Abstract

Two mirrors guiding laser light may experience an either attractive or repulsive force, according to the type of eigenmode they guide. We propose a method for the control over the motion of a mirror by changing the operation wavelength along the dispersion curve of the mode. In addition, a novel method for trapping a mirror in a stable equilibrium, based on a superposition of two modes, is presented. The mirror is then trapped by being exposed to light only from one of its sides.

© 2005 Optical Society of America

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References

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  1. A. Ashkin , “ Acceleration and trapping of particles by radiation pressure ,” Phys. Rev. Lett.   24 (4), 156 – 159 ( 1970 ).
    [Crossref]
  2. A. Ashkin , “ History of optical trapping and manipulation of small-neutral particle, atoms and molecules ,” IEEE J. Sel. Top. Quantum Electron.   6 (6), 841 – 856 ( 2000 ).
    [Crossref]
  3. A. Dorsel , J. D. McCullen , P. Meystre , E. Vignes , and H. Walther , “ Optical bistability and mirror confinement induced by radiation pressure ,” Phys. Rev. Lett.   51 (17), 1550 – 1553 ( 1983 ).
    [Crossref]
  4. P. Meystre , E. M. Wright , J. D. McCullen , and E. Vignes , “ Theory of radiation-pressure-driven interferometers ,” J. Opt. Soc. Am. B   2 (11), 1830 – 1840 ( 1985 ).
    [Crossref]
  5. P. F. Cohadon , A. Heidmann , and M. Pinard , “ Cooling of a mirror by radiation pressure ,” Phys. Rev. Lett.   83 (16), 3174 – 3177 ( 1999 ).
    [Crossref]
  6. M. Lester and M. Nieto-Vesperinas , “ Optical forces on microparticles in an evanescent laser field ,” Opt. Lett.   24 (14), 936 – 938 ( 1999 ).
    [Crossref]
  7. P. C. Chaumet , A. Rahmani , and M. Nieto-Vesperinas , “ Optical trapping and manipulation of nano-objects with an apertureless probe ,” Phys. Rev. Lett.   88 (12), 123601 ( 2002 ).
    [Crossref] [PubMed]
  8. M. I. Antonoyiannakis and J. B. Pendry , “ Electromagnetic forces in photonic crystals ,” Phys. Rev. B   60 (4), 2363 – 2374 ( 1999 ).
    [Crossref]
  9. C. Henkel , K. Joulain , J.-P. Mulet , and J.-J. Greffet , “ Coupled surface polaritons and the Casimir force ,” Phys. Rev. A   69 (2), 023808 ( 2004 ).
    [Crossref]
  10. A. Mizrahi and L. Schächter , “ Optical Bragg accelerators ,” Phys. Rev. E   70 (1), 016505 ( 2004 ).
    [Crossref]
  11. J. A. Stratton , Electromagnetic Theory ( Mcgraw-Hill, New York , 1941 ).
  12. R. F. Harrington , Time-Harmonic Electromagnetic Fields ( McGraw-Hill, New York , 1961 ).
  13. M. Planck , The Theory of Heat Radiation ( Dover Publications, New York , 1959 ). Translated by M. Masius from the German edition of 1914.
  14. P. Yeh and A. Yariv , “ Bragg reflection waveguides ,” Opt. Commun.   19 (3), 427 – 430 ( 1976 ).
    [Crossref]
  15. M. L. Povinelli , M. Ibanescu , S. G. Johnson , and J. D. Joannopoulos , “ Slow-light enhancement of radiation pressure in an omnidirectional-reflector waveguide ,” Appl. Phys. Lett.   85 (9), 1466 – 1468 ( 2004 ).
    [Crossref]
  16. A. Mizrahi and L. Schächter , “ Bragg reflection waveguides with a matching layer ,” Opt. Express   12 (14), 3156 – 3170 ( 2004 ). URL http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-14-3156 .
    [Crossref] [PubMed]
  17. Y. Fink , D. J. Ripin , S. Fan , C. Chen , J. D. Joannopoulos , and E. L. Thomas , “ Guiding optical light in air using an all-dielectric structure ,” J. Lightwave Technol.   17 (11), 2039 – 2041 ( 1999 ).
    [Crossref]
  18. J. Schwinger , L. L. DeRadd , K. A. Milton , and W.-Y. Tsai , Classical Electrodynamics ( Perseus Books, Reading, MA , 1998 ).
  19. M. Mansuripur , “ Radiation Pressure and the Linear Momentum of the Electromagnetic Field ,” Opt. Express   12 (22), 5375 – 5401 ( 2004 ). URL http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-22-5375 .
    [Crossref] [PubMed]
  20. M. M. Burns , J.-M. Fournier , and J. A. Golovchenko , “ Optical binding ,” Phys. Rev. Lett.   63 (12), 1233 – 1236 ( 1989 ).
    [Crossref] [PubMed]

