Abstract

Two alternative formulations of the Lorentz force theory of radiation pressure on macroscopic bodies are reviewed. The theories treat the medium respectively as formed from individual dipoles and from individual charges. The former theory is applied to the systems of dielectric slab and dielectric prism, where it is shown that the total torque and force respectively agree with the results of the latter theory. The longitudinal shift of the slab caused by the passage of a single-photon pulse is calculated by Einstein box and Lorentz force theories, with identical results. The Lorentz forces on a single dielectric surface are shown to differ in the two theories and the basic reasons for the discrepancy are discussed. Both top-hat and Gaussian transverse beam profiles are considered.

©2006 Optical Society of America

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References

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  1. I. Brevik, “Experiments in phenomenological electrodynamics and the electromagnetic energy-momentum tensor,” Phys. Reps. 52, 133–201 (1979).
    [Crossref]
  2. J. P. Gordon, “Radiation forces and momenta in dielectric media,” Phys. Rev. A 8, 14–21 (1973).
    [Crossref]
  3. R. Loudon, “Theory of the radiation pressure on dielectric surfaces,” J. Mod. Opt. 49, 812–836 (2002).
    [Crossref]
  4. R. Loudon, “Theory of the forces exerted by Laguerre-Gaussian light beams on dielectrics,” Phys. Rev. A 68, 013806 (2003).
    [Crossref]
  5. M. Padgett, S. M. Barnett, and R. Loudon, “The angular momentum of light inside a dielectric,” J. Mod. Opt. 50, 1555–1562 (2003).
  6. 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]
  7. R. Loudon, “Radiation pressure and momentum in dielectrics,” Fortschr. Phys. 52, 1132–1140 (2004).
    [Crossref]
  8. M. Mansuripur, “Radiation pressure and the linear momentum of the electromagnetic field,” Opt. Express 13, 5375–5401 (2004).
    [Crossref]
  9. M. Mansuripur, A. R. Zakharian, and J. V. Moloney, “Radiation pressure on a dielectric wedge,” Opt. Express 13, 2064–2074 (2005).
    [Crossref] [PubMed]
  10. M. Mansuripur, “Radiation pressure and the linear momentum of light in dispersive dielectric media,” Opt. Express 13, 2245–2250 (2005).
    [Crossref] [PubMed]
  11. M. Mansuripur, “Angular momentum of circularly polarized light in dielectric media,” Opt. Express 13, 5315–5324 (2005).
    [Crossref] [PubMed]
  12. M. Mansuripur, “Radiation pressure and the distribution of electromagnetic force in dielectric media,” in Optical Trapping and Optical Micromanipulation II, K. Dholakia and G. C. Spalding, eds., Proc. SPIE 5930, 154–160 (2005).
  13. S. M. Barnett and R. Loudon, “On the electromagnetic force on a dielectric medium,” J. Phys. B 39, S671–S684 (2006).
    [Crossref]
  14. A. R. Zakharian, P. Polynkin, M. Mansuripur, and J. V. Moloney, “Single-beam trapping of micro-beads in polarized light: numerical simulations,” Opt. Express 14, 3660–3676 (2006).
    [Crossref] [PubMed]
  15. G. Barlow, “On the torque produced by a beam of light in oblique refraction through a glass plate,” Proc. Roy. Soc. Lond. A 87, 1–16 (1912).
    [Crossref]
  16. A. Einstein, “Das Prinzip von der Erhaltung der Schwerpunktsbewegung und die Trägheit der Energie,” Ann. Phys. (Leipzig)  20, 627–633 (1906).
    [Crossref]
  17. N. L. Balazs, “The energy-momentum tensor of the electromagnetic field inside matter,” Phys. Rev. 91, 408–411 (1953).
    [Crossref]
  18. S. M. Barnett, “Optical angular-momentum flux,” J. Opt. B Quantum Semiclassical Opt. 4, S7–S16 (2002).
    [Crossref]
  19. A. Ashkin and J. M. Dziedzic, “Radiation pressure on a free liquid surface,” Phys. Rev. Lett. 30, 139–142 (1973).
    [Crossref]

2006 (2)

2005 (5)

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]

M. Mansuripur, A. R. Zakharian, and J. V. Moloney, “Radiation pressure on a dielectric wedge,” Opt. Express 13, 2064–2074 (2005).
[Crossref] [PubMed]

M. Mansuripur, “Radiation pressure and the linear momentum of light in dispersive dielectric media,” Opt. Express 13, 2245–2250 (2005).
[Crossref] [PubMed]

M. Mansuripur, “Angular momentum of circularly polarized light in dielectric media,” Opt. Express 13, 5315–5324 (2005).
[Crossref] [PubMed]

M. Mansuripur, “Radiation pressure and the distribution of electromagnetic force in dielectric media,” in Optical Trapping and Optical Micromanipulation II, K. Dholakia and G. C. Spalding, eds., Proc. SPIE 5930, 154–160 (2005).

