Propagação de ondas eletromagnéticas em meios materiais com parâmetros dependentes do tempo

Abstract

In our study on eletromagnetic waves we find exact solutions for electric and magnetic fields in an homogeneous and isotropic material media with linear response, considering time-dependent permittivity, pemeability and conductivity. This time-dependence allows one to say that the media is time-dependent. Taking Maxwell’s equations in materal media and using the Coulomb gauge, we assume periodic boundary condition to solve the problem. We also considered the potential vector to obtain the modes inside the cavity. Then, we got an expretion type damping harmonic oscilator for the amplitude modos, where the coeficients are time-dependent. To solve the main problem we use the Lewis-Riesenfeld dynamical invariants to investigate the dynamics of the amplitudes. By using Fock states we find the solution for Schr¨odinger’s equation associated to the time-dependent Hamiltonian. Assuming that the parameters varying exponentially with time, we find a Caldirola-Kanai Hamiltonian and we obtain an exact solution in classical and quantum regime. We also find the Berry’s fase and Hannay’s angle for an adiabatic evolution. In the end, we compare the radiation propagation in a dialetric time-dependent media and the propagation of scalar field in de Sitter spacetime.