Abstract

We demonstrate the feasibility of optical bistability in an axially modulated nonlinear OmniGuide fiber through analytical theory and detailed numerical experiments. At 1.55µm carrier wavelength, the in-fiber devices that we propose can operate with only a few tens of milliwatts of power, can have a nearly instantaneous response and recovery time, and can be shorter than 100 µm.

© 2003 Optical Society of America

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  1. Y. Fink, D. J. Ripin, S. Fan, C. Chen, J. D. Joannopoulos, and E. L. Thomas, J. Lightwave Technol. 17, 2039 (1999).
    [CrossRef]
  2. S. G. Johnson, M. Ibanescu, M. Skorobogatiy, O. Weisberg, T. D. Engeness, M. Soljačić, S. A. Jacobs, J. D. Joannopoulos, and Y. Fink, Opt. Express 9, 748 (2001), http://www.opticesexpress.org .
    [CrossRef] [PubMed]
  3. S. D. Hart, G. R. Maskaly, B. Temelkuran, P. H. Prideaux, J. D. Joannopoulos, and Y. Fink, Science 296, 511 (2002).
    [CrossRef]
  4. B. E. A. Saleh and M. C. Teich, Fundamentals Of Photonics (Wiley, New York, 1991).
    [CrossRef]
  5. M. Soljačić, M. Ibanescu, S. G. Johnson, Y. Fink, and J. D. Joannopoulos, Phys. Rev. E 66, 055601(R) (2002).
    [CrossRef]
  6. J. S. Foresi, P. R. Villeneuve, J. Ferrera, E. R. Thoen, G. Steinmeyer, S. Fan, J. D. Joannopoulos, L. C. Kimerling, H. I. Smith, and E. P. Ippen, Nature 390, 143 (1997).
    [CrossRef]
  7. S. G. Johnson and J. D. Joannopoulos, Opt. Express 8, 173 (2001), http://www.opticesexpress.org .
    [CrossRef] [PubMed]
  8. For a review, see A. Taflove, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech House, Norwood, Mass., 1995).
  9. See, e.g., S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and H. A. Haus, Phys. Rev. B 64, 245302 (2001), and H. A. Haus, Waves And Fields in Optoelectronics (Prentice-Hall, Englewood Cliffs, N.J., 1984).
    [CrossRef]
  10. S. G. Johnson, S. Fan, A. Mekis, and J. D. Joannopoulos, Appl. Phys. Lett. 78, 3388 (2001).
    [CrossRef]
  11. S. Coen and M. Haelterman, Opt. Lett. 24, 80 (1999).
    [CrossRef]
  12. S. Radić, N. George, and G. P. Agrawal, J. Opt. Soc. Am. B 12, 671 (1995).
    [CrossRef]
  13. A. Yariv, IEEE Photon. Technol. Lett. 14, 483 (2002).
    [CrossRef]
  14. J. E. Heebner and R. Boyd, Opt. Lett. 24, 847 (1999).
    [CrossRef]
  15. B. Temelkuran, Massachusetts Institute of Technology, Cambridge, Mass. 02139. (personal communication, November, 2001).
  16. C. Kerbage and B. J. Eggleton, Opt. Photon. News 13(9), 38 (2002).
    [CrossRef]

2002 (4)

S. D. Hart, G. R. Maskaly, B. Temelkuran, P. H. Prideaux, J. D. Joannopoulos, and Y. Fink, Science 296, 511 (2002).
[CrossRef]

M. Soljačić, M. Ibanescu, S. G. Johnson, Y. Fink, and J. D. Joannopoulos, Phys. Rev. E 66, 055601(R) (2002).
[CrossRef]

A. Yariv, IEEE Photon. Technol. Lett. 14, 483 (2002).
[CrossRef]

C. Kerbage and B. J. Eggleton, Opt. Photon. News 13(9), 38 (2002).
[CrossRef]

2001 (4)

S. G. Johnson, M. Ibanescu, M. Skorobogatiy, O. Weisberg, T. D. Engeness, M. Soljačić, S. A. Jacobs, J. D. Joannopoulos, and Y. Fink, Opt. Express 9, 748 (2001), http://www.opticesexpress.org .
[CrossRef] [PubMed]

