Abstract

A two-input configuration for microresonators, exhibiting bistability owing to Kerr nonlinearity, could be used for the realization of optical flip-flops with switching speeds that are not limited by thermal effects. We present design considerations for such devices. The concept of phase switching is explained, and the results of numerical simulations clarify the conditions under which it will succeed. A thermal model is presented and used to understand the influence of the material properties and cavity structure on important operating parameters that will be relevant to any experimental effort to realize the device.

© 2012 Optical Society of America

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  1. D. N. Maywar, K. P. Solomon, and G. P. Agrawal, “Remote optical control of an optical flip-flop,” Opt. Lett. 32, 3260–3262 (2007).
    [CrossRef]
  2. L. Liu, R. Kumar, K. Huybrechts, T. Spuesens, G. Roelkens, E. Geluk, T. de Vries, P. Regreny, D. V. Thourhout, R. Baets, and G. Morthier, “An ultra-small, low-power, all-optical flip-flop memory on a silicon chip,” Nat. Photon. 4, 182–187 (2010).
    [CrossRef]
  3. V. B. Braginsky, M. L. Gorodetsky, and V. S. Ilchenko, “Quality-factor and nonlinear properties of optical whispering-gallery modes,” Phys. Lett. A 137, 393–397 (1989).
    [CrossRef]
  4. V. S. Ilchenko and M. L. Gorodetsky, “Thermal nonlinear effects in optical whispering gallery microresonators,” Laser Phys. 2, 1004–1009 (1992).
  5. V. R. Almeida and M. Lipson, “Optical bistability on a silicon chip,” Opt. Lett. 29, 2387–2389 (2004).
    [CrossRef]
  6. H. Rokhsari and K. J. Vahala, “Observation of Kerr nonlinearity in microcavities at room temperature,” Opt. Lett. 30, 427–429 (2005).
    [CrossRef]
  7. K. Ikeda, R. E. Saperstein, N. Alic, and Y. Fainman, “Thermal and Kerr nonlinear properties of plasma-deposited silicon nitride/silicon dioxide waveguides,” Opt. Express 16, 12987–12994 (2008).
    [CrossRef]
  8. F. Treussart, V. S. Ilchenko, J.-F. Roch, J. Hare, V. Lefèvre-Seguin, J.-M. Raimond, and S. Haroche, “Evidence for intrinsic Kerr bistability of high-Q microsphere resonators in superfluid helium,” Eur. Phys. J. D 1, 235–238 (1998).
    [CrossRef]
  9. M. Pöllinger and A. Rauschenbeutel, “All-optical signal processing at ultra-low powers in bottle microresonators using the Kerr effect,” Opt. Express 18, 17764–17775 (2010).
    [CrossRef]
  10. A. E. Kaplan and P. Meystre, “Directionally asymmetrical bistability in a symmetrically pumped nonlinear ring interferometer,” Opt. Commun. 40, 229–232 (1982).
    [CrossRef]
  11. B. A. Daniel and G. P. Agrawal, “Phase-switched all-optical flip-flops using two-input bistable resonators,” IEEE Photon. Technol. Lett. 24, 479–481 (2012).
    [CrossRef]
  12. M. Haelterman, P. Mandel, J. Danckaert, H. Thienpont, and I. Veretennicoff, “Two-beam nonlinear Fabry–Perot transmission characteristics,” Opt. Commun. 74, 238–244 (1989).
    [CrossRef]
  13. M. Haelterman and P. Mandel, “Pitchfork bifurcation using a two-beam nonlinear Fabry–Perot interferometer: an analytical study,” Opt. Lett. 15, 1412–1414 (1990).
    [CrossRef]
  14. M. Haelterman, “All-optical set-reset flip-flop operation in the nonlinear Fabry–Pérot interferometer,” Opt. Commun. 86, 189–191 (1991).
    [CrossRef]
  15. G. P. Agrawal and C. Flytzanis, “Two-photon double-beam optical bistability,” Phys. Rev. Lett. 44, 1058–1061 (1980).
    [CrossRef]
  16. R. W. Boyd, Nonlinear Optics, 3rd ed. (Academic, 2008).
  17. B. A. Daniel, D. N. Maywar, and G. P. Agrawal, “Dynamic mode theory of optical resonators undergoing refractive index changes,” J. Opt. Soc. Am. B 28, 2207–2215 (2011).
    [CrossRef]
  18. F. A. Hopf, P. Meystre, P. D. Drummond, and D. F. Walls, “Anomalous switching in dispersive optical bistability,” Opt. Commun. 31, 245–250 (1979).
    [CrossRef]
  19. F. A. Hopf and P. Meystre, “Phase-switching of a dispersive non-linear interferometer,” Opt. Commun. 33, 225–230(1980).
    [CrossRef]
  20. H. Kawashima, Y. Tanaka, N. Ikeda, Y. Sugimoto, T. Hasama, and H. Ishikawa, “Numerical study of impulsive switching of bistable states in nonlinear etalons,” IEEE Photon. Technol. Lett. 19, 913–915 (2007).
    [CrossRef]
  21. S. Sandhu, M. L. Povinelli, and S. Fan, “Enhancing optical switching with coherent control,” Appl. Phys. Lett. 96, 231108 (2010).
    [CrossRef]
  22. H. A. Haus, Waves and Fields in Optoelectronics (Prentice-Hall, 1984).
  23. M. Tien, J. F. Bauters, M. J. R. Heck, D. T. Spencer, D. J. Blumenthal, and J. E. Bowers, “Ultra-high quality factor planar Si3N4 ring resonators on Si substrates,” Opt. Express 19, 13551–13556 (2011).
    [CrossRef]

