Abstract

It is demonstrated that a waveguide consisting of two dielectric slabs may become an all-optical spring when guiding a superposition of two transverse evanescent modes. Both slabs are transversally trapped in stable equilibrium due to the optical forces developed. A condition for stable equilibrium on the wavenumbers of the two modes is expressed analytically. The spring constant characterizing the system is shown to have a maximal value as a function of the equilibrium distance between the slabs and their width.

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References

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  1. A. Ashkin, IEEE J. Sel. Top. Quantum Electron. 6, 841 (2000).
  2. A. Dorsel, J. D. McCullen, P. Meystre, E. Vignes, and H. Walther, Phys. Rev. Lett. 51, 1550 (1983).
  3. P. Meystre, E. M. Wright, J. D. McCullen, and E. Vignes, J. Opt. Soc. Am. B 2, 1830 (1985).
  4. B. S. Sheard, M. B. Gray, C. M. Mow-Lowry, D. E. McClelland, and S. E. Whitcomb, Phys. Rev. A 69, 051801 (2004).
  5. M. L. Povinelli, M. Ibanescu, S. G. Johnson, and J. D. Joannopoulos, Appl. Phys. Lett. 85, 1466 (2004).
  6. M. L. Povinelli, M. Loncar, M. Ibanescu, E. J. Smythe, S. G. Johnson, F. Capasso, and J. D. Joannopoulos, Opt. Lett. 30, 3042 (2005).
    [PubMed]
  7. A. Mizrahi and L. Schächter, Opt. Express 13, 9804 (2005).
    [PubMed]
  8. A. Mizrahi and L. Schächter, Phys. Rev. E 74, 036504 (2006).
  9. M. M. Burns, J.-M. Fournier, and J. A. Golovchenko, Phys. Rev. Lett. 63, 1233 (1989).
    [PubMed]
  10. Y.-F. Li and J. W. Y. Lit, J. Opt. Soc. Am. A 4, 671 (1987).
  11. Q. Xu, V. R. Almeida, R. R. Panepucci, and M. Lipson, Opt. Lett. 29, 1626 (2004).
    [PubMed]
  12. J. A. Stratton, Electromagnetic Theory (McGraw-Hill, 1941).
  13. M. L. Povinelli, S. G. Johnson, M. Loncar, M. Ibanescu, E. J. Smythe, F. Capasso, and J. D. Joannopoulos, Opt. Express 13, 8286 (2005).
    [PubMed]

2006

A. Mizrahi and L. Schächter, Phys. Rev. E 74, 036504 (2006).

2005

2004

Q. Xu, V. R. Almeida, R. R. Panepucci, and M. Lipson, Opt. Lett. 29, 1626 (2004).
[PubMed]

B. S. Sheard, M. B. Gray, C. M. Mow-Lowry, D. E. McClelland, and S. E. Whitcomb, Phys. Rev. A 69, 051801 (2004).

M. L. Povinelli, M. Ibanescu, S. G. Johnson, and J. D. Joannopoulos, Appl. Phys. Lett. 85, 1466 (2004).

2000

A. Ashkin, IEEE J. Sel. Top. Quantum Electron. 6, 841 (2000).

1989

M. M. Burns, J.-M. Fournier, and J. A. Golovchenko, Phys. Rev. Lett. 63, 1233 (1989).
[PubMed]

1987

1985

1983

A. Dorsel, J. D. McCullen, P. Meystre, E. Vignes, and H. Walther, Phys. Rev. Lett. 51, 1550 (1983).

Almeida, V. R.

Ashkin, A.

A. Ashkin, IEEE J. Sel. Top. Quantum Electron. 6, 841 (2000).

Burns, M. M.

M. M. Burns, J.-M. Fournier, and J. A. Golovchenko, Phys. Rev. Lett. 63, 1233 (1989).
[PubMed]

Capasso, F.

Dorsel, A.

A. Dorsel, J. D. McCullen, P. Meystre, E. Vignes, and H. Walther, Phys. Rev. Lett. 51, 1550 (1983).

Fournier, J.-M.

M. M. Burns, J.-M. Fournier, and J. A. Golovchenko, Phys. Rev. Lett. 63, 1233 (1989).
[PubMed]

Golovchenko, J. A.

M. M. Burns, J.-M. Fournier, and J. A. Golovchenko, Phys. Rev. Lett. 63, 1233 (1989).
[PubMed]

Gray, M. B.

B. S. Sheard, M. B. Gray, C. M. Mow-Lowry, D. E. McClelland, and S. E. Whitcomb, Phys. Rev. A 69, 051801 (2004).

Ibanescu, M.

Joannopoulos, J. D.

Johnson, S. G.

Li, Y.-F.

Lipson, M.

Lit, J. W. Y.

Loncar, M.

McClelland, D. E.

B. S. Sheard, M. B. Gray, C. M. Mow-Lowry, D. E. McClelland, and S. E. Whitcomb, Phys. Rev. A 69, 051801 (2004).

McCullen, J. D.

P. Meystre, E. M. Wright, J. D. McCullen, and E. Vignes, J. Opt. Soc. Am. B 2, 1830 (1985).

A. Dorsel, J. D. McCullen, P. Meystre, E. Vignes, and H. Walther, Phys. Rev. Lett. 51, 1550 (1983).

Meystre, P.

