Abstract

We examine the force of the electromagnetic radiation on linear, isotropic, homogeneous media specified in terms of their permittivity ε and permeability μ . A formula is proposed for the electromagnetic Lorentz force on the magnetization M, which is treated here as an Amperian current loop. Using the proposed formula, we demonstrate conservation of momentum in several cases that are amenable to rigorous analysis based on the classical Maxwell equations, the Lorentz law of force, and the constitutive relations. Our analysis yields precise expressions for the density of the electromagnetic and mechanical momenta inside the media that are specified by their (ε,μ ) parameters. An interesting consequence of this analysis is the identification of an “intrinsic” mechanical momentum density, ½E ×M/c2, analogous to the electromagnetic (or Abraham) momentum density, ½E ×H/c2. (Here E and H are the magnitudes of the electric and magnetic fields, respectively, and c is the speed of light in vacuum.) This intrinsic mechanical momentum, associated with the magnetization M in the presence of an electric field E, is apparently the same “hidden” momentum that was predicted by W. Shockley and R. P. James nearly four decades ago.

© 2007 Optical Society of America

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  1. J. P. Gordon, "Radiation forces and momenta in dielectric media," Phys. Rev. A 8, 14-21 (1973).
    [CrossRef]
  2. D. F. Nelson, "Momentum, pseudomomentum, and wave momentum: Toward resolving the Minkowski-Abraham controversy," Phys. Rev. A 44, 3985 (1991).
    [CrossRef]
  3. I. Brevik, "Experiments in phenomenological electrodynamics and the electromagnetic energy-momentum. tensor," Phys. Reports 52, 133-201 (1979).
    [CrossRef]
  4. R. Loudon, "Theory of the radiation pressure on dielectric surfaces," J. Mod. Opt. 49, 821-838 (2002).
  5. R. Loudon, "Radiation pressure and momentum in dielectrics," Fortschr. Phys. 52, 1134-1140 (2004).
    [CrossRef]
  6. R. Loudon, S. M. Barnett, and C. Baxter, "Radiation pressure and momentum transfer in dielectrics: the photon drag effect," Phys. Rev. A 71, 063802 (2005).
    [CrossRef]
  7. M. Mansuripur, "Radiation pressure and the linear momentum of the electromagnetic field," Opt. Express 12, 5375-5401 (2004).
    [CrossRef]
  8. M. Mansuripur, A. R. Zakharian, and J. V. Moloney, "Radiation pressure on a dielectric wedge," Opt. Express 13, 2064-2074 (2005).
    [CrossRef]
  9. M. Mansuripur, "Radiation pressure and the linear momentum of light in dispersive dielectric media," Opt. Express 13, 2245-2250 (2005).
    [CrossRef]
  10. M. Mansuripur, "Angular momentum of circularly polarized light in dielectric media," Opt. Express 13, 5315-5324 (2005).
    [CrossRef]
  11. M. Mansuripur, "Radiation pressure and the distribution of electromagnetic force in dielectric media," SPIE Proc. 5930, 154-160 (2005).
  12. M. Mansuripur, A. R. Zakharian, and J. V. Moloney, "Equivalence of total force (and torque) for two formulations of the Lorentz law," SPIE Proc. 6326, 63260G (2006).
  13. M. Mansuripur, "Radiation Pressure on Submerged Mirrors: Implications for the Momentum of Light in Dielectric Media," Opt. Express 15, 2677-2682 (2007).
    [CrossRef]
  14. B. D. H. Tellegen, "Magnetic-Dipole Models," Am. J. Phys. 30, 650 (1962).
    [CrossRef]
  15. S. M. Barnett and R. Loudon, "On the electromagnetic force on a dielectric medium," J. Phys. B: At. Mol. Opt. Phys. 39, S671-S684 (2006).
    [CrossRef]
  16. B. Kemp, T. Grzegorczyk, and J. Kong, "Ab initio study of the radiation pressure on dielectric and magnetic media," Opt. Express 13, 9280-9291 (2005).
    [CrossRef]
  17. B. A. Kemp, J. A. Kong, and T. Grzegorczyk, "Reversal of wave momentum in isotropic left-handed media," Phys. Rev. A 75, 053810 (2007).
    [CrossRef]
  18. L. Vaidman, "Torque and force on a magnetic dipole," Am. J. Phys. 58, 978-983 (1990).
    [CrossRef]
  19. A. D. Yaghjian, "Electromagnetic forces on point dipoles," IEEE Anten. Prop. Soc. Symp. 4, 2868-2871 (1999).
  20. W. Shockley, "Hidden linear momentum related to the ?·E term for a Dirac-electron wave packet in an electric field," Phys. Rev. Lett. 20, 343-346 (1968).
    [CrossRef]
  21. M. Mansuripur, "Momentum of the electromagnetic field in transparent dielectric media," SPIE Proc. 6644, 664413 (2007).
  22. W. Shockley and R. P. James, "Try simplest cases discovery of hidden momentum forces on magnetic currents," Phys. Rev. Lett. 18, 876-879 (1967).
    [CrossRef]
  23. P. Penfield and H. A. Haus, Electrodynamics of Moving Media, (MIT Press, Cambridge, 1967).
  24. R. P.  Feynman, R. B.  Leighton, and M. Sands, The Feynman Lectures on Physics, (Addison-Wesley, Reading, Massachusetts 1964) Vol. 2, Chap. 27.

