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Waves in inhomogeneous isotropic media James, Christopher Robert

Abstract

For the case of a lossless medium containing no free charges and possessing a continuous and sufficiently differentiable spatially dependent permeability and permittivity, two vectorial differential wave equations, one for the electric and one for the magnetic field, are derived through the use of Maxwell's equations. From these two equations necessary conditions for E- and H-modes to exist in a waveguide are established,. The field equations for the case of constant permeability and z-dependent permittivity as well as the interchanged case are investigated. A test is developed which, if met, assures that the solutions are oscillatory for the ordinary differential equations containing the z-dependent part of the wave function. For the dielectric loaded periodic structure the theory for inhomogeneous isotropic media is used to determine the restrictions on the field components which are necessary before E-modes can exist and to find the E-mode wave solutions for the solid disc case when the dielectric regions are matched into the air regions. An investigation is carried out into the behaviour of plane waves in a medium with the permeability constant and the permittivity varying in the direction of propagation.

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