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Finite element modeling of electromagnetic properties in photonic bianisotropic structures

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Abstract

Given a constitutive relation of the bianisotropic medium, it is not trivial to study how light interacts with the photonic bianisotropic structure due to the limited available means of studying electromagnetic properties in bianisotropic media. In this paper, we study the electromagnetic properties of photonic bianisotropic structures using the finite element method. We prove that the vector wave equation with the presence of bianisotropic is self-adjoint under scalar inner product. we propose a balanced formulation of weak form in the practical implementation, which outperforms the standard formulation in finite element modeling. Furthermore, we benchmark our numerical results obtained from finite element simulation in three different scenarios. These are bianisotropy-dependent reflection and transmission of plane waves incident onto a bianisotropic slab, band structure of bianisotropic photonic crystals with valley-dependent phenomena, and the modal properties of bianisotropic ring resonators. The first two simulated results obtained from our modified weak form yield excellent agreements either with theoretical predictions or available data from the literature, and the modal properties in the last example, i.e., bianisotropic ring resonators as a polarization-dependent optical insulator, are also consistent with the theoretical analyses.

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References

  1. Gansel J K, Thiel M, Rill M S, Decker M, Bade K, Saile V, von Freymann G, Linden S, Wegener M. Gold helix photonic metamaterial as broadband circular polarizer. Science, 2009, 325(5947): 1513–1515

    Article  Google Scholar 

  2. Kriegler C E, Rill M S, Linden S, Wegener M M. Bianisotropic photonic metamaterials. IEEE Journal of Selected Topics in Quantum Electronics, 2010, 16(2): 367–375

    Article  Google Scholar 

  3. Soukoulis C M, Wegener M. Past achievements and future challenges in the development of three-dimensional photonic metamaterials. Nature Photonics, 2011, 5(9): 523–530

    Article  Google Scholar 

  4. Guo Q, Gao W, Chen J, Liu Y, Zhang S. Line degeneracy and strong spin-orbit coupling of light with bulk bianisotropic metamaterials. Physical Review Letters, 2015, 115(6): 067402

    Article  Google Scholar 

  5. Slobozhanyuk A P, Khanikaev A B, Filonov D S, Smirnova D A, Miroshnichenko A E, Kivshar Y S. Experimental demonstration of topological effects in bianisotropic metamaterials. Scientific Reports, 2016, 6(1): 22270

    Article  Google Scholar 

  6. Moritake Y, Tanaka T. Bi-anisotropic Fano resonance in three-dimensional metamaterials. Scientific Reports, 2018, 8(1): 9012

    Article  Google Scholar 

  7. Yu Y Z, Kuo C Y, Chern R L, Chan C T. Photonic topological semimetals in bianisotropic metamaterials. Scientific Reports, 2019, 9(1): 18312

    Article  Google Scholar 

  8. Pfeiffer C, Grbic A. Bianisotropic metasurfaces for optimal polarization control: analysis and synthesis. Physical Review Applied, 2014, 2(4): 044011

    Article  Google Scholar 

  9. Pfeiffer C, Zhang C, Ray V, Guo L J, Grbic A. Polarization rotation with ultra-thin bianisotropic metasurfaces. Optica, 2016, 3(4): 427–432

    Article  Google Scholar 

  10. Pfeiffer C, Zhang C, Ray V, Guo L J, Grbic A. High performance bianisotropic metasurfaces: asymmetric transmission of light. Physical Review Letters, 2014, 113(2): 023902

    Article  Google Scholar 

  11. Odit M, Kapitanova P, Belov P, Alaee R, Rockstuhl C, Kivshar Y S. Experimental realisation of all-dielectric bianisotropic metasurfaces. Applied Physics Letters, 2016, 108(22): 221903

    Article  Google Scholar 

  12. Epstein A, Eleftheriades G V. Arbitrary power-conserving field transformations with passive lossless omega-type bianisotropic metasurfaces. IEEE Transactions on Antennas and Propagation, 2016, 64(9): 3880–3895

    Article  MathSciNet  Google Scholar 

  13. Asadchy V S, Díaz-Rubio A, Tretyakov S A. Bianisotropic metasurfaces: physics and applications. Nanophotonics, 2018, 7(6): 1069–1094

    Article  Google Scholar 

  14. Li J, Shen C, Díaz-Rubio A, Tretyakov S A, Cummer S A. Systematic design and experimental demonstration of bianisotropic metasurfaces for scattering-free manipulation of acoustic wave-fronts. Nature Communications, 2018, 9(1): 1342

    Article  Google Scholar 

  15. Li J, Díaz-Rubio A, Shen C, Jia Z, Tretyakov S A, Cummer S. Highly efficient generation of angular momentum with cylindrical bianisotropic metasurfaces. Physical Review Applied, 2019, 11(2): 024016

    Article  Google Scholar 

  16. Chen X, Wu B I, Kong J A, Grzegorczyk T M. Retrieval of the effective constitutive parameters of bianisotropic metamaterials. Physical Review E, 2005, 71(4): 046610

    Article  Google Scholar 

  17. Li Z, Aydin K, Ozbay E. Determination of the effective constitutive parameters of bianisotropic metamaterials from reflection and transmission coefficients. Physical Review E, 2009, 79(2): 026610

    Article  Google Scholar 

  18. Ouchetto O, Qiu C W, Zouhdi S, Li L W, Razek A. Homogenization of 3-D periodic bianisotropic metamaterials. IEEE Transactions on Microwave Theory and Techniques, 2006, 54(11): 3893–3898

