Bandgap analysis of 2D photonic crystals with Auxiliary Functions of Generalized Scattering Matrix (AFGSM) method |
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| Affiliation: | 1. Literature and Information Center, Zhejiang Wanli University, Ningbo 315100, China;2. College of Electronics and Computer Science, Zhejiang Wanli University, Ningbo 315100, China;1. Department of Physics, Chemistry and Mathematics, Alabama A&M University, Normal, AL 35762, USA;2. Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia;3. Department of Mathematics and Statistics, Tshwane University of Technology, Pretoria 0008, South Africa;4. Department of Mathematics, Faculty of Science and Arts, Bozok University, 66100 Yozgat, Turkey;5. Department of Engineering Sciences, Faculty of Technology and Engineering, East of Guilan, University of Guilan, P.C. 44891-63157 Rudsar-Vajargah, Iran;6. School of Electronics and Information Engineering, Wuhan Donghu University, Wuhan 430212, People''s Republic of China;7. Science Program, Texas A&M University at Qatar, PO Box 23874, Doha, Qatar;1. School of Electronic and Information Engineering, Xi’an Jiaotong University, Xi’an, China;2. Shenzhen Research School, Xi’an Jiaotong University, Shenzhen, China;1. Dept of Computer and Communication Engineering, Ho Chi Minh City University of Technology and Education, Viet Nam;2. Dept of Telecommunications and Systems Engineering, School of Engineering, Autonomous University of Barcelona, Spain;1. Department of Physics, Ohio State University, Columbus, OH 43210, USA;2. Laboratory of Atomic and Solid State Physics, Cornell University, Ithaca, NY 14853, USA;3. Department of Earth Sciences and Department of Physics and Astronomy, University College London, London, WC1E 6BT, UK;4. Department of Material Science and Engineering, University of Florida, Gainesville, FL 32611, USA;1. Department of Mechanical Engineering, Bursa Technical University, Bursa, 16310, Turkey;2. School of Engineering, Newcastle University, Newcastle-Upon-Tyne, NE1 7RU, UK |
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| Abstract: | In this paper, an accurate and rapid method is presented to characterize bandgaps of photonic crystals (PCs) constituted by two-dimensional (2D) arrays of dielectric rods with rectangular and circular cross sections. The transmittance and reflectance spectrums of finitely periodic 2D PCs are analyzed using the combination of Rigorous Coupled Wave Analysis (RCWA) and Generalized Scattering Matrix (GSM) methods. In the proposed method, band-edge frequencies of infinitely periodic 2D PCs are determined via Auxiliary Functions of Generalized Scattering Matrix (AFGSM) method using RCWA as a sub-block code. Numerical investigations show that estimating the band-edge frequencies of ideal 2D PCs via AFGSM method is identical with determining the bandgaps of the finite periodic global structure. The high convergence rate of the proposed technique also allows us to perform a bandgap characterization including the higher order Floquet modes without solving the eigenvalue equations for each cascaded layer. Furthermore, the variation of bandgaps when modifying the incidence angle, physical and geometrical parameters are presented for both TE and TM polarizations. The effect of introducing defect in 2D PC structure and resulting band natures are outlined. Our results are in excellent agreement with both theoretical and experimental results in the literature. |
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| Keywords: | Electromagnetic bandgap (EBG) Periodic structures Photonic bandgaps (PBGs) Photonic crystals |
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