volume | PIER Journals

Abstract

This study presents an effective solution on the basis of Discontinuous-Galerkin Time-Domain (DGTD) scheme for the injection of elliptically polarized plane wave through total-field/scattered-field (TF/SF) boundary. Generally, the elliptically polarized wave can be resolved into two linearly polarized waves in phase quadrature with the polarization planes at right angles to each other, but the proposed methodology is focused to utilize the principle of wave field formation to induce left-handed or right-handed elliptically polarized waves by regulating the phase and amplitude of the incident waves. The outcome of the proposed technique is achieved by deriving the EB-scheme equations and employing the explicit fourth order Runge-Kutta (RK4) time integration scheme in the DGTD methodology. An anisotropic Riemann solver and non-conformal mesh schemes are introduced for domain decomposition to allow efficient spatial discretization. Additionally, the proposed work is extended from single frequency to broadband elliptical polarized plane wave injection in the DGTD method, and the significance of this study is observed in the results. The experimental outcomes reveal that the proposed method is consistent with the analytical solution in free space and expected to provide efficient numerical solutions for analyzing scattering characteristics generated by various elliptically polarized waves.

1. Merewether, E., R. Fisher, and F. W. Smith, "On implementing a numeric Huygen's source scheme in a finite difference program to illuminate scattering bodies," IEEE Trans. Nucl. Sci., Vol. 27, No. 6, 1829-1833, Dec. 1980.
doi:10.1109/TNS.1980.4331114

2. Taflove, A. and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method, Artech House, 2005.

3. Schneider, J. B., "Plane waves in FDTD simulations and a nearly perfect total-field/scattered-field boundary," IEEE Trans. Antennas Propag., Vol. 52, No. 12, 3280-3287, Dec. 2004.
doi:10.1109/TAP.2004.836403

4. Hadi, M. F., "A versatile split-field 1-D propagator for perfect plane wave injection," IEEE Trans. Antennas Propag., Vol. 57, No. 9, 2691-2697, Sept. 2009.
doi:10.1109/TAP.2009.2027171

5. Tan, T. and M. Potter, "Optimized analytic filed propagator (O-AFP) for plane wave injection in FDTD simulations," IEEE Trans. Antennas Propag., Vol. 58, No. 3, 824-831, Mar. 2010.
doi:10.1109/TAP.2009.2039310

6. Tan, T. and M. Potter, "FDTD discrete plane wave (FDTD-DPW) formulation for a perfectly matched source in TFSF simulations," IEEE Trans. Antennas Propag., Vol. 58, No. 8, 2641-2648, Aug. 2010.
doi:10.1109/TAP.2010.2050446

7. Anantha, V. and A. Taflove, "Efficient modeling of infinite scatterers using a generalized total-field/scattered-field FDTD boundary partially embedded within PML," IEEE Trans. Antennas Propag., Vol. 50, No. 10, 1111-1119, Oct. 2002.

8. Capoglu, I. R. and G. S. Smith, "A total-field/scattered-field plane wave source for the FDTD analysis of layered media," IEEE Trans. Antennas Propag., Vol. 56, No. 1, 158-169, Jan. 2008.
doi:10.1109/TAP.2007.913088

9. Riley, D. J., J. M. Jin, Z. Lou, and L. E. R. Petersson, "Total-and scattered-field decomposition technique for the finite-element time-domain method," IEEE Trans. Antennas Propag., Vol. 54, No. 1, 35-41, Jan. 2006.
doi:10.1109/TAP.2005.861524

10. Yang, Q., B. Wei, L. Li, and D. Ge, "Implementation of corner-free truncation strategy in DGTD method," Waves Random Complex Media, Vol. 27, No. 2, 367-380, Apr. 2017.
doi:10.1080/17455030.2016.1249439

11. Alvarez, J., L. D. Angulo, A. R. Bretones, and S. G. Garcia, "3-D Discontinuous Galerk in time-domain method for anisotropic materials," IEEE Antennas Wireless Propag. Lett., Vol. 11, 1182-1185, 2012.
doi:10.1109/LAWP.2012.2220952

12. Bao, H., L. Kang, S. D. Campbell, and D. H. Werner, "PML implementation in a nonconforming mixed-element DGTD method for periodic structureanalysis," IEEE Trans. Antennas Propag., Vol. 67, No. 11, 6979-6988, Nov. 2019.
doi:10.1109/TAP.2019.2927663

13. Alvarez, J., L. D. Angulo, M. R. Cabello, A. R. Bretones, and S. G. Garcia, "Ananalysis of the leap-frog discontinuous Galerkin method for Maxwell's equations," IEEE Trans. Microw. Theory Tech., Vol. 62, No. 2, 197-207, Feb. 2014.
doi:10.1109/TMTT.2013.2295775

