Abstract

We study cascaded microring resonator (CMRR) configurations as general nonlinear phase-shifting elements that exhibit enhanced nonlinear sensitivity and flattened transmission characteristics. We show that even when the material itself has large two-photon absorption, CMRR devices with five rings facilitate a factor-of-10 enhancement of the optical nonlinearity when compared with a channel waveguide having the same group delay. In addition, high throughput in intensity can be maintained up to a 3π phase shift.

© 2003 Optical Society of America

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References

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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  9. V. Van, T. A. Ibrahim, K. Ritter, P. Absil, F. Johnson, R. Grover, J. Goldhar, and P.-T. Ho, “All-optical nonlinear switching in GaAs-Al-GaAs microring resonators,” IEEE Photon. Technol. Lett. 14, 74–76 (2002).
    [CrossRef]
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2002 (4)

V. Van, T. A. Ibrahim, P. Absil, F. Johnson, R. Grover, and P.-T. Ho, “Optical signal processing using nonlinear semiconductor microring resonators,” IEEE J. Sel. Top. Quantum Electron. 8, 705–713 (2002).
[CrossRef]

V. Van, T. A. Ibrahim, K. Ritter, P. Absil, F. Johnson, R. Grover, J. Goldhar, and P.-T. Ho, “All-optical nonlinear switching in GaAs-Al-GaAs microring resonators,” IEEE Photon. Technol. Lett. 14, 74–76 (2002).
[CrossRef]

S. Blair, J. Heebner, and R. W. Boyd, “Beyond the absorption-limited nonlinear phase shift with microring resonators,” Opt. Lett. 27, 357–359 (2002).
[CrossRef]

J. E. Heebner and R. W. Boyd, “Scissor solitons and other novel propagation effects in microresonator modified waveguides,” J. Opt. Soc. Am. B 19, 722–731 (2002).
[CrossRef]

2000 (2)

1999 (2)

L. V. Hau, S. E. Harris, Z. Dutton, and C. H. Behroozi, “Light speed reduction to 17 metres per second in an ultracold atomic gas,” Nature 397, 594–598 (1999).
[CrossRef]

J. E. Heebner and R. W. Boyd, “Enhanced all-optical switching by use of a nonlinear fiber ring resonator,” Opt. Lett. 24, 847–849 (1999).
[CrossRef]

1997 (1)

1996 (1)

1989 (1)

Absil, P.

V. Van, T. A. Ibrahim, P. Absil, F. Johnson, R. Grover, and P.-T. Ho, “Optical signal processing using nonlinear semiconductor microring resonators,” IEEE J. Sel. Top. Quantum Electron. 8, 705–713 (2002).
[CrossRef]

V. Van, T. A. Ibrahim, K. Ritter, P. Absil, F. Johnson, R. Grover, J. Goldhar, and P.-T. Ho, “All-optical nonlinear switching in GaAs-Al-GaAs microring resonators,” IEEE Photon. Technol. Lett. 14, 74–76 (2002).
[CrossRef]

Absil, P. P.

Andrejco, M. J.

Behroozi, C. H.

L. V. Hau, S. E. Harris, Z. Dutton, and C. H. Behroozi, “Light speed reduction to 17 metres per second in an ultracold atomic gas,” Nature 397, 594–598 (1999).
[CrossRef]

Blair, S.

Boyd, R. W.

Cho, P. S.

DeLong, K. W.

Dutton, Z.

L. V. Hau, S. E. Harris, Z. Dutton, and C. H. Behroozi, “Light speed reduction to 17 metres per second in an ultracold atomic gas,” Nature 397, 594–598 (1999).
[CrossRef]

Goldhar, J.

V. Van, T. A. Ibrahim, K. Ritter, P. Absil, F. Johnson, R. Grover, J. Goldhar, and P.-T. Ho, “All-optical nonlinear switching in GaAs-Al-GaAs microring resonators,” IEEE Photon. Technol. Lett. 14, 74–76 (2002).
[CrossRef]

Grover, R.

V. Van, T. A. Ibrahim, K. Ritter, P. Absil, F. Johnson, R. Grover, J. Goldhar, and P.-T. Ho, “All-optical nonlinear switching in GaAs-Al-GaAs microring resonators,” IEEE Photon. Technol. Lett. 14, 74–76 (2002).
[CrossRef]

V. Van, T. A. Ibrahim, P. Absil, F. Johnson, R. Grover, and P.-T. Ho, “Optical signal processing using nonlinear semiconductor microring resonators,” IEEE J. Sel. Top. Quantum Electron. 8, 705–713 (2002).
[CrossRef]

Hagness, S. C.

Harris, S. E.

