Abstract
Accurate and unconditionally stable finite difference time domain (FDTD) algorithm is presented for modeling electromagnetic wave propagation in double-negative (DNG) meta-material domains. The proposed algorithm is based on incorporating the Bilinear transformation technique into the FDTD implementations of Maxwell’s equations. The stability of the proposed approach is studied by combining the von Neumann method with the Routh-Huwitz criterion and it has been observed that the proposed algorithm is free from the Courant-Friedrichs-Lewy (CFL) stability limit of the conventional FDTD scheme. Furthermore, the proposed algorithm is incorporated with the split-step FDTD scheme to model two-dimensional problems. Numerical examples carried out in one and two dimensional domains are included to show the validity of the proposed algorithm.
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References
V. G. Veselago, “The electrodynamics of substances with simultaneously negative values of ε and μ,” Soviet Physics. Uspekhi 10 (4), 509–514 (1968).
A. Taflove and S.C. Hangess, Computational electrodynamics: The Finite-Difference Time-Domain Method, 2nd ed. (Artech House, Boston, MA, 2000).
R. W. Ziolkowski and E. Heyman,“Wave propagation in media having negative permittivity and permeability,” Physical Review E 64, 056625 (2001).
M. K. Kärkkäinen, “Numerical study of wave propagation in uniaxially anisotropic Lorentzian backward-wave slabs,” Physical Review E 68, 026602 (2003).
T. Namiki, “A new FDTD algorithm based on alternating-direction implicit method,” IEEE Transactions on Microwave Theory and Techniques 47 (10), 2003–2007 (1999).
N. V. Kantartzis, D. L. Sounas, C. S. Antonopoulos, and T. D. Tsiboukis, “A Wideband ADI-FDTD algorithm for the design of double negative meta-material-based waveguides and antenna substrates,” IEEE Transactions on Magnetics 43 (4), 1329–1332 (2007).
J. G. Proakis and D. G. Manolakis, Digital Signal Processing: Principles, Algorithms and Applications, 3rd ed. (Prentice Hall, International Editions, Englewood Cliffs, NJ, 1995).
J. A. Pereda, L. A. Vielva, A. Vegas, and A. Prieto, “Analyzing the stability of the FDTD technique by combining the Von Neumann method with Routh-Hurwitz criterion,” IEEE Transactions on Microwave Theory and Techniques 49 (2), 377–381 (2001).
J. Lee and B. Fornberg, “A split step approach for the 3-D Maxwell’s equations,” Journal of Computational and Applied Mathematics 158 (2), 485–505 (2003).
D. Correia and J.-M. Jin, “3D-FDTD-PML analysis of left-handed metamaterials,” Microwave and Optical Technology Letters 40 (3), 201–205 (2004).
A. Grande, J. A. Pereda, O. Gonzalez, and A. Vegas, “Stability and accuracy of a finite-difference time-domain scheme for modelling double-negative media with high-order rational constitutive parameters,” IEEE Transactions on Microwave Theory and Techniques 56 (1), 94–104 (2008).
J.-P. Berenger, “A perfectly matched layer for the absorption of electromagnetic waves,” Journal of Computational Physics 114, 185–200 (1994).
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Ramadan, O.S. Unconditionally Stable Bilinear Transformation FDTD Algorithm for Modeling Double-Negative Meta-material Electromagnetic Problems. J Infrared Milli Terahz Waves 31, 288–301 (2010). https://doi.org/10.1007/s10762-009-9585-4
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DOI: https://doi.org/10.1007/s10762-009-9585-4