2012 (1)

B. A. Daniel and G. P. Agrawal, “Phase-switched all-optical flip-flops using two-input bistable resonators,” IEEE Photon. Technol. Lett. 24, 479–481 (2012).
[CrossRef]

2011 (2)

2010 (3)

S. Sandhu, M. L. Povinelli, and S. Fan, “Enhancing optical switching with coherent control,” Appl. Phys. Lett. 96, 231108 (2010).
[CrossRef]

M. Pöllinger and A. Rauschenbeutel, “All-optical signal processing at ultra-low powers in bottle microresonators using the Kerr effect,” Opt. Express 18, 17764–17775 (2010).
[CrossRef]

L. Liu, R. Kumar, K. Huybrechts, T. Spuesens, G. Roelkens, E. Geluk, T. de Vries, P. Regreny, D. V. Thourhout, R. Baets, and G. Morthier, “An ultra-small, low-power, all-optical flip-flop memory on a silicon chip,” Nat. Photon. 4, 182–187 (2010).
[CrossRef]

2008 (1)

2007 (2)

D. N. Maywar, K. P. Solomon, and G. P. Agrawal, “Remote optical control of an optical flip-flop,” Opt. Lett. 32, 3260–3262 (2007).
[CrossRef]

H. Kawashima, Y. Tanaka, N. Ikeda, Y. Sugimoto, T. Hasama, and H. Ishikawa, “Numerical study of impulsive switching of bistable states in nonlinear etalons,” IEEE Photon. Technol. Lett. 19, 913–915 (2007).
[CrossRef]

2005 (1)

2004 (1)

1998 (1)

F. Treussart, V. S. Ilchenko, J.-F. Roch, J. Hare, V. Lefèvre-Seguin, J.-M. Raimond, and S. Haroche, “Evidence for intrinsic Kerr bistability of high-Q microsphere resonators in superfluid helium,” Eur. Phys. J. D 1, 235–238 (1998).
[CrossRef]

1992 (1)

V. S. Ilchenko and M. L. Gorodetsky, “Thermal nonlinear effects in optical whispering gallery microresonators,” Laser Phys. 2, 1004–1009 (1992).

