Abstract

It is proposed a natural and consistent division of the momentum of electromagnetic waves in linear, non-dispersive and non-absorptive dielectric and magnetic media into material and electromagnetic parts. The material part is calculated using directly the Lorentz force law and the electromagnetic momentum density has the form ε 0 E × B, without an explicit dependence on the properties of the media. The consistency of the treatment is verified through the obtention of a correct momentum balance equation in many examples and showing the compatibility of the division with the Einstein’s theory of relativity by the use of a gedanken experiment. An experimental prediction for the radiation pressure on mirrors immersed in linear dielectric and magnetic media is also made.

© 2010 Optical Society of America

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  1. R. N. C. Pfeifer, T. A. Nieminen, N. R. Heckenberg and H. Rubinsztein-Dunlop, "Colloquium: Momentum of an electromagnetic wave in dielectric media," Rev. Mod. Phys. 79, 1197-1216 (2007).
    [CrossRef]
  2. R. V. Jones and J. C. S. Richards, "The Pressure of Radiation in a Refracting Medium," Proc. R. Soc. London A 221, 480-498 (1954).
    [CrossRef]
  3. R. V. Jones and B. Leslie, "The measurement of optical radiation pressure in dispersive media," Proc. R. Soc. London A 360, 347-363 (1978).
    [CrossRef]
  4. A. Ashkin and J. M. Dziedzic, "Radiation pressure on a free liquid surface," Phys. Rev. Lett. 30, 139-142 (1973).
    [CrossRef]
  5. A. F. Gibson, M. F. Kimmitt, A. O. Koohian, D. E. Evans and G. F. D. Levy, "A study of radiation pressure in a refractive medium by the photon drag effect," Proc. R. Soc. London A 370, 303-311 (1980).
    [CrossRef]
  6. G. K. Campbell, A. E. Leanhardt, J. Mun, M. Boyd, E.W. Streed, W. Ketterle and D. E. Pritchard, "Photon recoil momentum in dispersive media," Phys. Rev. Lett. 94, 170403 (2005).
    [CrossRef] [PubMed]
  7. O. R. Frisch, "Take a photon...," Contemp. Phys. 7, 45-53 (1965).
    [CrossRef]
  8. I. Brevik, "Phenomenological photons and the uncertainty principle," Eur. J. Phys. 2, 37-43 (1981).
    [CrossRef]
  9. R. Loudon, "Radiation pressure and momentum in dielectrics," Fortschr. Phys. 52, 1134-1140 (2004).
    [CrossRef]
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    [CrossRef]
  11. G. B. Walker and G. Walker, "Mechanical forces in a dielectric due to electromagnetic fields," Can. J. Phys. 55, 2121-2127 (1977).
    [CrossRef]
  12. W. She, J. Yu and R. Feng, "Observation of a Push Force on the End Face of a Nanometer Silica Filament Exerted by Outgoing Light," Phys. Rev. Lett. 101, 243601 (2008).
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    [CrossRef]
  16. 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]
  17. U. Leonhardt, "Energy-momentum balance in quantum dielectrics," Phys. Rev. A 73, 032108 (2006).
    [CrossRef]
  18. W. Israel, "Relativistic effects in dielectrics: an experimental decision between Abraham and Minkowski?," Phys. Lett. 67B, 125-128 (1977).
  19. M. Mansuripur, "Comment on 'Observation of a Push Force on the End Face of a Nanometer Silica Filament Exerted by Outgoing Light'," Phys. Rev. Lett. 103, 019301 (2009).
    [CrossRef] [PubMed]
  20. M. Mansuripur and A. R. Zakharian, "Theoretical analysis of the force on the end face of a nanofilament exerted by an outgoing light pulse," Phys. Rev. A 80, 023823 (2009).
    [CrossRef]
  21. I. Brevik, "Comment on ‘Observation of a Push Force on the End Face of a Nanometer Silica Filament Exerted by Outgoing Light’," Phys. Rev. Lett. 103, 219301 (2009).
    [CrossRef]
  22. R. N. C. Pfeifer, T. A. Nieminen, N. R. Heckenberg and H. Rubinsztein-Dunlop, "Constraining validity of the Minkowski energy-momentum tensor," Phys. Rev. A 79, 023813 (2009).
    [CrossRef]
  23. Y. N. Obukhov and F. W. Hehl, "Electromagnetic energy-momentum and forces in matter," Phys. Lett. A 311, 277-284 (2003).
    [CrossRef]
  24. R. Loudon, "Theory of the forces exerted by Laguerre-Gaussian light beams on dielectrics," Phys. Rev. A 68, 013806 (2003).
    [CrossRef]
  25. M. Mansuripur, "Radiation pressure and the linear momentum of the electromagnetic field," Opt. Express 12, 5375-5401 (2004).
    [CrossRef] [PubMed]
  26. M. Scalora, G. D’Aguanno, N. Mattiucci, M. J. Bloemer, M. Centini, C. Sibilia and J. W. Haus, "Radiation pressure of light pulses and conservation of linear momentum in dispersive media," Phys. Rev. E 73, 056604 (2006).
    [CrossRef]
  27. E. A. Hinds and S. M. Barnett, "Momentum Exchange between Light and a Single Atom: Abraham or Minkowski?," Phys. Rev. Lett. 102, 050403 (2009).
    [CrossRef] [PubMed]
  28. M. Mansuripur, "Radiation pressure and the linear momentum of the electromagnetic field in magnetic media," Opt. Express 15, 13502-13518 (2007).
    [CrossRef] [PubMed]
  29. M. Mansuripur, "Radiation pressure on submerged mirrors: implications for the momentum of light in dielectric media," Opt. Express 15, 2677-2682 (2007).
    [CrossRef] [PubMed]
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  32. W. Schockley and R. P. James, "Try simple cases discovery of hidden momentum forces on magnetic currents," Phys. Rev. Lett. 18, 876-879 (1967).
    [CrossRef]
  33. L. Vaidman, "Torque and force on a magnetic dipole," Am. J. Phys. 58, 978-983 (1990).
    [CrossRef]

