Abstract

Separatrices and scaling laws in the switching dynamics of spatial solitary wave pixels are investigated. We show that the dynamics in the full model are similar to those in the plane-wave limit. Switching features may be indicated and explained by the motion of the (complex) solitary wave amplitude in the phase plane. We report generalization, into the domain of transverse effects, of the pulse area theorem for the switching process and a logarithmic law for the transient dynamics. We also consider, for what is the first time to our knowledge, phase-encoded address of solitary pixels and find that a near-square-wave temporal switching pattern is permitted without (transverse) cross switching.

© 1993 Optical Society of America

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References

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  1. N. B. Abraham and W. J. Firth, “Overview of transverse effects in nonlinear-optical systems,” J. Opt. Soc. Am. B 7, 951 (1990).
    [CrossRef]
  2. R. De La Fuente, A. Barthelemy, and C. Froehly, “Spatial-soliton-induced guided waves in a homogeneous nonlinear Kerr medium,” Opt. Lett. 16, 793 (1991).
    [CrossRef] [PubMed]
  3. S. Maneuf and F. Reynaud, “Quasi-steady state self-trapping of first, second and third order subnanosecond soliton beams,” Opt. Commun. 66, 325 (1988).
    [CrossRef]
  4. J. S. Aitchison, A. M. Weiner, Y. Silberberg, M. K. Oliver, J. L. Jackel, D. E. Leaird, E. M. Vogel, and P. W. E. Smith, “Observation of spatial optical solitons in a nonlinear glass waveguide,” Opt. Lett. 15, 471 (1990).
    [CrossRef] [PubMed]
  5. H. Adachihara, D. W. McLaughlin, J. V. Moloney, and A. C. Newell, “Solitary waves as fixed points of infinite-dimensional maps for an optical bistable ring cavity: analysis,” J. Math. Phys. 29, 63 (1988).
    [CrossRef]
  6. G. S. McDonald and W. J. Firth, “All-optical switching in a nonlinear resonator,” J. Mod. Opt. 37, 613 (1990).
    [CrossRef]
  7. G. S. McDonald and W. J. Firth, “Spatial solitary-wave optical memory,” J. Opt. Soc. Am. B 7, 1328 (1990).
    [CrossRef]
  8. H. A. Haus and A. Mecozzi, “Long-term storage of a bit stream of solitons,” Opt. Lett. 17, 1500 (1992).
    [CrossRef] [PubMed]
  9. N. A. Whitaker and H. Avramopoulos, “Addressable fiber loop memory,” presented at the International Quantum Electronics Conference, Vienna, Austria, June 14–19, 1992.
  10. R. Bonifacio and L. Lugiato, “Cooperative effects and bistability for resonance fluorescence,” Opt. Commun. 19, 172 (1976).
    [CrossRef]
  11. R. Bonifacio and P. Meystre, “Critical slowing down in optical bistability,” Opt. Commun. 29, 131 (1979).
    [CrossRef]
  12. F. A. Hopf and P. Meystre, “Numerical studies of the switching of a bistable optical memory,” Opt. Commun. 29, 235 (1979).
    [CrossRef]
  13. T. Erneux and P. Mandel, “Temporal aspects of absorptive optical bistability,” Phys. Rev. A 28, 896 (1983).
    [CrossRef]
  14. P. Mandel, “Switching pulses for an optical transistor,” Opt. Commun. 54, 374 (1985).
    [CrossRef]
  15. G. Grynberg and S. Cribier, “Critical exponents in dispersive optical bistability,” J. Phys. Lett. 44, 449 (1983).
    [CrossRef]
  16. E. Abraham and C. Rae, “Cross talk in nonlinear interference filters: loop narrowing and critical slowing down,” J. Opt. Soc. Am. B 4, 490 (1987).
    [CrossRef]
  17. P. Mandel, “Scaling properties of switching pulses,” Opt. Commun. 55, 293 (1985).
    [CrossRef]
  18. B. Segard, J. Zemmouri, and B. Macke, “Switching delays in optical bistability: an experimental study,” Opt. Commun. 60, 323 (1986).
    [CrossRef]
  19. J. Y. Bigot, A. Daunois, and P. Mandel, “Slowing down far from the limit points in optical bistability,” Phys. Lett. A 123, 123 (1987).
    [CrossRef]
  20. B. Segard and B. Macke, “Non critical slowing down in optical bistability,” J. Phys. 49, 115 (1988).
  21. B. Segard, J. Zemmouri, and B. Macke, “Noncritical slowing down in optical bistability,” Opt. Commun. 63, 339 (1987).
    [CrossRef]
  22. J. Y. Bigot, A. Daunois, and J. B. Grun, “Switching dynamics of thermally induced optical bistability: theoretical analysis,” Phys. Rev. A 35, 3810 (1987).
    [CrossRef] [PubMed]
  23. B. Honerlage and J. B. Grun, “Switching dynamics of dispersive optical bistable devices, using three-level systems as active media,” Europhys. Lett. 3, 681 (1987).
    [CrossRef]
  24. F. Mitschke, C. Boden, W. Lange, and P. Mandel, “Exploring the dynamics of the unstable branch of bistable systems,” Opt. Commun. 71, 385 (1989).
    [CrossRef]
  25. S. M. Hammel, C. K. R. T. Jones, and J. V. Moloney, “Global dynamical behavior of the optical field in a ring cavity,” J. Opt. Soc. Am. B 2, 552 (1985).
    [CrossRef]
  26. G. S. McDonald, “Spatial solitary wave optical memory,” Ph.D. dissertation (Strathclyde University, Glasgow, Scotland, 1989).
  27. F. A. Hopf, P. Meystre, F. D. Drummond, and D. F. Walls, “Anomalous switching in dispersive optical bistability,” Opt. Commun. 31, 245 (1979).
    [CrossRef]
  28. F. A. Hopf and P. Meystre, “Phase-switching of a dispersive non-linear interferometer,” Opt. Commun. 33, 225 (1980).
    [CrossRef]

