Abstract

An exact theory describing the electromagnetic plane-wave force density on a scattering slab having various constitutive parameters and embedded in a background material with complex impedance is presented. It is shown that the constitutive parameters of the background medium contribute to the force density only through the impedance and not the refractive index. Asymptotic expressions show that the total force per unit area for sufficiently thick slabs having overall loss or gain remains positive, irrespective of the refractive index sign in the slab. However, example material responses indicate that for thin slabs the total force per unit area can be negative for both positive and negative refractive index slabs with gain.

© 2012 Optical Society of America

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  1. H. A. Lorentz, The Theory of Electrons, 2nd ed. (Dover, 1952). These are notes from lectures given at Columbia University in the spring of 1906, as collected by H. A.Lorentz in 1909 and then in revised form in 1915.
  2. A. Einstein and J. Laub, “Über die im elektromagnetischen Felde auf ruhende Körper ausgübten ponderomotorischen Kräfte,” Ann. Phys. 331, 541–550 (1908). English commentary on this paper and a reprint of the original paper appears in The Collected Papers of Albert Einstein (Princeton University, 1989), Vol. 2.
    [CrossRef]
  3. P. Penfield and H. A. Haus, Electrodynamics of Moving Media (MIT, 1967).
  4. J. P. Gordon, “Radiation forces and momenta in dielectric media,” Phys. Rev. A 8, 14–21 (1973).
    [CrossRef]
  5. I. Brevik, “Experiments in phenomenological electrodynamics and the electromagnetic energy-momentum tensor,” Phys. Rep. 52, 133–201 (1979).
    [CrossRef]
  6. M. Mansuripur, “Radiation pressure and the linear momentum of the electromagnetic field,” Opt. Express 12, 5375–5401 (2004).
    [CrossRef]
  7. 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]
  8. R. N. C. Pfeifer, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Momentum of an electromagentic wave in dielectric media,” Rev. Mod. Phys. 79, 1197–1216 (2007).
    [CrossRef]
  9. B. A. Kemp, J. A. Kong, and T. M. Grzegorczyk, “Reversal of wave momentum in isotropic left-handed media,” Phys. Rev. A 75, 053810 (2007).
    [CrossRef]
  10. M. Mansuripur, “Resolution of the Abraham-Minkowski controversy,” Opt. Commun. 283, 1997–2005 (2010).
    [CrossRef]
  11. C. Baxter and R. Loudon, “Radiation pressure and photon momentum in dielectrics,” J. Mod. Opt. 57, 830–842 (2010).
    [CrossRef]
  12. S. M. Barnett, “Resolution of the Abraham-Minkowski dilemma,” Phys. Rev. Lett. 104, 070401 (2010).
    [CrossRef]
  13. K. J. Webb and Shivanand, “Negative electromagnetic plane-wave force in gain media,” Phys. Rev. E 84, 057602 (2011).
    [CrossRef]
  14. K. J. Webb and Shivanand, “Electromagnetic plane-wave forces on homogeneous material,” J. Opt. Soc. Am. B 29, 1904–1910 (2012).
  15. K. J. Chau and H. J. Lezec, “Revisiting the Balazs thought experiment in the case of a left-handed material: electromagnetic-pulse-induced displacement of a dispersive, dissipative negative-index slab,” Opt. Express 20, 10138–10162 (2012).
    [CrossRef]
  16. M. Mansuripur, “Trouble with the Lorentz law of force: incompatibility with special relativity and momentum conservation,” Phys. Rev. Lett. 108, 193901 (2012).
    [CrossRef]
  17. E. F. Nichols and G. F. Hull, “The pressure due to radiation,” Phys. Rev. 17, 26–50 (1903).
    [CrossRef]
  18. R. V. Jones and B. Leslie, “The measurement of optical radiation pressure in dispersive media,” Proc. Roy. Soc. A 360, 347–363 (1978).
    [CrossRef]
  19. A. Ashkin, J. M. Dziedzic, J. E. Bjorkholm, and S. Chu, “Observation of a single-beam gradient force optical trap for dielectric particles,” Opt. Lett. 11, 288–290 (1986).
    [CrossRef]
  20. D. G. Grier, “A revolution in optical manipulation,” Nature 424, 810–816 (2003).
    [CrossRef]
  21. 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]
  22. V. G. Veselagao, “Energy, linear momentum, and mass transfer by an electromagnetic wave in a negative-refraction medium,” Phys. Usp. 52, 649–654 (2009).
    [CrossRef]
  23. V. Yannopapas and P. G. Galiatsatos, “Electromagnetic forces in negative-refractive-index metamaterials: a first-principles study,” Phys. Rev. A 77, 043819 (2008).
    [CrossRef]
  24. R. W. Ziolkowski, “Superluminal transmission of information through an electromagnetic metamaterial,” Phys. Rev. E 63, 046604 (2001).
    [CrossRef]
  25. 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]
  26. M. Mansuripur and A. R. Zakharian, “Energy, momentum, and force in classical electrodynamics: application to negative-index media,” Opt. Commun. 283, 4594–4600 (2010).
    [CrossRef]