2004 (5)

C. Henkel , K. Joulain , J.-P. Mulet , and J.-J. Greffet , “ Coupled surface polaritons and the Casimir force ,” Phys. Rev. A   69 (2), 023808 ( 2004 ).
[Crossref]

A. Mizrahi and L. Schächter , “ Optical Bragg accelerators ,” Phys. Rev. E   70 (1), 016505 ( 2004 ).
[Crossref]

M. L. Povinelli , M. Ibanescu , S. G. Johnson , and J. D. Joannopoulos , “ Slow-light enhancement of radiation pressure in an omnidirectional-reflector waveguide ,” Appl. Phys. Lett.   85 (9), 1466 – 1468 ( 2004 ).
[Crossref]

A. Mizrahi and L. Schächter , “ Bragg reflection waveguides with a matching layer ,” Opt. Express   12 (14), 3156 – 3170 ( 2004 ). URL http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-14-3156 .
[Crossref] [PubMed]

M. Mansuripur , “ Radiation Pressure and the Linear Momentum of the Electromagnetic Field ,” Opt. Express   12 (22), 5375 – 5401 ( 2004 ). URL http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-22-5375 .
[Crossref] [PubMed]

2002 (1)

P. C. Chaumet , A. Rahmani , and M. Nieto-Vesperinas , “ Optical trapping and manipulation of nano-objects with an apertureless probe ,” Phys. Rev. Lett.   88 (12), 123601 ( 2002 ).
[Crossref] [PubMed]

2000 (1)

A. Ashkin , “ History of optical trapping and manipulation of small-neutral particle, atoms and molecules ,” IEEE J. Sel. Top. Quantum Electron.   6 (6), 841 – 856 ( 2000 ).
[Crossref]

1999 (4)

M. I. Antonoyiannakis and J. B. Pendry , “ Electromagnetic forces in photonic crystals ,” Phys. Rev. B   60 (4), 2363 – 2374 ( 1999 ).
[Crossref]

P. F. Cohadon , A. Heidmann , and M. Pinard , “ Cooling of a mirror by radiation pressure ,” Phys. Rev. Lett.   83 (16), 3174 – 3177 ( 1999 ).
[Crossref]

M. Lester and M. Nieto-Vesperinas , “ Optical forces on microparticles in an evanescent laser field ,” Opt. Lett.   24 (14), 936 – 938 ( 1999 ).
[Crossref]

Y. Fink , D. J. Ripin , S. Fan , C. Chen , J. D. Joannopoulos , and E. L. Thomas , “ Guiding optical light in air using an all-dielectric structure ,” J. Lightwave Technol.   17 (11), 2039 – 2041 ( 1999 ).
[Crossref]

1989 (1)

M. M. Burns , J.-M. Fournier , and J. A. Golovchenko , “ Optical binding ,” Phys. Rev. Lett.   63 (12), 1233 – 1236 ( 1989 ).
[Crossref] [PubMed]

1985 (1)

1983 (1)

A. Dorsel , J. D. McCullen , P. Meystre , E. Vignes , and H. Walther , “ Optical bistability and mirror confinement induced by radiation pressure ,” Phys. Rev. Lett.   51 (17), 1550 – 1553 ( 1983 ).
[Crossref]

1976 (1)

P. Yeh and A. Yariv , “ Bragg reflection waveguides ,” Opt. Commun.   19 (3), 427 – 430 ( 1976 ).
[Crossref]

1970 (1)

A. Ashkin , “ Acceleration and trapping of particles by radiation pressure ,” Phys. Rev. Lett.   24 (4), 156 – 159 ( 1970 ).
[Crossref]

1961 (1)

R. F. Harrington , Time-Harmonic Electromagnetic Fields ( McGraw-Hill, New York , 1961 ).

Antonoyiannakis, M. I.

