Search search
submit Submit
Publication Date
to
Vol. 116
Latest Volume
All Volumes
PIER 180 [2024] PIER 179 [2024] PIER 178 [2023] PIER 177 [2023] PIER 176 [2023] PIER 175 [2022] PIER 174 [2022] PIER 173 [2022] PIER 172 [2021] PIER 171 [2021] PIER 170 [2021] PIER 169 [2020] PIER 168 [2020] PIER 167 [2020] PIER 166 [2019] PIER 165 [2019] PIER 164 [2019] PIER 163 [2018] PIER 162 [2018] PIER 161 [2018] PIER 160 [2017] PIER 159 [2017] PIER 158 [2017] PIER 157 [2016] PIER 156 [2016] PIER 155 [2016] PIER 154 [2015] PIER 153 [2015] PIER 152 [2015] PIER 151 [2015] PIER 150 [2015] PIER 149 [2014] PIER 148 [2014] PIER 147 [2014] PIER 146 [2014] PIER 145 [2014] PIER 144 [2014] PIER 143 [2013] PIER 142 [2013] PIER 141 [2013] PIER 140 [2013] PIER 139 [2013] PIER 138 [2013] PIER 137 [2013] PIER 136 [2013] PIER 135 [2013] PIER 134 [2013] PIER 133 [2013] PIER 132 [2012] PIER 131 [2012] PIER 130 [2012] PIER 129 [2012] PIER 128 [2012] PIER 127 [2012] PIER 126 [2012] PIER 125 [2012] PIER 124 [2012] PIER 123 [2012] PIER 122 [2012] PIER 121 [2011] PIER 120 [2011] PIER 119 [2011] PIER 118 [2011] PIER 117 [2011] PIER 116 [2011] PIER 115 [2011] PIER 114 [2011] PIER 113 [2011] PIER 112 [2011] PIER 111 [2011] PIER 110 [2010] PIER 109 [2010] PIER 108 [2010] PIER 107 [2010] PIER 106 [2010] PIER 105 [2010] PIER 104 [2010] PIER 103 [2010] PIER 102 [2010] PIER 101 [2010] PIER 100 [2010] PIER 99 [2009] PIER 98 [2009] PIER 97 [2009] PIER 96 [2009] PIER 95 [2009] PIER 94 [2009] PIER 93 [2009] PIER 92 [2009] PIER 91 [2009] PIER 90 [2009] PIER 89 [2009] PIER 88 [2008] PIER 87 [2008] PIER 86 [2008] PIER 85 [2008] PIER 84 [2008] PIER 83 [2008] PIER 82 [2008] PIER 81 [2008] PIER 80 [2008] PIER 79 [2008] PIER 78 [2008] PIER 77 [2007] PIER 76 [2007] PIER 75 [2007] PIER 74 [2007] PIER 73 [2007] PIER 72 [2007] PIER 71 [2007] PIER 70 [2007] PIER 69 [2007] PIER 68 [2007] PIER 67 [2007] PIER 66 [2006] PIER 65 [2006] PIER 64 [2006] PIER 63 [2006] PIER 62 [2006] PIER 61 [2006] PIER 60 [2006] PIER 59 [2006] PIER 58 [2006] PIER 57 [2006] PIER 56 [2006] PIER 55 [2005] PIER 54 [2005] PIER 53 [2005] PIER 52 [2005] PIER 51 [2005] PIER 50 [2005] PIER 49 [2004] PIER 48 [2004] PIER 47 [2004] PIER 46 [2004] PIER 45 [2004] PIER 44 [2004] PIER 43 [2003] PIER 42 [2003] PIER 41 [2003] PIER 40 [2003] PIER 39 [2003] PIER 38 [2002] PIER 37 [2002] PIER 36 [2002] PIER 35 [2002] PIER 34 [2001] PIER 33 [2001] PIER 32 [2001] PIER 31 [2001] PIER 30 [2001] PIER 29 [2000] PIER 28 [2000] PIER 27 [2000] PIER 26 [2000] PIER 25 [2000] PIER 24 [1999] PIER 23 [1999] PIER 22 [1999] PIER 21 [1999] PIER 20 [1998] PIER 19 [1998] PIER 18 [1998] PIER 17 [1997] PIER 16 [1997] PIER 15 [1997] PIER 14 [1996] PIER 13 [1996] PIER 12 [1996] PIER 11 [1995] PIER 10 [1995] PIER 09 [1994] PIER 08 [1994] PIER 07 [1993] PIER 06 [1992] PIER 05 [1991] PIER 04 [1991] PIER 03 [1990] PIER 02 [1990] PIER 01 [1989]
All Journals
PIER PIER B PIER C PIER M PIER Letters
2011-04-27
Consistent Formalism for the Momentum of Electromagnetic Waves in Lossless Dispersive Metamaterials and the Conservation of Momentum
By
Yingran He,

