Abstract

By considering a perfect reflector submerged in a dielectric fluid, we show that the Minkowski formulation describes the optical momentum transfer to submerged objects. This result is required by global energy conservation, regardless of the phase of the reflected wave. While the electromagnetic pressure on a submerged reflector can vary with phase of the mirror reflection coefficient between twice the Abraham momentum and twice the Minkowski momentum, the Minkowski momentum is always restored due to the additional pressure on the dielectric surface. This analysis also gives further evidence for use of the Minkowski stress tensor at the boundary of a dielectric interface, which has been the subject of a long-standing debate in physics and the source of uncertainty in the modeling of optical forces on submerged particles.

© 2011 Optical Society of America

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References

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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]

2010 (6)

K. Dholakia and P. Zemnek, Rev. Mod. Phys. 82, 1767 (2010).
[CrossRef]

S. M. Barnett, Phys. Rev. Lett. 104, 070401 (2010).
[CrossRef] [PubMed]

M. Mansuripur, Opt. Commun. 283, 1997 (2010).
[CrossRef]

S. M. Barnett and R. Loudon, Phil. Trans. R. Soc. A 368, 927 (2010).
[CrossRef] [PubMed]

C. Baxter and R. Loudon, J. Mod. Opt. 57, 830 (2010).
[CrossRef]

A. Hirose, Can. J. Phys. 88, 247 (2010).
[CrossRef]

2008 (2)

R. Gordon, M. Kawano, and J. T. Blakely, Phys. Rev. B 77, 245125 (2008).
[CrossRef]

T. M. Grzegorczyk and B. A. Kemp, Proc. SPIE 7038, 70381S (2008).
[CrossRef]

2007 (4)

R. N. C. Pfeifer, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, Rev. Mod. Phys. 79, 1197 (2007).
[CrossRef]

M. L. Povinelli, Nat. Photon. 1, 370 (2007).
[CrossRef]

B. A. Kemp, J. A. Kong, and T. M. Grzegorczyk, Phys. Rev. A 75, 053810 (2007).
[CrossRef]

M. Mansuripur, Opt. Express 15, 2677 (2007).
[CrossRef] [PubMed]

2006 (3)

U. Leonhardt, Nature 444, 823 (2006).
[CrossRef] [PubMed]

D. Maystre and P. Vincent, J. Opt. A: Pure Appl. Opt. 8, 1059 (2006).
[CrossRef]

B. A. Kemp, T. M. Grzegorczyk, and J. A. Kong, Phys. Rev. Lett. 97, 133902 (2006).
[CrossRef] [PubMed]

2005 (1)

2004 (1)

2003 (1)

D. G. Grier, Nature 424, 810 (2003).
[CrossRef] [PubMed]

2002 (1)

R. Loudon, J. Mod. Opt. 49, 821 (2002).
[CrossRef]

1990 (1)

M. M. Burns, J. M. Fournier, and J. Golovchenko, Science 249, 749 (1990).
[CrossRef] [PubMed]

1978 (1)

R. V. Jones and B. Leslie, Proc. R. Soc. A 360, 347 (1978).
[CrossRef]

1970 (1)

A. Ashkin, Phys. Rev. Lett. 24, 156 (1970).
[CrossRef]

1967 (1)

P. Daly and H. Gruenberg, J. Appl. Phys. 38, 4486 (1967).
[CrossRef]

1954 (1)

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

Ashkin, A.

A. Ashkin, Phys. Rev. Lett. 24, 156 (1970).
[CrossRef]

Barnett, S. M.

S. M. Barnett, Phys. Rev. Lett. 104, 070401 (2010).
[CrossRef] [PubMed]

S. M. Barnett and R. Loudon, Phil. Trans. R. Soc. A 368, 927 (2010).
[CrossRef] [PubMed]

Baxter, C.

C. Baxter and R. Loudon, J. Mod. Opt. 57, 830 (2010).
[CrossRef]

Blakely, J. T.

R. Gordon, M. Kawano, and J. T. Blakely, Phys. Rev. B 77, 245125 (2008).
[CrossRef]

Burns, M. M.

M. M. Burns, J. M. Fournier, and J. Golovchenko, Science 249, 749 (1990).
[CrossRef] [PubMed]

Daly, P.

P. Daly and H. Gruenberg, J. Appl. Phys. 38, 4486 (1967).
[CrossRef]

Dholakia, K.

K. Dholakia and P. Zemnek, Rev. Mod. Phys. 82, 1767 (2010).
[CrossRef]

Fournier, J. M.

M. M. Burns, J. M. Fournier, and J. Golovchenko, Science 249, 749 (1990).
[CrossRef] [PubMed]

Golovchenko, J.

