Abstract

Using the Fresnel relations as axioms, we derive a generalized electromagnetic momentum for a piecewise homogeneous medium and a different generalized momentum for a medium with a spatially varying refractive index in the Wentzel–Kramers–Brillouin (WKB) limit. Both generalized momenta depend linearly on the field, but the refractive index appears to different powers due to the difference in translational symmetry. For the case of the slowly varying index, it is demonstrated that there is negligible transfer of momentum from the electromagnetic field to the material. Such a transfer occurs at the interface between the vacuum and a homogeneous material allowing us to derive the radiation pressure from the Fresnel reflection formula. The Lorentz volume force is shown to be nil.

© 2007 Optical Society of America

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  1. 1. H. Minkowski, Natches. Ges. Wiss. Göttingen 53 (1908); Math. Ann. 68, 472 (1910).
  2. M. Abraham, Rend. Circ. Mat. Palermo 28, 1 (1909); 30, 33 (1910).
    [CrossRef]
  3. A. Einstein and J. Laub, Ann. Phys. (Leipzig) 26, 541 (1908).
  4. R. Peierls, "The momentum of light in a refracting medium," Proc. R. Soc. Lond. A 347, 475-491 (1976).
    [CrossRef]
  5. M. Kranys, "The Minkowski and Abraham Tensors, and the non-uniqueness of non-closed systems," Int. J. Engng. Sci. 20, 1193-1213 (1982).
    [CrossRef]
  6. G. H. Livens, The Theory of Electricity, (Cambridge University Press, Cambridge, 1908).
  7. Y. N. Obukhov and F. W. Hehl, "Electromagnetic energy-momentum and forces in matter," Phys. Lett. A 311, 277-284 (2003).
    [CrossRef]
  8. J. C. Garrison and R. Y. Chiao, "Canonical and kinetic forms of the electromagnetic momentum in an ad hoc quantization scheme for a dispersive dielectric," Phys. Rev. A 70, 053826-1-8 (2004).
    [CrossRef]
  9. S. Antoci and L. Mihich, "A forgotten argument by Gordon uniquely selects Abraham’s tensor as the energy-momentum tensor of the electromagnetic field in homogeneous, isotropic matter," Nuovo Cim. B112, 991-1001 (1997).
  10. R. V. Jones and J. C. S. Richards, "The pressure of radiation in a refracting medium," Proc. R. Soc. London A 221, 480 (1954).
    [CrossRef]
  11. A. Ashkin and J. M. Dziedzic, "Radiation Pressure on a Free Liquid Surface," Phys. Rev. Lett. 30, 139-142 (1973).
    [CrossRef]
  12. 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, 303-318 (1980).
    [CrossRef]
  13. D. G. Lahoz and G. M. Graham, "Experimental decision on the electromagnetic momentum," J. Phys. A 15, 303-318 (1982).
    [CrossRef]
  14. I. Brevik, "Experiments in phenomenological electrodynamics and the electromagnetic energy-momentum tensor," Phys. Rep. 52, 133-201 (1979).
    [CrossRef]
  15. I. Brevik, "Photon-drag experiment and the electromagnetic momentum in matter," Phys. Rev. B 33, 1058-1062 (1986).
    [CrossRef]
  16. H. Goldstein, Classical Mechanics, 2nd Ed., (Addison-Wesley, Reading, MA, 1980).
  17. M. E. Crenshaw, "Generalized electromagnetic momentum and the Fresnel relations," Phys. Lett. A 346, 249-254, (2005).
    [CrossRef]
  18. J. D. Jackson, Classical Electrodynamics, 2nd Ed., (Wiley, New York, 1975).
  19. W. P. Huang, S. T. Chu, A. Goss, and S. K. Chaudhuri, "A scalar finite-difference time-domain approach to guided-wave optics," IEEE Photonics Tech. Lett. 3, 524 (1991).
    [CrossRef]
  20. A. Chubykalo, A. Espinoza, and R. Tzonchev, "Experimental test of the compatibility of the definitions of the electromagnetic energy density and the Poynting vector," Eur. Phys. J. D 31, 113-120 (2004).
    [CrossRef]
  21. M. Crenshaw and N. Akozbek, "Electromagnetic energy flux vector for a dispersive linear medium," Phys. Rev. E 73, 056613 (2006).
    [CrossRef]
  22. J. P. Gordon, "Radiation Forces and Momenta in Dielectric Media," Phys. Rev. A 8, 14-21 (1973).
    [CrossRef]
  23. M. Stone, "Phonons and Forces: Momentum versus Pseudomomentum in Moving Fluids," arXiv.org, condmat/0012316 (2000), http://arxiv.org/abs/cond-mat?papernum=0012316.
  24. M. Mansuripur, "Radiation pressure and the linear momentum of the electromagnetic field," Opt. Express 12, 5375-5401 (2004), http://www.opticsinfobase.org/abstract.cfm?URI=oe-12-22-5375.
    [CrossRef] [PubMed]
  25. R. Loudon, S. M. Barnett, and C. Baxter, "Theory of radiation pressure and momentum transfer in dielectrics: the photon drag effect," Phys. Rev. A 71, 063802 (2005).
    [CrossRef]
  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]

