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PIER PIER B PIER C PIER M PIER Letters
2024-02-05
Fast Calculations of Vector Electromagnetics in 3D Periodic Structures Based on Multiple Scattering Theory and Broadband Green's Function
By
Leung Tsang,

    Professor Leung Tsang

    Department of Electrical Engineering and Computer Science

    University of Michigan

    USA

    Homepage

Tien-Hao Liao,

    Dr. Tien-Hao Liao

    Department of Electrical Engineering and Computer Science

    University of Michigan

    USA

    Homepage

Shurun Tan,

    Professor Shurun Tan

    College of Information Science and Electronic Engineering

    Zhejiang University

    China

    Homepage

Xiaolan Xu,

    Dr. Xiaolan Xu

    California Institute of Technology

    USA

    Homepage

Xuyang Bai,

    Dr. Xuyang Bai

    Zhejiang University-University of Illinois at Urbana-Champaign Institute

    Zhejiang University

    China

    Homepage

Rouxing Gao

    Dr. Rouxing Gao

    University of Michigan

    USA

    Homepage

Progress In Electromagnetics Research, Vol. 179, 19-36, 2024
doi:10.2528/PIER23091003
Abstract
We have developed a fast method of using Multiple Scattering Theory-Broadband Green's Function (MST-BBGF) for band field calculations. In this paper, we successfully extended the method to the vector electromagnetic case of 3D periodic structures. In the MST-BBGF approach, the broadband transformation to vector spherical waves for 3D is derived using the Broadband Green's function. The band eigenvalue problem is expressed in terms of the single scatterer T matrix which is independent of the periodic lattice nor the Bloch vector. For the first five bands, the dimension of the KKR eigen equation is merely 6, as 6 vector spherical waves are utilized for the scattered waves. We make extensive comparisons of the results with the commercial software COMSOL in both accuracy and computation efficiency. The CPU requirementon a standard laptop for the MST-BBGF method is merely 0.309 seconds for the first 5 bands. The MST-BBGF method is accurate and is at least two orders of magnitude faster than commercial software COMSOL. In the band field calculations, we employ the approach of extended coefficient to use the low order eigenvector of 6 to extend to 240 vector spherical wave coefficients without the need of re-calculating the eigenvalue nor the eigenvector of the KKR equation. The extended coefficients approach gives accurate band field solutions for the entire (0,0,0) cell.
Citation
Leung Tsang, Tien-Hao Liao, Shurun Tan, Xiaolan Xu, Xuyang Bai, and Rouxing Gao, "Fast Calculations of Vector Electromagnetics in 3D Periodic Structures Based on Multiple Scattering Theory and Broadband Green's Function," Progress In Electromagnetics Research, Vol. 179, 19-36, 2024.
doi:10.2528/PIER23091003
References

1. Joannopoulos, John D., Steven G. Johnson, Joshua N. Winn, and Robert D. Meade, Photonic Crystals: Molding the Flow of Light, 2nd Ed., Princeton University Press, 2008.

2. Ozawa, Tomoki, Hannah M. Price, Alberto Amo, Nathan Goldman, Mohammad Hafezi, Ling Lu, Mikael C. Rechtsman, David Schuster, Jonathan Simon, Oded Zilberberg, and Iacopo Carusotto, "Topological photonics," Reviews of Modern Physics, Vol. 91, No. 1, 015006, Mar. 2019.
doi:10.1103/RevModPhys.91.015006

3. Wang, Zheng, Y. D. Chong, John D. Joannopoulos, and Marin Soljačić, "Reflection-free one-way edge modes in a gyromagnetic photonic crystal," Physical Review Letters, Vol. 100, 013905, 2008.

4. Yang, Zhaoju, Fei Gao, Xihang Shi, Xiao Lin, Zhen Gao, Yidong Chong, and Baile Zhang, "Topological acoustics," Physical Review Letters, Vol. 114, 114301, Mar. 2015.
doi:10.1103/PhysRevLett.114.114301

5. Ao, Xianyu, Zhifang Lin, and C. T. Chan, "One-way edge mode in a magneto-optical honeycomb photonic crystal," Physical Review B, Vol. 80, 033105, Jul. 2009.
doi:10.1103/PhysRevB.80.033105

6. Tasolamprou, Anna C., Maria Kafesaki, Costas M. Soukoulis, Eleftherios N. Economou, and Thomas Koschny, "Chiral topological surface states on a finite square photonic crystal bounded by air," Physical Review Applied, Vol. 16, 044011, 2021.

7. Xi, Xiang, Bei Yan, Linyun Yang, Yan Meng, Zhen-Xiao Zhu, Jing-Ming Chen, Ziyao Wang, Peiheng Zhou, Perry Ping Shum, Yihao Yang, et al., "Topological antichiral surface states in a magnetic Weyl photonic crystal," Nature Communications, Vol. 14, 1991, 2023.

8. Jin, Jian-Ming, The Finite Element Method in Electromagnetics, 3rd Ed., John Wiley & Sons, 2014.

9. Zhao, Ran, Guo-Da Xie, Menglin L. N. Chen, Zhihao Lan, Zhixiang Huang, and Wei E. I. Sha, "First-principle calculation of Chern number in gyrotropic photonic crystals," Optics Express, Vol. 28, No. 4, 4638-4649, 2020.

