FDTD Modeling of Lorentzian DNG Metamaterials by Auxiliary Differential Equation Method

Chiranjib Goswami, Saptarshi Mukherjee, Subrata Karmakar, Manimala Pal, Rowdra Ghatak

Department of AEIE, Asansol Engineering College, Asansol, India.
Microwave and Antenna Research Laboratory, Department of ECE, National Institute of Technology Durgapur, Durgapur, India.
Radio Engineering and Antenna Laboratory, ECE Department, NFET, NSHM Knowledge Campus Durgapur, Durgapur, India.

DOI: 10.4236/jemaa.2014.65010                

Abstract

In this paper, Finite Difference Time Domain (FDTD) is utilized to simulate metamaterials of Double Negative (DNG) origin that refers to those materials having simultaneous negative permittivity and permeability. The problem regarding space formulation is achieved by means of auxiliary differential equation method (ADE), which is easy, reliable and also causal process in nature thus making it proficient. It uses fair approximations to explicate the model. Mur’s boundary condition is used for 1-D problem space and convolution perfectly matched layer boundary is implemented for 2-D problem space. The properties of metamaterial conform their speculations of energy absorption, enhancement and backward propagation property with the aid of graphs engineered by Matlab simulation both in 1-D and 2-D. Also, the interaction of fields on DNG and Double Positive (DPS) layers is contrasted. The results achieved elucidate the validity and effectiveness of the ADE method and the Convolution Perfectly Match Layer (CPML) in designing DNG metamaterials.

