Abstract

From fundamental concepts of electromagnetic theory a mathematical development on the forces between radiating bodies is presented. A method is developed that evaluates the stationary volume energy density as a function of particle separation. A rudimentary description of particle scattering yields data that correspond to the sinusoidally varying force that has been shown to act on particles under intense illumination as a function of their proximity.

© 1998 Optical Society of America

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References

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  1. M. M. Burns, J.-M. Fournier, and J. A. Golovchenko, “Optical matter:crystallization and binding in intense optical fields,” Science 249, 749–754 (1990).
    [CrossRef] [PubMed]
  2. M. M. Burns, J.-Marc Fournier, and J. A. Golovchenko, “Optical binding,” Phys. Rev. Lett. 63, 1233–1235 (1989).
    [CrossRef] [PubMed]
  3. F. Depassse and J.-M. Vigoreux, “Optical binding force between two Rayleigh particles,” J. Phys. D 27, 914–919 (1994).
    [CrossRef]
  4. A. Ashkin, “The pressure of laser light,” Sci. Am. 226, 63–71 (1972).
    [CrossRef]
  5. J. P. Gordon, “Radiation forces and momenta in dielectric media,” Phys. Rev. A 8, 14 (1973).
    [CrossRef]
  6. H. A. Haus, “Momentum, energy and power densities of TEM wave packet,” Physica (Amsterdam) 43, 77–91 (1969).
    [CrossRef]
  7. I. I. Tarhan and G. Watson, “Photonic band structure of fcc colloidal crystals,” Phys. Rev. Lett. 76, 315 (1996).
    [CrossRef] [PubMed]
  8. D. F. Evans and H. Wennerstrom, The Colloidal Domain (VCH, Deefield Beach, Fla., 1994), p. 102.
  9. J. C. Slater and N. H. Frank, Electromagnetism (Dover, New York, 1969), p. 100.
  10. J. D. Jackson, Classical Electrodynamics (Wiley, New York, 1962), p. 23.
  11. Ref. 10, p. 100.
  12. J. N. Israelachvili and D. Tabor, “Van der Waals forces: theory and experiment” in Progress in Surface and Membrane Science, J. F. Danielli, M. D. Rosenberg, and D. A. Cadenhead, eds. (Academic, New York, 1973), pp. 2–11.
  13. R. W. Boyd, Nonlinear Optics (Academic, New York, 1992), p. 328.
  14. J. C. Slater and N. H. Frank, Electromagnetism (Dover, New York, 1969), pp. 152–157.
  15. H. G. Booker, Energy in Electromagnetism (Institute of Electrical Engineers, London, 1982), pp. 344–347.
  16. C. T. Tai, “Characteristics of linear antenna elements,” in Antenna Engineering Handbook, H. Jasik, ed. (McGraw-Hill, New York, 1961), pp. 3–8.
  17. M. Gastine, L. Courtois, and J. L. Dormann, “Electromagnetic resonances of free dielectric spheres,” IEEE Trans. Microwave Theory Tech. MTT-15, 694–700 (1967).
    [CrossRef]
  18. A. Ashkin and J. M. Dziedzic, “Observation of resonances in the radiation pressure on dielectric spheres,” Phys. Rev. Lett. 38, 1351–1354 (1977).
    [CrossRef]
  19. S. Arnold, A. Serpenguzel, and G. Griffel, “Microparticle photonics: Fiber optic excitation of MDR’s,” in Guided-Wave Optoelectronics, T. Tamir, G. Griffel, and H. L. Bertoni, eds. (Plenum, New York, 1995), p. 495.
  20. H.-B. Lin, J. D. Eversole, and A. J. Campillo, “Spectral properties of lasing microdroplets,” J. Opt. Soc. Am. B 9, 43 (1992).
    [CrossRef]
  21. J. Z. Buchwald, From Maxwell to Microphysics (U. Chicago Press, Chicago, 1985).
  22. H. C. van de Hulst, Multiple Light Scattering (Academic, New York, 1980), p. 303.

1996

I. I. Tarhan and G. Watson, “Photonic band structure of fcc colloidal crystals,” Phys. Rev. Lett. 76, 315 (1996).
[CrossRef] [PubMed]

1994

F. Depassse and J.-M. Vigoreux, “Optical binding force between two Rayleigh particles,” J. Phys. D 27, 914–919 (1994).
[CrossRef]

1992

1990

M. M. Burns, J.-M. Fournier, and J. A. Golovchenko, “Optical matter:crystallization and binding in intense optical fields,” Science 249, 749–754 (1990).
[CrossRef] [PubMed]

1989

M. M. Burns, J.-Marc Fournier, and J. A. Golovchenko, “Optical binding,” Phys. Rev. Lett. 63, 1233–1235 (1989).
[CrossRef] [PubMed]

1977

A. Ashkin and J. M. Dziedzic, “Observation of resonances in the radiation pressure on dielectric spheres,” Phys. Rev. Lett. 38, 1351–1354 (1977).
[CrossRef]

1973

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

1972

A. Ashkin, “The pressure of laser light,” Sci. Am. 226, 63–71 (1972).
[CrossRef]

1969

H. A. Haus, “Momentum, energy and power densities of TEM wave packet,” Physica (Amsterdam) 43, 77–91 (1969).
[CrossRef]

1967

M. Gastine, L. Courtois, and J. L. Dormann, “Electromagnetic resonances of free dielectric spheres,” IEEE Trans. Microwave Theory Tech. MTT-15, 694–700 (1967).
[CrossRef]

Ashkin, A.

