Photonic crystals (PhCs) are materials with periodically varying dielectric permittivity distributions. Under the right conditions, such devices can have photonic band gaps which prohibit electromagnetic wave propagation of certain frequency and polarization [1]. Such features make PhCs as waveguides – not only can very high transmittance quality be controlled [2], but light can be contained even with very sharp bends present in the waveguide channels [3]. For this reason, very small and intricate light guiding devices can be realized which makes them great for making photonic logical elements, that can work 5-10 times faster than top of the line electronic counter parts while using a fraction of the power (clock rates can reach values of 12.5 GHz [4], compared to approximately 3 GHz that moder GPU’s provide while using power in the order of microwatts [5]). In this work we present a photonic logical element design, with silicon waveguide channels, which is based on a ring resonator. All numerical simulations have been caried out using finite difference frequency domain method in Academic MATLAB Environment. Similar devices with air waveguiding channels have already been proposed [6], but they lack confinement since there is no total internal reflection and lead to a diverging wave. 
NUMERICAL ANALYSIS OF PHOTONIC CRYSTAL WAVEGUIDE LOGICAL CIRCUITS
Andrius Zinkevičius1, Ignas Lukošiūnas2
1 Vilnius University
2 Laser Research Center
[1] Cersonsky, R.K., Antonaglia, J., Dice, B.D. et al. The diversity of three-dimensional photonic crystals. Nat Commun 12, 2543 (2021). https://doi.org/10.1038/s41467-021-22809-6.
[2] Zhipeng Ma, Yuanjian Wan, Yu Zhang, and Jian Wang, "Broadband lateral leakage suppression for TM polarization empowered by slab-photonic-crystal-modified ridge waveguide," Opt. Express 32, 31730-31740 (2024).
[3] Liu, G.; Wang, F.; Gao, Y.; Jia, B.; Guan, X.; Lu, P.; Song, H. Topology Optimization of Low-Loss Z-Bend 2D Photonic Crystal Waveguide. Photonics 2023, 10, 202. https://doi.org/10.3390/photonics10020202.
[4] Luis Pedraza Caballero, Michelle L. Povinelli, Jhonattan C. Ramirez, Paulo S. S. Guimarães, and Omar P. Vilela Neto, "Photonic crystal integrated logic gates and circuits," Opt. Express 30, 1976-1993 (2022).
[5] M.A. Butt, S.N. Khonina, N.L. Kazanskiy, Recent advances in photonic crystal optical devices: A review, Optics & Laser Technology,Volume 142, 2021, 107265, ISSN 0030-3992, https://doi.org/10.1016/j.optlastec.2021.107265.
[6] Jeevan Jot Singh, Divya Dhawan, Neena Gupta, 2D photonic crystal hexagonal ring resonator-based all-optical logic gates, Optics & Laser Technology, Volume 165, 2023, 109624, ISSN 0030-3992, https://doi.org/10.1016/j.optlastec.2023.109624.