2009

M. Mansuripur, "Comment on 'Observation of a Push Force on the End Face of a Nanometer Silica Filament Exerted by Outgoing Light'," Phys. Rev. Lett. 103, 019301 (2009).
[CrossRef] [PubMed]

M. Mansuripur and A. R. Zakharian, "Theoretical analysis of the force on the end face of a nanofilament exerted by an outgoing light pulse," Phys. Rev. A 80, 023823 (2009).
[CrossRef]

I. Brevik, "Comment on ‘Observation of a Push Force on the End Face of a Nanometer Silica Filament Exerted by Outgoing Light’," Phys. Rev. Lett. 103, 219301 (2009).
[CrossRef]

R. N. C. Pfeifer, T. A. Nieminen, N. R. Heckenberg and H. Rubinsztein-Dunlop, "Constraining validity of the Minkowski energy-momentum tensor," Phys. Rev. A 79, 023813 (2009).
[CrossRef]

E. A. Hinds and S. M. Barnett, "Momentum Exchange between Light and a Single Atom: Abraham or Minkowski?," Phys. Rev. Lett. 102, 050403 (2009).
[CrossRef] [PubMed]

2008

W. She, J. Yu and R. Feng, "Observation of a Push Force on the End Face of a Nanometer Silica Filament Exerted by Outgoing Light," Phys. Rev. Lett. 101, 243601 (2008).
[CrossRef] [PubMed]

2007

R. N. C. Pfeifer, T. A. Nieminen, N. R. Heckenberg and H. Rubinsztein-Dunlop, "Colloquium: Momentum of an electromagnetic wave in dielectric media," Rev. Mod. Phys. 79, 1197-1216 (2007).
[CrossRef]

M. Mansuripur, "Radiation pressure and the linear momentum of the electromagnetic field in magnetic media," Opt. Express 15, 13502-13518 (2007).
[CrossRef] [PubMed]

M. Mansuripur, "Radiation pressure on submerged mirrors: implications for the momentum of light in dielectric media," Opt. Express 15, 2677-2682 (2007).
[CrossRef] [PubMed]

2006

M. Scalora, G. D’Aguanno, N. Mattiucci, M. J. Bloemer, M. Centini, C. Sibilia and J. W. Haus, "Radiation pressure of light pulses and conservation of linear momentum in dispersive media," Phys. Rev. E 73, 056604 (2006).
[CrossRef]

U. Leonhardt, "Energy-momentum balance in quantum dielectrics," Phys. Rev. A 73, 032108 (2006).
[CrossRef]

2005

G. K. Campbell, A. E. Leanhardt, J. Mun, M. Boyd, E.W. Streed, W. Ketterle and D. E. Pritchard, "Photon recoil momentum in dispersive media," Phys. Rev. Lett. 94, 170403 (2005).
[CrossRef] [PubMed]