S. E. Harris, “Pondermotive forces with slow light,” Phys. Rev. Lett. 85, 4032–4035 (2000).
[CrossRef] [PubMed]

L. V. Hau, S. E. Harris, Z. Dutton, and C. H. Behroozi, “Light speed reduction to 17 metres per second in an ultracold atomic gas,” Nature 397, 594–598 (1999).
[CrossRef]

Hau, L. V.

L. V. Hau, S. E. Harris, Z. Dutton, and C. H. Behroozi, “Light speed reduction to 17 metres per second in an ultracold atomic gas,” Nature 397, 594–598 (1999).
[CrossRef]

Heebner, J.

Heebner, J. E.

Ho, P.-T.

V. Van, T. A. Ibrahim, K. Ritter, P. Absil, F. Johnson, R. Grover, J. Goldhar, and P.-T. Ho, “All-optical nonlinear switching in GaAs-Al-GaAs microring resonators,” IEEE Photon. Technol. Lett. 14, 74–76 (2002).
[CrossRef]

V. Van, T. A. Ibrahim, P. Absil, F. Johnson, R. Grover, and P.-T. Ho, “Optical signal processing using nonlinear semiconductor microring resonators,” IEEE J. Sel. Top. Quantum Electron. 8, 705–713 (2002).
[CrossRef]

P. P. Absil, J. V. Hyrniewicz, B. E. Little, P. S. Cho, R. A. Wilson, L. G. Joneckis, and P.-T. Ho, “Wavelength conversion in GaAs microring resonators,” Opt. Lett. 25, 554–556 (2000).
[CrossRef]

Ho, S. T.

Hyrniewicz, J. V.

Ibrahim, T. A.

V. Van, T. A. Ibrahim, P. Absil, F. Johnson, R. Grover, and P.-T. Ho, “Optical signal processing using nonlinear semiconductor microring resonators,” IEEE J. Sel. Top. Quantum Electron. 8, 705–713 (2002).
[CrossRef]

V. Van, T. A. Ibrahim, K. Ritter, P. Absil, F. Johnson, R. Grover, J. Goldhar, and P.-T. Ho, “All-optical nonlinear switching in GaAs-Al-GaAs microring resonators,” IEEE Photon. Technol. Lett. 14, 74–76 (2002).
[CrossRef]

Johnson, F.

V. Van, T. A. Ibrahim, K. Ritter, P. Absil, F. Johnson, R. Grover, J. Goldhar, and P.-T. Ho, “All-optical nonlinear switching in GaAs-Al-GaAs microring resonators,” IEEE Photon. Technol. Lett. 14, 74–76 (2002).
[CrossRef]

V. Van, T. A. Ibrahim, P. Absil, F. Johnson, R. Grover, and P.-T. Ho, “Optical signal processing using nonlinear semiconductor microring resonators,” IEEE J. Sel. Top. Quantum Electron. 8, 705–713 (2002).
[CrossRef]

Joneckis, L. G.

Little, B. E.

McLeod, R.

Mizrahi, V.

Rafizadeh, D.

Ritter, K.

V. Van, T. A. Ibrahim, K. Ritter, P. Absil, F. Johnson, R. Grover, J. Goldhar, and P.-T. Ho, “All-optical nonlinear switching in GaAs-Al-GaAs microring resonators,” IEEE Photon. Technol. Lett. 14, 74–76 (2002).
[CrossRef]

Saifi, M. A.

Stair, K. A.

Stegeman, G. I.

Taflove, A.

Tiberio, R. C.

Van, V.

V. Van, T. A. Ibrahim, P. Absil, F. Johnson, R. Grover, and P.-T. Ho, “Optical signal processing using nonlinear semiconductor microring resonators,” IEEE J. Sel. Top. Quantum Electron. 8, 705–713 (2002).
[CrossRef]

V. Van, T. A. Ibrahim, K. Ritter, P. Absil, F. Johnson, R. Grover, J. Goldhar, and P.-T. Ho, “All-optical nonlinear switching in GaAs-Al-GaAs microring resonators,” IEEE Photon. Technol. Lett. 14, 74–76 (2002).
[CrossRef]

Wagner, K.

Wilson, R. A.

Zhang, J. P.

IEEE J. Sel. Top. Quantum Electron. (1)

V. Van, T. A. Ibrahim, P. Absil, F. Johnson, R. Grover, and P.-T. Ho, “Optical signal processing using nonlinear semiconductor microring resonators,” IEEE J. Sel. Top. Quantum Electron. 8, 705–713 (2002).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

V. Van, T. A. Ibrahim, K. Ritter, P. Absil, F. Johnson, R. Grover, J. Goldhar, and P.-T. Ho, “All-optical nonlinear switching in GaAs-Al-GaAs microring resonators,” IEEE Photon. Technol. Lett. 14, 74–76 (2002).
[CrossRef]

J. Opt. Soc. Am. B (2)

Nature (1)

L. V. Hau, S. E. Harris, Z. Dutton, and C. H. Behroozi, “Light speed reduction to 17 metres per second in an ultracold atomic gas,” Nature 397, 594–598 (1999).
[CrossRef]

Opt. Lett. (5)

Phys. Rev. Lett. (1)

S. E. Harris, “Pondermotive forces with slow light,” Phys. Rev. Lett. 85, 4032–4035 (2000).
[CrossRef] [PubMed]

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Figures (11)

Fig. 1
Fig. 1

Basic structures of single-ring resonator configurations: (a) single-coupler ring resonator (SCRR) and (b) double-coupler ring resonator (DCRR).