2006 (2)

M. Crenshaw and N. Akozbek, "Electromagnetic energy flux vector for a dispersive linear medium," Phys. Rev. E 73, 056613 (2006).
[CrossRef]

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]

2005 (2)

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

M. E. Crenshaw, "Generalized electromagnetic momentum and the Fresnel relations," Phys. Lett. A 346, 249-254, (2005).
[CrossRef]

2004 (3)

A. Chubykalo, A. Espinoza, and R. Tzonchev, "Experimental test of the compatibility of the definitions of the electromagnetic energy density and the Poynting vector," Eur. Phys. J. D 31, 113-120 (2004).
[CrossRef]

J. C. Garrison and R. Y. Chiao, "Canonical and kinetic forms of the electromagnetic momentum in an ad hoc quantization scheme for a dispersive dielectric," Phys. Rev. A 70, 053826-1-8 (2004).
[CrossRef]

M. Mansuripur, "Radiation pressure and the linear momentum of the electromagnetic field," Opt. Express 12, 5375-5401 (2004), http://www.opticsinfobase.org/abstract.cfm?URI=oe-12-22-5375.
[CrossRef] [PubMed]

2003 (1)

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

1997 (1)

S. Antoci and L. Mihich, "A forgotten argument by Gordon uniquely selects Abraham’s tensor as the energy-momentum tensor of the electromagnetic field in homogeneous, isotropic matter," Nuovo Cim. B112, 991-1001 (1997).

1991 (1)

W. P. Huang, S. T. Chu, A. Goss, and S. K. Chaudhuri, "A scalar finite-difference time-domain approach to guided-wave optics," IEEE Photonics Tech. Lett. 3, 524 (1991).
[CrossRef]

1986 (1)

I. Brevik, "Photon-drag experiment and the electromagnetic momentum in matter," Phys. Rev. B 33, 1058-1062 (1986).
[CrossRef]

1982 (2)

D. G. Lahoz and G. M. Graham, "Experimental decision on the electromagnetic momentum," J. Phys. A 15, 303-318 (1982).
[CrossRef]

M. Kranys, "The Minkowski and Abraham Tensors, and the non-uniqueness of non-closed systems," Int. J. Engng. Sci. 20, 1193-1213 (1982).
[CrossRef]

1980 (1)

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, 303-318 (1980).
[CrossRef]

1979 (1)

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

1976 (1)

R. Peierls, "The momentum of light in a refracting medium," Proc. R. Soc. Lond. A 347, 475-491 (1976).
[CrossRef]

1973 (2)

A. Ashkin and J. M. Dziedzic, "Radiation Pressure on a Free Liquid Surface," Phys. Rev. Lett. 30, 139-142 (1973).
[CrossRef]

J. P. Gordon, "Radiation Forces and Momenta in Dielectric Media," Phys. Rev. A 8, 14-21 (1973).
[CrossRef]

1954 (1)

R. V. Jones and J. C. S. Richards, "The pressure of radiation in a refracting medium," Proc. R. Soc. London A 221, 480 (1954).
[CrossRef]

1908 (1)

A. Einstein and J. Laub, Ann. Phys. (Leipzig) 26, 541 (1908).

Akozbek, N.

M. Crenshaw and N. Akozbek, "Electromagnetic energy flux vector for a dispersive linear medium," Phys. Rev. E 73, 056613 (2006).
[CrossRef]

Antoci, S.

S. Antoci and L. Mihich, "A forgotten argument by Gordon uniquely selects Abraham’s tensor as the energy-momentum tensor of the electromagnetic field in homogeneous, isotropic matter," Nuovo Cim. B112, 991-1001 (1997).

