PIER | |

Progress In Electromagnetics Research | ISSN: 1070-4698, E-ISSN: 1559-8985 |

Home > Vol. 116 > pp. 81-106
## CONSISTENT FORMALISM FOR THE MOMENTUM OF ELECTROMAGNETIC WAVES IN LOSSLESS DISPERSIVE METAMATERIALS AND THE CONSERVATION OF MOMENTUMBy Y. He, K. Maski, and S. He
Abstract:
A new formalism for electromagnetic and mechanical momenta in a metamaterial is developed by means of the technique of wave-packet integrals. The medium has huge mass density and can therefore be regarded as almost stationary upon incident electromagnetic waves. A clear identification of momentum density and momentum flow, including their electromagnetic and mechanical parts, is obtained by employing this formalism in a lossless dispersive metamaterial (including the cases of impedance matching and mismatching with vacuum). It is found that the ratio of the electromagnetic momentum density to the mechanical momentum density depends on the impedance and group velocity of the electromagnetic wave inside the metamaterial. One of the definite results is that both the electromagnetic momentum and the mechanical momentum in the metamaterial are in the same direction as the energy flow, instead of in the direction of the wave vector. The conservation of total momentum is verified. In addition, the law of energy conservation in the process of normal incidence is also verified by using the wave-packet integral of both the electromagnetic energy density and the electromagnetic p
2. Abraham, "M. Rend. Circ. Matem. Palermo,", Vol. 28, No. 1, 1909.
3. Minkowski, 4. Jones, R. V. and J. C. S. Richards, "The pressure of radiation in a refracting medium," 5. Gordon, J. P., "Radiation forces and momenta in dielectric media," 6. Mikura, Z., "Variational formulation of the electrodynamics of fluids and its application to the radiation pressure problem ," 7. Peierls, R., 8. Jones, R. V., 9. Nelson, D. F., "Momentum, pseudomomentum, and wave momentum: Toward resolving the Minkowski-Abraham controversy," 10. Loudon, R., L. Allen, and D. F. Nelson, "Propagation of electromagnetic energy and momentum through an absorbing dielectric," 11. Obukhov, Y. N. and F. W. Hehl, "Electromagnetic energy-momentum and forces in matter," 12. Mansuripur, M., "Radiation pressure and the linear momentum of the electromagnetic field," 13. Kemp, B., T. Grzegorczyk, and J. Kong, "Ab initio study of the radiation pressure on dielectric and magnetic media," 14. Mansuripur, M., "Radiation pressure and the linear momentum of light in dispersive dielectric media," 15. Scalora, M., et al., "Radiation pressure of light pulses and conservation of linear momentum in dispersive media," 16. Mansuripur, M., "Radiation pressure and the linear momentum of the electromagnetic field in magnetic media," 17. Obukhov, Y. N. and F. W. Hehl, "Electrodynamics of moving magnetoelectric media: Variational approach," 18. Ramos, T., G. F. Rubilar, and Y. N. Obukhov, "Relativistic analysis of the dielectric Einstein box: Abraham, Minkowski and total energy-momentum tensors," 19. Yaghjian, A. D., "Internal energy, Q-energy, Poynting's theorem, and the stress dyadic in dispersive material," 20. Brevik, I., "Experiments in phenomenological electrodynamics and the electromagnetic energy-momentum tensor," 21. Pfeifer, R. N. C., et al., "Colloquium: Momentum of an electromagnetic wave in dielectric media," 22. Obukhov, Y. N., "Electromagnetic energy and momentum in moving media," 23. Veselago, V. G., "The electrodynamics of substances with simultaneously negative values of permittivity and permeability," 24. Shelby, R. A., D. R. Smith, and S. Schultz, "Experimental verification of a negative index of refraction," 25. Pendry, J. B., "Negative refraction makes a perfect lens," 26. Kemp, B. A., J. A. Kong, and T. M. Grzegorczyk, "Reversal of wave momentum in isotropic left-handed media," 27. Veselago, V. G., "Energy, linear momentum, and mass transfer by an electromagnetic wave in a negative-refraction medium," 28. Barnett, S. M., "Resolution of the Abraham-Minkowski Dilemma," 29. Einstein, A. and J. Laub, |

© Copyright 2014 EMW Publishing. All Rights Reserved