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]

2004

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

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

2003

Y. N. Obukhov and F. W. Hehl, "Electromagnetic energy-momentum and forces in matter," Phys. Lett. A 311, 277-284 (2003).
[CrossRef]

R. Loudon, "Theory of the forces exerted by Laguerre-Gaussian light beams on dielectrics," Phys. Rev. A 68, 013806 (2003).
[CrossRef]

2002

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

1990

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

1981

I. Brevik, "Phenomenological photons and the uncertainty principle," Eur. J. Phys. 2, 37-43 (1981).
[CrossRef]

1980

A. F. Gibson, M. F. Kimmitt, A. O. Koohian, D. E. Evans and G. F. D. Levy, "A study of radiation pressure in a refractive medium by the photon drag effect," Proc. R. Soc. London A 370, 303-311 (1980).
[CrossRef]

1978

R. V. Jones and B. Leslie, "The measurement of optical radiation pressure in dispersive media," Proc. R. Soc. London A 360, 347-363 (1978).
[CrossRef]

1977

G. B. Walker and G. Walker, "Mechanical forces in a dielectric due to electromagnetic fields," Can. J. Phys. 55, 2121-2127 (1977).
[CrossRef]

W. Israel, "Relativistic effects in dielectrics: an experimental decision between Abraham and Minkowski?," Phys. Lett. 67B, 125-128 (1977).

1975

G. B. Walker, D. G. Lahoz and G. Walker, "Measurement of the Abraham force in a barium titanate specimen," Can. J. Phys. 53, 2577-2586 (1975).
[CrossRef]

1973

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

A. Ashkin and J. M. Dziedzic, "Radiation pressure on a free liquid surface," Phys. Rev. Lett. 30, 139-142 (1973).
[CrossRef]

1967

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

1965

O. R. Frisch, "Take a photon...," Contemp. Phys. 7, 45-53 (1965).
[CrossRef]

1954

R. V. Jones and J. C. S. Richards, "The Pressure of Radiation in a Refracting Medium," Proc. R. Soc. London A 221, 480-498 (1954).
[CrossRef]

Ashkin, A.

A. Ashkin and J. M. Dziedzic, "Radiation pressure on a free liquid surface," Phys. Rev. Lett. 30, 139-142 (1973).
[CrossRef]

Barnett, S. M.

E. A. Hinds and S. M. Barnett, "Momentum Exchange between Light and a Single Atom: Abraham or Minkowski?," Phys. Rev. Lett. 102, 050403 (2009).
[CrossRef] [PubMed]

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]

Bloemer, M. J.

M. Scalora, G. D’Aguanno, N. Mattiucci, M. J. Bloemer, M. Centini, C. Sibilia and J. W. Haus, "Radiation pressure of light pulses and conservation of linear momentum in dispersive media," Phys. Rev. E 73, 056604 (2006).
[CrossRef]

Boyd, M.

G. K. Campbell, A. E. Leanhardt, J. Mun, M. Boyd, E.W. Streed, W. Ketterle and D. E. Pritchard, "Photon recoil momentum in dispersive media," Phys. Rev. Lett. 94, 170403 (2005).
[CrossRef] [PubMed]

Brevik, I.

I. Brevik, "Comment on ‘Observation of a Push Force on the End Face of a Nanometer Silica Filament Exerted by Outgoing Light’," Phys. Rev. Lett. 103, 219301 (2009).
[CrossRef]

I. Brevik, "Phenomenological photons and the uncertainty principle," Eur. J. Phys. 2, 37-43 (1981).
[CrossRef]

Campbell, G. K.

G. K. Campbell, A. E. Leanhardt, J. Mun, M. Boyd, E.W. Streed, W. Ketterle and D. E. Pritchard, "Photon recoil momentum in dispersive media," Phys. Rev. Lett. 94, 170403 (2005).
[CrossRef] [PubMed]

Centini, M.

M. Scalora, G. D’Aguanno, N. Mattiucci, M. J. Bloemer, M. Centini, C. Sibilia and J. W. Haus, "Radiation pressure of light pulses and conservation of linear momentum in dispersive media," Phys. Rev. E 73, 056604 (2006).
[CrossRef]

D’Aguanno, G.

