Computer realization of geometric methods in Maxwellian optics

In the thesis we construct geometrical description of Maxwell’s equations in terms of the fiber bundles. Different variants of the permeability tensor are described and, accordingly, various variants of the geometrization of the Maxwell equations are proposed. In particular, we propose a variant of geometrization based on a quadratic metric. It leads to equations of the Yang–Mills type. We also construct a symplectic Hamiltonian for the Maxwell equations without a source. The described formalism is demonstrated in application to problems of transformational optics and lens calculations. Analytical calculations are verified using numerical methods.