14. Ren, Q., Q. Zhan, and Q. H. Liu, "An improved subdomain level nonconformal discontinuous galerkin time domain (DGTD) method for materials with full-tensor constitutive parameters," IEEE Photon. J., Vol. 9, No. 2, 1-13, Apr. 2017.
doi:10.1109/JPHOT.2017.2672644

15. Dosopoulos, S. and J.-F. Lee, "Interior penalty discontinuous galerkin finite element method for the time-dependent first order maxwell's equations," IEEE Trans. Antennas Propag., Vol. 58, No. 12, 4085-4090, Dec. 2010.
doi:10.1109/TAP.2010.2078445

16. Li, P., Y. Shi, L. J. Jiang, and H. Bagci, "DGTD analysis of electromagnetic scattering from penetrable conductive objects with IBC," IEEE Trans. Antennas Propag., Vol. 63, No. 12, 5686-5697, Dec. 2015.
doi:10.1109/TAP.2015.2491963

17. Li, P., L. J. Jiang, and H. Bagci, "Discontinuous galerkin time-domain modeling of graphene nanoribbon incorporating the spatial dispersion effects," IEEE Trans. Antennas Propag., Vol. 66, No. 7, 3590-3598, July 2018.
doi:10.1109/TAP.2018.2826567

18. Yang, Q., B. Wei, L. Li, and D. Ge, "Simulation of electromagnetic waves in a magnetized cold plasma by the SO-DGTD method," IEEE Trans. Antennas Propag., Vol. 66, No. 8, 4151-4157, Aug. 2018.
doi:10.1109/TAP.2018.2835727

19. Wang, P., Y. Shi, Z. G. Ban, S. C. Zhu, Q. Yang, and L. Li, "Penalty fac tor threshold and time step bound estimations for discontinuous Galerkin time-domain method based on Helmholtz equation," IEEE Trans. Antennas Propag., Vol. 68, No. 11, 7494-7506, Nov. 2020.
doi:10.1109/TAP.2020.2998585

20. Chen, G., L. Zhao, W. Yu, S. Yan, K. Zhang, and J. Jin, "A general scheme for the discontinuous Galerkin time-domain modeling and s-parameter extraction of inhomogeneous waveports," IEEE Trans. Microw. Theory Techn., Vol. 66, No. 4, 1701-1712, Apr. 2018.
doi:10.1109/TMTT.2017.2785800

21. Zhang, T., H. Bao, D. Ding, and R. Chen, "Interior penalty DGTD method for solving wave equation in dispersive media described with GDM model," IEEE Trans. Antennas Propag., Vol. 69, No. 9, 6105-6110, Sept. 2021.
doi:10.1109/TAP.2021.3064222

22. Gedney, S. D., C. Luo, J. A. Roden, R. D. Crawford, B. Guernsey, J. A. Miller, and E. W. Lucas, "A discontinuous galerkin finite element time domain method with PML," IEEE Antennas and Propagation Society International Symposium, 1-4, 2008.

23. Li, K., T. Huang, L. Li, S. Lanteri, L. Xu, and B. Li, "A reduced-order discontinuous Galerkin method based on POD for electromagnetic simulation," IEEE Trans. Antennas Propag., Vol. 66, No. 1, 242-254, Jan. 2018.
doi:10.1109/TAP.2017.2768562

24. Sun, Q., R. Zhang, Q. Zhan, and Q. H. Lu, "3D implicit-explicit hybrid finite difference/spectral element/finite element time domain method without a Buffer zone," IEEE Trans. Antennas Propag., Vol. 67, No. 8, 5469-5476, Aug. 2019.
doi:10.1109/TAP.2019.2913740

25. Zhan, Q., Y. Wang, Y. Fang, Q. Ren, S. Yang, W. Y. Yin, and Q. H. Liu, "An adaptive high-order transient algorithm to solve large-scale anisotropic Maxwell's equations," IEEE Trans. Antennas Propag., Vol. 70, No. 3, 2082-2092, Mar. 2022.
doi:10.1109/TAP.2021.3111639

26. Sankaran, K., C. Fumeaux, and R. Vahldieck, "Cell-centered finite-volume-based perfectly matched layer for time-domain Maxwell system," IEEE Trans. Microw. Theory Tech., Vol. 54, No. 3, 1269-1276, Mar. 2006.
doi:10.1109/TMTT.2006.869704

27. Lee, J. F., R. Lee, and A. Cangellaris, "Time-domain finite-element methods," IEEE Trans. Antennas Propag., Vol. 45, No. 3, 430-442, Mar. 1997.
doi:10.1109/8.558658

