Z-Transform Implementation of the CFS-PML for Truncating 3D Meta-Material FDTD Domains

Abstract:

Efficient Z-transform implementa-tion of the complex frequency-shifted perfectly matched layer (CFS-PML) based on the stretched coordinate PML (SC-PML) formulations and the D-B formulations is proposed for truncating meta-material finite-difference time-domain (FDTD) lattices. In the proposed PML formulations, the Z-transform method is incorporated into the CFS-PML FDTD implementation. The main advantage of the proposed formulations can allow direct FDTD implementation of the Maxwell’s equations in the PML regions. A numerical test has been carried out in a three dimensions (3-D) FDTD domain to validate the proposed formulations. It is shown that the proposed formulations with CFS scheme are efficient in holding good absorbing performances.

• Periodical: Advanced Materials Research (Volumes 986-987)
• Pages: 3-7
• DOI: https://doi.org/10.4028/www.scientific.net/AMR.986-987.3
• Online since: July 2014
• Authors: Yong Qing Yue*, Chun Hui Zhu, Nai Xing Feng
• Keywords: Finite-Difference Time-Domain (FDTD), Meta-Material, Perfectly Matched Layer (PML), Z-Transform Method

References

[1] Veselago V G, The electrodynamics of substances with simultaneously negative values of ε and μ[J]. Sov. Phys. Uspekhi, 1968, 10(4): 509–514.

DOI: 10.1070/pu1968v010n04abeh003699

[2] Taflove A, Hagness S C. Computational electrodynamics[M]. Boston: Artech house, (2000).

[3] Kärkkäinen M K. Numerical study of wave propagation in uniaxially anisotropic Lorentzian backward-wave slabs[J]. Physical Review E, 2003, 68(2): 026602.

DOI: 10.1103/physreve.68.026602

[4] Prokopidis K P, Zografopoulos D C. Efficient FDTD algorithms for dispersive Drude-critical points media based on bilinear z-transform[J]. Electronics Letters, 2013, 49(8): 534-536.

DOI: 10.1049/el.2013.0198

[5] Mukherjee S, Karmakar S, Goswami C, et al. Electromagnetic wave propagation modeling in Lorentzian DNG metamaterial by auxiliary differential equation based ADI-FDTD[C]. Emerging Technology Trends in Electronics, Communication and Networking, Surat, 2012: 1-4.

DOI: 10.1109/et2ecn.2012.6470071

[6] Li J, Yang Q, Miao J, et al. A Novel and Efficient Algorithm of the Uniaxial Perfectly Matched Layer Based on the Z-Transform Method[C]. Control, Automation and Systems Engineering , Auckland , 2011: 1-4.

DOI: 10.1109/iccase.2011.5997572

[7] Cummer S A, Perfectly matched layer behavior in negative refractive index materials[J], IEEE Antennas Wireless Propag. Lett, 2004, 3(1): 172–175.

DOI: 10.1109/lawp.2004.833710

[8] Ramadan O. DSP-PML algorithm for open region DNG meta-material FDTD simulations[J]. Electronics letters, 2010, 46(1): 16-18.

DOI: 10.1049/el.2010.2273

[9] Feng N, Li J. Novel and efficient FDTD implementation of higher-order perfectly matched layer based on ADE method[J]. Journal of Computational Physics, 2013, 232(1): 318-326.

DOI: 10.1016/j.jcp.2012.08.012

[10] Feng N X, Li J X, Zhao X M. Efficient FDTD Implementations of the Higher-Order PML Using DSP Techniques for Arbitrary Media[J]. IEEE Transactions on Antennas and Propagation, 2013, 61: 2623-2629.

DOI: 10.1109/tap.2013.2242825