1992 (1)

1991 (1)

1990 (4)

1989 (1)

F. Mitschke, C. Boden, W. Lange, and P. Mandel, “Exploring the dynamics of the unstable branch of bistable systems,” Opt. Commun. 71, 385 (1989).
[CrossRef]

1988 (3)

S. Maneuf and F. Reynaud, “Quasi-steady state self-trapping of first, second and third order subnanosecond soliton beams,” Opt. Commun. 66, 325 (1988).
[CrossRef]

H. Adachihara, D. W. McLaughlin, J. V. Moloney, and A. C. Newell, “Solitary waves as fixed points of infinite-dimensional maps for an optical bistable ring cavity: analysis,” J. Math. Phys. 29, 63 (1988).
[CrossRef]

B. Segard and B. Macke, “Non critical slowing down in optical bistability,” J. Phys. 49, 115 (1988).

1987 (5)

B. Segard, J. Zemmouri, and B. Macke, “Noncritical slowing down in optical bistability,” Opt. Commun. 63, 339 (1987).
[CrossRef]

J. Y. Bigot, A. Daunois, and J. B. Grun, “Switching dynamics of thermally induced optical bistability: theoretical analysis,” Phys. Rev. A 35, 3810 (1987).
[CrossRef] [PubMed]

B. Honerlage and J. B. Grun, “Switching dynamics of dispersive optical bistable devices, using three-level systems as active media,” Europhys. Lett. 3, 681 (1987).
[CrossRef]

J. Y. Bigot, A. Daunois, and P. Mandel, “Slowing down far from the limit points in optical bistability,” Phys. Lett. A 123, 123 (1987).
[CrossRef]

E. Abraham and C. Rae, “Cross talk in nonlinear interference filters: loop narrowing and critical slowing down,” J. Opt. Soc. Am. B 4, 490 (1987).
[CrossRef]

