Abstract

The Abraham-Minkowski dilemma relates to the disputed value of the optical momentum within a dielectric medium and whether the free-space value should be divided (Abraham) or multiplied (Minkowski) by the refractive index. Although undoubtedly simplistic, these two approaches provide intuitive insight to many subtle problems in optical physics. This paper reviews a modified version of the Einstein box argument that supports an Abraham formulation, then considers diffraction within a dielectric medium and shows it supports a simple Minkowski formulation, i.e. that the optical momentum should be multiplied by the refractive index.

© 2008 Optical Society of America

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  1. I. Brevik, "Experiments in phenomenological electrodynamics and the electromagnetic energy-momentum tensor," Phys. Rep. 52, 133-201 (1979).
    [CrossRef]
  2. D. Nelson, "Momentum, pseudomomentum, and wave momentum - toward resolving the Minkowski-Abraham controversy," Phys. Rev. A 44, 3985-3996 (1991).
    [CrossRef] [PubMed]
  3. M. Mansuripur, "Radiation pressure and the linear momentum of the electromagnetic field," Opt. Express 12, 5375-5401 (2004).
    [CrossRef] [PubMed]
  4. U. Leonhardt, "Optics: Momentum in an uncertain light," Nature 444, 823-824 (2006).
    [CrossRef] [PubMed]
  5. 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]
  6. M. Abraham, Rend. Circ. Matem. Palermo 28, 1 (1909).
  7. A. Einstein, "The principle of conservation of the centre of gravity movement and the inertia of energy," Ann. Phys. 20, 627-633 (1906).
    [CrossRef]
  8. S. Weinberg, "Gravitation and Cosmology: Principles and Applications of the General Theory, " p. 46 (1972).
  9. H. Minkowski, Nachr. Ges. Wiss. Gottn Math.-Phys. Kl. 53, 472-525 (1908).
  10. I. Brevik, "Phenomenological photons and the uncertainty principle," Eur. J. Phys. 2, 37-43 (1981).
    [CrossRef]
  11. T. F. Krauss, "Slow light in photonic crystal waveguides," J. Phys. D 40, 2666-2670 (2007)
    [CrossRef]
  12. 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]
  13. J. Guck, R. Ananthakrishnan, H. Mahmood, T. Moon, C. Cunningham, and J. Kas, "The optical stretcher: A novel laser tool to micromanipulate cells," Biophys. J. 81, 767-784 (2001).
    [CrossRef] [PubMed]
  14. A. Gibson, M. Kimmitt, and A. Walker, "Photon drag in germanium," Appl. Phys. Lett. 17, 75-77 (1970).
    [CrossRef]
  15. R. Loudon, S. Barnett, and C. Baxter, "Radiation pressure and momentum transfer in dielectrics: The photon drag effect," Phys. Rev. A 71, 063802 (2005).
    [CrossRef]
  16. M. Kristensen and J. P. Woerdman, "Is photon angular momentum conserved in a dielectric medium?" Phys. Rev. Lett. 72, 2171-2174 (1994).
    [CrossRef] [PubMed]
  17. R. Loudon, "Theory of the radiation pressure on dielectric surfaces," J. Mod. Opt. 49, 821-838 (2002).
    [CrossRef]
  18. R. Loudon and S. M. Barnett, "Theory of the radiation pressure on dielectric slabs, prisms and single surfaces," Opt. Express 14, 11855-11869 (2006).
    [CrossRef] [PubMed]
  19. M. Padgett, S. Barnett, and R. Loudon, "The angular momentum of light inside a dielectric," J. Mod. Opt. 50, 1555-1562 (2003).
  20. R. Loudon, "Theory of the forces exerted by Laguerre-Gaussian light beams on dielectrics," Phys. Rev. A 68, 013806 (2003).
    [CrossRef]
  21. R. Jones and B. Leslie, "The Measurement of Optical Radiation Pressure in Dispersive Media," Proc. Roy. Soc. London A 360, 347-363 (1978).
    [CrossRef]
  22. W. She, J. Yu, and R. Feng, "Observation of a push force on the end face of a nm fiber taper exerted by outgoing light," arXiv:0806.2442v1
  23. M. Mansuripur, "Radiation pressure on submerged mirrors: Implications for the momentum of light in dielectric media," Opt. Express 15, 2677-2682 (2007).
    [CrossRef] [PubMed]
  24. S. M. Barnett and R. Loudon, "On the electromagnetic force on a dielectric medium," J. Phys. B 39, S671-S684 (2006).
    [CrossRef]