M. M. Burns, J. M. Fournier, and J. Golovchenko, Science 249, 749 (1990).
[CrossRef] [PubMed]

Gordon, R.

R. Gordon, M. Kawano, and J. T. Blakely, Phys. Rev. B 77, 245125 (2008).
[CrossRef]

Grier, D. G.

D. G. Grier, Nature 424, 810 (2003).
[CrossRef] [PubMed]

Gruenberg, H.

P. Daly and H. Gruenberg, J. Appl. Phys. 38, 4486 (1967).
[CrossRef]

Grzegorczyk, T. M.

T. M. Grzegorczyk and B. A. Kemp, Proc. SPIE 7038, 70381S (2008).
[CrossRef]

B. A. Kemp, J. A. Kong, and T. M. Grzegorczyk, Phys. Rev. A 75, 053810 (2007).
[CrossRef]

B. A. Kemp, T. M. Grzegorczyk, and J. A. Kong, Phys. Rev. Lett. 97, 133902 (2006).
[CrossRef] [PubMed]

B. A. Kemp, T. M. Grzegorczyk, and J. A. Kong, Opt. Express 13, 9280 (2005).
[CrossRef] [PubMed]

Heckenberg, N. R.

R. N. C. Pfeifer, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, Rev. Mod. Phys. 79, 1197 (2007).
[CrossRef]

Hirose, A.

A. Hirose, Can. J. Phys. 88, 247 (2010).
[CrossRef]

Jones, R. V.

R. V. Jones and B. Leslie, Proc. R. Soc. A 360, 347 (1978).
[CrossRef]

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

Kawano, M.

R. Gordon, M. Kawano, and J. T. Blakely, Phys. Rev. B 77, 245125 (2008).
[CrossRef]

Kemp, B. A.

T. M. Grzegorczyk and B. A. Kemp, Proc. SPIE 7038, 70381S (2008).
[CrossRef]

B. A. Kemp, J. A. Kong, and T. M. Grzegorczyk, Phys. Rev. A 75, 053810 (2007).
[CrossRef]

B. A. Kemp, T. M. Grzegorczyk, and J. A. Kong, Phys. Rev. Lett. 97, 133902 (2006).
[CrossRef] [PubMed]

B. A. Kemp, T. M. Grzegorczyk, and J. A. Kong, Opt. Express 13, 9280 (2005).
[CrossRef] [PubMed]

Kong, J. A.

B. A. Kemp, J. A. Kong, and T. M. Grzegorczyk, Phys. Rev. A 75, 053810 (2007).
[CrossRef]

B. A. Kemp, T. M. Grzegorczyk, and J. A. Kong, Phys. Rev. Lett. 97, 133902 (2006).
[CrossRef] [PubMed]

B. A. Kemp, T. M. Grzegorczyk, and J. A. Kong, Opt. Express 13, 9280 (2005).
[CrossRef] [PubMed]

J. A. Kong, Electromagnetic Wave Theory (EMW, 2005).

Leonhardt, U.

U. Leonhardt, Nature 444, 823 (2006).
[CrossRef] [PubMed]

Leslie, B.

R. V. Jones and B. Leslie, Proc. R. Soc. A 360, 347 (1978).
[CrossRef]

Loudon, R.

C. Baxter and R. Loudon, J. Mod. Opt. 57, 830 (2010).
[CrossRef]

S. M. Barnett and R. Loudon, Phil. Trans. R. Soc. A 368, 927 (2010).
[CrossRef] [PubMed]

R. Loudon, J. Mod. Opt. 49, 821 (2002).
[CrossRef]

Mansuripur, M.

Maystre, D.

D. Maystre and P. Vincent, J. Opt. A: Pure Appl. Opt. 8, 1059 (2006).
[CrossRef]

Nieminen, T. A.

R. N. C. Pfeifer, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, Rev. Mod. Phys. 79, 1197 (2007).
[CrossRef]

Pfeifer, R. N. C.

R. N. C. Pfeifer, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, Rev. Mod. Phys. 79, 1197 (2007).
[CrossRef]

Povinelli, M. L.

M. L. Povinelli, Nat. Photon. 1, 370 (2007).
[CrossRef]

Richards, J. C. S.

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

Rubinsztein-Dunlop, H.

R. N. C. Pfeifer, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, Rev. Mod. Phys. 79, 1197 (2007).
[CrossRef]

Stratton, J. A.

J. A. Stratton, Electromagnetic Theory (Mcgraw-Hill, 1941).

Vincent, P.

D. Maystre and P. Vincent, J. Opt. A: Pure Appl. Opt. 8, 1059 (2006).
[CrossRef]

Zemnek, P.