1986 (1)

B. Segard, J. Zemmouri, and B. Macke, “Switching delays in optical bistability: an experimental study,” Opt. Commun. 60, 323 (1986).
[CrossRef]

1985 (3)

P. Mandel, “Switching pulses for an optical transistor,” Opt. Commun. 54, 374 (1985).
[CrossRef]

P. Mandel, “Scaling properties of switching pulses,” Opt. Commun. 55, 293 (1985).
[CrossRef]

S. M. Hammel, C. K. R. T. Jones, and J. V. Moloney, “Global dynamical behavior of the optical field in a ring cavity,” J. Opt. Soc. Am. B 2, 552 (1985).
[CrossRef]

1983 (2)

T. Erneux and P. Mandel, “Temporal aspects of absorptive optical bistability,” Phys. Rev. A 28, 896 (1983).
[CrossRef]

G. Grynberg and S. Cribier, “Critical exponents in dispersive optical bistability,” J. Phys. Lett. 44, 449 (1983).
[CrossRef]

1980 (1)

F. A. Hopf and P. Meystre, “Phase-switching of a dispersive non-linear interferometer,” Opt. Commun. 33, 225 (1980).
[CrossRef]

1979 (3)

F. A. Hopf, P. Meystre, F. D. Drummond, and D. F. Walls, “Anomalous switching in dispersive optical bistability,” Opt. Commun. 31, 245 (1979).
[CrossRef]

R. Bonifacio and P. Meystre, “Critical slowing down in optical bistability,” Opt. Commun. 29, 131 (1979).
[CrossRef]

F. A. Hopf and P. Meystre, “Numerical studies of the switching of a bistable optical memory,” Opt. Commun. 29, 235 (1979).
[CrossRef]

1976 (1)

R. Bonifacio and L. Lugiato, “Cooperative effects and bistability for resonance fluorescence,” Opt. Commun. 19, 172 (1976).
[CrossRef]

Abraham, E.

Abraham, N. B.

Adachihara, H.

H. Adachihara, D. W. McLaughlin, J. V. Moloney, and A. C. Newell, “Solitary waves as fixed points of infinite-dimensional maps for an optical bistable ring cavity: analysis,” J. Math. Phys. 29, 63 (1988).
[CrossRef]

Aitchison, J. S.

Avramopoulos, H.

N. A. Whitaker and H. Avramopoulos, “Addressable fiber loop memory,” presented at the International Quantum Electronics Conference, Vienna, Austria, June 14–19, 1992.

Barthelemy, A.

Bigot, J. Y.

J. Y. Bigot, A. Daunois, and P. Mandel, “Slowing down far from the limit points in optical bistability,” Phys. Lett. A 123, 123 (1987).
[CrossRef]

J. Y. Bigot, A. Daunois, and J. B. Grun, “Switching dynamics of thermally induced optical bistability: theoretical analysis,” Phys. Rev. A 35, 3810 (1987).
[CrossRef] [PubMed]

Boden, C.

F. Mitschke, C. Boden, W. Lange, and P. Mandel, “Exploring the dynamics of the unstable branch of bistable systems,” Opt. Commun. 71, 385 (1989).
[CrossRef]

Bonifacio, R.

R. Bonifacio and P. Meystre, “Critical slowing down in optical bistability,” Opt. Commun. 29, 131 (1979).
[CrossRef]

R. Bonifacio and L. Lugiato, “Cooperative effects and bistability for resonance fluorescence,” Opt. Commun. 19, 172 (1976).
[CrossRef]

Cribier, S.

G. Grynberg and S. Cribier, “Critical exponents in dispersive optical bistability,” J. Phys. Lett. 44, 449 (1983).
[CrossRef]

Daunois, A.

