Abstract

We have identified photothermal displacement as a mechanism for optical bistability (OB) in prism coupling into absorbing planar waveguides: heating by the absorbed incoupled power causes a buckling of the waveguide, a reduction in air-gap width, and thus an increase in incoupling efficiency and a positive feedback. We developed a theory of this OB that qualitatively agrees well with experimental results obtained by coupling argon-laser light into indium–tin oxide layers as strongly absorbing waveguides. This new OB is quite different from dispersive OB in prism or grating couplers caused by a power-dependent effective guide index.

© 1987 Optical Society of America

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References

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  1. W. Lukosz, J. Opt. Soc. Am. A 1, 1271 (1984).
  2. V. J. Montemayor, R. T. Deck, J. Opt. Soc. Am B 2, 1010 (1985).
    [CrossRef]
  3. R. Reinisch, P. Arlot, G. Vitrant, E. Pic, Appl. Phys. Lett. 47, 1248 (1985).
    [CrossRef]
  4. W. Lukosz, V. Briguet, in Optical Bistability III, H. M. Gibbs, P. Mandel, N. Peyghambarian, S. D. Smith, eds., Vol. 8 of Springer Proceedings in Physics (Springer-Verlag, Berlin, 1986), p. 87.
    [CrossRef]
  5. W. Lukosz, P. Pirani, V. Briguet, in OpticalBistability III, H. M. Gibbs, P. Mandel, N. Peyghambarian, S. D. Smith, eds., Vol. 8 of Springer Proceedings in Physics (Springer-Verlag, Berlin, 1986), p. 108.
  6. G. Assanto, B. Svensson, D. Kuchibhatia, U. J. Gibson, C. T. Seaton, G. I. Stegeman, Opt. Lett. 11, 644 (1986).
    [CrossRef] [PubMed]
  7. M. A. Olmstead, N. M. Amer, S. Kohn, D. Fournier, A. C. Boccara, Appl. Phys. A 32, 141 (1983).
    [CrossRef]
  8. C. Karner, A. Mandel, F. Träger, Appl. Phys. A 38, 19 (1985).
    [CrossRef]

1986 (1)

1985 (3)

V. J. Montemayor, R. T. Deck, J. Opt. Soc. Am B 2, 1010 (1985).
[CrossRef]

R. Reinisch, P. Arlot, G. Vitrant, E. Pic, Appl. Phys. Lett. 47, 1248 (1985).
[CrossRef]

C. Karner, A. Mandel, F. Träger, Appl. Phys. A 38, 19 (1985).
[CrossRef]

1984 (1)

W. Lukosz, J. Opt. Soc. Am. A 1, 1271 (1984).

1983 (1)

M. A. Olmstead, N. M. Amer, S. Kohn, D. Fournier, A. C. Boccara, Appl. Phys. A 32, 141 (1983).
[CrossRef]

Amer, N. M.

M. A. Olmstead, N. M. Amer, S. Kohn, D. Fournier, A. C. Boccara, Appl. Phys. A 32, 141 (1983).
[CrossRef]

Arlot, P.

R. Reinisch, P. Arlot, G. Vitrant, E. Pic, Appl. Phys. Lett. 47, 1248 (1985).
[CrossRef]

Assanto, G.

Boccara, A. C.

M. A. Olmstead, N. M. Amer, S. Kohn, D. Fournier, A. C. Boccara, Appl. Phys. A 32, 141 (1983).
[CrossRef]

Briguet, V.

W. Lukosz, V. Briguet, in Optical Bistability III, H. M. Gibbs, P. Mandel, N. Peyghambarian, S. D. Smith, eds., Vol. 8 of Springer Proceedings in Physics (Springer-Verlag, Berlin, 1986), p. 87.
[CrossRef]

W. Lukosz, P. Pirani, V. Briguet, in OpticalBistability III, H. M. Gibbs, P. Mandel, N. Peyghambarian, S. D. Smith, eds., Vol. 8 of Springer Proceedings in Physics (Springer-Verlag, Berlin, 1986), p. 108.

Deck, R. T.

V. J. Montemayor, R. T. Deck, J. Opt. Soc. Am B 2, 1010 (1985).
[CrossRef]

Fournier, D.

M. A. Olmstead, N. M. Amer, S. Kohn, D. Fournier, A. C. Boccara, Appl. Phys. A 32, 141 (1983).
[CrossRef]

Gibson, U. J.

Karner, C.

C. Karner, A. Mandel, F. Träger, Appl. Phys. A 38, 19 (1985).
[CrossRef]

Kohn, S.

M. A. Olmstead, N. M. Amer, S. Kohn, D. Fournier, A. C. Boccara, Appl. Phys. A 32, 141 (1983).
[CrossRef]

Kuchibhatia, D.

Lukosz, W.

W. Lukosz, J. Opt. Soc. Am. A 1, 1271 (1984).

W. Lukosz, V. Briguet, in Optical Bistability III, H. M. Gibbs, P. Mandel, N. Peyghambarian, S. D. Smith, eds., Vol. 8 of Springer Proceedings in Physics (Springer-Verlag, Berlin, 1986), p. 87.
[CrossRef]

W. Lukosz, P. Pirani, V. Briguet, in OpticalBistability III, H. M. Gibbs, P. Mandel, N. Peyghambarian, S. D. Smith, eds., Vol. 8 of Springer Proceedings in Physics (Springer-Verlag, Berlin, 1986), p. 108.

