Análise e síntese de redes de microcavidades em anel utilizando a teoria de modos acoplados com uma abordagem por grafos de fluxo de sinal

Abstract

This work presents a formalism based on two-port network theory for modeling filters composed of ring-shaped microcavities applied to integrated photonic circuits. As an equivalent alternative to the conventional matrix-based approach, signal-flow graph theory is employed to provide a graphical representation of the different device sections and their interactions. A direct connection between the graph-based description of cascaded network associations and the definition of the Redheffer star product is established. Coupled-mode theory is introduced to characterize the network parameters of the devices. Based on the signal-flow graph representation of time-domain coupled-mode equations, a methodology for the synthesis of cascaded coupled-cavity filters is presented, with application to a second-order Butterworth filter. The results are validated through numerical simulations using the finite-difference time-domain method, demonstrating the consistency of the proposed procedure.