J. Y. Bigot, A. Daunois, and P. Mandel, “Slowing down far from the limit points in optical bistability,” Phys. Lett. A 123, 123 (1987).
[CrossRef]

J. Y. Bigot, A. Daunois, and J. B. Grun, “Switching dynamics of thermally induced optical bistability: theoretical analysis,” Phys. Rev. A 35, 3810 (1987).
[CrossRef] [PubMed]

De La Fuente, R.

Drummond, F. D.

F. A. Hopf, P. Meystre, F. D. Drummond, and D. F. Walls, “Anomalous switching in dispersive optical bistability,” Opt. Commun. 31, 245 (1979).
[CrossRef]

Erneux, T.

T. Erneux and P. Mandel, “Temporal aspects of absorptive optical bistability,” Phys. Rev. A 28, 896 (1983).
[CrossRef]

Firth, W. J.

Froehly, C.

Grun, J. B.

J. Y. Bigot, A. Daunois, and J. B. Grun, “Switching dynamics of thermally induced optical bistability: theoretical analysis,” Phys. Rev. A 35, 3810 (1987).
[CrossRef] [PubMed]

B. Honerlage and J. B. Grun, “Switching dynamics of dispersive optical bistable devices, using three-level systems as active media,” Europhys. Lett. 3, 681 (1987).
[CrossRef]

Grynberg, G.

G. Grynberg and S. Cribier, “Critical exponents in dispersive optical bistability,” J. Phys. Lett. 44, 449 (1983).
[CrossRef]

Hammel, S. M.

Haus, H. A.

Honerlage, B.

B. Honerlage and J. B. Grun, “Switching dynamics of dispersive optical bistable devices, using three-level systems as active media,” Europhys. Lett. 3, 681 (1987).
[CrossRef]

Hopf, F. A.

F. A. Hopf and P. Meystre, “Phase-switching of a dispersive non-linear interferometer,” Opt. Commun. 33, 225 (1980).
[CrossRef]

F. A. Hopf, P. Meystre, F. D. Drummond, and D. F. Walls, “Anomalous switching in dispersive optical bistability,” Opt. Commun. 31, 245 (1979).
[CrossRef]

F. A. Hopf and P. Meystre, “Numerical studies of the switching of a bistable optical memory,” Opt. Commun. 29, 235 (1979).
[CrossRef]

Jackel, J. L.

Jones, C. K. R. T.

Lange, W.

F. Mitschke, C. Boden, W. Lange, and P. Mandel, “Exploring the dynamics of the unstable branch of bistable systems,” Opt. Commun. 71, 385 (1989).
[CrossRef]

Leaird, D. E.

Lugiato, L.

R. Bonifacio and L. Lugiato, “Cooperative effects and bistability for resonance fluorescence,” Opt. Commun. 19, 172 (1976).
[CrossRef]

Macke, B.

B. Segard and B. Macke, “Non critical slowing down in optical bistability,” J. Phys. 49, 115 (1988).

B. Segard, J. Zemmouri, and B. Macke, “Noncritical slowing down in optical bistability,” Opt. Commun. 63, 339 (1987).
[CrossRef]

B. Segard, J. Zemmouri, and B. Macke, “Switching delays in optical bistability: an experimental study,” Opt. Commun. 60, 323 (1986).
[CrossRef]

Mandel, P.

F. Mitschke, C. Boden, W. Lange, and P. Mandel, “Exploring the dynamics of the unstable branch of bistable systems,” Opt. Commun. 71, 385 (1989).
[CrossRef]

J. Y. Bigot, A. Daunois, and P. Mandel, “Slowing down far from the limit points in optical bistability,” Phys. Lett. A 123, 123 (1987).
[CrossRef]

P. Mandel, “Switching pulses for an optical transistor,” Opt. Commun. 54, 374 (1985).
[CrossRef]

P. Mandel, “Scaling properties of switching pulses,” Opt. Commun. 55, 293 (1985).
[CrossRef]

T. Erneux and P. Mandel, “Temporal aspects of absorptive optical bistability,” Phys. Rev. A 28, 896 (1983).
[CrossRef]

Maneuf, S.

