| Summary: | The formulation of the variational principle of Jones and Sondheimer, which they used to optimise the functional form of the electric field inside a semi-infinite specimen, is modified and extended to examine the effects of size and surfaces on the optical properties in the extreme anomalous relaxation region of a metallic thin film in a constant magnetic field. For this purpose, a variational integral is defined as an expression quadratic in the tangential components of the electric field at the surfaces of the film. The coefficients of this equation are related to four 2x2 tensors, closely related to the usual admittance tensor, in terms of which the reflection and transmission tensors can he written. With the magnetic field parallel to the surface of the specimen the high degree of symmetry enables the cases of longitudinal and transverse propagation to be treated separately. With the sum of two exponentials as a trial function for the electric field inside the film, both classical and non-classical reults for the longitudinal and transverse propagation are obtained for the reflectivity, transmittivity and absorptivity of the film. Numerical calculations have been carried out for a model of a degenerate semiconductor with N=10[18], m*=0.1m[o], epsilon=16, where N is the number of electrons per unit volume, m* the effective mass, m[o] the electronic mass and the permittivity, at various thicknesses, frequencies and magnetic fields. The Voigt effect is also included in the theory and numerical calculations for this hove also been carried out using the same model. The results show that the classical size effects greatly influence the behaviour of the transmittivity, reflectivity, absorptivity and the Voigt rotation. Enhanced absorption due to diffuse scattering of electrons at the surface is also observed.
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