M. I. Antonoyiannakis and J. B. Pendry , “ Electromagnetic forces in photonic crystals ,” Phys. Rev. B   60 (4), 2363 – 2374 ( 1999 ).
[Crossref]

Ashkin, A.

A. Ashkin , “ History of optical trapping and manipulation of small-neutral particle, atoms and molecules ,” IEEE J. Sel. Top. Quantum Electron.   6 (6), 841 – 856 ( 2000 ).
[Crossref]

A. Ashkin , “ Acceleration and trapping of particles by radiation pressure ,” Phys. Rev. Lett.   24 (4), 156 – 159 ( 1970 ).
[Crossref]

Burns, M. M.

M. M. Burns , J.-M. Fournier , and J. A. Golovchenko , “ Optical binding ,” Phys. Rev. Lett.   63 (12), 1233 – 1236 ( 1989 ).
[Crossref] [PubMed]

Chaumet, P. C.

P. C. Chaumet , A. Rahmani , and M. Nieto-Vesperinas , “ Optical trapping and manipulation of nano-objects with an apertureless probe ,” Phys. Rev. Lett.   88 (12), 123601 ( 2002 ).
[Crossref] [PubMed]

Chen, C.

Cohadon, P. F.

P. F. Cohadon , A. Heidmann , and M. Pinard , “ Cooling of a mirror by radiation pressure ,” Phys. Rev. Lett.   83 (16), 3174 – 3177 ( 1999 ).
[Crossref]

DeRadd, L. L.

J. Schwinger , L. L. DeRadd , K. A. Milton , and W.-Y. Tsai , Classical Electrodynamics ( Perseus Books, Reading, MA , 1998 ).

Dorsel, A.

A. Dorsel , J. D. McCullen , P. Meystre , E. Vignes , and H. Walther , “ Optical bistability and mirror confinement induced by radiation pressure ,” Phys. Rev. Lett.   51 (17), 1550 – 1553 ( 1983 ).
[Crossref]

Fan, S.

Fink, Y.

Fournier, J.-M.

M. M. Burns , J.-M. Fournier , and J. A. Golovchenko , “ Optical binding ,” Phys. Rev. Lett.   63 (12), 1233 – 1236 ( 1989 ).
[Crossref] [PubMed]

Golovchenko, J. A.

M. M. Burns , J.-M. Fournier , and J. A. Golovchenko , “ Optical binding ,” Phys. Rev. Lett.   63 (12), 1233 – 1236 ( 1989 ).
[Crossref] [PubMed]

Greffet, J.-J.

C. Henkel , K. Joulain , J.-P. Mulet , and J.-J. Greffet , “ Coupled surface polaritons and the Casimir force ,” Phys. Rev. A   69 (2), 023808 ( 2004 ).
[Crossref]

Harrington, R. F.

R. F. Harrington , Time-Harmonic Electromagnetic Fields ( McGraw-Hill, New York , 1961 ).

Heidmann, A.

P. F. Cohadon , A. Heidmann , and M. Pinard , “ Cooling of a mirror by radiation pressure ,” Phys. Rev. Lett.   83 (16), 3174 – 3177 ( 1999 ).
[Crossref]

Henkel, C.

C. Henkel , K. Joulain , J.-P. Mulet , and J.-J. Greffet , “ Coupled surface polaritons and the Casimir force ,” Phys. Rev. A   69 (2), 023808 ( 2004 ).
[Crossref]

Ibanescu, M.