M. Scalora, G. D’Aguanno, N. Mattiucci, M. J. Bloemer, M. Centini, C. Sibilia and J. W. Haus, "Radiation pressure of light pulses and conservation of linear momentum in dispersive media," Phys. Rev. E 73, 056604 (2006).
[CrossRef]

Dziedzic, J. M.

A. Ashkin and J. M. Dziedzic, "Radiation pressure on a free liquid surface," Phys. Rev. Lett. 30, 139-142 (1973).
[CrossRef]

Evans, D. E.

A. F. Gibson, M. F. Kimmitt, A. O. Koohian, D. E. Evans and G. F. D. Levy, "A study of radiation pressure in a refractive medium by the photon drag effect," Proc. R. Soc. London A 370, 303-311 (1980).
[CrossRef]

Feng, R.

W. She, J. Yu and R. Feng, "Observation of a Push Force on the End Face of a Nanometer Silica Filament Exerted by Outgoing Light," Phys. Rev. Lett. 101, 243601 (2008).
[CrossRef] [PubMed]

Frisch, O. R.

O. R. Frisch, "Take a photon...," Contemp. Phys. 7, 45-53 (1965).
[CrossRef]

Gibson, A. F.

A. F. Gibson, M. F. Kimmitt, A. O. Koohian, D. E. Evans and G. F. D. Levy, "A study of radiation pressure in a refractive medium by the photon drag effect," Proc. R. Soc. London A 370, 303-311 (1980).
[CrossRef]

Gordon, J. P.

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

Haus, J. W.

M. Scalora, G. D’Aguanno, N. Mattiucci, M. J. Bloemer, M. Centini, C. Sibilia and J. W. Haus, "Radiation pressure of light pulses and conservation of linear momentum in dispersive media," Phys. Rev. E 73, 056604 (2006).
[CrossRef]

Heckenberg, N. R.

R. N. C. Pfeifer, T. A. Nieminen, N. R. Heckenberg and H. Rubinsztein-Dunlop, "Constraining validity of the Minkowski energy-momentum tensor," Phys. Rev. A 79, 023813 (2009).
[CrossRef]

R. N. C. Pfeifer, T. A. Nieminen, N. R. Heckenberg and H. Rubinsztein-Dunlop, "Colloquium: Momentum of an electromagnetic wave in dielectric media," Rev. Mod. Phys. 79, 1197-1216 (2007).
[CrossRef]

Hehl, F. W.

Y. N. Obukhov and F. W. Hehl, "Electromagnetic energy-momentum and forces in matter," Phys. Lett. A 311, 277-284 (2003).
[CrossRef]

Hinds, E. A.

E. A. Hinds and S. M. Barnett, "Momentum Exchange between Light and a Single Atom: Abraham or Minkowski?," Phys. Rev. Lett. 102, 050403 (2009).
[CrossRef] [PubMed]

Israel, W.

W. Israel, "Relativistic effects in dielectrics: an experimental decision between Abraham and Minkowski?," Phys. Lett. 67B, 125-128 (1977).

James, R. P.

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

Jones, R. V.

R. V. Jones and B. Leslie, "The measurement of optical radiation pressure in dispersive media," Proc. R. Soc. London A 360, 347-363 (1978).
[CrossRef]

R. V. Jones and J. C. S. Richards, "The Pressure of Radiation in a Refracting Medium," Proc. R. Soc. London A 221, 480-498 (1954).
[CrossRef]

Ketterle, W.

G. K. Campbell, A. E. Leanhardt, J. Mun, M. Boyd, E.W. Streed, W. Ketterle and D. E. Pritchard, "Photon recoil momentum in dispersive media," Phys. Rev. Lett. 94, 170403 (2005).
[CrossRef] [PubMed]

Kimmitt, M. F.

A. F. Gibson, M. F. Kimmitt, A. O. Koohian, D. E. Evans and G. F. D. Levy, "A study of radiation pressure in a refractive medium by the photon drag effect," Proc. R. Soc. London A 370, 303-311 (1980).
[CrossRef]

Koohian, A. O.

A. F. Gibson, M. F. Kimmitt, A. O. Koohian, D. E. Evans and G. F. D. Levy, "A study of radiation pressure in a refractive medium by the photon drag effect," Proc. R. Soc. London A 370, 303-311 (1980).
[CrossRef]

Lahoz, D. G.