S. G. Johnson and J. D. Joannopoulos, Opt. Express 8, 173 (2001), http://www.opticesexpress.org .
[CrossRef] [PubMed]

See, e.g., S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and H. A. Haus, Phys. Rev. B 64, 245302 (2001), and H. A. Haus, Waves And Fields in Optoelectronics (Prentice-Hall, Englewood Cliffs, N.J., 1984).
[CrossRef]

S. G. Johnson, S. Fan, A. Mekis, and J. D. Joannopoulos, Appl. Phys. Lett. 78, 3388 (2001).
[CrossRef]

1999 (3)

1997 (1)

J. S. Foresi, P. R. Villeneuve, J. Ferrera, E. R. Thoen, G. Steinmeyer, S. Fan, J. D. Joannopoulos, L. C. Kimerling, H. I. Smith, and E. P. Ippen, Nature 390, 143 (1997).
[CrossRef]

1995 (1)

Agrawal, G. P.

Boyd, R.

Chen, C.

Coen, S.

Eggleton, B. J.

C. Kerbage and B. J. Eggleton, Opt. Photon. News 13(9), 38 (2002).
[CrossRef]

Engeness, T. D.

Fan, S.

S. G. Johnson, S. Fan, A. Mekis, and J. D. Joannopoulos, Appl. Phys. Lett. 78, 3388 (2001).
[CrossRef]

See, e.g., S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and H. A. Haus, Phys. Rev. B 64, 245302 (2001), and H. A. Haus, Waves And Fields in Optoelectronics (Prentice-Hall, Englewood Cliffs, N.J., 1984).
[CrossRef]

Y. Fink, D. J. Ripin, S. Fan, C. Chen, J. D. Joannopoulos, and E. L. Thomas, J. Lightwave Technol. 17, 2039 (1999).
[CrossRef]

J. S. Foresi, P. R. Villeneuve, J. Ferrera, E. R. Thoen, G. Steinmeyer, S. Fan, J. D. Joannopoulos, L. C. Kimerling, H. I. Smith, and E. P. Ippen, Nature 390, 143 (1997).
[CrossRef]

Ferrera, J.

J. S. Foresi, P. R. Villeneuve, J. Ferrera, E. R. Thoen, G. Steinmeyer, S. Fan, J. D. Joannopoulos, L. C. Kimerling, H. I. Smith, and E. P. Ippen, Nature 390, 143 (1997).
[CrossRef]

Fink, Y.

Foresi, J. S.

J. S. Foresi, P. R. Villeneuve, J. Ferrera, E. R. Thoen, G. Steinmeyer, S. Fan, J. D. Joannopoulos, L. C. Kimerling, H. I. Smith, and E. P. Ippen, Nature 390, 143 (1997).
[CrossRef]

George, N.

Haelterman, M.

Hart, S. D.

S. D. Hart, G. R. Maskaly, B. Temelkuran, P. H. Prideaux, J. D. Joannopoulos, and Y. Fink, Science 296, 511 (2002).
[CrossRef]

Haus, H. A.

See, e.g., S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and H. A. Haus, Phys. Rev. B 64, 245302 (2001), and H. A. Haus, Waves And Fields in Optoelectronics (Prentice-Hall, Englewood Cliffs, N.J., 1984).
[CrossRef]

Heebner, J. E.

Ibanescu, M.

Ippen, E. P.

J. S. Foresi, P. R. Villeneuve, J. Ferrera, E. R. Thoen, G. Steinmeyer, S. Fan, J. D. Joannopoulos, L. C. Kimerling, H. I. Smith, and E. P. Ippen, Nature 390, 143 (1997).
[CrossRef]

Jacobs, S. A.

Joannopoulos, J. D.

