First and Second Order Mur Type ABCs for DNG Media
Keywords:
Absorbing Boundary Conditions (ABC), Double Negative Media (DNG), Finite Difference Time Domain (FDTD), Lorentz model, MUR, one-way wave equationAbstract
Reflections from boundaries of the FDTD computational domain lead to inaccurate, even unstable codes when dealing with problems involving double negative (DNG) materials. Here, an efficient and simple algorithm is presented for terminating FDTD in DNG medium which is based on first and second order Mur’s absorbing boundary conditions (ABC). FDTD update equations for Mur’s ABC formulations are obtained from frequency domain one-way wave equations using piecewise linear recursive convolution (PLRC) method. Numerical examples are given both for 1D and 2D scenarios to demonstrate the validity and stability of the proposed Mur formulations, and its advantages over uniaxial perfectly matched layer (UPML) in reducing computational time and memory requirements.
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References
G. Mur, “Absorbing boundary conditions for the finite difference approximation of the time-domain electromagnetic-field equations,” IEEE Trans. Electromagn. Compat., vol. 23, no. 4, pp.377-382, 1981.
J. P. Berenger, “Three-dimensional perfectly matched layer for the absorption of electromagnetic waves,” J. Computat. Phys., vol. 127, pp. 363-379, 1996.
S. D. Gedney, “An anisotropic perfectly matched layer-absorbing medium for the truncation of FDTD lattices,” IEEE Trans. Antennas Propag., vol. 44, pp. 1630-1639, Dec. 1996.
M. Kuzuoglu and R. Mittra, “Frequency dependence of the constitutive parameters of causal perfectly matched anisotropic absorbers,” IEEE Microw. Guided Wave Lett., vol. 6, pp. 447-449, 1996.
J. Roden and S. D. Gedney, “Convolution PML (CPML): An efficient FDTD implementation of the CFS-PML for arbitrary media,” Microw. Opt. Technol. Lett., vol. 27, pp. 334-339, 2000.
Y. Mao, A. Z. Elsherbeni, S. Li, and T. Jiang, “Surface impedance absorbing boundary for terminating FDTD simulations,” ACES Journal, vol. 29, no. 12, pp. 1035-1046, 2014.
Y. Mao, A. Z. Elsherbeni, S. Li, and T. Jiang, “Nonuniform surface impedance absorbing boundary condition for FDTD method,” ACES Express Journal, vol. 1, no. 7, pp. 197-200, July 2016.
S. D. Gedney, “An anisotropic PML absorbing media for the FDTD simulation of fields in lossy and dispersive media,” Electromagnetics, vol. 16, no. 4, pp. 399-415, 1996.
S. A. Cummer, “Perfectly matched layer behavior in negative refractive index materials,” IEEE Antennas Wireless Propagat. Lett., vol. 3, pp. 172- 175, 2004.
K. Zheng, W.-Y. Tam, D.-B. Ge, and J.-D. Xu, “Uniaxial PML absorbing boundary condition for truncating the boundary of DNG metamaterials,” PIERL, vol. 8, 125-134, 2009.
D. Correia and J. M Jin, “3D-FDTD-PML analysis of left-handed metamaterials,” Microw. Opt. Technol. Lett., vol. 40, no. 3, pp. 201-205, Feb. 2004.
P. Kosmas and C. Rappaport, “A simple absorbing boundary condition for FDTD modeling of lossy, dispersive media based on the one-way wave equation,” IEEE Trans. Antennas Propagat., vol. 52, no. 9, pp. 2476-2479, Sept. 2004.
D. Kelley and R. J. Luebbers, “Piecewise linear recursive convolution for dispersive media using FDTD,” IEEE Trans. Antennas Propagat., vol. 44, no. 6, pp. 792-797, 1996.
A. Pekmezci and L. Sevgi, “FDTD-based metamaterial (MTM) modeling and simulation,” IEEE Antennas and Propagat. Magazine, vol. 56, no. 5, pp. 289-303, Oct. 2014.
R. W. Ziolkowski and E. Heyman, “Wave propagation in media having negative permittivity and permeability,” Phys. Rev. E, vol. 64, 056625, 2001.
J. B. Pendry, “Negative refraction makes a perfect lens,” Physical Review Letters, vol. 85, no. 18, pp. 3966-3969, Oct. 2000.
