of the wave equation by means of orthogonal waves. When the direction of propagation of the incident wave is such that the angle between the wave normal and the normal to the boundary surfaces of the layers is sufficiently large, the orthogonal waves approximate closely the solution to the wave equation. However, in order to relate the transmitted field in each of the layers to the incident field, further approximations are necessaiy. In particular, in the approach used by Iogansen the orthogonal waves are expanded in a Taylor series and only the first linear term of the series is retained. Clearly, such an expansion yields a reasonable approximation to the actual solution if, and only if, the thickness of each of the layers is of the order of a wavelength of the incident light or smaller. When the thickness of the layers is large compared with the wavelength, the approximation becomes poor and the method of analysis breaks down completely. The approximation is therefore limited to the analysis of frustrated total equation filters or similar resonant systems involving a limited number of layers of limited thickness. In contrast, the method of plane wave expansion as proposed in our paper does not basically involve any approximations (assuming of course that the model of blackbody boundaries is accepted). It can, therefore, be used independently of the thickness and the number of layers involved. All results of interest
The frustrated total reflection filter. 1. Spectral analysis.
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.
A Birefringent Frustrated Total Reflection Filter
In the standard Turner Frustrated Total Reflection filter the pass bands occur in pairs which are oppositely polarized. The maximum theoretical transmission in any band is thus 50 percent. In this paper it is shown that if the high index layer of the filter is made of a birefringent material the oppositely polarized pass bands can be made to coincide so that the maximum theoretical transmission becomes 100 percent and the bands occur singly. Measurements are shown on a filter made with such a birefringent layer.