    Dr. Yingran He

    Centre for Optical and Electromagnetic Research

    Zhejiang University

    China

    Homepage

Katus Maski,

    Dr. Katus Maski

    Royal Inst Technol

    USA

    Homepage

Sailing He

    Prof. Sailing He

    Department of Electromagnetic Theory

    Royal Institute of Technology

    Sweden

    Homepage

Progress In Electromagnetics Research, Vol. 116, 81-106, 2011
doi:10.2528/PIER11032006
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
Citation
Yingran He, Katus Maski, and Sailing 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.
doi:10.2528/PIER11032006
References

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.
doi:10.1098/rspa.1954.0043

5. Gordon, J. P., "Radiation forces and momenta in dielectric media," Physical Review A, Vol. 8, No. 1, 14-21, 1973.
doi:10.1103/PhysRevA.8.14

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.
doi:10.1103/PhysRevA.13.2265

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.
doi:10.1103/PhysRevA.44.3985

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.
doi:10.1103/PhysRevE.55.1071

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.
doi:10.1016/S0375-9601(03)00503-6

12. Mansuripur, M., "Radiation pressure and the linear momentum of the electromagnetic field," Opt. Express, Vol. 12, No. 22, 5375-5401, 2004.
doi:10.1364/OPEX.12.005375

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.
doi:10.1364/OPEX.13.009280

14. Mansuripur, M., "Radiation pressure and the linear momentum of light in dispersive dielectric media," Opt. Express, Vol. 13, No. 6, 2245-2250, 2005.
doi:10.1364/OPEX.13.002245

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.
doi:10.1103/PhysRevE.73.056604

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.
doi:10.1364/OE.15.013502

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.
doi:10.1016/j.physleta.2007.08.026

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.
doi:10.1016/j.physleta.2011.03.015

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.
doi:10.1109/TAP.2007.897350

20. Brevik, I., "Experiments in phenomenological electrodynamics and the electromagnetic energy-momentum tensor," Physics Reports, Vol. 52, No. 3, 133-201, 1979.
doi:10.1016/0370-1573(79)90074-7

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.
doi:10.1103/RevModPhys.79.1197

22. Obukhov, Y. N., "Electromagnetic energy and momentum in moving media," Annalen der Physik, Vol. 17, No. 9-10, 830-851, 2008.
doi:10.1002/andp.200810313

23. Veselago, V. G., "The electrodynamics of substances with simultaneously negative values of permittivity and permeability," Sov. Phys. Usp., Vol. 10, 509-514, 1968.
doi:10.1070/PU1968v010n04ABEH003699

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.
doi:10.1126/science.1058847

25. Pendry, J. B., "Negative refraction makes a perfect lens," Physical Review Letters, Vol. 85, No. 18, 3966-3969, 2000.
doi:10.1103/PhysRevLett.85.3966

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.
doi:10.1103/PhysRevA.75.053810

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.
doi:10.3367/UFNe.0179.200906j.0689

28. Barnett, S. M., "Resolution of the Abraham-Minkowski Dilemma," Physical Review Letters, Vol. 104, No. 7, 070401, 2010.
doi:10.1103/PhysRevLett.104.070401

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

Download Full Article (323) View Full Article volume
The EM Academy piers.org jpier.org Who's Who in EM
Copyright © 2022 The Electromagnetics Academy. All Rights Reserved.