28. Jin, J.-M., The Finite Element Method in Electromagnetics, 2nd Ed., Wiley, 2002.

29. Ren, Q., L. E. Tobon, Q. Sun, and Q. H. Liu, "A new 3-D nonspurious discontinuous galerkin spectral element time-domain (DG-SETD) method for Maxwell's equations," IEEE Trans. Antennas Propag., Vol. 63, No. 6, 2585-2594, Jun. 2015.
doi:10.1109/TAP.2015.2417891

30. Chen, J., L. E. Tobon, M. Chai, J. A. Mix, and Q. H. Liu, "Efficient implicit-explicit time stepping scheme with domain decomposition for multiscale modeling of layered structures," IEEE Trans. Compon. Pack. Manuf. Technol., Vol. 1, No. 9, 1438-1446, Sept. 2011.
doi:10.1109/TCPMT.2011.2162726

31. Sun, Q., Q. Zhan, Q. Ren, and Q. H. Liu, "Wave equation-based implicit subdomain DGTD method for modeling of electrically small problems," IEEE Trans. Microw. Theory Techn., Vol. 65, No. 4, 1111-1119, Apr. 2017.
doi:10.1109/TMTT.2016.2640312

32. Wen, P., Q. Ren, J. Chen, A. Chen, and Y. Zhang, "Improved memory-efficient subdomain level discontinuous galerkin time domain method for periodic/quasi-periodic structures," IEEE Trans. Antennas Propag., Vol. 68, No. 11, 7471-7479, Nov. 2020.
doi:10.1109/TAP.2020.2998215

33. Zhou, Y., L. Shi, N. Liu, C. Zhu, H. Liu, and Q. H. Liu, "Spectral element method and domain decomposition for low-frequency fubsurface EM simulation," IEEE Geosci. Remote. Sens. Lett., Vol. 13, No. 4, 550-554, Apr. 2016.
doi:10.1109/LGRS.2016.2524558

34. Zhan, Q., Q. Ren, Q. Sun, H. Chen, and Q. H. Liu, "Isotropic riemann solver for a nonconformal discontinuous galerkin pseudospectral time-domain algorithm," IEEE Trans. Geosci. Remote. Sens., Vol. 55, No. 3, 1254-1261, Mar. 2017.
doi:10.1109/TGRS.2016.2621124

35. Zhou, Y., L. Shi, N. Liu, C. Zhu, H. Liu, and Q. H. Liu, "Spectral element method and domain decomposition for low-frequency subsurface EM simulation," IEEE Geosci. Remote Sens. Lett., Vol. 13, No. 4, 550-554, Apr. 2016.
doi:10.1109/LGRS.2016.2524558

36. Shi, L., M. Zhuang, Y. Zhou, N. Liu, and Q. H. Liu, "Domain decomposition based on the spectral element method for frequency-domain computational elastodynamics," Sci. China Earth Sci., Vol. 64, 388-403, 2021.
doi:10.1007/s11430-020-9696-4

37. Shi, L., Y. Zhou, J. Wang, M. Zhuang, N. Liu, and Q. H. Liu, "Spectral element method for elastic and acoustic waves in frequency domain," J. Comput. Phys., Vol. 327, No. 15, 19-38, Dec. 2016.
doi:10.1016/j.jcp.2016.09.036

38. Zhan, Q., M. Zhuang, Y. Mao, and Q. H. Liu, "Unified Riemann solution for multi-physics coupling: Anisotropic poroelastic/elastic/fluid interfaces," Journal of Computational Physics, Vol. 402, No. 108961, 1-25, Feb. 2020.

39. Zeng, C., J. Xia, R. D. Miller, and G. P. Tsoflias, "Application of the multiaxial perfectly matched layer (M-PML) to near-surface seismic modeling with rayleigh waves," Geophys., Vol. 76, No. 3, T43-T52, May 2011.
doi:10.1190/1.3560019

40. Meza-Fajardo, K. C. and A. S. Papageorgiou, "On the stability of a non-convolutional perfectly matched layer for isotropic elastic media," Soil Dyn. Earthq. Eng., Vol. 30, No. 3, 68-81, 2010.
doi:10.1016/j.soildyn.2009.09.002

41. Zhan, Q., Y. Fang, M. Zhuang, M. Yuan, and Q. H. Liu, "Stabilized DG-PSTD method with nonconformal meshes for electromagnetic waves," IEEE Trans. Antennas Propag., Vol. 68, No. 6, 4714-4726, Jun. 2020.
doi:10.1109/TAP.2020.2970036

Dr. Xiaobing Han

Dr. Hang Li

Prof. Yuanguo Zhou

Dr. Lin Wang

Dr. Shangqing Liang

Dr. Fawad Javaid