2012 (3)

2011 (1)

K. J. Webb and Shivanand, “Negative electromagnetic plane-wave force in gain media,” Phys. Rev. E 84, 057602 (2011).
[CrossRef]

2010 (4)

M. Mansuripur, “Resolution of the Abraham-Minkowski controversy,” Opt. Commun. 283, 1997–2005 (2010).
[CrossRef]

C. Baxter and R. Loudon, “Radiation pressure and photon momentum in dielectrics,” J. Mod. Opt. 57, 830–842 (2010).
[CrossRef]

S. M. Barnett, “Resolution of the Abraham-Minkowski dilemma,” Phys. Rev. Lett. 104, 070401 (2010).
[CrossRef]

M. Mansuripur and A. R. Zakharian, “Energy, momentum, and force in classical electrodynamics: application to negative-index media,” Opt. Commun. 283, 4594–4600 (2010).
[CrossRef]

2009 (1)

V. G. Veselagao, “Energy, linear momentum, and mass transfer by an electromagnetic wave in a negative-refraction medium,” Phys. Usp. 52, 649–654 (2009).
[CrossRef]

2008 (1)

V. Yannopapas and P. G. Galiatsatos, “Electromagnetic forces in negative-refractive-index metamaterials: a first-principles study,” Phys. Rev. A 77, 043819 (2008).
[CrossRef]

2007 (2)

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

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

2006 (1)

2005 (2)

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]

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]

2004 (1)

2003 (1)

D. G. Grier, “A revolution in optical manipulation,” Nature 424, 810–816 (2003).
[CrossRef]

2001 (1)

R. W. Ziolkowski, “Superluminal transmission of information through an electromagnetic metamaterial,” Phys. Rev. E 63, 046604 (2001).
[CrossRef]

1986 (1)

1979 (1)

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

1978 (1)

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

1973 (1)

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

1908 (1)

A. Einstein and J. Laub, “Über die im elektromagnetischen Felde auf ruhende Körper ausgübten ponderomotorischen Kräfte,” Ann. Phys. 331, 541–550 (1908). English commentary on this paper and a reprint of the original paper appears in The Collected Papers of Albert Einstein (Princeton University, 1989), Vol. 2.
[CrossRef]

1903 (1)

E. F. Nichols and G. F. Hull, “The pressure due to radiation,” Phys. Rev. 17, 26–50 (1903).
[CrossRef]

Ashkin, A.

Barnett, S. M.

S. M. Barnett, “Resolution of the Abraham-Minkowski dilemma,” Phys. Rev. Lett. 104, 070401 (2010).
[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]

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.

C. Baxter and R. Loudon, “Radiation pressure and photon momentum in dielectrics,” J. Mod. Opt. 57, 830–842 (2010).
[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]

Bjorkholm, J. E.

