Maxwell’s equations in Fourier space and coupling between elementary excitations in solids

Equações de Maxwell no espaço de Fourier e acoplamento entre excitações elementares em sólidos

Maxwell’s equations are fundamental to the understanding of electromagnetic events, as they describe the totality of experimentally verified electromagnetic phenomena from its boundary conditions and constitutive relations. Although, they are normally presented in the time and space domain, many physical effects and their associated mathematical manipulation are easier to understand when we use Maxwell’s equations in Fourier space. In this work we give a general introduction about Maxwell’s equations in Fourier domain in material media. The simplicity of the obtained equations in comparison with the ones in space-time domain is emphasized, and the link between them and the elementary excitations in solids is presented and explored. In particular, the coupling between various types of quasiparticles in solids is explained.

Keywords:
Maxwell equations; Fourier space; elementary excitations; plasmon; phonon-polariton