Using Linear Regression Method to Provide a Mathematical Relation to Investigate the Gap Wavelength Band in Photon Structures for Use in the Design of Optoelectronic Devices
Subject Areas : Electronics Engineering
Mozhgan Javahernia
1
,
Sahel Javahernia
2
1 - Department of Mathematics, Faculty of Mathematical Sciences, Islamic Azad University, Shabestar Branch, Shabestar, Iran
2 - Department of Electrical Engineering, Faculty of Engineering, Islamic Azad University, Sofian Branch, Sofian, Iran
Keywords: Flat wave expansion method, Photons, Photon Gap Band, Regression, Band Structure,
Abstract :
Photon crystals are on of the most common structures for designing and implementing electronic optical circuits. The photon gap band is of great importance in these structures. The most common mathematical methods for analyzing and calculating photon band diagrams and extracting the forbidden photon band of photon crystals is the flat wave expansion method. This method has many complexities that require special commercial software to perform its calculations. In two-dimensional photonic crystals, two parameters in the photon band are affected, which are the refractive index of the dielectric material and the ratio of the radius of the holes to the constant of the crystal lattice (r / a). In this paper, using mathematics and linear regression, simpler relations for extracting the photon band range of photon crystals are presented. Comparison of the results obtained from the relations with the results obtained with BandSOLVE software for photonic crystals shows that the maximum difference between the two calculation methods for fl and fu is 0.007 and 0.028, respectively, and the average difference is , respectively 0.004 and is 0.01.
[1] J. Chen, F. Mehdizadeh, M. Soroosh, and H. Alipour-Banaei, “A proposal for 5-bit all optical analog to digital converter using nonlinear photonic crystal based ring resonators,” Opt. Quantum Electron., vol. 53, no. 9, p. 510, 2021,doi:/10.1007/s11082-021-03166-6.
[2] Z. A. Zaky and A. H. Aly, “Modeling of a biosensor using Tamm resonance excited by graphene,” Appl. Opt., vol. 60, no. 5, pp. 1411–1419, Feb. 2021,doi:/10.1364/AO.412896.
[3] S. Johnson and J. Joannopoulos, “Block-iterative frequency-domain methods for Maxwell’s equations in a planewave basis,” Opt. Express, vol. 8, no. 3, p. 173, Jan. 2001, doi:/10.1364/OE.8.000173.
[4] M. Baghbanzadeh and A. Andalib, “A novel proposal for PhC-based OADC for Gray code generation,” Photonics Nanostructures - Fundam. Appl., vol. 43, p. 100847, 2021, doi:/10.1016/j.photonics.2020.100847.
[5] A. Taflove, Computational Electrodynamics: The Finite-difference Time-domain Method. Artech House, 1995,doi:/10.1007/978-1-4757-5124-6_3.
[6] D. G. S. Rao, S. Swarnakar, and S. Kumar, “Design of photonic crystal based compact all-optical 2 × 1 multiplexer for optical processing devices,” Microelectronics J., vol. 112, p. 105046, 2021, doi:/10.1016/j.mejo.2021.105046.
[7] A. Askarian, “Design and analysis of all optical half subtractor in 2D photonic crystal platform,” Optik (Stuttg)., vol. 228, no. April 2020, p. 166126, 2021, doi:/10.1016/j.ijleo.2020.166126.
[8] M. Zavvari, “Design of Photonic Crystal-Based Demultiplexer with High-Quality Factor for DWDM Applications,” J. Opt. Commun., vol. 0, no. 0, 2017, doi:/10.1515/joc-2017-0058.
[9] L. Zhu, F. Mehdizadeh, and R. Talebzadeh, “Application of photonic-crystal-based nonlinear ring resonators for realizing an all-optical comparator,” Appl. Opt., vol. 58, no. 30, pp. 8316–8321, Oct. 2019, doi:/10.1364/AO.58.008316.
[10] R. Talebzadeh, M. Soroosh, Y. S. Kavian, and F. Mehdizadeh, “All-optical 6- and 8-channel demultiplexers based on photonic crystal multilayer ring resonators in Si/C rods,” Photonic Netw. Commun., vol. 34, pp. 248–257, Feb. 2017, doi:/10.1007/s11107-017-0688-x.
[11] M. Youcef Mahmoud, G. Bassou, A. Taalbi, and Z. M. Chekroun, “Optical channel drop filters based on photonic crystal ring resonators,” Opt. Commun., vol. 285, no. 3, pp. 368–372, Feb. 2012,doi:/10.1016/j.optcom.2011.09.068.