M. L. Povinelli , M. Ibanescu , S. G. Johnson , and J. D. Joannopoulos , “ Slow-light enhancement of radiation pressure in an omnidirectional-reflector waveguide ,” Appl. Phys. Lett.   85 (9), 1466 – 1468 ( 2004 ).
[Crossref]

Joannopoulos, J. D.

M. L. Povinelli , M. Ibanescu , S. G. Johnson , and J. D. Joannopoulos , “ Slow-light enhancement of radiation pressure in an omnidirectional-reflector waveguide ,” Appl. Phys. Lett.   85 (9), 1466 – 1468 ( 2004 ).
[Crossref]

Y. Fink , D. J. Ripin , S. Fan , C. Chen , J. D. Joannopoulos , and E. L. Thomas , “ Guiding optical light in air using an all-dielectric structure ,” J. Lightwave Technol.   17 (11), 2039 – 2041 ( 1999 ).
[Crossref]

Johnson, S. G.

M. L. Povinelli , M. Ibanescu , S. G. Johnson , and J. D. Joannopoulos , “ Slow-light enhancement of radiation pressure in an omnidirectional-reflector waveguide ,” Appl. Phys. Lett.   85 (9), 1466 – 1468 ( 2004 ).
[Crossref]

Joulain, K.

C. Henkel , K. Joulain , J.-P. Mulet , and J.-J. Greffet , “ Coupled surface polaritons and the Casimir force ,” Phys. Rev. A   69 (2), 023808 ( 2004 ).
[Crossref]

Lester, M.

Mansuripur, M.

McCullen, J. D.

P. Meystre , E. M. Wright , J. D. McCullen , and E. Vignes , “ Theory of radiation-pressure-driven interferometers ,” J. Opt. Soc. Am. B   2 (11), 1830 – 1840 ( 1985 ).
[Crossref]

A. Dorsel , J. D. McCullen , P. Meystre , E. Vignes , and H. Walther , “ Optical bistability and mirror confinement induced by radiation pressure ,” Phys. Rev. Lett.   51 (17), 1550 – 1553 ( 1983 ).
[Crossref]

Meystre, P.

P. Meystre , E. M. Wright , J. D. McCullen , and E. Vignes , “ Theory of radiation-pressure-driven interferometers ,” J. Opt. Soc. Am. B   2 (11), 1830 – 1840 ( 1985 ).
[Crossref]

A. Dorsel , J. D. McCullen , P. Meystre , E. Vignes , and H. Walther , “ Optical bistability and mirror confinement induced by radiation pressure ,” Phys. Rev. Lett.   51 (17), 1550 – 1553 ( 1983 ).
[Crossref]

Milton, K. A.

J. Schwinger , L. L. DeRadd , K. A. Milton , and W.-Y. Tsai , Classical Electrodynamics ( Perseus Books, Reading, MA , 1998 ).

Mizrahi, A.

Mulet, J.-P.

C. Henkel , K. Joulain , J.-P. Mulet , and J.-J. Greffet , “ Coupled surface polaritons and the Casimir force ,” Phys. Rev. A   69 (2), 023808 ( 2004 ).
[Crossref]

Nieto-Vesperinas, M.

P. C. Chaumet , A. Rahmani , and M. Nieto-Vesperinas , “ Optical trapping and manipulation of nano-objects with an apertureless probe ,” Phys. Rev. Lett.   88 (12), 123601 ( 2002 ).
[Crossref] [PubMed]

M. Lester and M. Nieto-Vesperinas , “ Optical forces on microparticles in an evanescent laser field ,” Opt. Lett.   24 (14), 936 – 938 ( 1999 ).
[Crossref]

Pendry, J. B.

M. I. Antonoyiannakis and J. B. Pendry , “ Electromagnetic forces in photonic crystals ,” Phys. Rev. B   60 (4), 2363 – 2374 ( 1999 ).
[Crossref]

Pinard, M.

P. F. Cohadon , A. Heidmann , and M. Pinard , “ Cooling of a mirror by radiation pressure ,” Phys. Rev. Lett.   83 (16), 3174 – 3177 ( 1999 ).
[Crossref]

Planck, M.

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

Povinelli, M. L.