    Article  Google Scholar 

  19. Hasar U C, Muratoglu A, Bute M, Barroso J J, Ertugrul M. Effective constitutive parameters retrieval method for bianisotropic metamaterials using waveguide measurements. IEEE Transactions on Microwave Theory and Techniques, 2017, 65(5): 1488–1497

    Article  Google Scholar 

  20. Zhao J, Jing X, Wang W, Tian Y, Zhu D, Shi G. Steady method to retrieve effective electromagnetic parameters of bianisotropic metamaterials at one incident direction in the terahertz region. Optics & Laser Technology, 2017, 95: 56–62

    Article  Google Scholar 

  21. Shaltout A, Shalaev V, Kildishev A. Homogenization of bianisotropic metasurfaces. Optics Express, 2013, 21(19): 21941–21950

    Article  Google Scholar 

  22. Albooyeh M, Tretyakov S, Simovski C. Electromagnetic characterization of bianisotropic metasurfaces on refractive substrates: General theoretical framework. Annalen der Physik, 2016, 528(9–10): 721–737

    Article  Google Scholar 

  23. Lindell I V, Sihvola A H, Viitanen A J, Tretyakov S A. Electromagnetic Waves in Chiral and Bi-Isotropic Media. Boston: Artech House on Demand, 1994

    Google Scholar 

  24. Serdiukov A, Semchenk I, Tertyakov S, Sihvola A. Electromagnetics of Bi-Anisotropic Materials-Theory and Application. Singapore: Gordon and Breach, 2001

    Google Scholar 

  25. Sersic I, Tuambilangana C, Kampfrath T, Koenderink A F. Magnetoelectric point scattering theory for metamaterial scatterers. Physical Review B, 2011, 83(24): 245102

    Article  Google Scholar 

  26. Peng L, Zheng X, Wang K, Sang S, Chen Y, Wang Y G. Layer-by-layer design of bianisotropic metamaterial and its homogenization. Progress In Electromagnetics Research, 2017, 159: 39–47

    Article  Google Scholar 

  27. Xu J, Wu B, Chen Y. Elimination of polarization degeneracy in circularly symmetric bianisotropic waveguides: a decoupled case. Optics Express, 2015, 23(9): 11566–11575

    Article  Google Scholar 

  28. Multiphysics COMSOL. 5.2: a finite element analysis, solver and simulation software

  29. Dong J W, Chen X D, Zhu H, Wang Y, Zhang X. Valley photonic crystals for control of spin and topology. Nature Materials, 2017, 16(3): 298–302

    Article  Google Scholar 

Download references

Acknowledgements

The authors acknowledge the financial support from the National Key Research and Development Program of China (No. 2019YFB2203100) and the National Natural Science Foundation of China (Grant No. 11874026).

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Authors and Affiliations

  1. School of Optical and Electronic Information, Huazhong University of Science and Technology, Wuhan, 430074, China

    Zhongfei Xiong, Weijin Chen, Zhuoran Wang, Jing Xu & Yuntian Chen

  2. Department of Electrical and Computer Engineering (ECE), National University of Singapore, Singapore, 117583, Singapore

    Weijin Chen

  3. Wuhan National Laboratory of Optoelectronics, Huazhong University of Science and Technology, Wuhan, 430074, China

    Jing Xu & Yuntian Chen

Authors
  1. Zhongfei Xiong
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  2. Weijin Chen
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  3. Zhuoran Wang
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  4. Jing Xu
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  5. Yuntian Chen
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Correspondence to Yuntian Chen.

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Zhongfei Xiong received his B.S. degree in Optoelectronic Information Engineering from Huazhong University of Science and Technology, China. He is currently pursuing his Ph.D. degree in Optical Engineering at School of Optical and Electronic Information, Huazhong University of Science and Technology. His major research interests include topological photonics, symmetry in optics and thermodynamics optics.

Weijin Chen received his Bachelor degree from Harbin Institute of Technology, China, in 2015, and Ph.D. degree from Huazhong University of Science and Technology, China, in 2020. He is currently a Research Fellow in Department of Electrical and Computer Engineering (ECE), National University of Singapore, Singapore. Chen’s research focuses on the Mie scattering, scattering invariance, and coupledmode theory.

Zhuoran Wang is a research assistant in School of Optical and Electrical Information, Huazhong University of Science and Technology, China. He received the Master degree in Engineering from University of Science and Technology, China, in 2020. His research area involved computational electromagnetics, topological photonics, and Non-Hermition photonics. He proposed a new boundary condition, Non-Hermition port, so as to numerically calculate the S parameters of a Non-Hermition system. Besides, he used finite element method to calculate the eigenmodes of bianisotropic waveguide. Currently, he is focusing on developing an optical simulation software in order to replace the COMSOL, FDTD.

Jing Xu received her Ph.D. degree in Optical Engineering from Huazhong University of Science and Technology (HUST), China, in 2008. During 2009–2013, she has been a postdoctoral fellow at Technical University of Denmark (DTU), Denmark. From November 2013, Dr. Xu joined School of Optical and Electronic Information, HUST, as an associate professor. Since 2020, Dr. Xu become a full professor at HUST.

Yuntian Chen received his Ph.D. degree from Technical University of Denmark (DTU), Denmark, in 2010. During 2010–2013, he has been a postdoctoral fellow at Technical University of Denmark. From September 2013, Dr. Yuntian Chen joined School of Optical and Electronic Information in Huazhong University of Science and Technology, China, as an associate professor.

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Xiong, Z., Chen, W., Wang, Z. et al. Finite element modeling of electromagnetic properties in photonic bianisotropic structures. Front. Optoelectron. 14, 148–153 (2021). https://doi.org/10.1007/s12200-021-1213-5

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  • DOI: https://doi.org/10.1007/s12200-021-1213-5

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