Mandel, A.

C. Karner, A. Mandel, F. Träger, Appl. Phys. A 38, 19 (1985).
[CrossRef]

Montemayor, V. J.

V. J. Montemayor, R. T. Deck, J. Opt. Soc. Am B 2, 1010 (1985).
[CrossRef]

Olmstead, M. A.

M. A. Olmstead, N. M. Amer, S. Kohn, D. Fournier, A. C. Boccara, Appl. Phys. A 32, 141 (1983).
[CrossRef]

Pic, E.

R. Reinisch, P. Arlot, G. Vitrant, E. Pic, Appl. Phys. Lett. 47, 1248 (1985).
[CrossRef]

Pirani, P.

W. Lukosz, P. Pirani, V. Briguet, in OpticalBistability III, H. M. Gibbs, P. Mandel, N. Peyghambarian, S. D. Smith, eds., Vol. 8 of Springer Proceedings in Physics (Springer-Verlag, Berlin, 1986), p. 108.

Reinisch, R.

R. Reinisch, P. Arlot, G. Vitrant, E. Pic, Appl. Phys. Lett. 47, 1248 (1985).
[CrossRef]

Seaton, C. T.

Stegeman, G. I.

Svensson, B.

Träger, F.

C. Karner, A. Mandel, F. Träger, Appl. Phys. A 38, 19 (1985).
[CrossRef]

Vitrant, G.

R. Reinisch, P. Arlot, G. Vitrant, E. Pic, Appl. Phys. Lett. 47, 1248 (1985).
[CrossRef]

Appl. Phys. A (2)

M. A. Olmstead, N. M. Amer, S. Kohn, D. Fournier, A. C. Boccara, Appl. Phys. A 32, 141 (1983).
[CrossRef]

C. Karner, A. Mandel, F. Träger, Appl. Phys. A 38, 19 (1985).
[CrossRef]

Appl. Phys. Lett. (1)

R. Reinisch, P. Arlot, G. Vitrant, E. Pic, Appl. Phys. Lett. 47, 1248 (1985).
[CrossRef]

J. Opt. Soc. Am B (1)

V. J. Montemayor, R. T. Deck, J. Opt. Soc. Am B 2, 1010 (1985).
[CrossRef]

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

W. Lukosz, J. Opt. Soc. Am. A 1, 1271 (1984).

Opt. Lett. (1)

Other (2)

W. Lukosz, V. Briguet, in Optical Bistability III, H. M. Gibbs, P. Mandel, N. Peyghambarian, S. D. Smith, eds., Vol. 8 of Springer Proceedings in Physics (Springer-Verlag, Berlin, 1986), p. 87.
[CrossRef]

W. Lukosz, P. Pirani, V. Briguet, in OpticalBistability III, H. M. Gibbs, P. Mandel, N. Peyghambarian, S. D. Smith, eds., Vol. 8 of Springer Proceedings in Physics (Springer-Verlag, Berlin, 1986), p. 108.

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Figures (5)

Fig. 1
Fig. 1

Prism coupling into a planar waveguide. P, input power; α, angle of incidence; PR, output (reflected) power; F, waveguiding film; S, substrate; R, reflectance of low-power probe beam (dashed lines) used to monitor the air-gap width d.

Fig. 2
Fig. 2

Calculated incoupling efficiency ηa versus gap width d for different angular detunings 0. Intersections of the straight line with ηa(d) are the stationary states for constant input power P.

Fig. 3
Fig. 3

Output power PR versus input power P for different angular detunings 0 (in units of 10−3). Left: Experimental results for ITO waveguide, TE0 mode, λ = 514.5 nm; d0(exp) ≃ 210 nm; dashed lines, reflectance Rs of probe beam versus P; scan time 120 sec. Right: Theoretical results for d0 = 250 nm; dashed lines, gap width d versus P.

Fig. 4
Fig. 4

Output power PR versus angular detuning 0 for constant input power P = 50 mW. ↔’s half-widths of low-power incoupling efficiency ηa(0) curves at large gap widths. Top: Theoretical results for d0 = 250 nm (dashed lines) and d0 = 180 nm (solid lines). Bottom: Experimental results for d0(exp) ≃ 220 nm. (dashed lines) and d0(exp) ≃ 150 nm (solid lines); scan time 10 min.

Fig. 5
Fig. 5

Periodic switching between bistable states. Output power PR, reflectance Rs of He–Ne probe beam, and input power P versus time t; period T = 5.6 sec; d0 ≃ 250 nm.; 0 = −4.9 × l0−3

Equations (4)

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η i = 4 ( γ c / γ ) ( γ L ) - 1 [ 1 - exp ( - γ L / 2 ) ] 2
η a = 4 ( γ c γ a / γ 2 ) { 1 - ( γ L ) - 1 × [ 3 - 4 exp ( - γ L / 2 ) + exp ( - γ L ) ] } ,
N ¯ 0 N 0 - n p sin α = n p ( sin α 0 - sin α ) ,
d = d 0 - η a ( d ) tan θ ,

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