2007

B. A. Kemp, J. A. Kong, and T. Grzegorczyk, "Reversal of wave momentum in isotropic left-handed media," Phys. Rev. A 75, 053810 (2007).
[CrossRef]

M. Mansuripur, "Momentum of the electromagnetic field in transparent dielectric media," SPIE Proc. 6644, 664413 (2007).

M. Mansuripur, "Radiation Pressure on Submerged Mirrors: Implications for the Momentum of Light in Dielectric Media," Opt. Express 15, 2677-2682 (2007).
[CrossRef]

2006

S. M. Barnett and R. Loudon, "On the electromagnetic force on a dielectric medium," J. Phys. B: At. Mol. Opt. Phys. 39, S671-S684 (2006).
[CrossRef]

M. Mansuripur, A. R. Zakharian, and J. V. Moloney, "Equivalence of total force (and torque) for two formulations of the Lorentz law," SPIE Proc. 6326, 63260G (2006).

2005

2004

M. Mansuripur, "Radiation pressure and the linear momentum of the electromagnetic field," Opt. Express 12, 5375-5401 (2004).
[CrossRef]

R. Loudon, "Radiation pressure and momentum in dielectrics," Fortschr. Phys. 52, 1134-1140 (2004).
[CrossRef]

2002

R. Loudon, "Theory of the radiation pressure on dielectric surfaces," J. Mod. Opt. 49, 821-838 (2002).

1999

A. D. Yaghjian, "Electromagnetic forces on point dipoles," IEEE Anten. Prop. Soc. Symp. 4, 2868-2871 (1999).

1991

D. F. Nelson, "Momentum, pseudomomentum, and wave momentum: Toward resolving the Minkowski-Abraham controversy," Phys. Rev. A 44, 3985 (1991).
[CrossRef]

1990

L. Vaidman, "Torque and force on a magnetic dipole," Am. J. Phys. 58, 978-983 (1990).
[CrossRef]

1979

I. Brevik, "Experiments in phenomenological electrodynamics and the electromagnetic energy-momentum. tensor," Phys. Reports 52, 133-201 (1979).
[CrossRef]

1973

J. P. Gordon, "Radiation forces and momenta in dielectric media," Phys. Rev. A 8, 14-21 (1973).
[CrossRef]

1968

W. Shockley, "Hidden linear momentum related to the ?·E term for a Dirac-electron wave packet in an electric field," Phys. Rev. Lett. 20, 343-346 (1968).
[CrossRef]

1967

W. Shockley and R. P. James, "Try simplest cases discovery of hidden momentum forces on magnetic currents," Phys. Rev. Lett. 18, 876-879 (1967).
[CrossRef]

1962

B. D. H. Tellegen, "Magnetic-Dipole Models," Am. J. Phys. 30, 650 (1962).
[CrossRef]

Barnett, S. M.