S. Maneuf and F. Reynaud, “Quasi-steady state self-trapping of first, second and third order subnanosecond soliton beams,” Opt. Commun. 66, 325 (1988).
[CrossRef]

McDonald, G. S.

G. S. McDonald and W. J. Firth, “Spatial solitary-wave optical memory,” J. Opt. Soc. Am. B 7, 1328 (1990).
[CrossRef]

G. S. McDonald and W. J. Firth, “All-optical switching in a nonlinear resonator,” J. Mod. Opt. 37, 613 (1990).
[CrossRef]

G. S. McDonald, “Spatial solitary wave optical memory,” Ph.D. dissertation (Strathclyde University, Glasgow, Scotland, 1989).

McLaughlin, D. W.

H. Adachihara, D. W. McLaughlin, J. V. Moloney, and A. C. Newell, “Solitary waves as fixed points of infinite-dimensional maps for an optical bistable ring cavity: analysis,” J. Math. Phys. 29, 63 (1988).
[CrossRef]

Mecozzi, A.

Meystre, P.

F. A. Hopf and P. Meystre, “Phase-switching of a dispersive non-linear interferometer,” Opt. Commun. 33, 225 (1980).
[CrossRef]

F. A. Hopf, P. Meystre, F. D. Drummond, and D. F. Walls, “Anomalous switching in dispersive optical bistability,” Opt. Commun. 31, 245 (1979).
[CrossRef]

F. A. Hopf and P. Meystre, “Numerical studies of the switching of a bistable optical memory,” Opt. Commun. 29, 235 (1979).
[CrossRef]

R. Bonifacio and P. Meystre, “Critical slowing down in optical bistability,” Opt. Commun. 29, 131 (1979).
[CrossRef]

Mitschke, F.

F. Mitschke, C. Boden, W. Lange, and P. Mandel, “Exploring the dynamics of the unstable branch of bistable systems,” Opt. Commun. 71, 385 (1989).
[CrossRef]

Moloney, J. V.

H. Adachihara, D. W. McLaughlin, J. V. Moloney, and A. C. Newell, “Solitary waves as fixed points of infinite-dimensional maps for an optical bistable ring cavity: analysis,” J. Math. Phys. 29, 63 (1988).
[CrossRef]

S. M. Hammel, C. K. R. T. Jones, and J. V. Moloney, “Global dynamical behavior of the optical field in a ring cavity,” J. Opt. Soc. Am. B 2, 552 (1985).
[CrossRef]

Newell, A. C.

H. Adachihara, D. W. McLaughlin, J. V. Moloney, and A. C. Newell, “Solitary waves as fixed points of infinite-dimensional maps for an optical bistable ring cavity: analysis,” J. Math. Phys. 29, 63 (1988).
[CrossRef]

Oliver, M. K.

Rae, C.

Reynaud, F.

S. Maneuf and F. Reynaud, “Quasi-steady state self-trapping of first, second and third order subnanosecond soliton beams,” Opt. Commun. 66, 325 (1988).
[CrossRef]

Segard, B.

B. Segard and B. Macke, “Non critical slowing down in optical bistability,” J. Phys. 49, 115 (1988).

B. Segard, J. Zemmouri, and B. Macke, “Noncritical slowing down in optical bistability,” Opt. Commun. 63, 339 (1987).
[CrossRef]

B. Segard, J. Zemmouri, and B. Macke, “Switching delays in optical bistability: an experimental study,” Opt. Commun. 60, 323 (1986).
[CrossRef]

Silberberg, Y.

Smith, P. W. E.

Vogel, E. M.

Walls, D. F.

F. A. Hopf, P. Meystre, F. D. Drummond, and D. F. Walls, “Anomalous switching in dispersive optical bistability,” Opt. Commun. 31, 245 (1979).
[CrossRef]

Weiner, A. M.

Whitaker, N. A.