M. Soljačić, M. Ibanescu, S. G. Johnson, Y. Fink, and J. D. Joannopoulos, Phys. Rev. E 66, 055601(R) (2002).
[CrossRef]

S. D. Hart, G. R. Maskaly, B. Temelkuran, P. H. Prideaux, J. D. Joannopoulos, and Y. Fink, Science 296, 511 (2002).
[CrossRef]

S. G. Johnson, M. Ibanescu, M. Skorobogatiy, O. Weisberg, T. D. Engeness, M. Soljačić, S. A. Jacobs, J. D. Joannopoulos, and Y. Fink, Opt. Express 9, 748 (2001), http://www.opticesexpress.org .
[CrossRef] [PubMed]

S. G. Johnson and J. D. Joannopoulos, Opt. Express 8, 173 (2001), http://www.opticesexpress.org .
[CrossRef] [PubMed]

See, e.g., S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and H. A. Haus, Phys. Rev. B 64, 245302 (2001), and H. A. Haus, Waves And Fields in Optoelectronics (Prentice-Hall, Englewood Cliffs, N.J., 1984).
[CrossRef]

S. G. Johnson, S. Fan, A. Mekis, and J. D. Joannopoulos, Appl. Phys. Lett. 78, 3388 (2001).
[CrossRef]

Y. Fink, D. J. Ripin, S. Fan, C. Chen, J. D. Joannopoulos, and E. L. Thomas, J. Lightwave Technol. 17, 2039 (1999).
[CrossRef]

J. S. Foresi, P. R. Villeneuve, J. Ferrera, E. R. Thoen, G. Steinmeyer, S. Fan, J. D. Joannopoulos, L. C. Kimerling, H. I. Smith, and E. P. Ippen, Nature 390, 143 (1997).
[CrossRef]

Johnson, S. G.

Kerbage, C.

C. Kerbage and B. J. Eggleton, Opt. Photon. News 13(9), 38 (2002).
[CrossRef]

Kimerling, L. C.

J. S. Foresi, P. R. Villeneuve, J. Ferrera, E. R. Thoen, G. Steinmeyer, S. Fan, J. D. Joannopoulos, L. C. Kimerling, H. I. Smith, and E. P. Ippen, Nature 390, 143 (1997).
[CrossRef]

Maskaly, G. R.

S. D. Hart, G. R. Maskaly, B. Temelkuran, P. H. Prideaux, J. D. Joannopoulos, and Y. Fink, Science 296, 511 (2002).
[CrossRef]

Mekis, A.

S. G. Johnson, S. Fan, A. Mekis, and J. D. Joannopoulos, Appl. Phys. Lett. 78, 3388 (2001).
[CrossRef]

Prideaux, P. H.

S. D. Hart, G. R. Maskaly, B. Temelkuran, P. H. Prideaux, J. D. Joannopoulos, and Y. Fink, Science 296, 511 (2002).
[CrossRef]

Radic, S.

Ripin, D. J.

Saleh, B. E. A.

B. E. A. Saleh and M. C. Teich, Fundamentals Of Photonics (Wiley, New York, 1991).
[CrossRef]

Skorobogatiy, M.

Smith, H. I.

J. S. Foresi, P. R. Villeneuve, J. Ferrera, E. R. Thoen, G. Steinmeyer, S. Fan, J. D. Joannopoulos, L. C. Kimerling, H. I. Smith, and E. P. Ippen, Nature 390, 143 (1997).
[CrossRef]

Soljacic, M.

Steinmeyer, G.

J. S. Foresi, P. R. Villeneuve, J. Ferrera, E. R. Thoen, G. Steinmeyer, S. Fan, J. D. Joannopoulos, L. C. Kimerling, H. I. Smith, and E. P. Ippen, Nature 390, 143 (1997).
[CrossRef]

Taflove, A.

For a review, see A. Taflove, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech House, Norwood, Mass., 1995).

Teich, M. C.

B. E. A. Saleh and M. C. Teich, Fundamentals Of Photonics (Wiley, New York, 1991).
[CrossRef]

Temelkuran, B.

S. D. Hart, G. R. Maskaly, B. Temelkuran, P. H. Prideaux, J. D. Joannopoulos, and Y. Fink, Science 296, 511 (2002).
[CrossRef]

B. Temelkuran, Massachusetts Institute of Technology, Cambridge, Mass. 02139. (personal communication, November, 2001).

Thoen, E. R.

