Time-domain electromagnetic energy in a frequency-dispersive left-handed medium

From Maxwell's equations and the Poynting theorem, the time-domain electric and magnetic energy densities are generally defined in the frequency-dispersive media based on the conservation of energy. As a consequence, a general definition of electric and magnetic energy is proposed. Comparing with existing formulations of electric and magnetic energy in frequency-dispersive media, the new definition is more reasonable and is valid in any case. Using the new definition and staring from the equation of motion, we have shown rigorously that the total energy density and the individual electric and magnetic energy densities are always positive in a realistic artificial left-handed medium (LHM) [R. A. Shelby, D. R. Smith, and S. Schultz, Science 292, 77 (2001)], which obeys actually the Lorentz medium model, although such a LHM has negative permittivity and negative permeability simultaneously in a certain frequency range. We have also shown that the conservation of energy is not violated in LHM. The earlier conclusions can be easily extended to the Drude medium model and the cold plasma medium model. Through an exact analysis of a one-dimensional transient current source radiating in LHM, numerical results are given to demonstrate that the work done by source, the power flowing outwards a surface, and the electric and magnetic energy stored in a volume are all positive in the time domain.

[1]  Stewart,et al.  Extremely low frequency plasmons in metallic mesostructures. , 1996, Physical review letters.

[2]  Sailing He,et al.  Band structure for a one-dimensional photonic crystal containing left-handed materials , 2003 .

[3]  Willie J Padilla,et al.  Composite medium with simultaneously negative permeability and permittivity , 2000, Physical review letters.

[4]  R. Ziolkowski,et al.  Superluminal transmission of information through an electromagnetic metamaterial. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[5]  V. Veselago.  The Electrodynamics of Substances with Simultaneously Negative Values of ∊ and μ , 1968 .

[6]  David R. Smith,et al.  Negative refractive index in left-handed materials. , 2000, Physical review letters.

[7]  R. Ziolkowski,et al.  Wave propagation in media having negative permittivity and permeability. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[8]  J. Kong,et al.  Power propagation in homogeneous isotropic frequency-dispersive left-handed media. , 2002, Physical review letters.

[9]  R. Shelby,et al.  Experimental Verification of a Negative Index of Refraction , 2001, Science.

[10]  Jin Au Kong,et al.  Lateral displacement of a Gaussian beam reflected from a grounded slab with negative permittivity and permeability , 2002 .

[11]  Rodney Loudon,et al.  CORRIGENDUM: The propagation of electromagnetic energy through an absorbing dielectric , 1970 .

[12]  C. K. Ong,et al.  Amplification of evanescent waves in a lossy left-handed material slab , 2003 .

[13]  David R. Smith,et al.  Microwave transmission through a two-dimensional, isotropic, left-handed metamaterial , 2001 .

[14]  N Garcia,et al.  Left-handed materials do not make a perfect lens. , 2002, Physical review letters.

[15]  J. Askne,et al.  Energy of Electromagnetic Waves in the Presence of Absorption and Dispersion , 1970 .

[16]  R. Ruppin,et al.  Electromagnetic energy density in a dispersive and absorptive material , 2002 .

[17]  J. Pendry,et al.  Negative refraction makes a perfect lens , 2000, Physical review letters.

[18]  V. Agranovich,et al.  Crystal Optics with Spatial Dispersion and Excitons , 1984 .

[19]  M. Rosenbluth,et al.  Limitations on subdiffraction imaging with a negative refractive index slab , 2002, cond-mat/0206568.

[20]  John B. Schneider,et al.  Effects of surface waves on the behavior of perfect lenses , 2002 .

[21]  Jin Au Kong,et al.  ELECTROMAGNETIC WAVE INTERACTION WITH STRATIFIED NEGATIVE ISOTROPIC MEDIA , 2002 .

[22]  J. Pendry,et al.  Magnetism from conductors and enhanced nonlinear phenomena , 1999 .

[23]  Jin Au Kong,et al.  Study of lossy effects on the propagation of propagating and evanescent waves in left-handed materials☆ , 2004 .

[24]  Richard W. Ziolkowski,et al.  Metamaterial special issue introduction , 2003 .

[25]  T. Musha.  Electrodynamics of anisotropic media with space and time dispersion , 1972 .

[26]  R M Walser,et al.  Wave refraction in negative-index media: always positive and very inhomogeneous. , 2002, Physical review letters.