Fig. 2
Fig. 2

Linear response of critical-coupled SCRR versus frequency: (a) intensity transmittance, (b) output phase shift, and (c) group delay. Nonlinear response versus incident intensity: (d) intensity transmittance, (e) output phase shift.

Fig. 3
Fig. 3

Linear response of overcoupled SCRR versus frequency: (a) intensity transmittance, (b) output phase shift, and (c) group delay. Nonlinear response versus incident intensity: (d) intensity transmittance, (e) output phase shift.

Fig. 4
Fig. 4

Linear response of a symmetric DCRR near critical-coupling versus frequency: (a) intensity transmittance, (b) output phase shift, and (c) group delay. Nonlinear response versus incident intensity: (d) intensity transmittance, (e) output phase shift.

Fig. 5
Fig. 5

Nonlinear phase sensitivity of SCRRs and DCRRs: (a) SCRRs of fixed FSR, (b) SCRRs of constant Q, (c) DCRRs of fixed FSR, and (d) DCRRs of constant Q. The marks indicate calculated points and the lines are fitted curves. The values of Q are reasonable with advanced microfabrication technology.9

Fig. 6
Fig. 6

CMRR devices: (a) CMRR(5); (b) CMRR(4+1).

Fig. 7
Fig. 7

Linear response of CMRR(5) (light curves) and CMRR(4+1) (heavy curves) versus frequency: (a) intensity transmittance, (b) output phase shift, and (c) group delay. Nonlinear response versus incident intensity: (d) intensity transmittance, (e) output phase shift.

Fig. 8
Fig. 8

Nonlinear detuning of the CMRR (heavy curves) and the channel waveguide (light curves) at different TPA coefficients K=0, 0.03, 0.1: intensity transmittance (upper panel) and output phase-shift (lower panel) response with incident intensity n2Iin. The incident frequency is νm. The channel waveguide has a length of the same group delay as the CMRR.

Fig. 9
Fig. 9

FOM of the CMRR (heavy curves) and the channel waveguide (light curves) at different TPA coefficients K=0, 0.03, 0.1. The channel waveguide has a length of the same group delay as the CMRR.

Fig. 10
Fig. 10

CMRR under incident intensity of Iπ at different TPA coefficients K=0, 0.03, 0.1: intensity buildup inside the rings (top panel); refractive index change due to nonlinear refraction and TPA (middle panel); attenuation coefficient change due to TPA (bottom panel). n2Iπ=5.4×10-6, 5.9×10-6, 7.2×10-6 for K=0, 0.03, 0.1, respectively.

Fig. 11
Fig. 11

Comparison of the linear and nonlinear detuning at different TPA coefficients K=0, 0.03, 0.1. For nonlinear detuning the incident beam comprises a strong pump beam of intensity Iπ and fixed frequency νm and a weak probe beam of central frequency νm but detuned from -0.0005νm to +0.0005νm.

Equations (14)

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E(0)E(L)=irttir EinEout,
EoutEin=t-a exp(+iϕ)1-ta exp(+iϕ).
ΔΦ=π+ϕ+arctant sin ϕa-t cos ϕ+arctanta sin ϕ1-ta cos ϕ.
ϕ=ϕL+ϕNL=kL+2πn2Iringλf Leff,
EoutEin=r0r1[a exp(+iϕ)]1/21-t0t1a exp(+iϕ),
ΔΦ=π+ϕ2+arctant2a sin ϕ1-t2a cos ϕ.
dΔΦdIin=dΔΦdϕNLdϕNLdIringdIringdIin,
dΔΦdIinFQ.
EoutEin=t-a exp(+iϕ)1-ta exp(+iϕ)N.
EoutEin=t-a exp(+iϕ)1-ta exp(+iϕ)N-1-r2a exp(+iϕ)1-t2a exp(+iϕ)
a2=exp(-αL)1+2kfn2K|E(0)|2Leff.
ϕ=ϕL+ϕNL=kL+1/2K ln(1+2kfn2K|E(0)|2Leff).
FOM=e|Eout|2|Ein|2ΔΦπ,
αNL=β2Iring=dα,

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