P. Meystre, E. M. Wright, J. D. McCullen, and E. Vignes, J. Opt. Soc. Am. B 2, 1830 (1985).

A. Dorsel, J. D. McCullen, P. Meystre, E. Vignes, and H. Walther, Phys. Rev. Lett. 51, 1550 (1983).

Mizrahi, A.

A. Mizrahi and L. Schächter, Phys. Rev. E 74, 036504 (2006).

A. Mizrahi and L. Schächter, Opt. Express 13, 9804 (2005).
[PubMed]

Mow-Lowry, C. M.

B. S. Sheard, M. B. Gray, C. M. Mow-Lowry, D. E. McClelland, and S. E. Whitcomb, Phys. Rev. A 69, 051801 (2004).

Panepucci, R. R.

Povinelli, M. L.

Schächter, L.

A. Mizrahi and L. Schächter, Phys. Rev. E 74, 036504 (2006).

A. Mizrahi and L. Schächter, Opt. Express 13, 9804 (2005).
[PubMed]

Sheard, B. S.

B. S. Sheard, M. B. Gray, C. M. Mow-Lowry, D. E. McClelland, and S. E. Whitcomb, Phys. Rev. A 69, 051801 (2004).

Smythe, E. J.

Stratton, J. A.

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

Vignes, E.

P. Meystre, E. M. Wright, J. D. McCullen, and E. Vignes, J. Opt. Soc. Am. B 2, 1830 (1985).

A. Dorsel, J. D. McCullen, P. Meystre, E. Vignes, and H. Walther, Phys. Rev. Lett. 51, 1550 (1983).

Walther, H.

A. Dorsel, J. D. McCullen, P. Meystre, E. Vignes, and H. Walther, Phys. Rev. Lett. 51, 1550 (1983).

Whitcomb, S. E.

B. S. Sheard, M. B. Gray, C. M. Mow-Lowry, D. E. McClelland, and S. E. Whitcomb, Phys. Rev. A 69, 051801 (2004).

Wright, E. M.

Xu, Q.

Appl. Phys. Lett.

M. L. Povinelli, M. Ibanescu, S. G. Johnson, and J. D. Joannopoulos, Appl. Phys. Lett. 85, 1466 (2004).

IEEE J. Sel. Top. Quantum Electron.

A. Ashkin, IEEE J. Sel. Top. Quantum Electron. 6, 841 (2000).

J. Opt. Soc. Am. A

J. Opt. Soc. Am. B

Opt. Express

Opt. Lett.

Phys. Rev. A

B. S. Sheard, M. B. Gray, C. M. Mow-Lowry, D. E. McClelland, and S. E. Whitcomb, Phys. Rev. A 69, 051801 (2004).

Phys. Rev. E

A. Mizrahi and L. Schächter, Phys. Rev. E 74, 036504 (2006).

Phys. Rev. Lett.

M. M. Burns, J.-M. Fournier, and J. A. Golovchenko, Phys. Rev. Lett. 63, 1233 (1989).
[PubMed]

A. Dorsel, J. D. McCullen, P. Meystre, E. Vignes, and H. Walther, Phys. Rev. Lett. 51, 1550 (1983).

Other

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

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Figures (5)

Fig. 1
Fig. 1

Two-slab waveguide. H z for the odd TE mode is superimposed on the schematic of the system.

Fig. 2
Fig. 2

Contours of the transverse force per unit area per unit power in the two-slab waveguide normalized by ( c λ 0 Δ y ) 1 as a function of the slabs’ width and the distance between the slabs. (a) Even TM attractive force ( F A ) (dB). (b) Odd TE repulsive force F B (dB).

Fig. 3
Fig. 3

(a) Spring constant K of the two-slab waveguide normalized by K 0 ( c λ 0 2 Δ y ) 1 as a function of the slabs’ width and the equilibrium distance between the slabs. Negative values of K were replaced by zeros. (b) Power ratio α (dB) of the repulsive and attractive modes.

Fig. 4
Fig. 4

(a) Maximal spring constant of the two-slab waveguide as a function of the slabs’ permittivity ϵ r . (b) Slabs’ width and equilibrium distance corresponding to the optimal spring, as a function of ϵ r .

Fig. 5
Fig. 5

(a) Longitudinal wavenumber functions of the attractive mode β A , the repulsive mode β R , and their weighted sum β T , normalized by β 0 ω 0 c , for the optimal spring with ϵ r = 3.45 2 . (b) Magnification of the stable equilibrium region of β A . The equilibrium distance is indicated by a vertical dotted line.

Equations (9)

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F T ( D ) = [ F A ( D ) + α F R ( D ) ] ( 1 + α ) .
α = F A ( D 0 ) F R ( D 0 ) .
K = d F T d D D = D 0 ,
F = 1 ω 0 Δ y ω D W P ,
F = 1 ω 0 Δ y ( β D ω β ) W P = 1 ω 0 Δ 0 β D ,
β A + α β R = 0 .
β A + α β R < 0 ,
K = 1 ω 0 Δ y β A β R β R β A β R β A ,
( β R β A ) > 0 .

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