K. Dholakia and P. Zemnek, Rev. Mod. Phys. 82, 1767 (2010).
[CrossRef]

Can. J. Phys. (1)

A. Hirose, Can. J. Phys. 88, 247 (2010).
[CrossRef]

J. Appl. Phys. (1)

P. Daly and H. Gruenberg, J. Appl. Phys. 38, 4486 (1967).
[CrossRef]

J. Mod. Opt. (2)

R. Loudon, J. Mod. Opt. 49, 821 (2002).
[CrossRef]

C. Baxter and R. Loudon, J. Mod. Opt. 57, 830 (2010).
[CrossRef]

J. Opt. A: Pure Appl. Opt. (1)

D. Maystre and P. Vincent, J. Opt. A: Pure Appl. Opt. 8, 1059 (2006).
[CrossRef]

Nat. Photon. (1)

M. L. Povinelli, Nat. Photon. 1, 370 (2007).
[CrossRef]

Nature (2)

D. G. Grier, Nature 424, 810 (2003).
[CrossRef] [PubMed]

U. Leonhardt, Nature 444, 823 (2006).
[CrossRef] [PubMed]

Opt. Commun. (1)

M. Mansuripur, Opt. Commun. 283, 1997 (2010).
[CrossRef]

Opt. Express (3)

Phil. Trans. R. Soc. A (1)

S. M. Barnett and R. Loudon, Phil. Trans. R. Soc. A 368, 927 (2010).
[CrossRef] [PubMed]

Phys. Rev. A (1)

B. A. Kemp, J. A. Kong, and T. M. Grzegorczyk, Phys. Rev. A 75, 053810 (2007).
[CrossRef]

Phys. Rev. B (1)

R. Gordon, M. Kawano, and J. T. Blakely, Phys. Rev. B 77, 245125 (2008).
[CrossRef]

Phys. Rev. Lett. (3)

S. M. Barnett, Phys. Rev. Lett. 104, 070401 (2010).
[CrossRef] [PubMed]

A. Ashkin, Phys. Rev. Lett. 24, 156 (1970).
[CrossRef]

B. A. Kemp, T. M. Grzegorczyk, and J. A. Kong, Phys. Rev. Lett. 97, 133902 (2006).
[CrossRef] [PubMed]

Proc. R. Soc. A (2)

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

R. V. Jones and B. Leslie, Proc. R. Soc. A 360, 347 (1978).
[CrossRef]

Proc. SPIE (1)

T. M. Grzegorczyk and B. A. Kemp, Proc. SPIE 7038, 70381S (2008).
[CrossRef]

Rev. Mod. Phys. (2)

R. N. C. Pfeifer, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, Rev. Mod. Phys. 79, 1197 (2007).
[CrossRef]

K. Dholakia and P. Zemnek, Rev. Mod. Phys. 82, 1767 (2010).
[CrossRef]

Science (1)

M. M. Burns, J. M. Fournier, and J. Golovchenko, Science 249, 749 (1990).
[CrossRef] [PubMed]

Other (2)

J. A. Stratton, Electromagnetic Theory (Mcgraw-Hill, 1941).

J. A. Kong, Electromagnetic Wave Theory (EMW, 2005).

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Figures (2)

Fig. 1
Fig. 1

A plane wave is normally incident from a dielectric fluid onto a perfect reflector. The reflection coefficient of the perfect reflector is R = e i ϕ . The dielectric fluid has an index of refraction n = ϵ / ϵ 0 and is separated by a small gap of thickness δ to facilitate application of the Maxwell stress tensor to both the dielectric and the reflector. Integration paths for the two force calculations are shown by the dashed boxes.

Fig. 2
Fig. 2

Electromagnetic force on a submerged perfect mirror with reflection coefficient R = e i ϕ as a function of the mirror reflection phase ϕ. The plane wave has average power S i = 1 and is normally incident from a dielectric with n = 3 .

Equations (8)

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F ¯ m = z ^ 1 2 [ ϵ 0 2 | E x ( z = 0 + ) | 2 + μ 0 2 | H y ( z = 0 + ) | 2 ] .
F ¯ m = z ^ 1 n c [ 1 + n 2 + Re { R } ( 1 n 2 ) ] S i ,
Re { R } = n 2 cos 2 ( k 0 δ + ϕ / 2 ) sin 2 ( k 0 δ + ϕ / 2 ) n 2 cos 2 ( k 0 δ + ϕ / 2 ) + sin 2 ( k 0 δ + ϕ / 2 ) .
F ¯ l = z ^ { 2 n c 1 n c [ 1 + n 2 + Re { R } ( 1 n 2 ) ] } S i .
F ¯ total = F ¯ m + F ¯ l = z ^ 2 n c S i ,
ω = ω ( 1 n v c ) ,
ω = 1 2 m v 2 + ω ( 1 n v c ) .
v = 2 m n ω c .

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