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]

Brevik, I.

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]

Chau, K. J.

Chu, S.

Dziedzic, J. M.

Einstein, A.

A. Einstein and J. Laub, “Über die im elektromagnetischen Felde auf ruhende Körper ausgübten ponderomotorischen Kräfte,” Ann. Phys. 331, 541–550 (1908). English commentary on this paper and a reprint of the original paper appears in The Collected Papers of Albert Einstein (Princeton University, 1989), Vol. 2.
[CrossRef]

Galiatsatos, P. G.

V. Yannopapas and P. G. Galiatsatos, “Electromagnetic forces in negative-refractive-index metamaterials: a first-principles study,” Phys. Rev. A 77, 043819 (2008).
[CrossRef]

Gordon, J. P.

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

Grier, D. G.

D. G. Grier, “A revolution in optical manipulation,” Nature 424, 810–816 (2003).
[CrossRef]

Grzegorczyk, T. M.

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

Haus, H. A.

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

Heckenberg, N. R.

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

Hull, G. F.

E. F. Nichols and G. F. Hull, “The pressure due to radiation,” Phys. Rev. 17, 26–50 (1903).
[CrossRef]

Jones, R. V.

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

Kemp, B. A.

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

Kong, J. A.

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

Laub, J.

A. Einstein and J. Laub, “Über die im elektromagnetischen Felde auf ruhende Körper ausgübten ponderomotorischen Kräfte,” Ann. Phys. 331, 541–550 (1908). English commentary on this paper and a reprint of the original paper appears in The Collected Papers of Albert Einstein (Princeton University, 1989), Vol. 2.
[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]

Leslie, B.

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

Lezec, H. J.

Lorentz, H. A.

H. A. Lorentz, The Theory of Electrons, 2nd ed. (Dover, 1952). These are notes from lectures given at Columbia University in the spring of 1906, as collected by H. A.Lorentz in 1909 and then in revised form in 1915.

Loudon, R.

C. Baxter and R. Loudon, “Radiation pressure and photon momentum in dielectrics,” J. Mod. Opt. 57, 830–842 (2010).
[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]

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]

Mansuripur, M.

M. Mansuripur, “Trouble with the Lorentz law of force: incompatibility with special relativity and momentum conservation,” Phys. Rev. Lett. 108, 193901 (2012).
[CrossRef]

M. Mansuripur, “Resolution of the Abraham-Minkowski controversy,” Opt. Commun. 283, 1997–2005 (2010).
[CrossRef]

M. Mansuripur and A. R. Zakharian, “Energy, momentum, and force in classical electrodynamics: application to negative-index media,” Opt. Commun. 283, 4594–4600 (2010).
[CrossRef]

M. Mansuripur, “Radiation pressure and the linear momentum of the electromagnetic field,” Opt. Express 12, 5375–5401 (2004).
[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]

Nichols, E. F.

E. F. Nichols and G. F. Hull, “The pressure due to radiation,” Phys. Rev. 17, 26–50 (1903).
[CrossRef]

Nieminen, T. A.

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

Penfield, P.

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

Pfeifer, R. N. C.

R. N. C. Pfeifer, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Momentum of an electromagentic 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]

Rubinsztein-Dunlop, H.

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

Shivanand,

K. J. Webb and Shivanand, “Electromagnetic plane-wave forces on homogeneous material,” J. Opt. Soc. Am. B 29, 1904–1910 (2012).

K. J. Webb and Shivanand, “Negative electromagnetic plane-wave force in gain media,” Phys. Rev. E 84, 057602 (2011).
[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]

Veselagao, V. G.

V. G. Veselagao, “Energy, linear momentum, and mass transfer by an electromagnetic wave in a negative-refraction medium,” Phys. Usp. 52, 649–654 (2009).
[CrossRef]

Webb, K. J.

