Abstract

A four-port nonlinear photonic crystal system is discussed that exhibits optical bistability with negligible backscattering to the inputs, making it particularly suitable for integration with other active devices on the same chip. Devices based on this system can be made to be small Oλ3 in volume, have a nearly instantaneous response, and consume only a few milliwatts of power. Among many possible applications, we focus on an all-optical transistor and integrated optical isolation.

© 2003 Optical Society of America

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References

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  1. B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics (Wiley, New York, 1991).
    [CrossRef]
  2. M. Soljačić, M. Ibanescu, S. G. Johnson, Y. Fink, and J. D. Joannopoulos, Phys. Rev. E 66, 055601(R) (2002).
    [CrossRef]
  3. S. F. Mingaleev and Y. S. Kivshar, J. Opt. Soc. Am. B 19, 2241 (2002).
    [CrossRef]
  4. S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and H. A. Haus, Phys. Rev. Lett. 80, 960 (1998).
    [CrossRef]
  5. There also exist stable states of the system that are not left–right symmetric; we were able to excite them with particular initial conditions purposely designed to ruin the left–right symmetry. Nevertheless, the states that respect left–right symmetry appear to be particularly stable; various nonlinearly induced left–right asymmetries (at typcial operating power levels) with as large as 10% differences in the energies stored in the two cavities did not destabilize them.
  6. For a review, see A. Taflove, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech House, Norwood, Mass., 1995).
  7. M. L. Povinelli, S. G. Johnson, S. Fan, and J. D. Joannopoulos, Phys. Rev. B 64, 075313 (2001).
    [CrossRef]
  8. M. Scalora, J. P. Dowling, M. J. Bloemer, and C. M. Bowden, J. Appl. Phys. 76, 2023 (1994).
    [CrossRef]
  9. K. Gallo, G. Assanto, K. R. Parameswaran, and M. M. Fejer, Appl. Phys. Lett. 79, 314 (2001).
    [CrossRef]

2002 (2)

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

S. F. Mingaleev and Y. S. Kivshar, J. Opt. Soc. Am. B 19, 2241 (2002).
[CrossRef]

2001 (2)

M. L. Povinelli, S. G. Johnson, S. Fan, and J. D. Joannopoulos, Phys. Rev. B 64, 075313 (2001).
[CrossRef]

K. Gallo, G. Assanto, K. R. Parameswaran, and M. M. Fejer, Appl. Phys. Lett. 79, 314 (2001).
[CrossRef]

1998 (1)

S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and H. A. Haus, Phys. Rev. Lett. 80, 960 (1998).
[CrossRef]

1994 (1)

M. Scalora, J. P. Dowling, M. J. Bloemer, and C. M. Bowden, J. Appl. Phys. 76, 2023 (1994).
[CrossRef]

Assanto, G.

K. Gallo, G. Assanto, K. R. Parameswaran, and M. M. Fejer, Appl. Phys. Lett. 79, 314 (2001).
[CrossRef]

Bloemer, M. J.

M. Scalora, J. P. Dowling, M. J. Bloemer, and C. M. Bowden, J. Appl. Phys. 76, 2023 (1994).
[CrossRef]

Bowden, C. M.

M. Scalora, J. P. Dowling, M. J. Bloemer, and C. M. Bowden, J. Appl. Phys. 76, 2023 (1994).
[CrossRef]

Dowling, J. P.

M. Scalora, J. P. Dowling, M. J. Bloemer, and C. M. Bowden, J. Appl. Phys. 76, 2023 (1994).
[CrossRef]

Fan, S.

M. L. Povinelli, S. G. Johnson, S. Fan, and J. D. Joannopoulos, Phys. Rev. B 64, 075313 (2001).
[CrossRef]

S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and H. A. Haus, Phys. Rev. Lett. 80, 960 (1998).
[CrossRef]

Fejer, M. M.

K. Gallo, G. Assanto, K. R. Parameswaran, and M. M. Fejer, Appl. Phys. Lett. 79, 314 (2001).
[CrossRef]

Fink, Y.

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

Gallo, K.

K. Gallo, G. Assanto, K. R. Parameswaran, and M. M. Fejer, Appl. Phys. Lett. 79, 314 (2001).
[CrossRef]

Haus, H. A.

