Matrix analysis of microring coupled-resonator optical waveguides

TLDR

The matrix formalism is a powerful approach for microring CROWs since it can be applied to structures and geometries for which analyses with the commonly used tight‑binding approach are not applicable. We use the coupling matrix formalism to investigate continuous‑wave and pulse propagation through microring coupled‑resonator optical waveguides (CROWs). The study shows that in the weak‑coupling limit the dispersion relation matches the tight‑binding model, provides an analytical pulse‑propagation expression for semi‑infinite CROWs, predicts intensity enhancement inversely proportional to coupling, and demonstrates that finite CROWs can exhibit negative group velocity leading to apparent superluminal pulse emergence.

Abstract

We use the coupling matrix formalism to investigate continuous wave and pulse propagation through microring coupled-resonator optical waveguides (CROWs). The dispersion relation agrees with that derived using the tight-binding model in the limit of weak inter-resonator coupling. We obtain an analytical expression for pulse propagation through a semi-infinite CROW in the case of weak coupling which fully accounts for the nonlinear dispersive characteristics. We also show that intensity of a pulse in a CROW is enhanced by a factor inversely proportional to the inter-resonator coupling. In finite CROWs, anomalous dispersions allows for a pulse to propagate with a negative group velocity such that the output pulse appears to emerge before the input as in "superluminal" propagation. The matrix formalism is a powerful approach for microring CROWs since it can be applied to structures and geometries for which analyses with the commonly used tight-binding approach are not applicable.