Keywords

ABC, ADE Method, CPML, DNG, FDTD Method

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	Veselago, V.G. (1968) The Electrodynamics of Substance with Simultaneously Negative Values of ε and μ. Soviet Physics Uspekhi, 10, 509. http://dx.doi.org/10.1070/PU1968v010n04ABEH003699
[2]	Taflove, A. (1995) Computational Electrodynamics: The Finite-Difference Time-Domain Method. Artech House, Norwood.
[3]	Luebbers, R.J., Hunsberger, F., Kunz, K.S., Standler, R.B. and Schneider, M. (1990) A Frequency Dependent Finite-Difference Time-Domain Formulation for Dispersive Materials. IEEE Transactions on Electromagnetic Compatibility, 32, 222-227. http://dx.doi.org/10.1109/15.57116
[4]	Luebbers, R.J., Hunsberger, F. and Kunz, K.S. (1991) A Frequency-Dependent Finite-Difference Time-Domain Formulation for Transient Propagation in Plasma. IEEE Transactions on Antennas and Propagation, 39, 29-34. http://dx.doi.org/10.1109/8.64431
[5]	Luebbers, R.J. and Hunsberger, F. (1992) FDTD for Nth-Order Dispersive Media. IEEE Transactions on Antennas and Propagation, 40, 1297-1301. http://dx.doi.org/10.1109/8.202707
[6]	Zhang, Y.-Q. and Ge, D.-B. (2009) A Unified FDTD Approach for Electromagnetic Analysis of Dispersive Objects. Progress in Electromagnetics Research, PIER96, 155-172.
[7]	Jiang, Y.-N., Ge, D.-B. and Ding, S.-J. (2008) Analysis of TF-SF Boundary for 2D-FDTD with Plane P-Wave Propagation in Layered Dispersive and Lossy Media. Progress in Electromagnetics Research, PIER83, 157-172.
[8]	Akyurtlu, A. and Werner, D.H. (1990) A Novel Dispersive FDTD Formulation for Modeling Transient Propagation in Chiral Metamaterials. IEEE Transactions on Antennas and Propagation, 52, 2267-2276. http://dx.doi.org/10.1109/TAP.2004.834153
[9]	Kashiwa, T., Yoshida, N. and Fukai, I. (1990) A treatment by the Finite-Difference Time-Domain Method of the Dispersive Characteristics Associated with Orientation Polarization. IEEE Transactions on Antennas and Propagation, E73, 1326-1328.
[10]	Kashiwa, T. and Fukai, I. (1990) A Treatment by the FD-TD Method of the Dispersive Characteristics Associated with Electronic Polarization. Microwave and Optical Technology Letters, 3, 203-205. http://dx.doi.org/10.1002/mop.4650030606
[11]	Kashiwa, T., Ohtomo, Y. and Fukai, I. (1990) A Finite-Difference Time-Domain Formulation for Transient Propagation in Dispersive Media Associated with Cole-Cole’s Circular ARC Law. Microwave and Optical Technology Letters, 3, 416-419. http://dx.doi.org/10.1002/mop.4650031204
[12]	Joseph, R.M., Hagness, S.C. and Taflove, A. (1991) Direct Time Integration of Maxwell’s Equations in Linear Dispersive Media with Absorption for Scattering and Propagation of Femtosecond Electrogmagnetic Pulses. Optics Letters, 16, 1412-1414. http://dx.doi.org/10.1364/OL.16.001412
[13]	Gandhi, P., Gao, B.Q. and Chen, J.Y. (1992) A Frequency-Dependent Finite-Difference Time Domain Formulation for Induced Current Calculations in Human Beings. Bioelectromagentics, 13, 543-556. http://dx.doi.org/10.1002/bem.2250130609
[14]	Gandhi, P., Gao, B.Q. and Chen, J.Y. (1993) A Frequency-Dependent Finite-Difference Time Domain Formulation for General Dispersive Media. IEEE Transactions on Microwave Theory and Techniques, 41, 658-665. http://dx.doi.org/10.1109/22.231661
[15]	Goorjian, P.M. and Taflove, A. (1992) Direct Time Integration of Maxwell’s Equations in Nonlinear Dispersive Media for Propagation and Scattering of Femto Second Electromagnetic Solutions. Optics Letters, 17, 180-182. http://dx.doi.org/10.1364/OL.17.000180
[16]	Sullivan, D.M. (1992) Frequency-Dependent FDTD Methods Using Z Transforms. IEEE Transactions on Antennas and Propagations, 40, 1223-1230. http://dx.doi.org/10.1109/8.182455
[17]	Demir, V., Elsherbeni, A.Z. and Arvas, E. (2005) FDTD Formulation for Dispersive Chiral Media Using the Z Transform Method. IEEE Transactions on Antennas and Propagations, 53, 3374-3384. http://dx.doi.org/10.1109/TAP.2005.856328
[18]	Feise, M.W., Schneider, J.B. and Bevelacqua, P.J. (2004) Finite-Difference and Pseudospectraltime-Domain Methods Applied to Backward-Wave Metamaterials. IEEE Transactions on Antennas and Propagations, 52, 2955-2962. http://dx.doi.org/10.1109/TAP.2004.835274
[19]	Lee, J.Y., Lee, J.H., Kim, H.S., Kang, N.W. and Jung, H.K. (2005) Effective Medium Approach of Left Handed Material Using a Dispersive FDTD Method. IEEE Transactions on Magnetics, 41, 1484-1487. http://dx.doi.org/10.1109/TMAG.2005.844566
[20]	Ziolkowski, R.W. and Heyman, E. (2001) Wave Propagation in Media Having Negative Permittivity and Permeability. Physical Review E, 64, Article No. 056625. http://dx.doi.org/10.1103/PhysRevE.64.056625
[21]	Ziolkowski, R.W. (2001) Superluminal Transmission of Information through an Electromagnetic Metamaterial. Physical Review E, 63, Article No. 046604.
[22]	Suwailam, M.M.B. and Chen, Z.Z. (2004) FDTD Modeling of Lorentzian DNG Meta-Materials with the Z-Transform. In: 3rd International Conference on Computational Electromagnetics and Its Applications Proceedings, IEEE, New York, 40-43.
[23]	Lee, K.H., Ahmed, I., Goh, R.S.M., Khoo, E.H., Li, E.P. and Hung, T.G.G. (2011) Implementation of the FDTD Method Based on Lorentz-Drude Dispersive Model on GPU for Plasmonic Applications. Progress in Electromagnetics Research, 116, 441-456.
[24]	Berenger, J.P. (1994) A Perfectly Matched Layer for the Absorption of Electromagnetic Waves. Journal of Computational Physics, 114, 185-200. http://dx.doi.org/10.1006/jcph.1994.1159
[25]	Roden, A. and Gedney, S.D. (2000) Convolutional PML (CPML): An Efficient FDTD Implementation of the CFSPML for Arbitrary Media. Microwave and Optical Technical Letter, 27, 334-339.
[26]	Mukherjee, S., Karmakar, S., Goswami, C. and Ghatak, R. (2012) Electromagnetic Wave Propagation Modeling in Lorentzian DNG Metamaterial by Auxiliary Differential Equation Based ADI-FDTD. In: Proceedings of 2012 1st International Conference on Emerging Technology Trends in Electronics, Communication and Networking, IEEE, New York, 1-4.