Matrix analysis of microring coupled-resonator optical waveguides

Abstract

Abstract:We use the coupling matrix formalism to investigate continuouswave 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.

Time-Domain Numerical Investigation of Ring Resonator Optical Delay Devices

“…The calculated FSR is 0.8 nm which is the same as the theoretical one, and the delay time at the resonant wavelength is about 138ps. The phase and delay response calculated from the analytical formula [17][18][19] is also shown in Fig. 4 which exhibits the same result as shown in Fig.…”

“…The numerical model described in Section II can be checked by comparing the phase and delay responses as a function of wavelength calculated from the numerical model with the analytical and numerical spectral analysis [17][18][19] for a single-ring resonator APF. The waveguide is assumed to be lossless throughout the discussions in this section.…”

“…Even though several approaches in analytical and numerical analysis of the CROW's provides lots of information regarding the delay performance of the devices [17][18][19], the quality of delayed pulse shapes can be directly investigated through a time-domain analysis.…”

Design and Simulation of Two-Dimensional OCDMA En/Decoder Composed of Double Ring Add/Drop Filters and Delay Waveguides

“…2 is considered to illustrate the transfer matrix method [14]. In this method, the transfer matrix through i-th coupler relating the input and output waves of two waveguides is given by (1) where κ i and ti are the cross-coupling and the passthrough ratios of the i-th coupler, respectively, and…”

All-Optical Delay Module Using Cascaded Polymer All-Pass-Filter Ring Resonators

“…The resonator slow-wave structure can be implemented using Fabry-Perot resonators [10,11], coupled ring resonators [12][13][14][15][16][17][18][19][20], or coupled defect mode resonators in photonic crystals [21]. CROW's (Coupled Resonator Optical Waveguides), in which a few tens ring resonators are coupled together, have been implemented in the form of glass waveguides or polymer waveguide [12][13][14][15][16][17][18][19][20]. In addition, fixed delay modules in the form of CROW and all pass filters composed of a few hundreds micro-ring resonators have been realized in SOI (Silicon on Insulator) photonic wire waveguide.…”