1991 (1)

M. Haelterman, “All-optical set-reset flip-flop operation in the nonlinear Fabry–Pérot interferometer,” Opt. Commun. 86, 189–191 (1991).
[CrossRef]

1990 (1)

1989 (2)

M. Haelterman, P. Mandel, J. Danckaert, H. Thienpont, and I. Veretennicoff, “Two-beam nonlinear Fabry–Perot transmission characteristics,” Opt. Commun. 74, 238–244 (1989).
[CrossRef]

V. B. Braginsky, M. L. Gorodetsky, and V. S. Ilchenko, “Quality-factor and nonlinear properties of optical whispering-gallery modes,” Phys. Lett. A 137, 393–397 (1989).
[CrossRef]

1982 (1)

A. E. Kaplan and P. Meystre, “Directionally asymmetrical bistability in a symmetrically pumped nonlinear ring interferometer,” Opt. Commun. 40, 229–232 (1982).
[CrossRef]

1980 (2)

G. P. Agrawal and C. Flytzanis, “Two-photon double-beam optical bistability,” Phys. Rev. Lett. 44, 1058–1061 (1980).
[CrossRef]

F. A. Hopf and P. Meystre, “Phase-switching of a dispersive non-linear interferometer,” Opt. Commun. 33, 225–230(1980).
[CrossRef]

1979 (1)

F. A. Hopf, P. Meystre, P. D. Drummond, and D. F. Walls, “Anomalous switching in dispersive optical bistability,” Opt. Commun. 31, 245–250 (1979).
[CrossRef]

Agrawal, G. P.

B. A. Daniel and G. P. Agrawal, “Phase-switched all-optical flip-flops using two-input bistable resonators,” IEEE Photon. Technol. Lett. 24, 479–481 (2012).
[CrossRef]

B. A. Daniel, D. N. Maywar, and G. P. Agrawal, “Dynamic mode theory of optical resonators undergoing refractive index changes,” J. Opt. Soc. Am. B 28, 2207–2215 (2011).
[CrossRef]

D. N. Maywar, K. P. Solomon, and G. P. Agrawal, “Remote optical control of an optical flip-flop,” Opt. Lett. 32, 3260–3262 (2007).
[CrossRef]

G. P. Agrawal and C. Flytzanis, “Two-photon double-beam optical bistability,” Phys. Rev. Lett. 44, 1058–1061 (1980).
[CrossRef]

Alic, N.

Almeida, V. R.

Baets, R.

L. Liu, R. Kumar, K. Huybrechts, T. Spuesens, G. Roelkens, E. Geluk, T. de Vries, P. Regreny, D. V. Thourhout, R. Baets, and G. Morthier, “An ultra-small, low-power, all-optical flip-flop memory on a silicon chip,” Nat. Photon. 4, 182–187 (2010).
[CrossRef]

Bauters, J. F.

Blumenthal, D. J.

Bowers, J. E.

Boyd, R. W.

R. W. Boyd, Nonlinear Optics, 3rd ed. (Academic, 2008).

Braginsky, V. B.

V. B. Braginsky, M. L. Gorodetsky, and V. S. Ilchenko, “Quality-factor and nonlinear properties of optical whispering-gallery modes,” Phys. Lett. A 137, 393–397 (1989).
[CrossRef]

Danckaert, J.

M. Haelterman, P. Mandel, J. Danckaert, H. Thienpont, and I. Veretennicoff, “Two-beam nonlinear Fabry–Perot transmission characteristics,” Opt. Commun. 74, 238–244 (1989).
[CrossRef]

Daniel, B. A.

B. A. Daniel and G. P. Agrawal, “Phase-switched all-optical flip-flops using two-input bistable resonators,” IEEE Photon. Technol. Lett. 24, 479–481 (2012).
[CrossRef]

B. A. Daniel, D. N. Maywar, and G. P. Agrawal, “Dynamic mode theory of optical resonators undergoing refractive index changes,” J. Opt. Soc. Am. B 28, 2207–2215 (2011).
[CrossRef]

de Vries, T.

L. Liu, R. Kumar, K. Huybrechts, T. Spuesens, G. Roelkens, E. Geluk, T. de Vries, P. Regreny, D. V. Thourhout, R. Baets, and G. Morthier, “An ultra-small, low-power, all-optical flip-flop memory on a silicon chip,” Nat. Photon. 4, 182–187 (2010).
[CrossRef]

Drummond, P. D.

F. A. Hopf, P. Meystre, P. D. Drummond, and D. F. Walls, “Anomalous switching in dispersive optical bistability,” Opt. Commun. 31, 245–250 (1979).
[CrossRef]

Fainman, Y.

Fan, S.

S. Sandhu, M. L. Povinelli, and S. Fan, “Enhancing optical switching with coherent control,” Appl. Phys. Lett. 96, 231108 (2010).
[CrossRef]

Flytzanis, C.