2004 (2)

R. Loudon, “Radiation pressure and momentum in dielectrics,” Fortschr. Phys. 52, 1132–1140 (2004).
[Crossref]

M. Mansuripur, “Radiation pressure and the linear momentum of the electromagnetic field,” Opt. Express 13, 5375–5401 (2004).
[Crossref]

2003 (2)

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

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

2002 (2)

R. Loudon, “Theory of the radiation pressure on dielectric surfaces,” J. Mod. Opt. 49, 812–836 (2002).
[Crossref]

S. M. Barnett, “Optical angular-momentum flux,” J. Opt. B Quantum Semiclassical Opt. 4, S7–S16 (2002).
[Crossref]

1979 (1)

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

1973 (2)

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

A. Ashkin and J. M. Dziedzic, “Radiation pressure on a free liquid surface,” Phys. Rev. Lett. 30, 139–142 (1973).
[Crossref]

1953 (1)

N. L. Balazs, “The energy-momentum tensor of the electromagnetic field inside matter,” Phys. Rev. 91, 408–411 (1953).
[Crossref]

1912 (1)

G. Barlow, “On the torque produced by a beam of light in oblique refraction through a glass plate,” Proc. Roy. Soc. Lond. A 87, 1–16 (1912).
[Crossref]

1906 (1)

A. Einstein, “Das Prinzip von der Erhaltung der Schwerpunktsbewegung und die Trägheit der Energie,” Ann. Phys. (Leipzig)  20, 627–633 (1906).
[Crossref]

Ashkin, A.

A. Ashkin and J. M. Dziedzic, “Radiation pressure on a free liquid surface,” Phys. Rev. Lett. 30, 139–142 (1973).
[Crossref]

Balazs, N. L.

N. L. Balazs, “The energy-momentum tensor of the electromagnetic field inside matter,” Phys. Rev. 91, 408–411 (1953).
[Crossref]

Barlow, G.

G. Barlow, “On the torque produced by a beam of light in oblique refraction through a glass plate,” Proc. Roy. Soc. Lond. A 87, 1–16 (1912).
[Crossref]

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

S. M. Barnett, “Optical angular-momentum flux,” J. Opt. B Quantum Semiclassical Opt. 4, S7–S16 (2002).
[Crossref]

Baxter, C.

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]

Brevik, I.

I. Brevik, “Experiments in phenomenological electrodynamics and the electromagnetic energy-momentum tensor,” Phys. Reps. 52, 133–201 (1979).
[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, “Das Prinzip von der Erhaltung der Schwerpunktsbewegung und die Trägheit der Energie,” Ann. Phys. (Leipzig)  20, 627–633 (1906).
[Crossref]

Gordon, J. P.

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

Loudon, R.

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. M. Barnett, and C. Baxter, “Radiation pressure and momentum transfer in dielectrics: the photon drag effect,” Phys. Rev. A 71, 063802 (2005).
[Crossref]

R. Loudon, “Radiation pressure and momentum in dielectrics,” Fortschr. Phys. 52, 1132–1140 (2004).
[Crossref]

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

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

R. Loudon, “Theory of the radiation pressure on dielectric surfaces,” J. Mod. Opt. 49, 812–836 (2002).
[Crossref]

Mansuripur, M.

Moloney, J. V.

Padgett, M.

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

Polynkin, P.

Zakharian, A. R.

