Wave Propagation through a One-Dimensional Dielectric Slab and V-Symmetric Transformations

This paper contains an abstract theory of wave propagation through an inhomogeneous dielectric slab based on the splitting of waves into right and left propagating components. The mapping of right and left moving waves at one point in the slab to the waves at another point in the slab is found to have a symmetry called V-symmetry which is a generalization of that possessed by symplectic transformations. An analogue of Hamiltonian mechanics is then presented based on these generalized symplectic transformations