G. P. Agrawal and C. Flytzanis, “Two-photon double-beam optical bistability,” Phys. Rev. Lett. 44, 1058–1061 (1980).
[CrossRef]

Geluk, E.

L. Liu, R. Kumar, K. Huybrechts, T. Spuesens, G. Roelkens, E. Geluk, T. de Vries, P. Regreny, D. V. Thourhout, R. Baets, and G. Morthier, “An ultra-small, low-power, all-optical flip-flop memory on a silicon chip,” Nat. Photon. 4, 182–187 (2010).
[CrossRef]

Gorodetsky, M. L.

V. S. Ilchenko and M. L. Gorodetsky, “Thermal nonlinear effects in optical whispering gallery microresonators,” Laser Phys. 2, 1004–1009 (1992).

V. B. Braginsky, M. L. Gorodetsky, and V. S. Ilchenko, “Quality-factor and nonlinear properties of optical whispering-gallery modes,” Phys. Lett. A 137, 393–397 (1989).
[CrossRef]

Haelterman, M.

M. Haelterman, “All-optical set-reset flip-flop operation in the nonlinear Fabry–Pérot interferometer,” Opt. Commun. 86, 189–191 (1991).
[CrossRef]

M. Haelterman and P. Mandel, “Pitchfork bifurcation using a two-beam nonlinear Fabry–Perot interferometer: an analytical study,” Opt. Lett. 15, 1412–1414 (1990).
[CrossRef]

M. Haelterman, P. Mandel, J. Danckaert, H. Thienpont, and I. Veretennicoff, “Two-beam nonlinear Fabry–Perot transmission characteristics,” Opt. Commun. 74, 238–244 (1989).
[CrossRef]

Hare, J.

F. Treussart, V. S. Ilchenko, J.-F. Roch, J. Hare, V. Lefèvre-Seguin, J.-M. Raimond, and S. Haroche, “Evidence for intrinsic Kerr bistability of high-Q microsphere resonators in superfluid helium,” Eur. Phys. J. D 1, 235–238 (1998).
[CrossRef]

Haroche, S.

F. Treussart, V. S. Ilchenko, J.-F. Roch, J. Hare, V. Lefèvre-Seguin, J.-M. Raimond, and S. Haroche, “Evidence for intrinsic Kerr bistability of high-Q microsphere resonators in superfluid helium,” Eur. Phys. J. D 1, 235–238 (1998).
[CrossRef]

Hasama, T.

H. Kawashima, Y. Tanaka, N. Ikeda, Y. Sugimoto, T. Hasama, and H. Ishikawa, “Numerical study of impulsive switching of bistable states in nonlinear etalons,” IEEE Photon. Technol. Lett. 19, 913–915 (2007).
[CrossRef]

Haus, H. A.

H. A. Haus, Waves and Fields in Optoelectronics (Prentice-Hall, 1984).

Heck, M. J. R.

Hopf, F. A.

F. A. Hopf and P. Meystre, “Phase-switching of a dispersive non-linear interferometer,” Opt. Commun. 33, 225–230(1980).
[CrossRef]

F. A. Hopf, P. Meystre, P. D. Drummond, and D. F. Walls, “Anomalous switching in dispersive optical bistability,” Opt. Commun. 31, 245–250 (1979).
[CrossRef]

Huybrechts, K.

L. Liu, R. Kumar, K. Huybrechts, T. Spuesens, G. Roelkens, E. Geluk, T. de Vries, P. Regreny, D. V. Thourhout, R. Baets, and G. Morthier, “An ultra-small, low-power, all-optical flip-flop memory on a silicon chip,” Nat. Photon. 4, 182–187 (2010).
[CrossRef]

Ikeda, K.

Ikeda, N.

H. Kawashima, Y. Tanaka, N. Ikeda, Y. Sugimoto, T. Hasama, and H. Ishikawa, “Numerical study of impulsive switching of bistable states in nonlinear etalons,” IEEE Photon. Technol. Lett. 19, 913–915 (2007).
[CrossRef]

Ilchenko, V. S.