G. B. Walker, D. G. Lahoz and G. Walker, "Measurement of the Abraham force in a barium titanate specimen," Can. J. Phys. 53, 2577-2586 (1975).
[CrossRef]

Leanhardt, A. E.

G. K. Campbell, A. E. Leanhardt, J. Mun, M. Boyd, E.W. Streed, W. Ketterle and D. E. Pritchard, "Photon recoil momentum in dispersive media," Phys. Rev. Lett. 94, 170403 (2005).
[CrossRef] [PubMed]

Leonhardt, U.

U. Leonhardt, "Energy-momentum balance in quantum dielectrics," Phys. Rev. A 73, 032108 (2006).
[CrossRef]

Leslie, B.

R. V. Jones and B. Leslie, "The measurement of optical radiation pressure in dispersive media," Proc. R. Soc. London A 360, 347-363 (1978).
[CrossRef]

Levy, G. F. D.

A. F. Gibson, M. F. Kimmitt, A. O. Koohian, D. E. Evans and G. F. D. Levy, "A study of radiation pressure in a refractive medium by the photon drag effect," Proc. R. Soc. London A 370, 303-311 (1980).
[CrossRef]

Loudon, R.

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 forces exerted by Laguerre-Gaussian light beams on dielectrics," Phys. Rev. A 68, 013806 (2003).
[CrossRef]

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

Mansuripur, M.

M. Mansuripur, "Comment on 'Observation of a Push Force on the End Face of a Nanometer Silica Filament Exerted by Outgoing Light'," Phys. Rev. Lett. 103, 019301 (2009).
[CrossRef] [PubMed]

M. Mansuripur and A. R. Zakharian, "Theoretical analysis of the force on the end face of a nanofilament exerted by an outgoing light pulse," Phys. Rev. A 80, 023823 (2009).
[CrossRef]

M. Mansuripur, "Radiation pressure on submerged mirrors: implications for the momentum of light in dielectric media," Opt. Express 15, 2677-2682 (2007).
[CrossRef] [PubMed]

M. Mansuripur, "Radiation pressure and the linear momentum of the electromagnetic field in magnetic media," Opt. Express 15, 13502-13518 (2007).
[CrossRef] [PubMed]

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

Mattiucci, N.

M. Scalora, G. D’Aguanno, N. Mattiucci, M. J. Bloemer, M. Centini, C. Sibilia and J. W. Haus, "Radiation pressure of light pulses and conservation of linear momentum in dispersive media," Phys. Rev. E 73, 056604 (2006).
[CrossRef]

Mun, J.

G. K. Campbell, A. E. Leanhardt, J. Mun, M. Boyd, E.W. Streed, W. Ketterle and D. E. Pritchard, "Photon recoil momentum in dispersive media," Phys. Rev. Lett. 94, 170403 (2005).
[CrossRef] [PubMed]

Nieminen, T. A.

R. N. C. Pfeifer, T. A. Nieminen, N. R. Heckenberg and H. Rubinsztein-Dunlop, "Constraining validity of the Minkowski energy-momentum tensor," Phys. Rev. A 79, 023813 (2009).
[CrossRef]

R. N. C. Pfeifer, T. A. Nieminen, N. R. Heckenberg and H. Rubinsztein-Dunlop, "Colloquium: Momentum of an electromagnetic wave in dielectric media," Rev. Mod. Phys. 79, 1197-1216 (2007).
[CrossRef]

Obukhov, Y. N.

Y. N. Obukhov and F. W. Hehl, "Electromagnetic energy-momentum and forces in matter," Phys. Lett. A 311, 277-284 (2003).
[CrossRef]

Pfeifer, R. N. C.

R. N. C. Pfeifer, T. A. Nieminen, N. R. Heckenberg and H. Rubinsztein-Dunlop, "Constraining validity of the Minkowski energy-momentum tensor," Phys. Rev. A 79, 023813 (2009).
[CrossRef]

R. N. C. Pfeifer, T. A. Nieminen, N. R. Heckenberg and H. Rubinsztein-Dunlop, "Colloquium: Momentum of an electromagnetic wave in dielectric media," Rev. Mod. Phys. 79, 1197-1216 (2007).
[CrossRef]

Pritchard, D. E.

G. K. Campbell, A. E. Leanhardt, J. Mun, M. Boyd, E.W. Streed, W. Ketterle and D. E. Pritchard, "Photon recoil momentum in dispersive media," Phys. Rev. Lett. 94, 170403 (2005).
[CrossRef] [PubMed]

Richards, J. C. S.

