Abstract

Under the constraint of fixed pulse distortion, we study the bandwidth-delay product and nonlinear phase shift performance of coupled-resonator slow-light waveguides with designs that produce maximally-flat transmission and maximally-flat group delay responses. Even though improvement in bandwidth-delay product can be obtained with increasing number of resonators, the nonlinear response fails to improve beyond a certain number of resonators due to the increased filter bandwidth necessary to maintain a fixed pulse distortion. However, as expected, the nonlinear response improves with resonator finesse and degrades with resonator loss.

©2007 Optical Society of America

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References

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  1. N. Stefanou and A. Modinos “Impurity bands in photonic insulators,” Phys. Rev. B 57,12127–12133 (1998).
    [Crossref]
  2. A. Yariv, Y. Xu, R. K. Lee, and A. Scherer “Coupled-resonator optical waveguides: a proposal and analysis,” Opt. Lett. 24,711–713 (1999).
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  3. J. V. Hyrniewicz, P. P. Absil, B. E. Little, R. A. Wilson, and P.-T. Ho “Higher order filter response in coupled microring resonators,” IEEE Photon. Technol. Lett. 12,320–322 (2000).
    [Crossref]
  4. J. K. S. Poon, L. Zhu, G. A. DeRose, and A. Yariv “Transmission and group delay of microring coupled-resonator optical waveguides,” Opt. Lett. 31,456–458 (2006).
    [Crossref] [PubMed]
  5. S. Mookherjea and A. Yariv “Second harmonic generation with pulses in a coupled-resonator optical waveguide,” Phys. Rev. E 65,026607 (2002).
    [Crossref]
  6. A. Melloni, F. Morichetti, and M. Martinelli “Linear and nonlinear pulse propagation in coupled resonator slow-wave optical structures,” Opt. Quantum Electron. 35,365–379 (2003).
    [Crossref]
  7. Y. Chen and S. Blair “Nonlinearity enhancement in finite coupled-resonator slow-light waveguides,” Opt. Express 12,3353–3366 (2004). http://oe.osa.org/abstract.cfm?id=80620
    [Crossref] [PubMed]
  8. A. Melloni and M. Martinelli “Synthesis of direct-coupled-resonators bandpass filters for WDM systems,” J. Lightwave Technol. 20,296–303 (2002).
    [Crossref]
  9. C. K. Madsen and J. H. ZhaoOptical Filter Design and Analysis: A Signal Processing Approach. Wiley1999.
  10. M. D. Stenner, M. A. Neifeld, Z. Zhu, A. M. C. Dawes, and D. J. Gauthier “Distortion management in slow-light pulse delay,” Opt. Express 13,9995–10002 (2005). http://oe.osa.org/abstract.cfm?id=86492
    [Crossref] [PubMed]
  11. F. G. Sedgwick, C. J. Chang-Hasnain, P. C. Ku, and R. S. Tucker, “Storage-bit-rate product in slow-light optical buffers,” Electron. Lett. 41,1347–1348 (2005).
    [Crossref]
  12. Y. Chen and S. Blair “Nonlinear phase shift of cascaded microring resonators,” J. Opt. Soc. Am. B 20,2125–2132 (2003).
    [Crossref]

2006 (1)

2005 (2)

M. D. Stenner, M. A. Neifeld, Z. Zhu, A. M. C. Dawes, and D. J. Gauthier “Distortion management in slow-light pulse delay,” Opt. Express 13,9995–10002 (2005). http://oe.osa.org/abstract.cfm?id=86492
[Crossref] [PubMed]

F. G. Sedgwick, C. J. Chang-Hasnain, P. C. Ku, and R. S. Tucker, “Storage-bit-rate product in slow-light optical buffers,” Electron. Lett. 41,1347–1348 (2005).
[Crossref]

2004 (1)

2003 (2)

A. Melloni, F. Morichetti, and M. Martinelli “Linear and nonlinear pulse propagation in coupled resonator slow-wave optical structures,” Opt. Quantum Electron. 35,365–379 (2003).
[Crossref]

Y. Chen and S. Blair “Nonlinear phase shift of cascaded microring resonators,” J. Opt. Soc. Am. B 20,2125–2132 (2003).
[Crossref]

2002 (2)

A. Melloni and M. Martinelli “Synthesis of direct-coupled-resonators bandpass filters for WDM systems,” J. Lightwave Technol. 20,296–303 (2002).
[Crossref]

S. Mookherjea and A. Yariv “Second harmonic generation with pulses in a coupled-resonator optical waveguide,” Phys. Rev. E 65,026607 (2002).
[Crossref]

2000 (1)

J. V. Hyrniewicz, P. P. Absil, B. E. Little, R. A. Wilson, and P.-T. Ho “Higher order filter response in coupled microring resonators,” IEEE Photon. Technol. Lett. 12,320–322 (2000).
[Crossref]

1999 (1)

1998 (1)

N. Stefanou and A. Modinos “Impurity bands in photonic insulators,” Phys. Rev. B 57,12127–12133 (1998).
[Crossref]

Absil, P. P.