F. Treussart, V. S. Ilchenko, J.-F. Roch, J. Hare, V. Lefèvre-Seguin, J.-M. Raimond, and S. Haroche, “Evidence for intrinsic Kerr bistability of high-Q microsphere resonators in superfluid helium,” Eur. Phys. J. D 1, 235–238 (1998).
[CrossRef]

V. S. Ilchenko and M. L. Gorodetsky, “Thermal nonlinear effects in optical whispering gallery microresonators,” Laser Phys. 2, 1004–1009 (1992).

V. B. Braginsky, M. L. Gorodetsky, and V. S. Ilchenko, “Quality-factor and nonlinear properties of optical whispering-gallery modes,” Phys. Lett. A 137, 393–397 (1989).
[CrossRef]

Ishikawa, H.

H. Kawashima, Y. Tanaka, N. Ikeda, Y. Sugimoto, T. Hasama, and H. Ishikawa, “Numerical study of impulsive switching of bistable states in nonlinear etalons,” IEEE Photon. Technol. Lett. 19, 913–915 (2007).
[CrossRef]

Kaplan, A. E.

A. E. Kaplan and P. Meystre, “Directionally asymmetrical bistability in a symmetrically pumped nonlinear ring interferometer,” Opt. Commun. 40, 229–232 (1982).
[CrossRef]

Kawashima, H.

H. Kawashima, Y. Tanaka, N. Ikeda, Y. Sugimoto, T. Hasama, and H. Ishikawa, “Numerical study of impulsive switching of bistable states in nonlinear etalons,” IEEE Photon. Technol. Lett. 19, 913–915 (2007).
[CrossRef]

Kumar, R.

L. Liu, R. Kumar, K. Huybrechts, T. Spuesens, G. Roelkens, E. Geluk, T. de Vries, P. Regreny, D. V. Thourhout, R. Baets, and G. Morthier, “An ultra-small, low-power, all-optical flip-flop memory on a silicon chip,” Nat. Photon. 4, 182–187 (2010).
[CrossRef]

Lefèvre-Seguin, V.

F. Treussart, V. S. Ilchenko, J.-F. Roch, J. Hare, V. Lefèvre-Seguin, J.-M. Raimond, and S. Haroche, “Evidence for intrinsic Kerr bistability of high-Q microsphere resonators in superfluid helium,” Eur. Phys. J. D 1, 235–238 (1998).
[CrossRef]

Lipson, M.

Liu, L.

L. Liu, R. Kumar, K. Huybrechts, T. Spuesens, G. Roelkens, E. Geluk, T. de Vries, P. Regreny, D. V. Thourhout, R. Baets, and G. Morthier, “An ultra-small, low-power, all-optical flip-flop memory on a silicon chip,” Nat. Photon. 4, 182–187 (2010).
[CrossRef]

Mandel, P.

M. Haelterman and P. Mandel, “Pitchfork bifurcation using a two-beam nonlinear Fabry–Perot interferometer: an analytical study,” Opt. Lett. 15, 1412–1414 (1990).
[CrossRef]

M. Haelterman, P. Mandel, J. Danckaert, H. Thienpont, and I. Veretennicoff, “Two-beam nonlinear Fabry–Perot transmission characteristics,” Opt. Commun. 74, 238–244 (1989).
[CrossRef]

Maywar, D. N.

Meystre, P.

A. E. Kaplan and P. Meystre, “Directionally asymmetrical bistability in a symmetrically pumped nonlinear ring interferometer,” Opt. Commun. 40, 229–232 (1982).
[CrossRef]

F. A. Hopf and P. Meystre, “Phase-switching of a dispersive non-linear interferometer,” Opt. Commun. 33, 225–230(1980).
[CrossRef]

F. A. Hopf, P. Meystre, P. D. Drummond, and D. F. Walls, “Anomalous switching in dispersive optical bistability,” Opt. Commun. 31, 245–250 (1979).
[CrossRef]

Morthier, G.

L. Liu, R. Kumar, K. Huybrechts, T. Spuesens, G. Roelkens, E. Geluk, T. de Vries, P. Regreny, D. V. Thourhout, R. Baets, and G. Morthier, “An ultra-small, low-power, all-optical flip-flop memory on a silicon chip,” Nat. Photon. 4, 182–187 (2010).
[CrossRef]

Pöllinger, M.

Povinelli, M. L.