R. V. Jones and J. C. S. Richards, "The Pressure of Radiation in a Refracting Medium," Proc. R. Soc. London A 221, 480-498 (1954).
[CrossRef]

Rubinsztein-Dunlop, H.

R. N. C. Pfeifer, T. A. Nieminen, N. R. Heckenberg and H. Rubinsztein-Dunlop, "Constraining validity of the Minkowski energy-momentum tensor," Phys. Rev. A 79, 023813 (2009).
[CrossRef]

R. N. C. Pfeifer, T. A. Nieminen, N. R. Heckenberg and H. Rubinsztein-Dunlop, "Colloquium: Momentum of an electromagnetic wave in dielectric media," Rev. Mod. Phys. 79, 1197-1216 (2007).
[CrossRef]

Scalora, M.

M. Scalora, G. D’Aguanno, N. Mattiucci, M. J. Bloemer, M. Centini, C. Sibilia and J. W. Haus, "Radiation pressure of light pulses and conservation of linear momentum in dispersive media," Phys. Rev. E 73, 056604 (2006).
[CrossRef]

Schockley, W.

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

She, W.

W. She, J. Yu and R. Feng, "Observation of a Push Force on the End Face of a Nanometer Silica Filament Exerted by Outgoing Light," Phys. Rev. Lett. 101, 243601 (2008).
[CrossRef] [PubMed]

Sibilia, C.

M. Scalora, G. D’Aguanno, N. Mattiucci, M. J. Bloemer, M. Centini, C. Sibilia and J. W. Haus, "Radiation pressure of light pulses and conservation of linear momentum in dispersive media," Phys. Rev. E 73, 056604 (2006).
[CrossRef]

Streed, E.W.

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[CrossRef] [PubMed]

W. She, J. Yu and R. Feng, "Observation of a Push Force on the End Face of a Nanometer Silica Filament Exerted by Outgoing Light," Phys. Rev. Lett. 101, 243601 (2008).
[CrossRef] [PubMed]

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Figures (2)

Fig. 1.
Fig. 1.

(a) A pulse with total momentum P i propagates in medium 1 with electric and magnetic susceptibilities χ e1 and χ m1 towards the interface with medium 2 with electric and magnetic susceptibilities χ e2 and χ m2. (b) The resultant reflected and transmitted pulses with total momentum P r and P t.

Fig. 2.
Fig. 2.

(a) A pulse with total momentum P i propagates in medium 1 with electric and magnetic susceptibilities χ e1 and χ m1 towards medium 2 with electric and magnetic susceptibilities χ e2 and χ m2. There is an antireflection coating layer between media 1 and 2 consisted of a material with electric and magnetic susceptibilities χ e and χ m such that ( 1 + χ e ) = ( 1 + χ e 1 ) ( 1 + χ e 2 ) and ( 1 + χ m ) = ( 1 + χ m 1 ) ( 1 + χ m 2 ) . The thickness of the layer is λ′/4, λ′ being the wavelength of the central frequency of the pulse in this medium. Despite the figure, it is assumed that the pulse is much larger than the layer. (b) The pulse was totally transmitted to medium 2 and has total momentum P 2.

Equations (33)