A. Ashkin and J. M. Dziedzic, “Observation of resonances in the radiation pressure on dielectric spheres,” Phys. Rev. Lett. 38, 1351–1354 (1977).
[CrossRef]

A. Ashkin, “The pressure of laser light,” Sci. Am. 226, 63–71 (1972).
[CrossRef]

Burns, M. M.

M. M. Burns, J.-M. Fournier, and J. A. Golovchenko, “Optical matter:crystallization and binding in intense optical fields,” Science 249, 749–754 (1990).
[CrossRef] [PubMed]

M. M. Burns, J.-Marc Fournier, and J. A. Golovchenko, “Optical binding,” Phys. Rev. Lett. 63, 1233–1235 (1989).
[CrossRef] [PubMed]

Campillo, A. J.

Courtois, L.

M. Gastine, L. Courtois, and J. L. Dormann, “Electromagnetic resonances of free dielectric spheres,” IEEE Trans. Microwave Theory Tech. MTT-15, 694–700 (1967).
[CrossRef]

Depassse, F.

F. Depassse and J.-M. Vigoreux, “Optical binding force between two Rayleigh particles,” J. Phys. D 27, 914–919 (1994).
[CrossRef]

Dormann, J. L.

M. Gastine, L. Courtois, and J. L. Dormann, “Electromagnetic resonances of free dielectric spheres,” IEEE Trans. Microwave Theory Tech. MTT-15, 694–700 (1967).
[CrossRef]

Dziedzic, J. M.

A. Ashkin and J. M. Dziedzic, “Observation of resonances in the radiation pressure on dielectric spheres,” Phys. Rev. Lett. 38, 1351–1354 (1977).
[CrossRef]

Eversole, J. D.

Fournier, J.-M.

M. M. Burns, J.-M. Fournier, and J. A. Golovchenko, “Optical matter:crystallization and binding in intense optical fields,” Science 249, 749–754 (1990).
[CrossRef] [PubMed]

Fournier, J.-Marc

M. M. Burns, J.-Marc Fournier, and J. A. Golovchenko, “Optical binding,” Phys. Rev. Lett. 63, 1233–1235 (1989).
[CrossRef] [PubMed]

Gastine, M.

M. Gastine, L. Courtois, and J. L. Dormann, “Electromagnetic resonances of free dielectric spheres,” IEEE Trans. Microwave Theory Tech. MTT-15, 694–700 (1967).
[CrossRef]

Golovchenko, J. A.

M. M. Burns, J.-M. Fournier, and J. A. Golovchenko, “Optical matter:crystallization and binding in intense optical fields,” Science 249, 749–754 (1990).
[CrossRef] [PubMed]

M. M. Burns, J.-Marc Fournier, and J. A. Golovchenko, “Optical binding,” Phys. Rev. Lett. 63, 1233–1235 (1989).
[CrossRef] [PubMed]

Gordon, J. P.

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

Haus, H. A.

H. A. Haus, “Momentum, energy and power densities of TEM wave packet,” Physica (Amsterdam) 43, 77–91 (1969).
[CrossRef]

Lin, H.-B.

Tarhan, I. I.

I. I. Tarhan and G. Watson, “Photonic band structure of fcc colloidal crystals,” Phys. Rev. Lett. 76, 315 (1996).
[CrossRef] [PubMed]

Vigoreux, J.-M.

F. Depassse and J.-M. Vigoreux, “Optical binding force between two Rayleigh particles,” J. Phys. D 27, 914–919 (1994).
[CrossRef]

Watson, G.

I. I. Tarhan and G. Watson, “Photonic band structure of fcc colloidal crystals,” Phys. Rev. Lett. 76, 315 (1996).
[CrossRef] [PubMed]

IEEE Trans. Microwave Theory Tech.

M. Gastine, L. Courtois, and J. L. Dormann, “Electromagnetic resonances of free dielectric spheres,” IEEE Trans. Microwave Theory Tech. MTT-15, 694–700 (1967).
[CrossRef]

J. Opt. Soc. Am. B

J. Phys. D

F. Depassse and J.-M. Vigoreux, “Optical binding force between two Rayleigh particles,” J. Phys. D 27, 914–919 (1994).
[CrossRef]

Phys. Rev. A

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

Phys. Rev. Lett.