M. L. Povinelli , M. Ibanescu , S. G. Johnson , and J. D. Joannopoulos , “ Slow-light enhancement of radiation pressure in an omnidirectional-reflector waveguide ,” Appl. Phys. Lett.   85 (9), 1466 – 1468 ( 2004 ).
[Crossref]

Rahmani, A.

P. C. Chaumet , A. Rahmani , and M. Nieto-Vesperinas , “ Optical trapping and manipulation of nano-objects with an apertureless probe ,” Phys. Rev. Lett.   88 (12), 123601 ( 2002 ).
[Crossref] [PubMed]

Ripin, D. J.

Schächter, L.

Schwinger, J.

J. Schwinger , L. L. DeRadd , K. A. Milton , and W.-Y. Tsai , Classical Electrodynamics ( Perseus Books, Reading, MA , 1998 ).

Stratton, J. A.

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

Thomas, E. L.

Tsai, W.-Y.

J. Schwinger , L. L. DeRadd , K. A. Milton , and W.-Y. Tsai , Classical Electrodynamics ( Perseus Books, Reading, MA , 1998 ).

Vignes, E.

P. Meystre , E. M. Wright , J. D. McCullen , and E. Vignes , “ Theory of radiation-pressure-driven interferometers ,” J. Opt. Soc. Am. B   2 (11), 1830 – 1840 ( 1985 ).
[Crossref]

A. Dorsel , J. D. McCullen , P. Meystre , E. Vignes , and H. Walther , “ Optical bistability and mirror confinement induced by radiation pressure ,” Phys. Rev. Lett.   51 (17), 1550 – 1553 ( 1983 ).
[Crossref]

Walther, H.

A. Dorsel , J. D. McCullen , P. Meystre , E. Vignes , and H. Walther , “ Optical bistability and mirror confinement induced by radiation pressure ,” Phys. Rev. Lett.   51 (17), 1550 – 1553 ( 1983 ).
[Crossref]

Wright, E. M.

Yariv, A.

P. Yeh and A. Yariv , “ Bragg reflection waveguides ,” Opt. Commun.   19 (3), 427 – 430 ( 1976 ).
[Crossref]

Yeh, P.

P. Yeh and A. Yariv , “ Bragg reflection waveguides ,” Opt. Commun.   19 (3), 427 – 430 ( 1976 ).
[Crossref]

Appl. Phys. Lett. (1)

M. L. Povinelli , M. Ibanescu , S. G. Johnson , and J. D. Joannopoulos , “ Slow-light enhancement of radiation pressure in an omnidirectional-reflector waveguide ,” Appl. Phys. Lett.   85 (9), 1466 – 1468 ( 2004 ).
[Crossref]

IEEE J. Sel. Top. Quantum Electron. (1)

A. Ashkin , “ History of optical trapping and manipulation of small-neutral particle, atoms and molecules ,” IEEE J. Sel. Top. Quantum Electron.   6 (6), 841 – 856 ( 2000 ).
[Crossref]

J. Lightwave Technol. (1)

J. Opt. Soc. Am. B (1)

Opt. Commun. (1)

P. Yeh and A. Yariv , “ Bragg reflection waveguides ,” Opt. Commun.   19 (3), 427 – 430 ( 1976 ).
[Crossref]

Opt. Express (2)

Opt. Lett. (1)

Phys. Rev. A (1)

C. Henkel , K. Joulain , J.-P. Mulet , and J.-J. Greffet , “ Coupled surface polaritons and the Casimir force ,” Phys. Rev. A   69 (2), 023808 ( 2004 ).
[Crossref]

Phys. Rev. B (1)

M. I. Antonoyiannakis and J. B. Pendry , “ Electromagnetic forces in photonic crystals ,” Phys. Rev. B   60 (4), 2363 – 2374 ( 1999 ).
[Crossref]

Phys. Rev. E (1)

A. Mizrahi and L. Schächter , “ Optical Bragg accelerators ,” Phys. Rev. E   70 (1), 016505 ( 2004 ).
[Crossref]

Phys. Rev. Lett. (5)