S. M. Barnett and R. Loudon, "On the electromagnetic force on a dielectric medium," J. Phys. B: At. Mol. Opt. Phys. 39, S671-S684 (2006).
[CrossRef]

R. Loudon, S. M. Barnett, and C. Baxter, "Radiation pressure and momentum transfer in dielectrics: the photon drag effect," Phys. Rev. A 71, 063802 (2005).
[CrossRef]

Baxter, C.

R. Loudon, S. M. Barnett, and C. Baxter, "Radiation pressure and momentum transfer in dielectrics: the photon drag effect," Phys. Rev. A 71, 063802 (2005).
[CrossRef]

Brevik, I.

I. Brevik, "Experiments in phenomenological electrodynamics and the electromagnetic energy-momentum. tensor," Phys. Reports 52, 133-201 (1979).
[CrossRef]

Gordon, J. P.

J. P. Gordon, "Radiation forces and momenta in dielectric media," Phys. Rev. A 8, 14-21 (1973).
[CrossRef]

Grzegorczyk, T.

B. A. Kemp, J. A. Kong, and T. Grzegorczyk, "Reversal of wave momentum in isotropic left-handed media," Phys. Rev. A 75, 053810 (2007).
[CrossRef]

B. Kemp, T. Grzegorczyk, and J. Kong, "Ab initio study of the radiation pressure on dielectric and magnetic media," Opt. Express 13, 9280-9291 (2005).
[CrossRef]

James, R. P.

W. Shockley and R. P. James, "Try simplest cases discovery of hidden momentum forces on magnetic currents," Phys. Rev. Lett. 18, 876-879 (1967).
[CrossRef]

Kemp, B.

Kemp, B. A.

B. A. Kemp, J. A. Kong, and T. Grzegorczyk, "Reversal of wave momentum in isotropic left-handed media," Phys. Rev. A 75, 053810 (2007).
[CrossRef]

Kong, J.

Kong, J. A.

B. A. Kemp, J. A. Kong, and T. Grzegorczyk, "Reversal of wave momentum in isotropic left-handed media," Phys. Rev. A 75, 053810 (2007).
[CrossRef]

Loudon, R.

S. M. Barnett and R. Loudon, "On the electromagnetic force on a dielectric medium," J. Phys. B: At. Mol. Opt. Phys. 39, S671-S684 (2006).
[CrossRef]

R. Loudon, S. M. Barnett, and C. Baxter, "Radiation pressure and momentum transfer in dielectrics: the photon drag effect," Phys. Rev. A 71, 063802 (2005).
[CrossRef]

R. Loudon, "Radiation pressure and momentum in dielectrics," Fortschr. Phys. 52, 1134-1140 (2004).
[CrossRef]

R. Loudon, "Theory of the radiation pressure on dielectric surfaces," J. Mod. Opt. 49, 821-838 (2002).

Mansuripur, M.

Moloney, J. V.

M. Mansuripur, A. R. Zakharian, and J. V. Moloney, "Equivalence of total force (and torque) for two formulations of the Lorentz law," SPIE Proc. 6326, 63260G (2006).

M. Mansuripur, A. R. Zakharian, and J. V. Moloney, "Radiation pressure on a dielectric wedge," Opt. Express 13, 2064-2074 (2005).
[CrossRef]

Nelson, D. F.

D. F. Nelson, "Momentum, pseudomomentum, and wave momentum: Toward resolving the Minkowski-Abraham controversy," Phys. Rev. A 44, 3985 (1991).
[CrossRef]

Shockley, W.

W. Shockley, "Hidden linear momentum related to the ?·E term for a Dirac-electron wave packet in an electric field," Phys. Rev. Lett. 20, 343-346 (1968).
[CrossRef]

W. Shockley and R. P. James, "Try simplest cases discovery of hidden momentum forces on magnetic currents," Phys. Rev. Lett. 18, 876-879 (1967).
[CrossRef]

Tellegen, B. D. H.

B. D. H. Tellegen, "Magnetic-Dipole Models," Am. J. Phys. 30, 650 (1962).
[CrossRef]

Vaidman, L.