Ann. Phys. (1)

A. Einstein, “Das Prinzip von der Erhaltung der Schwerpunktsbewegung und die Trägheit der Energie,” Ann. Phys. (Leipzig)  20, 627–633 (1906).
[Crossref]

Fortschr. Phys. (1)

R. Loudon, “Radiation pressure and momentum in dielectrics,” Fortschr. Phys. 52, 1132–1140 (2004).
[Crossref]

J. Mod. Opt. (2)

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

R. Loudon, “Theory of the radiation pressure on dielectric surfaces,” J. Mod. Opt. 49, 812–836 (2002).
[Crossref]

J. Opt. B Quantum Semiclassical Opt. (1)

S. M. Barnett, “Optical angular-momentum flux,” J. Opt. B Quantum Semiclassical Opt. 4, S7–S16 (2002).
[Crossref]

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]

Opt. Express (5)

Phys. Reps. (1)

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

Phys. Rev. (1)

N. L. Balazs, “The energy-momentum tensor of the electromagnetic field inside matter,” Phys. Rev. 91, 408–411 (1953).
[Crossref]

Phys. Rev. A (3)

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

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

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. Roy. Soc. Lond. A (1)

G. Barlow, “On the torque produced by a beam of light in oblique refraction through a glass plate,” Proc. Roy. Soc. Lond. A 87, 1–16 (1912).
[Crossref]

Proc. SPIE (1)

M. Mansuripur, “Radiation pressure and the distribution of electromagnetic force in dielectric media,” in Optical Trapping and Optical Micromanipulation II, K. Dholakia and G. C. Spalding, eds., Proc. SPIE 5930, 154–160 (2005).

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Figures (2)

Fig. 1.
Fig. 1. Representation of a dielectric slab with light beam incident at the Brewster angle, showing the orientations of the three forces at the entrance surface. The corresponding forces at the exit surface are identified by the same coloring as for the entrance surface. The red colored sections of beam edge indicate the regions of unbalanced force contributions of type 3.

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Fig. 2.
Fig. 2. Representation of a dielectric prism with light beam incident at the Brewster angle, showing the coordinate system used in the calculations. The natures of the three forces at both entrance and exit surfaces are identified by the same color convention as in Fig. 1.

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Equations (55)

