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.
Highlights
Coupled optical resonators are becoming important in nonlinear optics research as well as in telecommunication applications [1, 2, 3, 4, 5, 6]
In the tight-binding method, we approximate the electric field of an eigenmode EK of the coupled-resonator optical waveguides (CROWs) as a Bloch wave superposition of the individual resonator modes EΩ [1], EK(r,t) = E0 exp(iωKt) ∑ exp(−inKΛ)EΩ(r − nΛz), (1)
Even though much of the theoretical work on CROWs is based on the tight-binding method [2, 5], the formalism is not convenient for practical, physical systems
Summary
Coupled optical resonators are becoming important in nonlinear optics research as well as in telecommunication applications [1, 2, 3, 4, 5, 6]. The “large” chains (CROWs) have been previously analyzed using a tight-binding formalism [1]. Even though much of the theoretical work on CROWs is based on the tight-binding method [2, 5], the formalism is not convenient for practical, physical systems. It does not account for input/output coupling, loss, different resonator sizes, or variations in coupling strengths. With the aim of rigorously analyzing realistic CROW structures, we use a matrix approach [11, 12, 13] to study a system consisting of N coupled ring resonators with input and output waveguides. Since the modal properties of ring resonators can be tailored and their fabrication technology is mature [14, 15], they may enable practical implementations of CROWs
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