A. Ashkin and J. M. Dziedzic, “Observation of resonances in the radiation pressure on dielectric spheres,” Phys. Rev. Lett. 38, 1351–1354 (1977).
[CrossRef]

M. M. Burns, J.-Marc Fournier, and J. A. Golovchenko, “Optical binding,” Phys. Rev. Lett. 63, 1233–1235 (1989).
[CrossRef] [PubMed]

I. I. Tarhan and G. Watson, “Photonic band structure of fcc colloidal crystals,” Phys. Rev. Lett. 76, 315 (1996).
[CrossRef] [PubMed]

Physica (Amsterdam)

H. A. Haus, “Momentum, energy and power densities of TEM wave packet,” Physica (Amsterdam) 43, 77–91 (1969).
[CrossRef]

Sci. Am.

A. Ashkin, “The pressure of laser light,” Sci. Am. 226, 63–71 (1972).
[CrossRef]

Science

M. M. Burns, J.-M. Fournier, and J. A. Golovchenko, “Optical matter:crystallization and binding in intense optical fields,” Science 249, 749–754 (1990).
[CrossRef] [PubMed]

Other

S. Arnold, A. Serpenguzel, and G. Griffel, “Microparticle photonics: Fiber optic excitation of MDR’s,” in Guided-Wave Optoelectronics, T. Tamir, G. Griffel, and H. L. Bertoni, eds. (Plenum, New York, 1995), p. 495.

D. F. Evans and H. Wennerstrom, The Colloidal Domain (VCH, Deefield Beach, Fla., 1994), p. 102.

J. C. Slater and N. H. Frank, Electromagnetism (Dover, New York, 1969), p. 100.

J. D. Jackson, Classical Electrodynamics (Wiley, New York, 1962), p. 23.

Ref. 10, p. 100.

J. N. Israelachvili and D. Tabor, “Van der Waals forces: theory and experiment” in Progress in Surface and Membrane Science, J. F. Danielli, M. D. Rosenberg, and D. A. Cadenhead, eds. (Academic, New York, 1973), pp. 2–11.

R. W. Boyd, Nonlinear Optics (Academic, New York, 1992), p. 328.

J. C. Slater and N. H. Frank, Electromagnetism (Dover, New York, 1969), pp. 152–157.

H. G. Booker, Energy in Electromagnetism (Institute of Electrical Engineers, London, 1982), pp. 344–347.

C. T. Tai, “Characteristics of linear antenna elements,” in Antenna Engineering Handbook, H. Jasik, ed. (McGraw-Hill, New York, 1961), pp. 3–8.

J. Z. Buchwald, From Maxwell to Microphysics (U. Chicago Press, Chicago, 1985).

H. C. van de Hulst, Multiple Light Scattering (Academic, New York, 1980), p. 303.

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Figures (7)

Fig. 1
Fig. 1

Geometry of induced dipole interaction.

Fig. 2
Fig. 2

Configuration of two particles simultaneously polarized by an external field.

Fig. 3
Fig. 3

Stationary far-field volume energy density of two externally driven scatterers in the equatorial plane, R=5λ.

Fig. 4
Fig. 4

View of stationary interaction along the equatorial plane.

Fig. 5
Fig. 5

Stationary total field for R=12λ.

Fig. 6
Fig. 6

As in Fig. 5, seen along the equatorial plane.

Fig. 7
Fig. 7

Total interaction energy of driven scatterers as a function of R (in wavelengths).

Equations (22)

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Etot=E1+E2,
we=12 εE2=12 ε[(E1x+E2x)2+(E1y+E2y)2]2=12 ε(E1x2+2E1xE2x+E2x2+E1y2+2E1yE2y+E2y2).
WE=V 12 ε|E|2dτ=-RFdR,
F=-WER=-12 εV R (E1x2+2E1xE2x+E2x2+E1y2+2E1yE2y+E2y2)dτRˆ.
FR=-12 ε R 4π00E2ρdρdzRˆ=-004πεR E1xE2x+R E1yE2yρdρdzRˆ=-004πεR E1E2ρdρdzRˆ.
-pE=p1p24πεR3.
We=-12 p2E1=p1p28πεR3,
p2=αE1=-αp18πεR3,
We=-αp1p1(8πε)2R6.
p4πεr3 exp(jωt)(2 cos θrˆ+sin θθˆ).
WE1=2πε0R/20l2E1E2ρdρdz.
E=jηI0 exp[j(ωt-kr)]2πr cos(kl cos θ)-cos klsin θθˆ.
l=λ4,
θ=90°,
I0=qtp(t)=0=ωp2l,
r=ρ2+z2,
E(r, z, t)=-ηωp4πlr cos(ωt-kz).
E1(z, t)=-ηωp1(t-z/c)4πlr1.
E2(z, t)=-ηωp2[t+(z-R)/c]4πl(R-r2)=-ηω4πl(R-r2) p2 cos(ωt+kz-kR).
E1E2=(ηωp)2(4πl)2(z2+ρ2)1/2[(z-R)2+ρ2]1/2×cos(ωt-kz)cos(ωt+kz-kR)=(ηωp)2(4πl)2(z2+ρ2)1/2[(z-R)2+ρ2]1/2×12[cos(2ωt-kR)+cos(kR-2kz)],
2we/ε=E1E2=(ηωp)2(4πl)2(z2+ρ2)1/2[(z-R)2+ρ2]1/2×12 cos(kR-2kz),
Q=1.3 ln2la.

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