2007 (3)

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]

T. F. Krauss, "Slow light in photonic crystal waveguides," J. Phys. D 40, 2666-2670 (2007)
[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]

2006 (3)

R. Loudon and S. M. Barnett, "Theory of the radiation pressure on dielectric slabs, prisms and single surfaces," Opt. Express 14, 11855-11869 (2006).
[CrossRef] [PubMed]

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

U. Leonhardt, "Optics: Momentum in an uncertain light," Nature 444, 823-824 (2006).
[CrossRef] [PubMed]

2005 (2)

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

2004 (1)

2003 (2)

M. Padgett, S. Barnett, and R. Loudon, "The angular momentum of light inside a dielectric," J. Mod. Opt. 50, 1555-1562 (2003).

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

2002 (1)

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

2001 (1)

J. Guck, R. Ananthakrishnan, H. Mahmood, T. Moon, C. Cunningham, and J. Kas, "The optical stretcher: A novel laser tool to micromanipulate cells," Biophys. J. 81, 767-784 (2001).
[CrossRef] [PubMed]

1994 (1)

M. Kristensen and J. P. Woerdman, "Is photon angular momentum conserved in a dielectric medium?" Phys. Rev. Lett. 72, 2171-2174 (1994).
[CrossRef] [PubMed]

1991 (1)

D. Nelson, "Momentum, pseudomomentum, and wave momentum - toward resolving the Minkowski-Abraham controversy," Phys. Rev. A 44, 3985-3996 (1991).
[CrossRef] [PubMed]

1981 (1)

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

1979 (1)

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

1978 (1)

R. Jones and B. Leslie, "The Measurement of Optical Radiation Pressure in Dispersive Media," Proc. Roy. Soc. London A 360, 347-363 (1978).
[CrossRef]

1970 (1)

A. Gibson, M. Kimmitt, and A. Walker, "Photon drag in germanium," Appl. Phys. Lett. 17, 75-77 (1970).
[CrossRef]

1909 (1)

M. Abraham, Rend. Circ. Matem. Palermo 28, 1 (1909).

1908 (1)

H. Minkowski, Nachr. Ges. Wiss. Gottn Math.-Phys. Kl. 53, 472-525 (1908).

1906 (1)

A. Einstein, "The principle of conservation of the centre of gravity movement and the inertia of energy," Ann. Phys. 20, 627-633 (1906).
[CrossRef]

Abraham, M.

M. Abraham, Rend. Circ. Matem. Palermo 28, 1 (1909).

Ananthakrishnan, R.

J. Guck, R. Ananthakrishnan, H. Mahmood, T. Moon, C. Cunningham, and J. Kas, "The optical stretcher: A novel laser tool to micromanipulate cells," Biophys. J. 81, 767-784 (2001).
[CrossRef] [PubMed]

Barnett, S.

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

M. Padgett, S. Barnett, and R. Loudon, "The angular momentum of light inside a dielectric," J. Mod. Opt. 50, 1555-1562 (2003).

Barnett, S. M.

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

R. Loudon and S. M. Barnett, "Theory of the radiation pressure on dielectric slabs, prisms and single surfaces," Opt. Express 14, 11855-11869 (2006).
[CrossRef] [PubMed]

Baxter, C.

R. Loudon, S. Barnett, and C. Baxter, "Radiation pressure and momentum transfer in dielectrics: The photon drag effect," Phys. Rev. A 71, 063802 (2005).
[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, "Phenomenological photons and the uncertainty principle," Eur. J. Phys. 2, 37-43 (1981).
[CrossRef]

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

Cunningham, C.

