Integrated time delays are important for self-forced oscillation techniques in opto-electronic oscillators (OEO). Add-drop filters (ADFs) resonators using optical waveguide coupled to micro-ring resonators (MRR) are suitable for integrated optical time delays but suffer from a limited expected delay. 2-dimensional (2-D) photonic crystals (PhCs) with line defect are employed as confined optical waveguide to realize ADF resonators where longer optical delays than standard homogenous resonators are achieved by leveraging the slow-light effect. Moreover, achieving time delay up to microseconds (μs) is envisioned by cascading multiple identical ADF based on dispersive 2-D PhC micro-resonators. The focus of this paper is to devise a hybrid modeling procedure for accurate calculations of achieved time delays in various complex structures, while a combined electromagnetic modeling and analytical calculation technique overcomes a substantial computational resources and long computation times for a brute forced full-wave design and modeling. This innovative hybrid modeling for time delay estimation of cascaded ADFs is proposed for the first time to optimize physical design within short time period. First, transfer function performance of a homogenous ADF resonator is simulated using finite-difference-time-domain (FDTD) for both the full structure and structures with bi-fold symmetry and compared against proven analytical solutions to demonstrate accuracy of bi-fold symmetry while the computational resources are economized. The same modeling procedure is then extended to predicting performance of 2-D PhC based ADF resonator by quantifying key physical parameters of coupling factor, complex optical propagation constant, and optical transfer function for ADF resonator for the ring radius of curvature about 1.5 μm with various coupling gaps between feed waveguide and resonator guide. These parameters and the effective group index calculated by OptiFDTD software are applied to the analytical expressions to estimate single 2-D PhC ADF and attain a simulated time delay of 200 ps. The estimated time delay of 70 cascaded 2-D PhC based ADF resonators with R of 100 μm is estimated to be about 925 ns for the on-resonance frequency of 1534 nm.
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