[12] S. M. Mirjalili and S. Z. Mirjalili, “Asymmetric Oval-Shaped-Hole Photonic Crystal Waveguide Design by Artificial Intelligence Optimizers,” IEEE J. Sel. Top. Quantum Electron., vol. 22, no. 2, pp. 258–264, 2016, doi:/10.1109/JSTQE.2015.2469760.
[13] H. G. Teo, A. Q. Liu, J. Singh, M. B. Yu, and T. Bourouina, “Design and simulation of MEMS optical switch using photonic bandgap crystal,” Microsyst. Technol., vol. 10, no. 5, pp. 400–406, Aug. 2004, doi:/10.1007/BF02637111.
_||_[1] J. Chen, F. Mehdizadeh, M. Soroosh, and H. Alipour-Banaei, “A proposal for 5-bit all optical analog to digital converter using nonlinear photonic crystal based ring resonators,” Opt. Quantum Electron., vol. 53, no. 9, p. 510, 2021,doi:/10.1007/s11082-021-03166-6.
[2] Z. A. Zaky and A. H. Aly, “Modeling of a biosensor using Tamm resonance excited by graphene,” Appl. Opt., vol. 60, no. 5, pp. 1411–1419, Feb. 2021,doi:/10.1364/AO.412896.
[3] S. Johnson and J. Joannopoulos, “Block-iterative frequency-domain methods for Maxwell’s equations in a planewave basis,” Opt. Express, vol. 8, no. 3, p. 173, Jan. 2001, doi:/10.1364/OE.8.000173.
[4] M. Baghbanzadeh and A. Andalib, “A novel proposal for PhC-based OADC for Gray code generation,” Photonics Nanostructures - Fundam. Appl., vol. 43, p. 100847, 2021, doi:/10.1016/j.photonics.2020.100847.
[5] A. Taflove, Computational Electrodynamics: The Finite-difference Time-domain Method. Artech House, 1995,doi:/10.1007/978-1-4757-5124-6_3.
[6] D. G. S. Rao, S. Swarnakar, and S. Kumar, “Design of photonic crystal based compact all-optical 2 × 1 multiplexer for optical processing devices,” Microelectronics J., vol. 112, p. 105046, 2021, doi:/10.1016/j.mejo.2021.105046.
[7] A. Askarian, “Design and analysis of all optical half subtractor in 2D photonic crystal platform,” Optik (Stuttg)., vol. 228, no. April 2020, p. 166126, 2021, doi:/10.1016/j.ijleo.2020.166126.
[8] M. Zavvari, “Design of Photonic Crystal-Based Demultiplexer with High-Quality Factor for DWDM Applications,” J. Opt. Commun., vol. 0, no. 0, 2017, doi:/10.1515/joc-2017-0058.
[9] L. Zhu, F. Mehdizadeh, and R. Talebzadeh, “Application of photonic-crystal-based nonlinear ring resonators for realizing an all-optical comparator,” Appl. Opt., vol. 58, no. 30, pp. 8316–8321, Oct. 2019, doi:/10.1364/AO.58.008316.
[10] R. Talebzadeh, M. Soroosh, Y. S. Kavian, and F. Mehdizadeh, “All-optical 6- and 8-channel demultiplexers based on photonic crystal multilayer ring resonators in Si/C rods,” Photonic Netw. Commun., vol. 34, pp. 248–257, Feb. 2017, doi:/10.1007/s11107-017-0688-x.
[11] M. Youcef Mahmoud, G. Bassou, A. Taalbi, and Z. M. Chekroun, “Optical channel drop filters based on photonic crystal ring resonators,” Opt. Commun., vol. 285, no. 3, pp. 368–372, Feb. 2012,doi:/10.1016/j.optcom.2011.09.068.
[12] S. M. Mirjalili and S. Z. Mirjalili, “Asymmetric Oval-Shaped-Hole Photonic Crystal Waveguide Design by Artificial Intelligence Optimizers,” IEEE J. Sel. Top. Quantum Electron., vol. 22, no. 2, pp. 258–264, 2016, doi:/10.1109/JSTQE.2015.2469760.
[13] H. G. Teo, A. Q. Liu, J. Singh, M. B. Yu, and T. Bourouina, “Design and simulation of MEMS optical switch using photonic bandgap crystal,” Microsyst. Technol., vol. 10, no. 5, pp. 400–406, Aug. 2004, doi:/10.1007/BF02637111.