J. Guck, R. Ananthakrishnan, H. Mahmood, T. Moon, C. Cunningham, and J. Kas, "The optical stretcher: A novel laser tool to micromanipulate cells," Biophys. J. 81, 767-784 (2001).
[CrossRef] [PubMed]

Einstein, A.

A. Einstein, "The principle of conservation of the centre of gravity movement and the inertia of energy," Ann. Phys. 20, 627-633 (1906).
[CrossRef]

Gibson, A.

A. Gibson, M. Kimmitt, and A. Walker, "Photon drag in germanium," Appl. Phys. Lett. 17, 75-77 (1970).
[CrossRef]

Guck, J.

J. Guck, R. Ananthakrishnan, H. Mahmood, T. Moon, C. Cunningham, and J. Kas, "The optical stretcher: A novel laser tool to micromanipulate cells," Biophys. J. 81, 767-784 (2001).
[CrossRef] [PubMed]

Heckenberg, N. R.

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]

Jones, R.

R. Jones and B. Leslie, "The Measurement of Optical Radiation Pressure in Dispersive Media," Proc. Roy. Soc. London A 360, 347-363 (1978).
[CrossRef]

Kas, J.

J. Guck, R. Ananthakrishnan, H. Mahmood, T. Moon, C. Cunningham, and J. Kas, "The optical stretcher: A novel laser tool to micromanipulate cells," Biophys. J. 81, 767-784 (2001).
[CrossRef] [PubMed]

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.

A. Gibson, M. Kimmitt, and A. Walker, "Photon drag in germanium," Appl. Phys. Lett. 17, 75-77 (1970).
[CrossRef]

Krauss, T. F.

T. F. Krauss, "Slow light in photonic crystal waveguides," J. Phys. D 40, 2666-2670 (2007)
[CrossRef]

Kristensen, M.

M. Kristensen and J. P. Woerdman, "Is photon angular momentum conserved in a dielectric medium?" Phys. Rev. Lett. 72, 2171-2174 (1994).
[CrossRef] [PubMed]

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, "Optics: Momentum in an uncertain light," Nature 444, 823-824 (2006).
[CrossRef] [PubMed]

Leslie, B.

R. Jones and B. Leslie, "The Measurement of Optical Radiation Pressure in Dispersive Media," Proc. Roy. Soc. London A 360, 347-363 (1978).
[CrossRef]

Loudon, R.

R. Loudon and S. M. Barnett, "Theory of the radiation pressure on dielectric slabs, prisms and single surfaces," Opt. Express 14, 11855-11869 (2006).
[CrossRef] [PubMed]

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

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

M. Padgett, S. Barnett, and R. Loudon, "The angular momentum of light inside a dielectric," J. Mod. Opt. 50, 1555-1562 (2003).

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]

Mahmood, H.

J. Guck, R. Ananthakrishnan, H. Mahmood, T. Moon, C. Cunningham, and J. Kas, "The optical stretcher: A novel laser tool to micromanipulate cells," Biophys. J. 81, 767-784 (2001).
[CrossRef] [PubMed]

Mansuripur, M.

Minkowski, H.

H. Minkowski, Nachr. Ges. Wiss. Gottn Math.-Phys. Kl. 53, 472-525 (1908).

Moon, T.

J. Guck, R. Ananthakrishnan, H. Mahmood, T. Moon, C. Cunningham, and J. Kas, "The optical stretcher: A novel laser tool to micromanipulate cells," Biophys. J. 81, 767-784 (2001).
[CrossRef] [PubMed]

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]

Nelson, D.

D. Nelson, "Momentum, pseudomomentum, and wave momentum - toward resolving the Minkowski-Abraham controversy," Phys. Rev. A 44, 3985-3996 (1991).
[CrossRef] [PubMed]

Nieminen, T. A.

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]

Padgett, M.

M. Padgett, S. Barnett, and R. Loudon, "The angular momentum of light inside a dielectric," J. Mod. Opt. 50, 1555-1562 (2003).

Pfeifer, R. N. C.

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]

Rubinsztein-Dunlop, H.