K. J. Webb and Shivanand, “Electromagnetic plane-wave forces on homogeneous material,” J. Opt. Soc. Am. B 29, 1904–1910 (2012).

K. J. Webb and Shivanand, “Negative electromagnetic plane-wave force in gain media,” Phys. Rev. E 84, 057602 (2011).
[CrossRef]

Yannopapas, V.

V. Yannopapas and P. G. Galiatsatos, “Electromagnetic forces in negative-refractive-index metamaterials: a first-principles study,” Phys. Rev. A 77, 043819 (2008).
[CrossRef]

Zakharian, A. R.

M. Mansuripur and A. R. Zakharian, “Energy, momentum, and force in classical electrodynamics: application to negative-index media,” Opt. Commun. 283, 4594–4600 (2010).
[CrossRef]

Ziolkowski, R. W.

R. W. Ziolkowski, “Superluminal transmission of information through an electromagnetic metamaterial,” Phys. Rev. E 63, 046604 (2001).
[CrossRef]

Ann. Phys. (1)

A. Einstein and J. Laub, “Über die im elektromagnetischen Felde auf ruhende Körper ausgübten ponderomotorischen Kräfte,” Ann. Phys. 331, 541–550 (1908). English commentary on this paper and a reprint of the original paper appears in The Collected Papers of Albert Einstein (Princeton University, 1989), Vol. 2.
[CrossRef]

J. Mod. Opt. (1)

C. Baxter and R. Loudon, “Radiation pressure and photon momentum in dielectrics,” J. Mod. Opt. 57, 830–842 (2010).
[CrossRef]

J. Opt. Soc. Am. B (1)

Nature (1)

D. G. Grier, “A revolution in optical manipulation,” Nature 424, 810–816 (2003).
[CrossRef]

Opt. Commun. (2)

M. Mansuripur, “Resolution of the Abraham-Minkowski controversy,” Opt. Commun. 283, 1997–2005 (2010).
[CrossRef]

M. Mansuripur and A. R. Zakharian, “Energy, momentum, and force in classical electrodynamics: application to negative-index media,” Opt. Commun. 283, 4594–4600 (2010).
[CrossRef]

Opt. Express (3)

Opt. Lett. (1)

Phys. Rep. (1)

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

Phys. Rev. (1)

E. F. Nichols and G. F. Hull, “The pressure due to radiation,” Phys. Rev. 17, 26–50 (1903).
[CrossRef]

Phys. Rev. A (4)

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

V. Yannopapas and P. G. Galiatsatos, “Electromagnetic forces in negative-refractive-index metamaterials: a first-principles study,” Phys. Rev. A 77, 043819 (2008).
[CrossRef]

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

Phys. Rev. E (2)

R. W. Ziolkowski, “Superluminal transmission of information through an electromagnetic metamaterial,” Phys. Rev. E 63, 046604 (2001).
[CrossRef]

K. J. Webb and Shivanand, “Negative electromagnetic plane-wave force in gain media,” Phys. Rev. E 84, 057602 (2011).
[CrossRef]

Phys. Rev. Lett. (3)

S. M. Barnett, “Resolution of the Abraham-Minkowski dilemma,” Phys. Rev. Lett. 104, 070401 (2010).
[CrossRef]

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]

M. Mansuripur, “Trouble with the Lorentz law of force: incompatibility with special relativity and momentum conservation,” Phys. Rev. Lett. 108, 193901 (2012).
[CrossRef]

Phys. Usp. (1)

V. G. Veselagao, “Energy, linear momentum, and mass transfer by an electromagnetic wave in a negative-refraction medium,” Phys. Usp. 52, 649–654 (2009).
[CrossRef]

Proc. Roy. Soc. A (1)

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

Rev. Mod. Phys. (1)

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

Other (2)

H. A. Lorentz, The Theory of Electrons, 2nd ed. (Dover, 1952). These are notes from lectures given at Columbia University in the spring of 1906, as collected by H. A.Lorentz in 1909 and then in revised form in 1915.

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

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