Dielectric and magnetic properties of continuum with dislocations

More than twenty years ago, we were invited by professor V.B. Braginsky at the seminar of the Molecular Physics and Physical Measurements Department to make a report on using gauge fields, fibre bundles, and geometry to describe solids with structural defects. After the seminar, he proposed us to consider a possibility of using the above-mentioned exact mathematical and geometrical methods to create theoretical models of description of optomechanical properties of media with defects. It was the starting point for us to investigate the electromagnetic wave propagation in solids with defects. This paper is dedicated to the memory of professor Vladimir Borisovich Braginsky. The solutions of the electrostatics and magnetostatics equations for a continuous medium with dislocations are found. The expressions for the dependence of the electric permittivity and magnetic permeability on the dislocation distribution in a solid are found. The expression for the refractive index in a continuum with dislocations is obtained.