S. Sandhu, M. L. Povinelli, and S. Fan, “Enhancing optical switching with coherent control,” Appl. Phys. Lett. 96, 231108 (2010).
[CrossRef]

Raimond, J.-M.

F. Treussart, V. S. Ilchenko, J.-F. Roch, J. Hare, V. Lefèvre-Seguin, J.-M. Raimond, and S. Haroche, “Evidence for intrinsic Kerr bistability of high-Q microsphere resonators in superfluid helium,” Eur. Phys. J. D 1, 235–238 (1998).
[CrossRef]

Rauschenbeutel, A.

Regreny, P.

L. Liu, R. Kumar, K. Huybrechts, T. Spuesens, G. Roelkens, E. Geluk, T. de Vries, P. Regreny, D. V. Thourhout, R. Baets, and G. Morthier, “An ultra-small, low-power, all-optical flip-flop memory on a silicon chip,” Nat. Photon. 4, 182–187 (2010).
[CrossRef]

Roch, J.-F.

F. Treussart, V. S. Ilchenko, J.-F. Roch, J. Hare, V. Lefèvre-Seguin, J.-M. Raimond, and S. Haroche, “Evidence for intrinsic Kerr bistability of high-Q microsphere resonators in superfluid helium,” Eur. Phys. J. D 1, 235–238 (1998).
[CrossRef]

Roelkens, G.

L. Liu, R. Kumar, K. Huybrechts, T. Spuesens, G. Roelkens, E. Geluk, T. de Vries, P. Regreny, D. V. Thourhout, R. Baets, and G. Morthier, “An ultra-small, low-power, all-optical flip-flop memory on a silicon chip,” Nat. Photon. 4, 182–187 (2010).
[CrossRef]

Rokhsari, H.

Sandhu, S.

S. Sandhu, M. L. Povinelli, and S. Fan, “Enhancing optical switching with coherent control,” Appl. Phys. Lett. 96, 231108 (2010).
[CrossRef]

Saperstein, R. E.

Solomon, K. P.

Spencer, D. T.

Spuesens, T.

L. Liu, R. Kumar, K. Huybrechts, T. Spuesens, G. Roelkens, E. Geluk, T. de Vries, P. Regreny, D. V. Thourhout, R. Baets, and G. Morthier, “An ultra-small, low-power, all-optical flip-flop memory on a silicon chip,” Nat. Photon. 4, 182–187 (2010).
[CrossRef]

Sugimoto, Y.

H. Kawashima, Y. Tanaka, N. Ikeda, Y. Sugimoto, T. Hasama, and H. Ishikawa, “Numerical study of impulsive switching of bistable states in nonlinear etalons,” IEEE Photon. Technol. Lett. 19, 913–915 (2007).
[CrossRef]

Tanaka, Y.

H. Kawashima, Y. Tanaka, N. Ikeda, Y. Sugimoto, T. Hasama, and H. Ishikawa, “Numerical study of impulsive switching of bistable states in nonlinear etalons,” IEEE Photon. Technol. Lett. 19, 913–915 (2007).
[CrossRef]

Thienpont, H.

M. Haelterman, P. Mandel, J. Danckaert, H. Thienpont, and I. Veretennicoff, “Two-beam nonlinear Fabry–Perot transmission characteristics,” Opt. Commun. 74, 238–244 (1989).
[CrossRef]

Thourhout, D. V.

L. Liu, R. Kumar, K. Huybrechts, T. Spuesens, G. Roelkens, E. Geluk, T. de Vries, P. Regreny, D. V. Thourhout, R. Baets, and G. Morthier, “An ultra-small, low-power, all-optical flip-flop memory on a silicon chip,” Nat. Photon. 4, 182–187 (2010).
[CrossRef]

Tien, M.

Treussart, F.

F. Treussart, V. S. Ilchenko, J.-F. Roch, J. Hare, V. Lefèvre-Seguin, J.-M. Raimond, and S. Haroche, “Evidence for intrinsic Kerr bistability of high-Q microsphere resonators in superfluid helium,” Eur. Phys. J. D 1, 235–238 (1998).
[CrossRef]

Vahala, K. J.

Veretennicoff, I.