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.

R. Loudon, S. M. Barnett, and C. Baxter, "Theory of 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, "Theory of 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]

Brevik, I.

I. Brevik, "Photon-drag experiment and the electromagnetic momentum in matter," Phys. Rev. B 33, 1058-1062 (1986).
[CrossRef]

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

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]

Chaudhuri, S. K.

W. P. Huang, S. T. Chu, A. Goss, and S. K. Chaudhuri, "A scalar finite-difference time-domain approach to guided-wave optics," IEEE Photonics Tech. Lett. 3, 524 (1991).
[CrossRef]

Chiao, R. Y.

J. C. Garrison and R. Y. Chiao, "Canonical and kinetic forms of the electromagnetic momentum in an ad hoc quantization scheme for a dispersive dielectric," Phys. Rev. A 70, 053826-1-8 (2004).
[CrossRef]

Chu, S. T.

W. P. Huang, S. T. Chu, A. Goss, and S. K. Chaudhuri, "A scalar finite-difference time-domain approach to guided-wave optics," IEEE Photonics Tech. Lett. 3, 524 (1991).
[CrossRef]

Chubykalo, A.

A. Chubykalo, A. Espinoza, and R. Tzonchev, "Experimental test of the compatibility of the definitions of the electromagnetic energy density and the Poynting vector," Eur. Phys. J. D 31, 113-120 (2004).
[CrossRef]

Crenshaw, M.

M. Crenshaw and N. Akozbek, "Electromagnetic energy flux vector for a dispersive linear medium," Phys. Rev. E 73, 056613 (2006).
[CrossRef]

Crenshaw, M. E.

M. E. Crenshaw, "Generalized electromagnetic momentum and the Fresnel relations," Phys. Lett. A 346, 249-254, (2005).
[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]

Einstein, A.

A. Einstein and J. Laub, Ann. Phys. (Leipzig) 26, 541 (1908).

Espinoza, A.

A. Chubykalo, A. Espinoza, and R. Tzonchev, "Experimental test of the compatibility of the definitions of the electromagnetic energy density and the Poynting vector," Eur. Phys. J. D 31, 113-120 (2004).
[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, 303-318 (1980).
[CrossRef]

Garrison, J. C.

J. C. Garrison and R. Y. Chiao, "Canonical and kinetic forms of the electromagnetic momentum in an ad hoc quantization scheme for a dispersive dielectric," Phys. Rev. A 70, 053826-1-8 (2004).
[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, 303-318 (1980).
[CrossRef]

Gordon, J. P.

J. P. Gordon, "Radiation Forces and Momenta in Dielectric Media," Phys. Rev. A 8, 14-21 (1973).
[CrossRef]

Goss, A.

W. P. Huang, S. T. Chu, A. Goss, and S. K. Chaudhuri, "A scalar finite-difference time-domain approach to guided-wave optics," IEEE Photonics Tech. Lett. 3, 524 (1991).
[CrossRef]

Graham, G. M.

D. G. Lahoz and G. M. Graham, "Experimental decision on the electromagnetic momentum," J. Phys. A 15, 303-318 (1982).
[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]

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]

Huang, W. P.

W. P. Huang, S. T. Chu, A. Goss, and S. K. Chaudhuri, "A scalar finite-difference time-domain approach to guided-wave optics," IEEE Photonics Tech. Lett. 3, 524 (1991).
[CrossRef]

Jones, R. V.

R. V. Jones and J. C. S. Richards, "The pressure of radiation in a refracting medium," Proc. R. Soc. London A 221, 480 (1954).
[CrossRef]

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, 303-318 (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, 303-318 (1980).
[CrossRef]

Kranys, M.

M. Kranys, "The Minkowski and Abraham Tensors, and the non-uniqueness of non-closed systems," Int. J. Engng. Sci. 20, 1193-1213 (1982).
[CrossRef]

Lahoz, D. G.

D. G. Lahoz and G. M. Graham, "Experimental decision on the electromagnetic momentum," J. Phys. A 15, 303-318 (1982).
[CrossRef]

Laub, J.

A. Einstein and J. Laub, Ann. Phys. (Leipzig) 26, 541 (1908).

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, 303-318 (1980).
[CrossRef]

Loudon, R.

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

Mansuripur, M.

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]

Mihich, L.