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f d = ( P . ∇ ) E + ∂ P ∂ t × B
f c = − ( ∇ . P ) E + ∂ P ∂ t × B
sin i = η sin r and η cos i = cos r
sin i = cos r = η η 2 + 1 and cos i = sin r = 1 η 2 + 1 .
Δ = D cos r sin ( i − r ) = D η 2 − 1 η η 2 + 1 .
T L = − ℏ ω f c Δ = − ℏ ω f D c η 2 − 1 η η 2 + 1
1 2 A ε 0 c ∣ E ∣ 2 = ℏ ω f ,
A cos i = A η cos r = A η 2 + 1 .
F 1 = ℏ ω f c η 2 − 1 2 η .
∂ E z ∂ z = E sin i η 2 − 1 η 2 δ ( z ) .
P z = ε 0 ( η 2 − 1 ) ( E sin r η ) ϑ ( − z ) .
F 2 = A η 2 + 1 ∫ d z P z ∂ E z ∂ z = 1 4 A ε 0 ∣ E ∣ 2 ( η 2 − 1 ) 2 η 2 η 2 + 1 = ℏ ω f c ( η 2 − 1 ) 2 2 η 2 η 2 + 1 ,
T 2 = ℏ ω f D c ( η 2 − 1 ) 2 2 η 3 η 2 + 1 .
∂ E ζ ∂ ζ = E η δ ( ζ ) and P ζ = ε 0 ( η 2 − 1 ) ( E η ) ϑ ( ζ ) .
F 3 = ℏ ω f c η 2 − 1 2 η 2 .
T 3 = ℏ ω f D c η 2 − 1 2 η 3 η 2 + 1 .
T s = T 2 + T 3 = ℏ ω f D c η 2 − 1 η η 2 + 1 = − T L
( F 2 + F 3 ) ∥ = − F 2 cos i + F 3 sin ( i − r ) = 0
( F 2 + F 3 ) ⊥ = F 2 sin i + F 3 cos ( i − r ) = ℏ ω f c η 2 − 1 2 η .
D cos r cos ( i − r ) = 2 D η 2 + 1 .
τ = D η c cos r = D c η 2 + 1 .
D cos r { η − cos ( i − r ) } = D η 2 − 1 η 2 + 1 ,
M c 2 Δ Z = ℏ ω D η 2 − 1 η 2 + 1 ,
p 2 + p 3 = ℏ ω c η 2 − 1 2 η
p 1 = ℏ ω c { η 2 − 1 2 η ︸ surface + 1 η ︸ bulk } = η 2 + 1 2 η ℏ ω c ︸ total .
p 1 cos ( i − r ) = ℏ ω c and − p 1 sin ( i − r ) = − ℏ ω c η 2 − 1 2 η
Δ Z = ℏ ω M c η 2 − 1 2 η τ cos ( i − r ) = ℏ ω D M c 2 η 2 − 1 η 2 + 1 ,
F L = − 2 ℏ ω f c cos 2 r = − 2 ℏ ω f c η 2 − 1 η 2 + 1 .
F P = 2 F 2 cos i + 2 F 3 = ℏ ω f c ( η 2 − 1 ) 2 η 2 ( η 2 + 1 ) + ℏ ω f c η 2 − 1 η 2 = − F L .
E incid ( r ) = E exp { − ( x ′ 2 + y 2 ) 2 w 2 } exp [ − i ( ω c ) ( z ′ + p + c t ) ] x ̂ ′ ,
x ′ = ( x − p ) cos ( i − r ) + z sin ( i − r ) and z ′ = − ( x − p ) sin ( i − r ) + z cos ( i − r ) .
E prism ( r ) = ( E η ) exp { − [ ( x η ) 2 + y 2 ] 2 w 2 } exp [ − i ( ω c ) ( η z + c t ) ] x ̂ ,
η p cot ( i − r ) ≫ w ,
1 2 π w 2 ε 0 c ∣ E ∣ 2 = ℏ ω f .
T i j = 1 2 ℜ { 1 2 δ i j ( ε 0 ∣ E ∣ 2 + μ 0 − 1 ∣ B ∣ 2 ) − ε 0 E i * E j − μ 0 − 1 B i * B j } .
F in = 1 2 π w 2 ε 0 ∣ E ∣ 2 { − η 2 − 1 η 2 + 1 x ̂ + 2 η η 2 + 1 z ̂ } .
f i d = 1 2 ℜ ( P j * ∇ j E i ) = 1 4 ε 0 ( η 2 − 1 ) ∇ i ∣ E ( r ) ∣ 2 ,
n = x cos i + [ z − p cot ( i − r ) ] sin i
n ̂ = ( x ̂ + η z ̂ ) η 2 + 1 .
∂ E n ∂ n = ( E n incid − E n prism ) δ ( n ) and P n = ε 0 ( η 2 − 1 ) E n prism ϑ ( − n ) .
F 2 = 1 2 ∫ d V ℜ ( P n * ∂ E n ∂ n ) n ̂ ,
− ∞ < x < η p cot ( i − r ) .
F 2 = 1 4 π w 2 ε 0 ∣ E ∣ 2 ( η 2 − 1 ) 2 η 2 η 2 + 1 n ̂ .
F 3 = 1 4 ε 0 ( η 2 − 1 ) ∫ d V ∂ ∣ E ( r ) ∣ 2 ∂ x x ̂ .
− ∞ < x < η p cot ( i − r ) − η z ,
F 3 = 1 4 ε 0 η 2 − 1 η 2 π w ∣ E ∣ 2 ∫ 0 ∞ d z exp { − [ p cot ( i − r ) − z ] 2 w 2 } x ̂
= 1 8 ε 0 η 2 − 1 η 2 π w 2 ∣ E ∣ 2 { 1 + erf [ p cot ( i − r ) w ] } x ̂ .
F = 2 c η − 1 η + 1 Q ≈ 10 − 9 N for η = 1.33 and Q = 1 W ,
u ( x , y ) = exp [ − ( x 2 + y 2 ) 2 w 2 ] π w ,
E z = 2 c Q ε 0 ω 2 2 η η + 1 ∂ u ∂ x for z > 0 , and E z = 2 c Q ε 0 ω 2 2 η ( η + 1 ) ∂ u ∂ x for z < 0 .
P z = 2 ε 0 2 c Q ε 0 ω 2 η − 1 η ∂ u ∂ x ϑ ( − z ) and ∂ E z ∂ z = 2 2 c Q ε 0 ω 2 η − 1 η ∂ u ∂ x δ ( z ) ,
F z = ∫ d r P z ∂ E z ∂ z = Q c w 2 ( c ω ) 2 ( η − 1 η ) 2 .
F z ≈ 10 − 12 N for η = 1.33 , Q = 1 W , ω = 3 × 10 15 s − 1 and w = 1.5 μ m ,
F z ′ = − ∫ d r ∂ P z ∂ z E z = 2 Q c w 2 ( c ω ) 2 ( η − 1 ) ( η 2 + 1 ) η 2 ( η + 1 ) ,
F z − F z ′ = ∫ d r ∂ ∂ z ( P z E z ) ,

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