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F dip . = ( p · ) E + d p d t × B ,
f diel . = χ e ε 0 [ ( 1 2 E 2 ) + t ( E × B ) ] .
f = χ e ε 0 ( 1 2 E 2 ) f 1 + χ e ε 0 t ( E × B ) f 2 + ( × M ) × B f 3 .
E i ( z , t ) = 1 2 π + d ω E ˜ ( ω ) exp [ i ( c z ωt ) ] x ̂ ,
f 1 = χ e ε 0 2 t ( E × B ) ,
f 3 = χ m ( 1 + χ e ) ε 0 2 t ( E × B ) .
p mat ( t ) = t d t f ( t ) = ( χ e + χ m + χ e χ m ) 2 ε 0 E ( t ) × B ( t ) .
P 0 = d 3 r ε 0 E i × B i = ε 0 dx d y + d ω E ˜ ( ω ) 2 z ̂ .
P i = ( 1 + χ e 1 + χ m 1 + χ e 1 χ m 1 2 ) P 0 , P r = r 2 P i , P t = t 2 ( 1 + χ e 2 + χ m 2 + χ e 2 χ m 2 2 ) P 0 ,
P 1 = + d t d x d y 0 d z χ e 1 ε 0 z ( E i · E r ) z ̂ = r χ e 1 P 0 ,
f 3 = χ m μ 0 ( 1 + χ m ) ( B 2 2 ) .
P ' 3 = r χ m 1 ( 1 + χ e 1 ) P 0 .
f 3 | z = 0 = 1 δz [ χ m 2 1 + χ m 2 B 2 χ m 1 1 + χ m 1 B 1 ] ( x ̂ ) μ 0 × B ,
P 4 = + d t d x d y δz / 2 + δz / 2 d z f 3 = ( χ m 1 χ m 2 ) ( 1 + χ e 1 ) ( 1 r ) 2 2 [ 1 + 1 + χ m 2 1 + χ m 1 ] P 0 .
r = ( 1 + χ e 1 ) ( 1 + χ m 2 ) ( 1 + χ e 2 ) ( 1 + χ m 1 ) ( 1 + χ e 1 ) ( 1 + χ m 2 ) + ( 1 + χ e 2 ) ( 1 + χ m 1 ) ,
t = 2 ( 1 + χ e 1 ) ( 1 + χ m 2 ) ( 1 + χ e 1 ) ( 1 + χ m 2 ) + ( 1 + χ e 2 ) ( 1 + χ m 1 ) ,
P r + P t + P 1 + P 3 + P 4 = P i .
B mir = 1 2 π + d ω 2 n 1 ( 1 + χ m 1 ) c E ˜ ( ω ) exp [ ( κ + ik ) z iωt ] y ̂ ,
P mir = d x d y 0 + d z + d t J mir × B mir = d x d y 0 + d ω 2 ε 0 ( 1 + χ e 1 ) ( 1 + χ m 1 ) E ˜ ( ω ) 2 ( κ ik ) κ z ̂ .
P mir = 2 ( 1 + χ e 1 1 + χ m 1 ) P 0 ,
U i = d 3 r ( 1 + χ e 1 ) ε 0 E i 2 = ( 1 + χ e 1 ) c n 1 P 0 .
P mir 2 [ 1 + ( χ e 1 χ m 1 χ e 1 χ m 1 ) sin 2 ( ϕ 2 ) ] P 0 ,
E 2 ( z , t ) = [ ( 1 + χ e 1 ) ( 1 + χ m 2 ) ( 1 + χ e 2 ) ( 1 + χ m 1 ) ] 1 / 4 1 2 π + d ω E ˜ ( ω ) exp [ i ( n 2 ω c z ωt ) ] x ̂ .
P i = ( 1 + χ e 1 + χ m 1 + χ e 1 χ m 1 2 ) P 0 ,
P 2 = [ ( 1 + χ e 1 ) ( 1 + χ m 2 ) ( 1 + χ e 2 ) ( 1 + χ m 1 ) ] 1 / 2 ( 1 + χ e 2 + χ m 2 + χ e 2 χ m 2 2 ) P 0 ,
E | z = 0 = E 1 | z = 0 , E | z = λ / 4 = E 2 | z = λ / 4 , B | z = 0 1 + χ m = B 1 | z = 0 1 + χ m 1 , B | z = λ / 4 1 + χ m = B 2 | z = λ / 4 1 + χ m 2 .
P a = d x d y 0 λ / 4 d z + d t f = χ e + χ m + χ e χ m 2 [ ( 1 + χ e 1 ) ( 1 + χ m 2 ) ( 1 + χ e 2 ) ( 1 + χ m 1 ) 1 ] P 0 .
P b = ( χ m 1 χ m ) ( 2 + χ m 1 + χ m ) ( 1 + χ e 1 ) 2 ( 1 + χ m 1 ) P 0 ,
P c = ( χ m χ m 2 ) ( 2 + χ m + χ m 2 ) ( 1 + χ e 2 ) 2 ( 1 + χ m 2 ) ( 1 + χ e 1 ) ( 1 + χ m 2 ) ( 1 + χ e 2 ) ( 1 + χ m 1 ) P 0 .
P 2 + P = P i
M c 2 Δ z = ħ ω ( n 2 1 ) L .
P slab = n 2 1 χ m 2 n 2 ħ ω c z ̂ .
Δ z = P slab P hid M n 2 L c = ħ ω ( n 2 1 ) L M c 2 ,

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