Abstract

We show that the nonlinear phase shift produced by a ring resonator constructed from a given nonlinear optical material can be greater than the phase shift produced by a single pass through an infinite length of the same material when linear and nonlinear absorption are taken into consideration. The figure of merit (defined by the phase shift times the throughput) also improves for the ring resonator over that of the native nonlinear absorbing material. We finally show that these benefits of using the ring resonator as a nonlinear phase-shifting element can enhance the switching characteristics of a Mach–Zehnder interferometer.

© 2002 Optical Society of America

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References

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  1. S. Blair, K. Wagner, and R. McLeod, J. Opt. Soc. Am. B 13, 2141 (1996).
    [CrossRef]
  2. H. M. Gibbs, Optical Bistability: Controlling Light with Light (Academic, San Diego, Calif., 1985).
  3. P. P. Absil, J. V. Hryniewicz, B. E. Little, R. A. Wilson, L. G. Joneckis, and P.-T. Ho, IEEE Photon. Technol. Lett. 12, 398 (2000).
    [CrossRef]
  4. J. E. Heebner and R. W. Boyd, Opt. Lett. 24, 847 (1999).
    [CrossRef]
  5. K. W. DeLong and G. I. Stegeman, Appl. Phys. Lett. 57, 2063 (1990).
    [CrossRef]

2000 (1)

P. P. Absil, J. V. Hryniewicz, B. E. Little, R. A. Wilson, L. G. Joneckis, and P.-T. Ho, IEEE Photon. Technol. Lett. 12, 398 (2000).
[CrossRef]

1999 (1)

1996 (1)

1990 (1)

K. W. DeLong and G. I. Stegeman, Appl. Phys. Lett. 57, 2063 (1990).
[CrossRef]

Absil, P. P.

P. P. Absil, J. V. Hryniewicz, B. E. Little, R. A. Wilson, L. G. Joneckis, and P.-T. Ho, IEEE Photon. Technol. Lett. 12, 398 (2000).
[CrossRef]

Blair, S.

Boyd, R. W.

DeLong, K. W.

K. W. DeLong and G. I. Stegeman, Appl. Phys. Lett. 57, 2063 (1990).
[CrossRef]

Gibbs, H. M.

H. M. Gibbs, Optical Bistability: Controlling Light with Light (Academic, San Diego, Calif., 1985).

Heebner, J. E.

Ho, P.-T.

P. P. Absil, J. V. Hryniewicz, B. E. Little, R. A. Wilson, L. G. Joneckis, and P.-T. Ho, IEEE Photon. Technol. Lett. 12, 398 (2000).
[CrossRef]

Hryniewicz, J. V.

P. P. Absil, J. V. Hryniewicz, B. E. Little, R. A. Wilson, L. G. Joneckis, and P.-T. Ho, IEEE Photon. Technol. Lett. 12, 398 (2000).
[CrossRef]

Joneckis, L. G.

P. P. Absil, J. V. Hryniewicz, B. E. Little, R. A. Wilson, L. G. Joneckis, and P.-T. Ho, IEEE Photon. Technol. Lett. 12, 398 (2000).
[CrossRef]

Little, B. E.

P. P. Absil, J. V. Hryniewicz, B. E. Little, R. A. Wilson, L. G. Joneckis, and P.-T. Ho, IEEE Photon. Technol. Lett. 12, 398 (2000).
[CrossRef]

McLeod, R.

Stegeman, G. I.

K. W. DeLong and G. I. Stegeman, Appl. Phys. Lett. 57, 2063 (1990).
[CrossRef]

Wagner, K.

Wilson, R. A.

P. P. Absil, J. V. Hryniewicz, B. E. Little, R. A. Wilson, L. G. Joneckis, and P.-T. Ho, IEEE Photon. Technol. Lett. 12, 398 (2000).
[CrossRef]

Appl. Phys. Lett. (1)

K. W. DeLong and G. I. Stegeman, Appl. Phys. Lett. 57, 2063 (1990).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

P. P. Absil, J. V. Hryniewicz, B. E. Little, R. A. Wilson, L. G. Joneckis, and P.-T. Ho, IEEE Photon. Technol. Lett. 12, 398 (2000).
[CrossRef]

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

Opt. Lett. (1)

Other (1)

H. M. Gibbs, Optical Bistability: Controlling Light with Light (Academic, San Diego, Calif., 1985).

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Figures (4)

Fig. 1
Fig. 1

Squared magnitude (solid curve) and phase (dashed curve) of the transfer function for a single-coupler RR near the critical coupling condition in which the rate of energy coupled into the cavity equals the rate of energy dissipated within the cavity. Insets, RR geometry used for Figs. 2 and 3 (left) and resonance-enhanced Mach–Zehnder interferometer geometry used for Fig. 4 (right).

Fig. 2
Fig. 2

Comparison of the FOM for the RR with δν=0 (solid curve) and nonlinear sections of lengths L, 10L, and FL.

Fig. 3
Fig. 3

Intensity transmission (heavier curves) for the RR (solid curves) with δν=0 and nonlinear sections of lengths L, 10L, and FL. The corresponding phase changes are shown as thinner curves. The dotted curve corresponds to a nonlinear section of infinite length, which is essentially the same as for a length FL.

Fig. 4
Fig. 4

Inverting and noninverting outputs of a Mach–Zehnder interferometer with a RR δν=0 used as a nonlinear element (solid curves) with inverting switching threshold n2Iinc=9×10-6. Because of slight overcoupling, the outputs do not reach their expected values of 0.25 at low input levels. Inverting Mach–Zehnder outputs with nonlinear sections of lengths L (threshold, 6×10-3), 10L (threshold, 7×10-4), and FL (switching threshold not reached owing to large absorption) are shown.

Equations (7)

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2jk0Az+2k02n2n01+jKA2A+jk0α0A=0.
a2=exp-αL1+2kfn2KE02Leff,
ϕ=k0L+12Kln1+2kfn2KE02Leff,
E0=τEL+jσEi,
Et=τEi+jσEL,
EtEi=τ-exp-αL/2expjk0L1-τ exp-αL/2expjk0L.
FOM=ΔϕtπeEt2Ei2,

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