Effect of negative permittivity and permeability on the transmission of electromagnetic waves through a structure containing left-handed material

ABSTRACT

We investigate the characteristics of electromagnetic wave reflection and transmission by multilayered structures consisting of a pair of left-handed material (LHM) and dielectric slabs inserted between two semi-infinite dielectric media. The theoretical aspect is based on Maxwell's equations and matching the boundary conditions for the electric and magnetic fields of the incident waves at each layer interface. We calculate the reflected and transmitted powers of the multilayered structure taking into account the widths of the slabs and the frequency dependence of permittivity and permeability of the LHM. The obtained results satisfy the law of conservation of energy. We show that if the semi-infinite dielectric media have the same refractive index and the slabs have the same width, then the reflected (and transmitted) powers can be minimized (and maximized) and the powers-frequency curves show no ripple. On the other hand if the semi-infinite dielectric media have different values of refractive indices and the slabs have different widths, then under certain conditions the situation of minimum and maximum values of the mentioned powers will be reversed.

We investigate the characteristics of electromagnetic wave reflection and transmission by multilayered structures consisting of a pair of left-handed material (LHM) and dielectric slabs inserted between two semi-infinite dielectric media. The theoretical aspect is based on Maxwell's equations and matching the boundary conditions for the electric and magnetic fields of the incident waves at each layer interface. We calculate the reflected and transmitted powers of the multilayered structure taking into account the widths of the slabs and the frequency dependence of permittivity and permeability of the LHM. The obtained results satisfy the law of conservation of energy. We show that if the semi-infinite dielectric media have the same refractive index and the slabs have the same width, then the reflected (and transmitted) powers can be minimized (and maximized) and the powers-frequency curves show no ripple. On the other hand if the semi-infinite dielectric media have different values of refractive indices and the slabs have different widths, then under certain conditions the situation of minimum and maximum values of the mentioned powers will be reversed.

Cite this paper

Ubeid, M. , Shabat, M. and Sid-Ahmed, M. (2011) Effect of negative permittivity and permeability on the transmission of electromagnetic waves through a structure containing left-handed material.*Natural Science*, **3**, 328-333. doi: 10.4236/ns.2011.34043.

Ubeid, M. , Shabat, M. and Sid-Ahmed, M. (2011) Effect of negative permittivity and permeability on the transmission of electromagnetic waves through a structure containing left-handed material.

References

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[2] Pendry, J.B. Holden, A.J. Sewart, W.J. Youngs, I. (1996) Extremely low frequency plasmons in metallic meso- structure. Phys. Rev. Lett., 76, 4773-4776.

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[5] Shadrivov, I.V. (2004) Nonlinear guided waves and symmetry breaking in left-handed waveguides. Photonic Nanostruct: Fundam Appl., 2, 175-180.

[6] Garcia, N. and Nieto-Vesperinoas, M. (2002) Left- handed materials do not make a perfect lens. Phys. Rev. Lett., 88, issue20, 7403.

[7] Kong, J.A. (2002) Electromagnetic wave interaction with stratified negative isotropic media. Prog. Electromagn. Res., 35, 1-52.

[8] Mousa, H.M. and Shabat, M.M. (2007) Nonlinear TE surface waves in a left-handed material and magnetic super lattice waveguide structure. Mod. Phys. B, 21, 895-906.

[9] Kourakis, I. and Shukla, P.K. (2005) Nonlinear propagation of electromagnetic waves in negative-refraction-index composite materials. Phys. Rev. E, 72, 016626.

[10] Cory, H. and Zach, C. (2004) Wave propagation in me- tamaterial multi-layered structures. Microwave and Optical Tech., 40, 460-465.

[11] Sabah, C. and Uckun, S. (2009) High reflection coating with negative and positive refractive index. Piers Online, 5, (7), 601-604.

[12] Oraizi, H. and Abdolali, A. (2009) Mathematical formulation for zero reflection from multilayered metamaterial structures. IET Microw. Antennas Progpag., 3, 987-996.

[13] Stancil, D.D. and Prabhakar, A. (2009) Spin waves. New York: Springer Sience.

