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.
 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
 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
 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.
 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
 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.
 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.
 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.
 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.
 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
 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
 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.
 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.
 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.
 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
 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.
 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.
 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.
 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
 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.
 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.
 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
 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.