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]

Streed, E. 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]

Walker, A.

A. Gibson, M. Kimmitt, and A. Walker, "Photon drag in germanium," Appl. Phys. Lett. 17, 75-77 (1970).
[CrossRef]

Woerdman, J. P.

M. Kristensen and J. P. Woerdman, "Is photon angular momentum conserved in a dielectric medium?" Phys. Rev. Lett. 72, 2171-2174 (1994).
[CrossRef] [PubMed]

Ann. Phys. (1)

A. Einstein, "The principle of conservation of the centre of gravity movement and the inertia of energy," Ann. Phys. 20, 627-633 (1906).
[CrossRef]

Appl. Phys. Lett. (1)

A. Gibson, M. Kimmitt, and A. Walker, "Photon drag in germanium," Appl. Phys. Lett. 17, 75-77 (1970).
[CrossRef]

Biophys. J. (1)

J. Guck, R. Ananthakrishnan, H. Mahmood, T. Moon, C. Cunningham, and J. Kas, "The optical stretcher: A novel laser tool to micromanipulate cells," Biophys. J. 81, 767-784 (2001).
[CrossRef] [PubMed]

Eur. J. Phys. (1)

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

J. Mod. Opt. (2)

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

M. Padgett, S. Barnett, and R. Loudon, "The angular momentum of light inside a dielectric," J. Mod. Opt. 50, 1555-1562 (2003).

J. Phys. B (1)

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

J. Phys. D (1)

T. F. Krauss, "Slow light in photonic crystal waveguides," J. Phys. D 40, 2666-2670 (2007)
[CrossRef]

Nature (1)

U. Leonhardt, "Optics: Momentum in an uncertain light," Nature 444, 823-824 (2006).
[CrossRef] [PubMed]

Opt. Express (3)

Phys. Kl. (1)

H. Minkowski, Nachr. Ges. Wiss. Gottn Math.-Phys. Kl. 53, 472-525 (1908).

Phys. Rep. (1)

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

Phys. Rev. A (3)

D. Nelson, "Momentum, pseudomomentum, and wave momentum - toward resolving the Minkowski-Abraham controversy," Phys. Rev. A 44, 3985-3996 (1991).
[CrossRef] [PubMed]

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

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

Phys. Rev. Lett. (2)

M. Kristensen and J. P. Woerdman, "Is photon angular momentum conserved in a dielectric medium?" Phys. Rev. Lett. 72, 2171-2174 (1994).
[CrossRef] [PubMed]

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]

Proc. Roy. Soc. London A (1)

R. Jones and B. Leslie, "The Measurement of Optical Radiation Pressure in Dispersive Media," Proc. Roy. Soc. London A 360, 347-363 (1978).
[CrossRef]

Rend. Circ. Matem. Palermo (1)

M. Abraham, Rend. Circ. Matem. Palermo 28, 1 (1909).

Rev. Mod. Phys. (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]

Other (2)

S. Weinberg, "Gravitation and Cosmology: Principles and Applications of the General Theory, " p. 46 (1972).

W. She, J. Yu, and R. Feng, "Observation of a push force on the end face of a nm fiber taper exerted by outgoing light," arXiv:0806.2442v1

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Figures (2)

Fig. 1.
Fig. 1.

a) Shows the traditional Einstein box Gedankenexperiment which equates the energy delay of the photon to the mass energy advance of the block b) Shows an equivalent example where the delay arises from a free-space delay line and the recoil force acting on the mirrors causes the block displacement. Both a) and b) are consistent with the Abraham formulation of optical momentum.

Fig. 2.
Fig. 2.

a) Shows how in single slit diffraction the width of the slit introduces a transverse moment spread, the ratio of which to the axial momentum gives the diffractive, angular spreading of the light b) Shows how increasing the refractive index of the medium reduces the angular spreading, which is consistent with an increase in the axial optical momentum and the Minkowski formulation.

Equations (2)

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Δ z = h ̅ ω ( n 1 ) L Mc 2 = h ̅ k 0 ( n 1 ) L Mc
Δ θ = 2 h ̅ Δ x p 0 .

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