J. V. Hyrniewicz, P. P. Absil, B. E. Little, R. A. Wilson, and P.-T. Ho “Higher order filter response in coupled microring resonators,” IEEE Photon. Technol. Lett. 12,320–322 (2000).
[Crossref]

Blair, S.

Chang-Hasnain, C. J.

F. G. Sedgwick, C. J. Chang-Hasnain, P. C. Ku, and R. S. Tucker, “Storage-bit-rate product in slow-light optical buffers,” Electron. Lett. 41,1347–1348 (2005).
[Crossref]

Chen, Y.

Dawes, A. M. C.

DeRose, G. A.

Gauthier, D. J.

Ho, P.-T.

J. V. Hyrniewicz, P. P. Absil, B. E. Little, R. A. Wilson, and P.-T. Ho “Higher order filter response in coupled microring resonators,” IEEE Photon. Technol. Lett. 12,320–322 (2000).
[Crossref]

Hyrniewicz, J. V.

J. V. Hyrniewicz, P. P. Absil, B. E. Little, R. A. Wilson, and P.-T. Ho “Higher order filter response in coupled microring resonators,” IEEE Photon. Technol. Lett. 12,320–322 (2000).
[Crossref]

Ku, P. C.

F. G. Sedgwick, C. J. Chang-Hasnain, P. C. Ku, and R. S. Tucker, “Storage-bit-rate product in slow-light optical buffers,” Electron. Lett. 41,1347–1348 (2005).
[Crossref]

Lee, R. K.

Little, B. E.

J. V. Hyrniewicz, P. P. Absil, B. E. Little, R. A. Wilson, and P.-T. Ho “Higher order filter response in coupled microring resonators,” IEEE Photon. Technol. Lett. 12,320–322 (2000).
[Crossref]

Madsen, C. K.

C. K. Madsen and J. H. ZhaoOptical Filter Design and Analysis: A Signal Processing Approach. Wiley1999.

Martinelli, M.

A. Melloni, F. Morichetti, and M. Martinelli “Linear and nonlinear pulse propagation in coupled resonator slow-wave optical structures,” Opt. Quantum Electron. 35,365–379 (2003).
[Crossref]

A. Melloni and M. Martinelli “Synthesis of direct-coupled-resonators bandpass filters for WDM systems,” J. Lightwave Technol. 20,296–303 (2002).
[Crossref]

Melloni, A.

A. Melloni, F. Morichetti, and M. Martinelli “Linear and nonlinear pulse propagation in coupled resonator slow-wave optical structures,” Opt. Quantum Electron. 35,365–379 (2003).
[Crossref]

A. Melloni and M. Martinelli “Synthesis of direct-coupled-resonators bandpass filters for WDM systems,” J. Lightwave Technol. 20,296–303 (2002).
[Crossref]

Modinos, A.

N. Stefanou and A. Modinos “Impurity bands in photonic insulators,” Phys. Rev. B 57,12127–12133 (1998).
[Crossref]

Mookherjea, S.

S. Mookherjea and A. Yariv “Second harmonic generation with pulses in a coupled-resonator optical waveguide,” Phys. Rev. E 65,026607 (2002).
[Crossref]

Morichetti, F.

A. Melloni, F. Morichetti, and M. Martinelli “Linear and nonlinear pulse propagation in coupled resonator slow-wave optical structures,” Opt. Quantum Electron. 35,365–379 (2003).
[Crossref]

Neifeld, M. A.

Poon, J. K. S.

Scherer, A.

Sedgwick, F. G.

F. G. Sedgwick, C. J. Chang-Hasnain, P. C. Ku, and R. S. Tucker, “Storage-bit-rate product in slow-light optical buffers,” Electron. Lett. 41,1347–1348 (2005).
[Crossref]

Stefanou, N.

N. Stefanou and A. Modinos “Impurity bands in photonic insulators,” Phys. Rev. B 57,12127–12133 (1998).
[Crossref]

Stenner, M. D.

Tucker, R. S.

F. G. Sedgwick, C. J. Chang-Hasnain, P. C. Ku, and R. S. Tucker, “Storage-bit-rate product in slow-light optical buffers,” Electron. Lett. 41,1347–1348 (2005).
[Crossref]

Wilson, R. A.

J. V. Hyrniewicz, P. P. Absil, B. E. Little, R. A. Wilson, and P.-T. Ho “Higher order filter response in coupled microring resonators,” IEEE Photon. Technol. Lett. 12,320–322 (2000).
[Crossref]

Xu, Y.

