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.
United Nations Convention on the Law of the Sea 1982, A Commentary
Volume VI is the sixth substantive volume to be published in the series. It deals with the work of the First Committee at the Third UN Conference on the Law of the Sea, namely the international seabed area. The volume thus embraces the deep seabed mining regime set out in Part XI of the 1982 Convention on the Law of the Sea together with the 1994 Agreement on its implementation. Completion of this commentary was delayed first by the consultations and negotiations that commenced in 1990 and led to the 1994 Agreement and the entry into force of the Convention. It was further delayed until the Assembly of the International Seabed Authority approved the detailed mining regulations in 2000. Additional supplementary material can be found at UNCLOS 1982 Commentary: Supplementary Documents.