[14] Sabah, C. and Uckun, S. (2007) Electromagnetic wave propagation through frequency-dis persive and lossy double-negative slab. Optp-Elec. Rev., 15, (3) 133-143.

[15] Shelby, R.A. (2001) Microwave Experiments with Left-Handed Materials. PhD. Dissertation, University of Calefornia, San Diego.

[16] Pendry, J.B. Holden, A.J. Robbins, D.J. Stewart, W.J. (1998) Low frequency plasmons in thin wire structures. Phys. Condens. Matter, 10, 4785-4809.

[17] Sievenpiper, D.F. Yablonovitch, E. Fan, J.N. Villeneuve, P.R. and Joannopoulos, J.D. (1998) 3D Metallo-Dielec- tric photonic crystals with strong capacitance coupling between metallic islands. Phys. Rev. Lett., 80, 2829-2832.

[1] Veselago, V.G. (1986) The electrodynamics of substances with simultaneously negative values of ε and μ. Soviet Phys Uspekhi., 10, 509-514.

[2] Pendry, J.B. Holden, A.J. Sewart, W.J. Youngs, I. (1996) Extremely low frequency plasmons in metallic meso- structure. Phys. Rev. Lett., 76, 4773-4776.

[3] Pendry, J.B. Holden, A.J. Robbins, D.J. Stewart, W.J. (1999) Magnetic from conductors and enhanced nonlinear phenomena. IEEE Transaction on Microwave Theory and Techniques, 47, 2075-2084.

[4] Shelby, R.A. Smith, D.R. and Schultz, S. (2001) Experimental verification of a negative index of refraction. science, 292, 77-79.

[5] Shadrivov, I.V. (2004) Nonlinear guided waves and symmetry breaking in left-handed waveguides. Photonic Nanostruct: Fundam Appl., 2, 175-180.

[6] Garcia, N. and Nieto-Vesperinoas, M. (2002) Left- handed materials do not make a perfect lens. Phys. Rev. Lett., 88, issue20, 7403.

[7] Kong, J.A. (2002) Electromagnetic wave interaction with stratified negative isotropic media. Prog. Electromagn. Res., 35, 1-52.

[8] Mousa, H.M. and Shabat, M.M. (2007) Nonlinear TE surface waves in a left-handed material and magnetic super lattice waveguide structure. Mod. Phys. B, 21, 895-906.

[9] Kourakis, I. and Shukla, P.K. (2005) Nonlinear propagation of electromagnetic waves in negative-refraction-index composite materials. Phys. Rev. E, 72, 016626.

[10] Cory, H. and Zach, C. (2004) Wave propagation in me- tamaterial multi-layered structures. Microwave and Optical Tech., 40, 460-465.

[11] Sabah, C. and Uckun, S. (2009) High reflection coating with negative and positive refractive index. Piers Online, 5, (7), 601-604.

[12] Oraizi, H. and Abdolali, A. (2009) Mathematical formulation for zero reflection from multilayered metamaterial structures. IET Microw. Antennas Progpag., 3, 987-996.

[13] Stancil, D.D. and Prabhakar, A. (2009) Spin waves. New York: Springer Sience.

[14] Sabah, C. and Uckun, S. (2007) Electromagnetic wave propagation through frequency-dis persive and lossy double-negative slab. Optp-Elec. Rev., 15, (3) 133-143.

[15] Shelby, R.A. (2001) Microwave Experiments with Left-Handed Materials. PhD. Dissertation, University of Calefornia, San Diego.

[16] Pendry, J.B. Holden, A.J. Robbins, D.J. Stewart, W.J. (1998) Low frequency plasmons in thin wire structures. Phys. Condens. Matter, 10, 4785-4809.

[17] Sievenpiper, D.F. Yablonovitch, E. Fan, J.N. Villeneuve, P.R. and Joannopoulos, J.D. (1998) 3D Metallo-Dielec- tric photonic crystals with strong capacitance coupling between metallic islands. Phys. Rev. Lett., 80, 2829-2832.