volume | PIER Journals

Abstract

In this paper, the Runge-Kutta exponential time differencing (RK-ETD) scheme is used for incorporating Graphene dispersion in the finite difference time domain (FDTD) simulations. The Graphene dispersion is described in the gigahertz and terahertz frequency regimes by Drude model, and the stability of the implementation is studied by means of the von Neumann method combined with the Routh-Hurwitz criterion. It is shown that the presented implementation retains the standard non- dispersive FDTD time step stability constraint. In addition, the RK-ETD scheme is used for the FDTD implementation of the complex-frequency shifted perfectly matched layer (CFS-PML) to truncated open region simulation domains. A numerical example is included to validate both the stability and accuracy of the given implementation.

1. Geim, K. and K. S. Novoselov, "The rise of Graphene," Nat. Mater., Vol. 6, No. 3, 183-191, 2007.
doi:10.1038/nmat1849

2. Novoselov, K. S., V. I. Falko, L. Colombo, P. R. Gellert, M. G. Schwab, and K. Kim, "A roadmap for Graphene," Nature, Vol. 490, 192-200, 2012.
doi:10.1038/nature11458

3. Taflove, A. and S. Hangess, Computational Electrodynamics: The Finite-Difference Time-Domain Method, 3rd Ed., Artech-House, Norwood, MA, 2005.

4. Bouzianas, D., N. Kantartzis, S. Antonopoulos, and T. Tsiboukis, "Optimal modeling of infinite Graphene sheets via a class of generalized FDTD schemes," IEEE Trans. Magn., Vol. 48, No. 2, 379-382, 2012.
doi:10.1109/TMAG.2011.2172778

5. Bouzianas, G. D., N. V. Kantartzis, T. V. Yioultsis, and T. Tsiboukis, "Consistent study of Graphene structures through the direct incorporation of surface conductivity," IEEE Trans. Magn., Vol. 50, No. 2, Art. No. 7003804, 2014.
doi:10.1109/TMAG.2013.2282332

6. Papadimopoulos, A. N., S. A. Amanatiadis, N. V. Kantartzis, I. T. Rekanos, T. T. Zygiridis, and T. D. Tsiboukis, "A convolutional PML scheme for the efficient modeling of Graphene structures through the ADE-FDTD technique," IEEE Trans. Magn., Vol. 53, No. 6, Art. No. 7204504, 2017.
doi:10.1109/TMAG.2017.2661812

7. Sounas, L. and C. Caloz, "Gyrotropy and nonreciprocity of Graphene for microwave applications dimitrios," IEEE Trans. Microw. Theory Tech., Vol. 60, No. 4, 901-914, 2012.
doi:10.1109/TMTT.2011.2182205

8. Young, J. L., A. Kittichartphayak, Y. M. Kwok, and D. Sullivan, "On the dispersion errors related to (FD)² TD type schemes," IEEE Trans. Microw. Theory Tech., Vol. 43, No. 8, 1902-1909, 1995.
doi:10.1109/22.402280

9. Cox, S. M. and P. C. Matthews, "Exponential time differencing for stiff systems," J. Comput. Phys., Vol. 176, 430-455, 2002.
doi:10.1006/jcph.2002.6995

10. Pereda, J. A., L. A. Vielva, A. Vegas, and A. Prieto, "Analyzing the stability of the FDTD technique by combining the Von Neumann method with the Routh-Hurwitz criterion," IEEE Trans. Microw. Theory Tech., Vol. 49, No. 2, 377-381, 2001.
doi:10.1109/22.903100

11. Kuzuoglu, M. and R. Mittra, "Frequency dependence of the constitutive parameters of causal perfectly matched anisotropic absorbers," IEEE Microw. Guided Wave Lett., Vol. 6, No. 12, 447-449, Dec. 1996.
doi:10.1109/75.544545

12. Hanson, G. W., "Dyadic Green’s functions and guided surface waves for a surface conductivity model of graphene," J. Appl. Phys., Vol. 103, No. 064302, 2008.

Prof. Omar Ramadan