J. S. Foresi, P. R. Villeneuve, J. Ferrera, E. R. Thoen, G. Steinmeyer, S. Fan, J. D. Joannopoulos, L. C. Kimerling, H. I. Smith, and E. P. Ippen, Nature 390, 143 (1997).
[CrossRef]

Thomas, E. L.

Villeneuve, P. R.

See, e.g., S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and H. A. Haus, Phys. Rev. B 64, 245302 (2001), and H. A. Haus, Waves And Fields in Optoelectronics (Prentice-Hall, Englewood Cliffs, N.J., 1984).
[CrossRef]

J. S. Foresi, P. R. Villeneuve, J. Ferrera, E. R. Thoen, G. Steinmeyer, S. Fan, J. D. Joannopoulos, L. C. Kimerling, H. I. Smith, and E. P. Ippen, Nature 390, 143 (1997).
[CrossRef]

Weisberg, O.

Yariv, A.

A. Yariv, IEEE Photon. Technol. Lett. 14, 483 (2002).
[CrossRef]

Appl. Phys. Lett. (1)

S. G. Johnson, S. Fan, A. Mekis, and J. D. Joannopoulos, Appl. Phys. Lett. 78, 3388 (2001).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

A. Yariv, IEEE Photon. Technol. Lett. 14, 483 (2002).
[CrossRef]

J. Lightwave Technol. (1)

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

Nature (1)

J. S. Foresi, P. R. Villeneuve, J. Ferrera, E. R. Thoen, G. Steinmeyer, S. Fan, J. D. Joannopoulos, L. C. Kimerling, H. I. Smith, and E. P. Ippen, Nature 390, 143 (1997).
[CrossRef]

Opt. Express (2)

Opt. Lett. (2)

Opt. Photon. News (1)

C. Kerbage and B. J. Eggleton, Opt. Photon. News 13(9), 38 (2002).
[CrossRef]

Phys. Rev. B (1)

See, e.g., S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and H. A. Haus, Phys. Rev. B 64, 245302 (2001), and H. A. Haus, Waves And Fields in Optoelectronics (Prentice-Hall, Englewood Cliffs, N.J., 1984).
[CrossRef]

Phys. Rev. E (1)

M. Soljačić, M. Ibanescu, S. G. Johnson, Y. Fink, and J. D. Joannopoulos, Phys. Rev. E 66, 055601(R) (2002).
[CrossRef]

Science (1)

S. D. Hart, G. R. Maskaly, B. Temelkuran, P. H. Prideaux, J. D. Joannopoulos, and Y. Fink, Science 296, 511 (2002).
[CrossRef]

Other (3)

B. E. A. Saleh and M. C. Teich, Fundamentals Of Photonics (Wiley, New York, 1991).
[CrossRef]

For a review, see A. Taflove, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech House, Norwood, Mass., 1995).

B. Temelkuran, Massachusetts Institute of Technology, Cambridge, Mass. 02139. (personal communication, November, 2001).

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Figures (3)

Fig. 1
Fig. 1

Schematic of a nonlinear OmniGuide device in which we demonstrate optical bistability. Left, longitudinal cross section; right, transverse cross section.

Fig. 2
Fig. 2

Numerical experiments with launching temporal Gaussian pulses into the nonlinear system of Fig. 1. The top left-hand panel shows the transmission as a function of the incoming pulse energy. The colored curves in the top right-hand panel display the output spectra for a few pulses, corresponding to the colored dots in the top left-hand panel. The spectrum of each pulse is normalized to its peak incoming power; i.e., the input pulse, normalized in the same manner, is displayed with the gray dashed curve. The bottom panels show the output shapes for the incoming pulses, denoted by the green and blue dots, respectively, in the top left-hand panel.

Fig. 3
Fig. 3

Plot of the observed POUTS versus PINS for the device from Fig. 1, when δ=3.2. The green squares are points obtained from numerical experiments. The red curve is the analytical prediction, which clearly matches the numerical experiments; the dotted part of the curve is unstable and therefore physically unobservable.

Equations (3)

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κcωRESd×VOLddrEr·Er2+2Er·E*r2n2rn2rVOLddrEr2n2r2n2r|MAX,
POUTSPINS=TP1+POUTS/P0-δ2,
P0TPκQ2ωRES/cd-1n2r|MAX.

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