10. Tsang, Leung, "Broadband calculations of band diagrams in periodic structures using the broadband Green's function with low wavenumber extraction (BBGFL)," Progress In Electromagnetics Research, Vol. 153, 57-68, 2015.

11. Tsang, Leung and Shurun Tan, "Calculations of band diagrams and low frequency dispersion relations of 2D periodic dielectric scatterers using broadband Green's function with low wavenumber extraction (BBGFL)," Optics Express, Vol. 24, No. 2, 945-965, 2016.

12. Gao, Rouxing, Leung Tsang, Shurun Tan, and Tien-Hao Liao, "Band calculations using broadband Green's functions and the KKR method with applications to magneto-optics and photonic crystals," Journal of the Optical Society of America B, Vol. 37, No. 12, 3896-3907, 2020.

13. Gao, Rouxing, Leung Tsang, Shurun Tan, and Tien-Hao Liao, "Broadband Green's function-KKR-Multiple Scattering Method for calculations of normalized band-field solutions in magneto-optics crystals," Journal of the Optical Society of America B, Vol. 38, No. 10, 3159-3171, 2021.

14. Tsang, Leung, Tien-Hao Liao, and Shurun Tan, "Calculations of bands and band field solutions in topological acoustics using the broadband Green's function-KKR-Multiple Scattering Method," Progress In Electromagnetics Research, Vol. 171, 137-158, 2021.

15. Tsang, Leung, Tien-Hao Liao, and Shurun Tan, "A fast computation method of bands and band field solutions of 3D periodic structures using broadband Green's Function-Multiple Scattering Theory," Progress In Electromagnetics Research, Vol. 176, 67-93, 2023.
doi:10.2528/PIER22080101

16. Tan, Shurun and Leung Tsang, "Efficient broadband evaluations of lattice Green's functions via imaginary wavenumber components extractions," Progress In Electromagnetics Research, Vol. 164, 63-74, 2019.

17. Foldy, Leslie L., "The multiple scattering of waves. I. General theory of isotropic scattering by randomly distributed scatterers," Physical Review, Vol. 67, 107-119, 1945.

18. Lax, Melvin, "Multiple scattering of waves," Reviews of Modern Physics, Vol. 23, No. 4, 287-310, 1951.

19. Waterman, Peter Cary and Rohn Truell, "Multiple scattering of waves," Journal of Mathematical Physics, Vol. 2, No. 4, 512-537, 1961.

20. Tsang, Leung, Jin Au Kong, and Robert T. Shin, Theory of Microwave Remote Sensing, Wiley-Interscience, New York, 1985.

21. Tsang, L., Jin Au Kong, Kung-Hau Ding, and Chi On Ao, Scattering of Electromagnetic Waves, Vol. 2: Numerical Simulations, Wiley Interscience, 2001.
doi:10.1002/0471224308

22. Korringa, J., "On the calculation of the energy of a Bloch wave in a metal," Physica, Vol. 13, No. 6-7, 392-400, 1947.

23. Tsang, L., Jin Au Kong, and Kung-Hau Ding, Scattering of Electromagnetic Waves, Vol. 1: Theory and Applications, Wiley Interscience, 2000.
doi:10.1002/0471224286

24. Wang, Xindong, X.-G. Zhang, Qingliang Yu, and B. N. Harmon, "Multiple-scattering theory for electromagnetic waves," Physical Review B, Vol. 47, No. 8, 4161-4167, 1993.

25. Kohn, W. and N. Rostoker, "Solution of the Schrödinger equation in periodic lattices with an application to metallic lithium," Physical Review, Vol. 94, 1111-1120, 1954.
doi:10.1103/PhysRev.94.1111

26. Kambe, Kyozaburo, "Theory of electron diffraction by crystals: I. Green's function and integral equation," Zeitschrift für Naturforschung A, Vol. 22, No. 4, 422-431, Apr. 1967.
doi:10.1515/zna-1967-0402

27. Gu, W., L. Tsang, A. Colliander, and S. Yueh, "Propagation of waves in vegetations using a hybrid method," IEEE Transactions on Antennas and Propagation, Vol. 69, No. 10, 6752-6761, Oct. 2021.
doi:10.1109/TAP.2021.3069487

28. Gu, Weihui, Leung Tsang, Andreas Colliander, and Simon H. Yueh, "Multifrequency full-wave simulations of vegetation using a hybrid method," IEEE Transactions on Microwave Theory and Techniques, Vol. 70, No. 1, 275-285, Jan. 2022.

29. Tsang, Leung, Tien-Hao Liao, Ruoxing Gao, Haokui Xu, Weihui Gu, and Jiyue Zhu, "Theory of microwave remote sensing of vegetation effects, soop and rough soil surface backscattering," Remote Sensing, Vol. 14, No. 15, 3640, 2022.

30. Huang, Huanting, Leung Tsang, Andreas Colliander, Rashmi Shah, Xiaolan Xu, and Simon Yueh, "Multiple scattering of waves by complex objects using hybrid method of T-matrix and Foldy-Lax equations using vector spherical waves and vector spheroidal waves," Progress In Electromagnetics Research, Vol. 168, 87-111, 2020.

31. Harrington, R. F., Time-harmonic Electromagnetic Fields, McGraw-Hill, 1961.

32. Sarabandi, K., Foundations of Applied Electromagnetics, Michigan Publishing, 2022.

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