S. Antoci and L. Mihich, "A forgotten argument by Gordon uniquely selects Abraham’s tensor as the energy-momentum tensor of the electromagnetic field in homogeneous, isotropic matter," Nuovo Cim. B112, 991-1001 (1997).

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]

Peierls, R.

R. Peierls, "The momentum of light in a refracting medium," Proc. R. Soc. Lond. A 347, 475-491 (1976).
[CrossRef]

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 (1954).
[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]

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]

Tzonchev, R.

A. Chubykalo, A. Espinoza, and R. Tzonchev, "Experimental test of the compatibility of the definitions of the electromagnetic energy density and the Poynting vector," Eur. Phys. J. D 31, 113-120 (2004).
[CrossRef]

Ann. Phys. (Leipzig) (1)

A. Einstein and J. Laub, Ann. Phys. (Leipzig) 26, 541 (1908).

Eur. Phys. J. D (1)

A. Chubykalo, A. Espinoza, and R. Tzonchev, "Experimental test of the compatibility of the definitions of the electromagnetic energy density and the Poynting vector," Eur. Phys. J. D 31, 113-120 (2004).
[CrossRef]

IEEE Photonics Tech. Lett. (1)

W. P. Huang, S. T. Chu, A. Goss, and S. K. Chaudhuri, "A scalar finite-difference time-domain approach to guided-wave optics," IEEE Photonics Tech. Lett. 3, 524 (1991).
[CrossRef]

Int. J. Engng. Sci. (1)

M. Kranys, "The Minkowski and Abraham Tensors, and the non-uniqueness of non-closed systems," Int. J. Engng. Sci. 20, 1193-1213 (1982).
[CrossRef]

J. Phys. A (1)

D. G. Lahoz and G. M. Graham, "Experimental decision on the electromagnetic momentum," J. Phys. A 15, 303-318 (1982).
[CrossRef]

Nuovo Cim. (1)

S. Antoci and L. Mihich, "A forgotten argument by Gordon uniquely selects Abraham’s tensor as the energy-momentum tensor of the electromagnetic field in homogeneous, isotropic matter," Nuovo Cim. B112, 991-1001 (1997).

Opt. Express (1)

Phys. Lett. A (2)

M. E. Crenshaw, "Generalized electromagnetic momentum and the Fresnel relations," Phys. Lett. A 346, 249-254, (2005).
[CrossRef]

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

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)

J. C. Garrison and R. Y. Chiao, "Canonical and kinetic forms of the electromagnetic momentum in an ad hoc quantization scheme for a dispersive dielectric," Phys. Rev. A 70, 053826-1-8 (2004).
[CrossRef]

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

J. P. Gordon, "Radiation Forces and Momenta in Dielectric Media," Phys. Rev. A 8, 14-21 (1973).
[CrossRef]

Phys. Rev. B (1)

I. Brevik, "Photon-drag experiment and the electromagnetic momentum in matter," Phys. Rev. B 33, 1058-1062 (1986).
[CrossRef]

Phys. Rev. E (2)

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]

M. Crenshaw and N. Akozbek, "Electromagnetic energy flux vector for a dispersive linear medium," Phys. Rev. E 73, 056613 (2006).
[CrossRef]

Phys. Rev. Lett. (1)

A. Ashkin and J. M. Dziedzic, "Radiation Pressure on a Free Liquid Surface," Phys. Rev. Lett. 30, 139-142 (1973).
[CrossRef]

Proc. R. Soc. Lond. A (1)

R. Peierls, "The momentum of light in a refracting medium," Proc. R. Soc. Lond. A 347, 475-491 (1976).
[CrossRef]

Proc. R. Soc. London A (2)

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, 303-318 (1980).
[CrossRef]

R. V. Jones and J. C. S. Richards, "The pressure of radiation in a refracting medium," Proc. R. Soc. London A 221, 480 (1954).
[CrossRef]

Other (6)

H. Goldstein, Classical Mechanics, 2nd Ed., (Addison-Wesley, Reading, MA, 1980).

1. H. Minkowski, Natches. Ges. Wiss. Göttingen 53 (1908); Math. Ann. 68, 472 (1910).

M. Abraham, Rend. Circ. Mat. Palermo 28, 1 (1909); 30, 33 (1910).
[CrossRef]

G. H. Livens, The Theory of Electricity, (Cambridge University Press, Cambridge, 1908).

J. D. Jackson, Classical Electrodynamics, 2nd Ed., (Wiley, New York, 1975).

M. Stone, "Phonons and Forces: Momentum versus Pseudomomentum in Moving Fluids," arXiv.org, condmat/0012316 (2000), http://arxiv.org/abs/cond-mat?papernum=0012316.

