2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/200051We use a functional approach to the Casimir effect in order to evaluate the exact vacuum energy for a real scalar field in $d+1$ dimensions, in the presence of backgrounds that, in a particular limit, impose Dirichlet boundary conditions on one or two parallel surfaces. Outside of that limit, the background may be thought of as describing finite-width mirrors with frequency-dependent transmission and reflection coefficients. We provide new explicit results for the Casimir energy in some particular backgrounds18 pages, no figures. Version to appear in Phys. Rev. DHigh Energy Physics - TheoryHigh Energy Physics - PhenomenologyQuantum Physicstext