M. Haelterman, P. Mandel, J. Danckaert, H. Thienpont, and I. Veretennicoff, “Two-beam nonlinear Fabry–Perot transmission characteristics,” Opt. Commun. 74, 238–244 (1989).
[CrossRef]

Walls, D. F.

F. A. Hopf, P. Meystre, P. D. Drummond, and D. F. Walls, “Anomalous switching in dispersive optical bistability,” Opt. Commun. 31, 245–250 (1979).
[CrossRef]

Appl. Phys. Lett. (1)

S. Sandhu, M. L. Povinelli, and S. Fan, “Enhancing optical switching with coherent control,” Appl. Phys. Lett. 96, 231108 (2010).
[CrossRef]

Eur. Phys. J. D (1)

F. Treussart, V. S. Ilchenko, J.-F. Roch, J. Hare, V. Lefèvre-Seguin, J.-M. Raimond, and S. Haroche, “Evidence for intrinsic Kerr bistability of high-Q microsphere resonators in superfluid helium,” Eur. Phys. J. D 1, 235–238 (1998).
[CrossRef]

IEEE Photon. Technol. Lett. (2)

B. A. Daniel and G. P. Agrawal, “Phase-switched all-optical flip-flops using two-input bistable resonators,” IEEE Photon. Technol. Lett. 24, 479–481 (2012).
[CrossRef]

H. Kawashima, Y. Tanaka, N. Ikeda, Y. Sugimoto, T. Hasama, and H. Ishikawa, “Numerical study of impulsive switching of bistable states in nonlinear etalons,” IEEE Photon. Technol. Lett. 19, 913–915 (2007).
[CrossRef]

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

Laser Phys. (1)

V. S. Ilchenko and M. L. Gorodetsky, “Thermal nonlinear effects in optical whispering gallery microresonators,” Laser Phys. 2, 1004–1009 (1992).

Nat. Photon. (1)

L. Liu, R. Kumar, K. Huybrechts, T. Spuesens, G. Roelkens, E. Geluk, T. de Vries, P. Regreny, D. V. Thourhout, R. Baets, and G. Morthier, “An ultra-small, low-power, all-optical flip-flop memory on a silicon chip,” Nat. Photon. 4, 182–187 (2010).
[CrossRef]

Opt. Commun. (5)

A. E. Kaplan and P. Meystre, “Directionally asymmetrical bistability in a symmetrically pumped nonlinear ring interferometer,” Opt. Commun. 40, 229–232 (1982).
[CrossRef]

M. Haelterman, P. Mandel, J. Danckaert, H. Thienpont, and I. Veretennicoff, “Two-beam nonlinear Fabry–Perot transmission characteristics,” Opt. Commun. 74, 238–244 (1989).
[CrossRef]

M. Haelterman, “All-optical set-reset flip-flop operation in the nonlinear Fabry–Pérot interferometer,” Opt. Commun. 86, 189–191 (1991).
[CrossRef]

F. A. Hopf, P. Meystre, P. D. Drummond, and D. F. Walls, “Anomalous switching in dispersive optical bistability,” Opt. Commun. 31, 245–250 (1979).
[CrossRef]

F. A. Hopf and P. Meystre, “Phase-switching of a dispersive non-linear interferometer,” Opt. Commun. 33, 225–230(1980).
[CrossRef]

Opt. Express (3)

Opt. Lett. (4)

Phys. Lett. A (1)

V. B. Braginsky, M. L. Gorodetsky, and V. S. Ilchenko, “Quality-factor and nonlinear properties of optical whispering-gallery modes,” Phys. Lett. A 137, 393–397 (1989).
[CrossRef]

Phys. Rev. Lett. (1)

G. P. Agrawal and C. Flytzanis, “Two-photon double-beam optical bistability,” Phys. Rev. Lett. 44, 1058–1061 (1980).
[CrossRef]

Other (2)

R. W. Boyd, Nonlinear Optics, 3rd ed. (Academic, 2008).

H. A. Haus, Waves and Fields in Optoelectronics (Prentice-Hall, 1984).

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Figures (5)

Fig. 1.
Fig. 1.

