Progress In Electromagnetics Research
ISSN: 1070-4698, E-ISSN: 1559-8985
Home | Search | Notification | Authors | Submission | PIERS Home | EM Academy
Home > Vol. 116 > pp. 81-106


By Y. He, J.-Q. Shen, and S. He

Full Article PDF (232 KB)

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

Y. He, J.-Q. Shen, and S. He, "Consistent Formalism for the Momentum of Electromagnetic Waves in Lossless Dispersive Metamaterials and the Conservation of Momentum," Progress In Electromagnetics Research, Vol. 116, 81-106, 2011.

1. Jackson, J. D., Classical Electrodynamics, New York, Wiley, 1999.

2. Abraham, "M. Rend. Circ. Matem. Palermo,", Vol. 28, No. 1, 1909.

3. Minkowski, Nachr. Ges. Wiss. Gottn Math. Phys. KI., Vol. 53, 1908.

4. Jones, R. V. and J. C. S. Richards, "The pressure of radiation in a refracting medium," Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences, Vol. 221, No. 1147, 480-498, 1954.

5. Gordon, J. P., "Radiation forces and momenta in dielectric media," Physical Review A, Vol. 8, No. 1, 14-21, 1973.

6. Mikura, Z., "Variational formulation of the electrodynamics of fluids and its application to the radiation pressure problem ," Physical Review A, Vol. 13, No. 6, 2265, 1976.

7. Peierls, R., The momentum of light in a refracting medium, Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences, Vol. 347, No. 1651, 475-491, 1976.

8. Jones, R. V., Radiation pressure of light in a dispersive medium, Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences, Vol. 360, No. 1702, 365-371, 1978.

9. Nelson, D. F., "Momentum, pseudomomentum, and wave momentum: Toward resolving the Minkowski-Abraham controversy," Physical Review A, Vol. 44, No. 6, 3985-3966, 1991.

10. Loudon, R., L. Allen, and D. F. Nelson, "Propagation of electromagnetic energy and momentum through an absorbing dielectric," Physical Review E, Vol. 55, No. 1, 1071-1085, 1997.

11. Obukhov, Y. N. and F. W. Hehl, "Electromagnetic energy-momentum and forces in matter," Physics Letters A, Vol. 311, No. 4-5, 277-284, 2003.

12. Mansuripur, M., "Radiation pressure and the linear momentum of the electromagnetic field," Opt. Express, Vol. 12, No. 22, 5375-5401, 2004.

13. Kemp, B., T. Grzegorczyk, and J. Kong, "Ab initio study of the radiation pressure on dielectric and magnetic media," Opt. Express, Vol. 13, No. 23, 9280-9291, 2005.

14. Mansuripur, M., "Radiation pressure and the linear momentum of light in dispersive dielectric media," Opt. Express, Vol. 13, No. 6, 2245-2250, 2005.

15. Scalora, M., et al., "Radiation pressure of light pulses and conservation of linear momentum in dispersive media," Physical Review E, Vol. 73, No. 5, 056604, 2006.

16. Mansuripur, M., "Radiation pressure and the linear momentum of the electromagnetic field in magnetic media," Opt. Express, Vol. 15, No. 21, 13502-13518, 2007.

17. Obukhov, Y. N. and F. W. Hehl, "Electrodynamics of moving magnetoelectric media: Variational approach," Physics Letters A, Vol. 371, No. 1-2, 11-19, 2007.

18. Ramos, T., G. F. Rubilar, and Y. N. Obukhov, "Relativistic analysis of the dielectric Einstein box: Abraham, Minkowski and total energy-momentum tensors," Physics Letters A, Vol. 375, No. 16, 1703-1709, 2011.

19. Yaghjian, A. D., "Internal energy, Q-energy, Poynting's theorem, and the stress dyadic in dispersive material," IEEE Transactions on Antennas and Propagation, Vol. 55, No. 6, 1495-1505, 2007.

20. Brevik, I., "Experiments in phenomenological electrodynamics and the electromagnetic energy-momentum tensor," Physics Reports, Vol. 52, No. 3, 133-201, 1979.

21. Pfeifer, R. N. C., et al., "Colloquium: Momentum of an electromagnetic wave in dielectric media," Reviews of Modern Physics, Vol. 79, No. 4, 1197-1216, 2007.

22. Obukhov, Y. N., "Electromagnetic energy and momentum in moving media," Annalen der Physik, Vol. 17, No. 9-10, 830-851, 2008.

23. Veselago, V. G., "The electrodynamics of substances with simultaneously negative values of permittivity and permeability," Sov. Phys. Usp., Vol. 10, 509-514, 1968.

24. Shelby, R. A., D. R. Smith, and S. Schultz, "Experimental verification of a negative index of refraction," Science, Vol. 292, No. 5514, 77-79, 2001.

25. Pendry, J. B., "Negative refraction makes a perfect lens," Physical Review Letters, Vol. 85, No. 18, 3966-3969, 2000.

26. Kemp, B. A., J. A. Kong, and T. M. Grzegorczyk, "Reversal of wave momentum in isotropic left-handed media," Physical Review A, Vol. 75, No. 5, 053810, 2007.

27. Veselago, V. G., "Energy, linear momentum, and mass transfer by an electromagnetic wave in a negative-refraction medium," Physics-Uspekhi, Vol. 52, No. 6, 649-654, 2009.

28. Barnett, S. M., "Resolution of the Abraham-Minkowski Dilemma," Physical Review Letters, Vol. 104, No. 7, 070401, 2010.

29. Einstein, A. and J. Laub, Ann. Physik, Vol. 26, No. 541, 1908.

© Copyright 2014 EMW Publishing. All Rights Reserved