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.
2. Smit, M., K. Williams, and J. van der Tol, "Past, present, and future of InP-based photonic integration," APL Photon., Vol. 4, No. 5, Art. No. 050901, May 2019.
3., "JePPIX MPW Platforms,", JePPIX, https://www.jeppix.eu/mpw-services/get-started/performance-summary-table/.
4. Liu, A. Y. and J. Bowers, "Photonic integration with epitaxial III-V on silicon," IEEE Journal of Selected Topics in Quantum Electronics, Vol. 24, No. 6, 1-12, Art No. 6000412, Nov.-Dec. 2018.
5. Daryoush, A. S., "Opto-electronically stabilized RF oscillators," Microwave and Wireless Synthesizers: Theory and Design, 701-759, 2nd Edition, Appendix F, John Wiley & Sons, Inc., 2021.
6. Yao, J., "Photonic integrated circuits for microwave photonics," 2017 IEEE Photonics Conference (IPC) Part II, 1-2, Orlando, FL, 2017.
7. Wei, K. and A. S. Daryoush, "Self-injection locked oscillation of multi-mode laser in heterogeneously integrated silicon photonics," The 2021 IEEE International Microwave Symposium (IMS), Atlanta, GA, June 6-11, 2021.
8. Hao, T., et al., "Recent advances in optoelectronic oscillators," Advanced Photonics, Vol. 2, No. 4, 044001, 2020.
9. Sun, T., K. Wei, and A. S. Daryoush, "Inter-modal laser based RF output stabilization using forced SILPLL technique," 2019 International Topical Meeting on Microwave Photonics (MWP), 1-3, Ottawa, ON, Canada, 2019.
10. Sun, T. and A. S. Daryoush, "Self-mode-locked multimode lasers for stabilized RF oscillators," Electronics Lett., Vol. 55, No. 25, 1351-1353, December 2019.
11. Sun, T. and A. S. Daryoush, "RF frequency synthesizer based on self-mode-locked multimode lasers," Journal of Lightwave Technology, Vol. 38, No. 8, 2262-2270, April 15, 2020.
12. Daryoush, A. S., K. Wei, T. Sun, L. Zhang, U. L. Rohde, and A. K. Poddar, "Compact highly stable frequency synthesizers for integrated RF front-end," Microwave Journal, Vol. 64, No. 8, August 2021.
13. Sun, T., L. Zhang, K. Receveur, A. K. Poddar, U. L. Rohde, and A. Daryoush, "Integrated implementation of ultra-stable VCO using optical self-ILPLL techniques," 2016 IEEE MTT-S International Microwave Symposium (IMS), 1-4, 2016.
14. Daryoush, A. S. and T. Sun, "Multi-mode lasers for self-forced opto-electronic oscillators in compact frequency synthesizers," IEEE Journal of Microwaves, Vol. 1, No. 2, 625-638, Spring, 2021.
15. Wei, K., "Photonic crystal enhanced electrooptic polymer based optical modulators for realization of integrated 40 Gs/s all-optical analog/digital converters with 8 effective number of bits,", Ph.D. thesis, Drexel University, August 2021.
16. Shahoei, H., M. Li, and J. Yao, "Continuously tunable time delay using an optically pumped linear chirped fiber bragg grating," Journal of Lightwave Technology, Vol. 29, No. 10, 1465-1472, May 15, 2011.
17. Savchenkov, A. A., et al., "Whispering-gallery mode based opto-electronic oscillators," 2010 IEEE International Frequency Control Symposium, 554-557, Newport Beach, CA, 2010.
18. Dai, J., et al., "Compact optoelectronic oscillator based on a Fabry-Perot resonant electro-optic modulator," Chinese Optics Letters, Vol. 14, No. 11, 110701, 2016.
19. Sun, T., "Forced oscillation in integrated opto-electronic circuits for realization of stable RF synthesizers,", 2019.
20. Bogaerts, W., et al., "Silicon microring resonators," Laser Photon. Rev., Vol. 6, No. 1, 47-73, 2012.
21. Bahadori, M., et al., "Design space exploration of microring resonators in silicon photonic interconnects: Impact of the ring curvature," Journal of Lightwave Technology, Vol. 36, No. 13, 2767-2782, July 1, 2018.
22. Zhang, L., A. K. Poddar, U. L. Rohde, and A. S. Daryoush, "Comparison of optical self-phase locked loop techniques for frequency stabilization of oscillators," IEEE Photonics Journal, Vol. 6, No. 5, 1-15, Art. No. 7903015, October 2014.
23. Bahadoran, M. and I. S. Amiri, "Double critical coupled ring resonator-based add-drop filter," Journal of Theoretical and Applied Physics, Vol. 13, 213-220, 2019.
24. Optiwave.s software OptiFDTD, , Version 15.0.1: http:// https://optiwave.com/, Capella Court, Ottawa, 2020.
25. Girault, P., et al., "Integrated polymer micro-ring resonators for optical sensing applications," J. Appl. Phys., Vol. 117, No. 10, Art. No. 104504, March 2015.
26. Talebi, N. and M. Shahabadi, "Analysis of a lossy microring using the generalized multipole technique," Progress In Electromagnetics Research, Vol. 66, 287-299, 2006.
27. Qiang, Z., W. Zhou, and R. A. Soref, "Optical add-drop filters based on photonic crystal ring resonators," Opt. Expr., Vol. 15, 1823-1831, 2007.
28. Zhang, W. and J. Yao, "Photonic integrated field-programmable disk array signal processor," Nat. Commun., Vol. 11, 406, 2020.
29. Takano, H., B. S. Song, T. Asano, and S. Noda, "Highly efficient multi-channel drop filter in a two-dimensional hetero photonic crystal," Opt. Express, Vol. 14, 3491-3496, April 2006.
30. Daryoush, A. S. and K. Wei, "Integrated opto-electronic chip as microwave and millmeter-wave frequency synthesizer," US Provisional Patent Application: 63/209,247, June 10, 2021.
31. Monroe, D., "Neuromorphic computing gets ready for the (really) big time," Commun. ACM, Vol. 57, No. 6, 13-15, June 2014.
32. Maan, A. K., D. A. Jayadevi, and A. P. James, "A survey of memristive threshold logic circuits," IEEE Transactions on Neural Networks and Learning Systems, Vol. 28, No. 8, 1734-1746, January 1, 2016.
33. Camacho, M., B. Edwards, and N. Engheta, "Simultaneous analog computing using multi-frequency inverse-designed metamaterial platforms," 2020 Conference on Lasers and Electro-Optics (CLEO), 1-2, 2020.