N. A. Whitaker and H. Avramopoulos, “Addressable fiber loop memory,” presented at the International Quantum Electronics Conference, Vienna, Austria, June 14–19, 1992.

Zemmouri, J.

B. Segard, J. Zemmouri, and B. Macke, “Noncritical slowing down in optical bistability,” Opt. Commun. 63, 339 (1987).
[CrossRef]

B. Segard, J. Zemmouri, and B. Macke, “Switching delays in optical bistability: an experimental study,” Opt. Commun. 60, 323 (1986).
[CrossRef]

Europhys. Lett. (1)

B. Honerlage and J. B. Grun, “Switching dynamics of dispersive optical bistable devices, using three-level systems as active media,” Europhys. Lett. 3, 681 (1987).
[CrossRef]

J. Math. Phys. (1)

H. Adachihara, D. W. McLaughlin, J. V. Moloney, and A. C. Newell, “Solitary waves as fixed points of infinite-dimensional maps for an optical bistable ring cavity: analysis,” J. Math. Phys. 29, 63 (1988).
[CrossRef]

J. Mod. Opt. (1)

G. S. McDonald and W. J. Firth, “All-optical switching in a nonlinear resonator,” J. Mod. Opt. 37, 613 (1990).
[CrossRef]

J. Opt. Soc. Am. B (4)

J. Phys. (1)

B. Segard and B. Macke, “Non critical slowing down in optical bistability,” J. Phys. 49, 115 (1988).

J. Phys. Lett. (1)

G. Grynberg and S. Cribier, “Critical exponents in dispersive optical bistability,” J. Phys. Lett. 44, 449 (1983).
[CrossRef]

Opt. Commun. (11)

P. Mandel, “Switching pulses for an optical transistor,” Opt. Commun. 54, 374 (1985).
[CrossRef]

B. Segard, J. Zemmouri, and B. Macke, “Noncritical slowing down in optical bistability,” Opt. Commun. 63, 339 (1987).
[CrossRef]

F. Mitschke, C. Boden, W. Lange, and P. Mandel, “Exploring the dynamics of the unstable branch of bistable systems,” Opt. Commun. 71, 385 (1989).
[CrossRef]

F. A. Hopf, P. Meystre, F. D. Drummond, and D. F. Walls, “Anomalous switching in dispersive optical bistability,” Opt. Commun. 31, 245 (1979).
[CrossRef]

F. A. Hopf and P. Meystre, “Phase-switching of a dispersive non-linear interferometer,” Opt. Commun. 33, 225 (1980).
[CrossRef]

P. Mandel, “Scaling properties of switching pulses,” Opt. Commun. 55, 293 (1985).
[CrossRef]

B. Segard, J. Zemmouri, and B. Macke, “Switching delays in optical bistability: an experimental study,” Opt. Commun. 60, 323 (1986).
[CrossRef]

R. Bonifacio and L. Lugiato, “Cooperative effects and bistability for resonance fluorescence,” Opt. Commun. 19, 172 (1976).
[CrossRef]

R. Bonifacio and P. Meystre, “Critical slowing down in optical bistability,” Opt. Commun. 29, 131 (1979).
[CrossRef]

F. A. Hopf and P. Meystre, “Numerical studies of the switching of a bistable optical memory,” Opt. Commun. 29, 235 (1979).
[CrossRef]

S. Maneuf and F. Reynaud, “Quasi-steady state self-trapping of first, second and third order subnanosecond soliton beams,” Opt. Commun. 66, 325 (1988).
[CrossRef]

Opt. Lett. (3)

Phys. Lett. A (1)

J. Y. Bigot, A. Daunois, and P. Mandel, “Slowing down far from the limit points in optical bistability,” Phys. Lett. A 123, 123 (1987).
[CrossRef]

Phys. Rev. A (2)

T. Erneux and P. Mandel, “Temporal aspects of absorptive optical bistability,” Phys. Rev. A 28, 896 (1983).
[CrossRef]

J. Y. Bigot, A. Daunois, and J. B. Grun, “Switching dynamics of thermally induced optical bistability: theoretical analysis,” Phys. Rev. A 35, 3810 (1987).
[CrossRef] [PubMed]

Other (2)

G. S. McDonald, “Spatial solitary wave optical memory,” Ph.D. dissertation (Strathclyde University, Glasgow, Scotland, 1989).