S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and H. A. Haus, Phys. Rev. Lett. 80, 960 (1998).
[CrossRef]

Ibanescu, M.

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

Joannopoulos, J. D.

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

M. L. Povinelli, S. G. Johnson, S. Fan, and J. D. Joannopoulos, Phys. Rev. B 64, 075313 (2001).
[CrossRef]

S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and H. A. Haus, Phys. Rev. Lett. 80, 960 (1998).
[CrossRef]

Johnson, S. G.

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

M. L. Povinelli, S. G. Johnson, S. Fan, and J. D. Joannopoulos, Phys. Rev. B 64, 075313 (2001).
[CrossRef]

Kivshar, Y. S.

Mingaleev, S. F.

Parameswaran, K. R.

K. Gallo, G. Assanto, K. R. Parameswaran, and M. M. Fejer, Appl. Phys. Lett. 79, 314 (2001).
[CrossRef]

Povinelli, M. L.

M. L. Povinelli, S. G. Johnson, S. Fan, and J. D. Joannopoulos, Phys. Rev. B 64, 075313 (2001).
[CrossRef]

Saleh, B. E. A.

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

Scalora, M.

M. Scalora, J. P. Dowling, M. J. Bloemer, and C. M. Bowden, J. Appl. Phys. 76, 2023 (1994).
[CrossRef]

Soljacic, M.

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

Villeneuve, P. R.

S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and H. A. Haus, Phys. Rev. Lett. 80, 960 (1998).
[CrossRef]

Appl. Phys. Lett. (1)

K. Gallo, G. Assanto, K. R. Parameswaran, and M. M. Fejer, Appl. Phys. Lett. 79, 314 (2001).
[CrossRef]

J. Appl. Phys. (1)

M. Scalora, J. P. Dowling, M. J. Bloemer, and C. M. Bowden, J. Appl. Phys. 76, 2023 (1994).
[CrossRef]

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

Phys. Rev. B (1)

M. L. Povinelli, S. G. Johnson, S. Fan, and J. D. Joannopoulos, Phys. Rev. B 64, 075313 (2001).
[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]

Phys. Rev. Lett. (1)

S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and H. A. Haus, Phys. Rev. Lett. 80, 960 (1998).
[CrossRef]

Other (3)

There also exist stable states of the system that are not left–right symmetric; we were able to excite them with particular initial conditions purposely designed to ruin the left–right symmetry. Nevertheless, the states that respect left–right symmetry appear to be particularly stable; various nonlinearly induced left–right asymmetries (at typcial operating power levels) with as large as 10% differences in the energies stored in the two cavities did not destabilize them.

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

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

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Figures (3)

Fig. 1
Fig. 1

Basic four-port nonlinear PC devices that we use to demonstrate optical bistability. The PC consists of high-index, ϵH=11.56, rods with radius 0.2a; a is the lattice constant. The green rods have ϵ=9.5; the small rods have ϵ=6.2 and radius 0.05a. As an example of the use of the device, we show the electrical fields when it performs optical isolation. Top, a strong forward-propagating pulse; bottom, a weak reflected backward-propagating pulse. We model the high-index rods as having an instantaneous Kerr nonlinearity.

Fig. 2
Fig. 2

Plots of the observed TPOUTS/PINS versus PINS for the device from Fig. 1. Top, power observed at output 2; bottom, power observed at output 4. The input signal enters the device at port 1. To observe the lower bistability hysteresis branch (red circles), we send smooth cw signals into port 1 of the system, and we vary the peak power of the incoming signals. To observe the upper bistability hysteresis branch (blue circles), we launch superpositions of wide Gaussian pulses that decay into smaller-intensity cw signals, thereby relaxing into the points on the upper hysteresis branch. The green curves are from an analytical model described in the text.

Fig. 3
Fig. 3

Results of launching Gaussian pulses into the device of Fig. 1. Top left, observations of launching various energy (otherwise equal) pulses into port 1 only. Top right, observations of launching a fixed signal (red circle from the top left) into port 1 of the device, in parallel with launching various energy (otherwise equal) pulses into port 3. The blue shaded area and curve in the bottom graphs correspond to the pulse observed at port 4 when a signal (blue circle in the top right graph) is launched into the device. The top right graph also shows (in green) the incoming pulse (both pulses in this panel are normalized to the peak power of the incoming pulse).

Equations (1)

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