Yariv, A.

Zhao, J. H.

C. K. Madsen and J. H. ZhaoOptical Filter Design and Analysis: A Signal Processing Approach. Wiley1999.

Zhu, L.

Zhu, Z.

Electron. Lett. (1)

F. G. Sedgwick, C. J. Chang-Hasnain, P. C. Ku, and R. S. Tucker, “Storage-bit-rate product in slow-light optical buffers,” Electron. Lett. 41,1347–1348 (2005).
[Crossref]

IEEE Photon. Technol. Lett. (1)

J. V. Hyrniewicz, P. P. Absil, B. E. Little, R. A. Wilson, and P.-T. Ho “Higher order filter response in coupled microring resonators,” IEEE Photon. Technol. Lett. 12,320–322 (2000).
[Crossref]

J. Lightwave Technol. (1)

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

Opt. Express (2)

Opt. Lett. (2)

Opt. Quantum Electron. (1)

A. Melloni, F. Morichetti, and M. Martinelli “Linear and nonlinear pulse propagation in coupled resonator slow-wave optical structures,” Opt. Quantum Electron. 35,365–379 (2003).
[Crossref]

Phys. Rev. B (1)

N. Stefanou and A. Modinos “Impurity bands in photonic insulators,” Phys. Rev. B 57,12127–12133 (1998).
[Crossref]

Phys. Rev. E (1)

S. Mookherjea and A. Yariv “Second harmonic generation with pulses in a coupled-resonator optical waveguide,” Phys. Rev. E 65,026607 (2002).
[Crossref]

Other (1)

C. K. Madsen and J. H. ZhaoOptical Filter Design and Analysis: A Signal Processing Approach. Wiley1999.

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Figures (12)

Fig. 1.
Fig. 1. Coupled-resonator optical waveguide (CROW) geometry.
Fig. 2.
Fig. 2. Maximally-flat transmission (left) and group delay (right) designs with six resonators (N = 6), plotted versus normalized frequency. These designs were optimized for 20% distortion of a 10 ps input pulse.
Fig. 3.
Fig. 3. Bandwidth-delay product versus number of resonators for maximally-flat transmission and group delay designs with the constraint of 20%, 10%, or 5% output pulse distortion. For each resonator, L = 50 μm.
Fig. 4.
Fig. 4. Input (dashed linestyle) and output (solid linestyle) pulse profiles for maximally-flat transmission (left) and group-delay (right) designs with N = 6, optimized for 20% output pulse distortion. The input pulse duration is 10 ps, and the pulse has Gaussian shape.
Fig. 5.
Fig. 5. Comparison of intensity required to produce π/10 (dashed linestyle) and π (solid linestyle) nonlinear phase change versus number of resonators for maximally-flat transmission (blue) and group delay (red) designs with 20% output pulse distortion in linear propagation.
Fig. 6.
Fig. 6. Output pulse distortion at intensity required to produce π/10 (dashed linestyle) and π (solid linestyle) nonlinear phase change versus number of resonators for maximally-flat transmission (blue) and group delay (red) designs with 20%output pulse distortion in linear propagation.
Fig. 7.
Fig. 7. Nonlinear detuning of maximally flat transmission (left) and group delay (right) designs optimized for 20% linear distortion with N = 6.
Fig. 8.
Fig. 8. Intensities required to produce π, π/4 and π/10 nonlinear phase changes versus number of resonators for maximally-flat transmission and group delay designs with 20% output pulse distortion in nonlinear propagation.
Fig. 9.
Fig. 9. Nonlinear detuning of maximally flat transmission design optimized for 20% nonlinear distortion with N = 6.
Fig. 10.
Fig. 10. Bandwidth-delay product versus number of resonators for maximally-flat transmission design with the constraint of 20% output pulse distortion in nonlinear propagation atIπ . For each resonator, L = 50 μm.
Fig. 11.
Fig. 11. Intensity required to produce π and π/10 nonlinear phase shifts versus number of resonators for maximally-flat transmission design of different rings lengths, with the constraint of 20% output pulse distortion in nonlinear propagation.
Fig. 12.
Fig. 12. Intensity required to produce π and π/10 nonlinear phase shifts for maximally-flat transmission design with ring loss, with the constraint of 20% output pulse distortion in nonlinear propagation. For each resonator, L = 50 μm, and loss is included at 1 cm-1.

Equations (3)

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D = E in ( t + t gd ) E out * ( t ) dt E in ( t ) 2 dt
t gd = t E out ( t ) 2 dt E out ( t ) 2 dt
Δ ϕ = 2 π n 2 , eff I in L eff λ ,

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