N. A. Whitaker and H. Avramopoulos, “Addressable fiber loop memory,” presented at the International Quantum Electronics Conference, Vienna, Austria, June 14–19, 1992.

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Figures (9)

Fig. 1
Fig. 1

Schematic of the ring cavity partially filled with a nonlinear medium, L1 = 0.3(L1 + L2). Mirrors M1 and M2, the input and output couplers, respectively, have a finite intensity reflectivity R = 0.9.

Fig. 2
Fig. 2

Separatrices in terms of electric field amplitudes. a, The static separatrix. Output amplitudes when noncritical slowing occurs is compared with those of the lower- and upper-branch fixed points. b, A dynamic separatrix. Variation across the bias range of the required switch amplitude AS for noncritical slowing.

Fig. 3
Fig. 3

Samples of the dynamic flow (arrows) and the stable and unstable manifolds (dotted curves) in the plane of the complex electric field. a, −2 ≤ Re[g] ≤ 2; b, −1 ≤ Re[g] ≤ 1; c, −0.5 ≤ Re[g] ≤ 0.5.

Fig. 4
Fig. 4

Temporal evolution of peak output amplitude at A = 0.12 for a selection of switch pulse amplitudes: AS = 0.0131 to 0.393, N is the number of cavity transits.

Fig. 5
Fig. 5

Rate of increase of the peak output amplitude (with respect to N) during a switch of amplitude AS. Data for three representative bias levels are marked with dots, while the best-fit curve type denotes different values of A. Curves 1, 2, and 3 represent A = 0.095, 0.12, and 0.1425, respectively.

Fig. 6
Fig. 6

Dependency of lethargy time, τ, on the difference between switch amplitude AS and its critical value AS*, where Δ = ln|ASAS*|. a, Curves 1, 2, and 3 represent A = 0.095, 0.12, and 0.1425, respectively. b, A range of curves representing A = 0.096 « 0.1375.

Fig. 7
Fig. 7

Evolution of the output field in the complex plane (A = 0.12). a, Developments during a range of switch phases, ψ ∈ [0, 2π). b, Trajectories during and after switching when ψ = 0. π/16, π/8.

Fig. 8
Fig. 8

Transverse profiles during a switch cycle of two address pulses, the second having an overall phase encoded (A = 0.095). a, Isometric plot; N is in multiples of 10, while |G| is in units of 0.1. b, Overlay of transverse profiles during solitary pixel reset.

Fig. 9
Fig. 9

Two solitary pixels, each adjacent to the central pixel site, are switched on and then off by use of address beams with AS = 0.3166 and T = 6. Switch-on is performed with a real address pulse (ψ = 0), whereas the reset pulse has ψ = 3.53. Shown are the peak amplitudes at beam center (dashed curve) and at one of the switched sites (bold curve).

Equations (6)

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

2 i G n z + γ p 2 G n x 2 + f ( G n 2 ) G n = 0 ,
G n + 1 ( x , 0 ) = A ( x ) + R exp ( i Φ 0 ) G n ( x , p ) .
A ( x ) = A 0 ( 1 + M cos k m x ) exp ( - x 2 ) .
g n + 1 = a + R exp { i [ Φ 0 + N ( g n g n * ) ( p / 2 ) ] } g n = a + R exp ( i Γ ) g n .
a 2 = g 2 [ 1 + R 2 - 2 R cos ( Γ ) ] ,
tan ( θ ) = sin ( ψ ) + R sin ( Γ - ψ ) cos ( ψ ) - R cos ( Γ - ψ ) Æ

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