Influence of the shape of a wavelength-tunable light filter on its spectral properties

A study has been made of the influence of the geometric shape of a wavelength-tunable light filter on its following properties: 1) the tuning range of the wavelength selected by the light filter; 2) the ratio of the geometric cross sections of the input and output light beams; 3) the angle between the incident radiation and the filtered radiation. A calculation is made of the optimal ratios of the prism faces and angles suitable for making light filters. The reasons for the formation of so-called “parasitic” rays are considered with methods for eliminating them. V. D. Kuznetsov Siberian Physicotechnical Institute at the State University, Tomsk. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 54–61, September, 1997.     

Calculation of the effective permeability of a randomly inhomogeneous porous medium

The effective permeability of a porous medium is calculated nonperturbatively. An exact expression for the permeability in terms of a double path integral is derived on the assumption that the permeability obeys a log-normal distribution function. Path integration is carried out in general form in the large-scale limit. The result confirms the well-known conjecture that the effective permeability is independent of the structure of the correlation function, but it disagrees with the hypothesis that the effective permeability depends exponentially on the variance. Zh. éksp. Teor. Fiz. 112, 313–324 (July 1997)     

Renormalization group method in the problem of the effective conductivity of a randomly heterogeneous porous medium

Within the field formulation of the renormalization group (RG) method, an expression for the Fourier transform of the integral kernel of the effective conductivity of a randomly heterogeneous porous medium is obtained. In the large-scale limit, the result obtained corresponds to the well-known Landau-Lifshits-Matheron formula. The validity of the technical tricks applied to the calculations performed within the RG approach is discussed.     

Problems in expanding the working range of wavelength-tunable light filters

The possibilities for expanding the range of tuning of the wavelength isolated by a tunable interference light filter, based on a combination of a nonuniform multilayer and a reflecting prism, are investigated. The degree of influence of the immersion liquid on the lower limit of wavelength tuning is studied. That influence is shown to be limited. A connection between the scheme for obtaining a nonuniform multilayer and the maximum wavelength of light reflected by the multilayer is demonstrated theoretically. The working range of a wavelength-tunable filter, the nonuniform multilayer of which is based on holographic photographic plates, is expanded by changing the scheme for obtaining the multilayer. The possibility of advancing into the near ultraviolet by using other materials (such as bichromized gelatin) is demonstrated experimentally. V. D. Kuznetsov Physics and Engineering Institute of Siberia at Tomsk State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 63–69, April, 1997.