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.
Natural Radioactivity of Intrusive-Metamorphic and Sedimentary Rocks of the Balkan Mountain Range (Serbia, Stara Planina)
Stara Planina (also known as the Balkan mountain range) is known for numerous occurrences and deposits of uranium and associated radionuclides. It is also famous for its geodiversity. The geologic framework is highly complex. The mountain is situated between the latitudes of 43° and 44° N and the longitudes from 22°16′ to 23°00′ E. Uranium exploration and radioactivity testing on Stara Planina began back in 1948. Uranium has also been mined in the zone of Kalna, within the Janja granite intrusive. The naturally radioactive geologic units of Stara Planina are presented in detail in this paper. The main sources of radioactivity on Stara Planina can be classified as: 1. Granitic endogenous—syngenetic–epigenetic deposits and occurrences; 2. Metamorphogenic—syngenetic; and 3. Sedimentary, including occurrences of uranium deposition and fluctuation caused by water in different types of sedimentary rocks formed in a continental setting, which could be classified under epigenetic types. The area of Stara Planina with increased radioactivity (higher than 200 cps), measured by airborne gamma spectrometry, is about 380 square kilometers. The highest values of measured radioactivity and uranium grade were obtained from a sample taken from the Mezdreja uranium mine tailing dump, where 226Ra measures 2600 ± 100 Bq/kg and the uranium grade is from 76.54 to 77.65 ppm U. The highest uranium (and lead) concentration, among all samples, is measured in graphitic schist with high concentrations of organic (graphitic) material from the Inovska Series—99.47 ppm U and 107.69 ppm Pb. Thorium related radioactivity is the highest in granite samples from the Janja granite in the vicinity of the Mezdreja granite mine and the Gabrovnica granite mine tailing dump, and it is the same—250 ± 10 Bq/kg for 232Th, while the thorium grade varies from 30.82 to 60.27 ppm Th. In gray siltstones with a small amount of organic material, the highest radioactivity is related to potassium—2080 ± 90 Bq/kg for 40K.