L. Vaidman, "Torque and force on a magnetic dipole," Am. J. Phys. 58, 978-983 (1990).
[CrossRef]

Yaghjian, A. D.

A. D. Yaghjian, "Electromagnetic forces on point dipoles," IEEE Anten. Prop. Soc. Symp. 4, 2868-2871 (1999).

Zakharian, A. R.

M. Mansuripur, A. R. Zakharian, and J. V. Moloney, "Equivalence of total force (and torque) for two formulations of the Lorentz law," SPIE Proc. 6326, 63260G (2006).

M. Mansuripur, A. R. Zakharian, and J. V. Moloney, "Radiation pressure on a dielectric wedge," Opt. Express 13, 2064-2074 (2005).
[CrossRef]

Am. J. Phys.

L. Vaidman, "Torque and force on a magnetic dipole," Am. J. Phys. 58, 978-983 (1990).
[CrossRef]

B. D. H. Tellegen, "Magnetic-Dipole Models," Am. J. Phys. 30, 650 (1962).
[CrossRef]

Fortschr. Phys.

R. Loudon, "Radiation pressure and momentum in dielectrics," Fortschr. Phys. 52, 1134-1140 (2004).
[CrossRef]

IEEE Anten. Prop. Soc. Symp.

A. D. Yaghjian, "Electromagnetic forces on point dipoles," IEEE Anten. Prop. Soc. Symp. 4, 2868-2871 (1999).

J. Mod. Opt.

R. Loudon, "Theory of the radiation pressure on dielectric surfaces," J. Mod. Opt. 49, 821-838 (2002).

J. Phys. B: At. Mol. Opt. Phys.

S. M. Barnett and R. Loudon, "On the electromagnetic force on a dielectric medium," J. Phys. B: At. Mol. Opt. Phys. 39, S671-S684 (2006).
[CrossRef]

Opt. Express

Phys. Reports

I. Brevik, "Experiments in phenomenological electrodynamics and the electromagnetic energy-momentum. tensor," Phys. Reports 52, 133-201 (1979).
[CrossRef]

Phys. Rev. A

J. P. Gordon, "Radiation forces and momenta in dielectric media," Phys. Rev. A 8, 14-21 (1973).
[CrossRef]

D. F. Nelson, "Momentum, pseudomomentum, and wave momentum: Toward resolving the Minkowski-Abraham controversy," Phys. Rev. A 44, 3985 (1991).
[CrossRef]

R. Loudon, S. M. Barnett, and C. Baxter, "Radiation pressure and momentum transfer in dielectrics: the photon drag effect," Phys. Rev. A 71, 063802 (2005).
[CrossRef]

B. A. Kemp, J. A. Kong, and T. Grzegorczyk, "Reversal of wave momentum in isotropic left-handed media," Phys. Rev. A 75, 053810 (2007).
[CrossRef]

Phys. Rev. Lett.

W. Shockley and R. P. James, "Try simplest cases discovery of hidden momentum forces on magnetic currents," Phys. Rev. Lett. 18, 876-879 (1967).
[CrossRef]

W. Shockley, "Hidden linear momentum related to the ?·E term for a Dirac-electron wave packet in an electric field," Phys. Rev. Lett. 20, 343-346 (1968).
[CrossRef]

SPIE Proc.

M. Mansuripur, "Momentum of the electromagnetic field in transparent dielectric media," SPIE Proc. 6644, 664413 (2007).

M. Mansuripur, "Radiation pressure and the distribution of electromagnetic force in dielectric media," SPIE Proc. 5930, 154-160 (2005).

M. Mansuripur, A. R. Zakharian, and J. V. Moloney, "Equivalence of total force (and torque) for two formulations of the Lorentz law," SPIE Proc. 6326, 63260G (2006).

Other

P. Penfield and H. A. Haus, Electrodynamics of Moving Media, (MIT Press, Cambridge, 1967).

R. P.  Feynman, R. B.  Leighton, and M. Sands, The Feynman Lectures on Physics, (Addison-Wesley, Reading, Massachusetts 1964) Vol. 2, Chap. 27.

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