One possible configuration for a two-input Kerr flip-flop. Two input fields at frequencies ω01 and ω02 couple to two different resonator modes with resonance frequencies ω1 and ω2. In the first state, input field Ain(1) fills the cavity with light, causing a Kerr-induced redshift of the resonance frequencies. The redshift of the mode 2 resonance is twice as large because the XPM is twice as strong as the SPM. In the second stable state, the roles of the input fields are reversed.

Fig. 2.
Fig. 2.

Map of possible bias points when the input fields have the same power P0 and detuning Δω0. The solid and dashed curves bound regions for which asymmetric solutions exist and multiple symmetric solutions exist, respectively [10]. The ideal bias points lie in the shaded region.

Fig. 3.
Fig. 3.

Stable and unstable states of the device when the detuning of input field 2 deviates from the initial biasing at Δω2τph=Δω1τph=2. The shaded region indicates where the flip-flop can be switched by modulating the phase of input field 2.

Fig. 4.
Fig. 4.

Phase switching for four different values of the maximum phase shift ϕ0 when the duration of the modulation is fixed at T0=2τph. Temporal variations of the phase (left) and transmission (right) are shown for input fields 1 (solid blue curves) and 2 (dashed red curves).

Fig. 5.
Fig. 5.

Phase switching for four different values of T0 when the maximum phase shift is fixed at ϕ0=π. Temporal variations of the phase (left) and transmission (right) are shown for input fields 1 (solid blue curves) and 2 (dashed red curves).

Equations (40)

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E(r,t)=a1(t)N1e1(r)+a2(t)N2e2(r),
Nk=12ε0ε(r)|ek|2d3r,
Pμ(3)(r,t)=3ε04α,β,γχμαβγ(3)Eα(r,t)Eβ*(r,t)Eγ(r,t),
dakdt=iωkakak2τph+κAin(k)(t)+iωk4Nkek*·P(3)d3r,
da1dt=iω1a1a12τph+κAin(1)(t)+i(γ11|a1|2+2γ12|a2|2)a1,
da2dt=iω2a2a22τph+κAin(2)(t)+i(γ22|a2|2+2γ21|a1|2)a2.
γkl=ωkn2cηkln02(VkVl)1/2.
Vk=(ε(r)|e(k)|2d3r)2n04(|e(k)|2)2d3r.
χc(3)=43ε0cn02n2,
ηkl=μαβγχμαβγ(3)eμ*(k)eα(k)eβ*(l)eγ(l)d3rχc(3)[(|e(k)|2)2d3r(|e(l)|2)2d3r]1/2.
γω1cn2/(n02Vcav).
Ain(k)(t)=Bkeiω0kt,
ak(t)=bkeiω0kt.
[i(Δωk+γ|bk|2+2γ|b3k|2)+1/2τph]bk=κBk,
[(Δωk+γEk+2γE3k)2+(1/2τph)2]Ek=|κ|2Pk,
Δω1=Δω2=Δω0,
P1=P2=P0,
Ain(k)(t)=Bkeiϕk(t)iω0kt,
Δωk(t)=Δω0kdϕkdt.
Tk=|κak/Ain(k)|2.
ϕk(t)=ϕ0e(ttp)2/T02,
ΔωkmaxΔω0+0.86ϕ0/T0.
ϕ0>T0/τph.
T0>τph.
1τph=1τphab+1τphsc+1τphe,
1τphabcαmn0,
dΔUTdt=cαmn0(|a1|2+|a2|2)ΔUTτT,
ΔnT=(n/T)ΔUTρCρVcav,
dΔnTdt=(n/T)cαmn0ρCρVcav(|a1|2+|a2|2)ΔnTτT.
dakdt=iωkakak2τph+κAin(k)(t)+iγ(|ak|2+2|a3k|2)ak+iωkΔnTn0ak.
ΔωTωkτTcαm(n/T)n02ρCρVcavEcav,
ΔωKerrω1cn2n02VcavEcav,
ϒT=|ΔωTΔωKerr|=τTαm(n/T)ρCρn2.
P0(VcavQ2)ω1n02cn2.
ΔT(1Q)2τTαmn0n2ρCρ,
ak(t)=bk[1+ck(t)]eiω0kt,
dcdt=iγSc,
S=(q12E2E12E22E1q22E1E2E12E2q1*2E22E1E22E1q2*),
Scm=λmcm.
Im{λm}>0,

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