A. Ashkin , “ Acceleration and trapping of particles by radiation pressure ,” Phys. Rev. Lett.   24 (4), 156 – 159 ( 1970 ).
[Crossref]

P. C. Chaumet , A. Rahmani , and M. Nieto-Vesperinas , “ Optical trapping and manipulation of nano-objects with an apertureless probe ,” Phys. Rev. Lett.   88 (12), 123601 ( 2002 ).
[Crossref] [PubMed]

P. F. Cohadon , A. Heidmann , and M. Pinard , “ Cooling of a mirror by radiation pressure ,” Phys. Rev. Lett.   83 (16), 3174 – 3177 ( 1999 ).
[Crossref]

A. Dorsel , J. D. McCullen , P. Meystre , E. Vignes , and H. Walther , “ Optical bistability and mirror confinement induced by radiation pressure ,” Phys. Rev. Lett.   51 (17), 1550 – 1553 ( 1983 ).
[Crossref]

M. M. Burns , J.-M. Fournier , and J. A. Golovchenko , “ Optical binding ,” Phys. Rev. Lett.   63 (12), 1233 – 1236 ( 1989 ).
[Crossref] [PubMed]

Other (4)

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

R. F. Harrington , Time-Harmonic Electromagnetic Fields ( McGraw-Hill, New York , 1961 ).

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

J. Schwinger , L. L. DeRadd , K. A. Milton , and W.-Y. Tsai , Classical Electrodynamics ( Perseus Books, Reading, MA , 1998 ).

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Figures (4)

Fig. 1.
Fig. 1.

A general configuration of two mirrors guiding light.

Fig. 2.
Fig. 2.

Dispersion curves for a configuration of two Bragg mirrors: Odd TM (left) and even TM (right). The three curves shown are D int = 0.3λ 0 (solid red), D int = 0.6λ 0 (dashed green), and D int = 1.0λ 0 (dotted blue). The transverse pass-bands of the infinite periodic structures are indicated in gray. The inset shows the odd modes near the lower band-gap edge magnified, emphasizing the difference between the curves.

Fig. 3.
Fig. 3.

The normalized time-averaged Maxwell stress-tensor component 〈Txx 〉 as a function of the frequency, for a configuration of two Bragg mirrors.

Fig. 4.
Fig. 4.

Trapping of a mirror by a superposition of an even mode and an odd mode. Top: Time-averaged Maxwell stress-tensor component 〈Txx 〉 for the odd TM mode, the even TE mode, and their sum. Bottom: Potential well of the total transverse force.

Tables (1)

Tables Icon

Table 1.Txx 〉 and the sign of the time-averaged force between two mirrors guiding light, for even and odd modes (either TE or TM).

Equations (16)

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

E z = E 0 cosh ( Γ x x ) e j k z z ,
E x = E 0 j k z Γ x sinh ( Γ x x ) e j k z z ,
H y = E 0 j ωε 0 Γ x sinh ( Γ x x ) e j k z z ,
E z = E 0 sinh ( Γ x x ) e j k z z ,
E x = E 0 j k z Γ x cosh ( Γ x x ) e j k z z ,
H y = E 0 j ωε 0 Γ x cosh ( Γ x x ) e j k z z ,
E z = E 0 e j ω c z ,
E x = E 0 j ω c x e j ω c z ,
H y = E 0 η 0 j ω c x e j ω c z .
E z = 0 ,
E x = E 0 e j ω c z ,
H y = E 0 η 0 e j ω c z .
T xx = 1 4 ε 0 E x 2 1 4 ε 0 E z 2 1 4 μ 0 H y 2 ;
T xx ( even ) = 1 4 ε 0 E 0 2 Γ x 2 sinh ( Γ x x ) 2 Γ x 2 cosh ( Γ x x ) 2 Γ x 2 ,
T xx ( odd ) = 1 4 ε 0 E 0 2 Γ x 2 cosh ( Γ x x ) 2 Γ x 2 sinh ( Γ x x ) 2 Γ x 2 .
f x = 1 4 1 ε 0 ρ s , e 2 1 4 ε 0 J s , m 2 1 4 μ 0 J s , e 2 .

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