Fresnel coefficients, coherent optical scattering, and planar waveguiding

Abstract

The Fresnel formalism of transmission and reflection of coherent waves on the abrupt interface between two different optical media is revisited and extended to study optical phenomena concerning guided waves. Using the Fresnel formalism, the propagation of light through different sequences of parallel layers of constant refractive index is analysed, revealing that, in all cases, the solutions corresponding to waveguiding share major features. In the analysis, aiming to connect waveguiding with coherent optical scattering, the possibility of the system having a resonance is examined, and it is shown that guided modes always emerge as singular solutions of the associated coherent scattering configuration. Invariably, the resonance condition that must be satisfied to obtain waveguiding corresponds to the pole of the associated total reflection and transmission coefficients. Even more, the fulfilment of the requirements to meet the resonance condition is a clear indication of the possibility of waveguiding.