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Figures (5)

Fig. 1.
Fig. 1.

Propagation of the vector potential from vacuum into a linear medium with a gradient-index antireflection layer on the the entry and exit faces. The shaded region is the profile of the index of refraction. The field travels to the right and the horizontal axis is scaled to the wavelength.

Fig. 2.
Fig. 2.

Same as Fig. 1 after the field has propagated out of the medium through the anti-reflection layer.

Fig. 3.
Fig. 3.

Propagation of the vector potential from vacuum into a linear medium through a step increase in the refractive index. The shaded region is the profile of the index of refraction. The field travels to the right and the horizontal axis is scaled to the wavelength.

Fig. 4.
Fig. 4.

Propagation of the vector potential from vacuum into a linear medium with a step-index for the entry and a gradient-index antireflection layer on the exit face. The shaded region is the profile of the index of refraction. The field travels to the right and the horizontal axis is scaled to the wavelength.

Fig. 5.
Fig. 5.

Same as Fig. 4 after the field has propagated out of the medium through the anti-reflection layer.

Equations (49)

Equations on this page are rendered with MathJax. Learn more.

E i = e x E i e i ( ω t k i z )
E r = e x E r e i ( ω t k r z )
E t = e x E t e i ( ω t k t z )
E r = n 2 n 1 n 1 + n 2 E i
E t = 2 n 1 n 1 + n 2 E i
n 1 E i 2 = n 2 E t 2 + n 1 E r 2
E i = E t + E r
S = γ n E 2
T = α E
ρ v = ρ t
S = γ n E 2 e z
T = α E e z
u = S v = n c γ n E 2
g = T v = n c α E .
V 1 n 1 2 E i 2 d v = V 1 n 1 2 E r 2 d v + V 2 n 2 2 E t 2 d v
V 1 n 1 E i d v = V 1 n 1 E r d v + V 2 n 2 E t d v .
G = α c V n E .
E i = E t E r + 2 E r .
V 1 n 1 E i d ν e z = V 2 n 2 E t d ν e z V 1 n 1 E r d ν e z + 2 V 1 n 1 E r d ν e z .
g = ρ 0 4 π n E e z
u e = 1 8 π n 2 E 2 = g 2 2 ρ 0 .
T = g v = ρ 0 4 π n E c n e z
G = V g d ν = ρ 0 4 π V n E d ν e z
n 2 E t = n 1 E i
T = α n E
T ( z ) = α n ( z ) E ( z ) e z
g ( z ) = T ( z ) v ( z ) = α c n 3 2 ( z ) E ( z ) .
G = V g d ν e z = ρ 0 4 π V n 3 2 E d v e z
2 A z 2 2 i k A z + n 2 c 2 2 A t 2 2 i ω n 2 c 2 A t = 0 ,
E i w = n 3 2 E i n w n
E i w = 2 n 1 n 2 n 2 + n 1 E i w n 2 + ( 2 1 ) n 2 n 1 n 2 + n 1 E i w .
U = 1 8 π V ( n 2 E 2 + B 2 ) d v
G x = 1 4 π c V n E × H dv ,
g x = 1 4 π c n E × H
g x v = g x t .
c 4 π E × H = c g x t
δ G = A ρ 0 4 π n 1 n + 1 E i c δ tda
P = 2 c ρ 0 4 π n 1 n + 1 E i
F = A 2 c ρ 0 2 π n 1 n + 1 E i da e z .
F = i q i ( E + v i c × B )
d P mech dt = V ( ρ E + 1 c J × B ) dv .
d P mech d t + d G M d t = 1 4 π V [ E ( D ) D × ( × E ) B × ( × B ) ] d v
G M = V 1 4 π c D × B d v
G A = V 1 4 π c E × B d v
G mech = V 1 c P × B d v
d P mech d t + d G mech d t + d G A d t = 1 4 π V [ E ( D ) E × ( × E ) 4 π P × ( × E ) B × ( × B ) ] d v
d P mech d t + d G mech d t = V ( ρ E + 1 c J × B P × ( × E ) + d P d t × B ) d v .
d P mech d t + d G mech d t = 1 c V d d t ( P × B ) d v
d P mech d t = 0 .

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