Abstract

We derive the force of the electromagnetic radiation on material objects by a direct application of the Lorentz law of classical electrodynamics. The derivation is straightforward in the case of solid metals and solid dielectrics, where the mass density and the optical constants of the media are assumed to remain unchanged under internal and external pressures, and where material flow and deformation can be ignored. For metallic mirrors, we separate the contribution to the radiation pressure of the electrical charge density from that of the current density of the conduction electrons. In the case of dielectric media, we examine the forces experienced by bound charges and currents, and determine the contribution of each to the radiation pressure. These analyses reveal the existence of a lateral radiation pressure inside the dielectric media, one that is exerted at and around the edges of a finite-diameter light beam. The lateral pressure turns out to be compressive for s-polarized light and expansive for p-polarized light. Along the way, we derive an expression for the momentum density of the light field inside dielectric media, one that has equal contributions from the traditional Minkowski and Abraham forms. This new expression for the momentum density, which contains both electromagnetic and mechanical terms, is used to explain the behavior of light pulses and individual photons upon entering and exiting a dielectric slab. In all the cases considered, the net forces and torques experienced by material bodies are consistent with the relevant conservation laws. Our method of calculating the radiation pressure can be used in conjunction with numerical simulations to yield the distribution of fields and forces in diverse systems of practical interest.

© 2004 Optical Society of America

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References

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  1. H. Minkowski, Nachr. Ges. Wiss. Gottingen 53 (1908).
  2. H. Minkowski, Math. Annalon 68, 472 (1910).
  3. M. Abraham, R. C. Circ. Mat. Palermo 28, 1 (1909).
  4. M. Abraham, R. C. Circ. Mat. Palermo 30, 33 (1910).
  5. J. P. Gordon, “Radiation forces and momenta in dielectric media,” Phys. Rev. A 8, 14-21 (1973).
    [CrossRef]
  6. R. Loudon, “Radiation Pressure and Momentum in Dielectrics,” De Martini lecture, to appear in Fortschritte der Physik (2004).
  7. R. Loudon, “Theory of the radiation pressure on dielectric surfaces,” J. Mod. Opt. 49, 821-838 (2002).
  8. L. Landau, E. Lifshitz, Electrodynamics of Continuous Media, Pergamon, New York, 1960.
  9. J. D. Jackson, Classical Electrodynamics, 2nd edition, Wiley, New York, 1975.
  10. M. Planck, The Theory of Heat Radiation, translated by M. Masius form the German edition of 1914, Dover Publications, New York (1959).
  11. R. V. Jones and J. C. S. Richards, Proc. Roy. Soc. A 221, 480 (1954).
  12. 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).
  13. A. Ashkin and J. M. Dziedzic, “Optical trapping and manipulation of viruses and bacteria,” Science 235, 1517-1520 (1987).
    [CrossRef]
  14. A. Rohrbach and E. Stelzer, “Trapping forces, force constants, and potential depths for dielectric spheres in the presence of spherical aberrations,” Appl. Opt. 41, 2494 (2002).
  15. Y. N. Obukhov and F. W.Hehl, “Electromagnetic energy-momentum and forces in matter,” Phys. Lett. A, 311, 277-284 (2003).
    [CrossRef]
  16. G. Barlow, Proc. Roy. Soc. Lond. A 87, 1-16 (1912).
  17. R. Loudon, “Theory of the forces exerted by Laguerre-Gaussian light beams on dielectrics,” Phys. Rev. A 68, 013806 (2003).
    [CrossRef]

Appl. Opt. (1)

Fortschritte der Physik (1)

R. Loudon, “Radiation Pressure and Momentum in Dielectrics,” De Martini lecture, to appear in Fortschritte der Physik (2004).

J. Mod. Opt. (1)

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

Math. Annalon (1)

H. Minkowski, Math. Annalon 68, 472 (1910).

Nachr. Ges. Wiss. Gottingen (1)

H. Minkowski, Nachr. Ges. Wiss. Gottingen 53 (1908).

Opt. Lett. (1)

Phys. Lett. A (1)

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

Phys. Rev. A (2)

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

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

Proc. Roy. Soc. A (1)

R. V. Jones and J. C. S. Richards, Proc. Roy. Soc. A 221, 480 (1954).

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

G. Barlow, Proc. Roy. Soc. Lond. A 87, 1-16 (1912).

R. C. Circ. Mat. Palermo (2)

M. Abraham, R. C. Circ. Mat. Palermo 28, 1 (1909).

M. Abraham, R. C. Circ. Mat. Palermo 30, 33 (1910).

Science (1)

A. Ashkin and J. M. Dziedzic, “Optical trapping and manipulation of viruses and bacteria,” Science 235, 1517-1520 (1987).
[CrossRef]

Other (3)

L. Landau, E. Lifshitz, Electrodynamics of Continuous Media, Pergamon, New York, 1960.

J. D. Jackson, Classical Electrodynamics, 2nd edition, Wiley, New York, 1975.

M. Planck, The Theory of Heat Radiation, translated by M. Masius form the German edition of 1914, Dover Publications, New York (1959).

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