Abstract

We propose a novel electro-optic modulator enhanced by nonlinear coupling dynamics. The design is similar to a conventional Mach–Zehnder modulator, but includes a nonlinear directional coupler at the output. At high enough intensities, this nonlinear coupler permits full switching for electro-optic phase shifts much less than the π required in a conventional linear device. Simulations confirm that this strategy can be used to design modulators with low drive voltage. Prospects for implementing this device are discussed.

© 2003 Optical Society of America

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  1. E. L. Wooten, K. M. Kissa, A. Yi-Yan, E. J. Murphy, D. A. Lafaw, P. F. Hallemeier, D. Maack, D. V. Attanasio, D. J. Fritz, G. J. McBrien, and D. E. Bossi, “A review of lithium niobate modulators for fiber-optic communications systems,” IEEE J. Sel. Top. Quantum Electron. 6, 69–82 (2000).
    [CrossRef]
  2. S. R. Friberg, A. M. Weiner, Y. Silberberg, B. G. Sfez, and P. S. Smith, “Femtosecond switching in a dual-core-fiber nonlinear coupler,” Opt. Lett. 13, 904–906 (1988).
    [CrossRef] [PubMed]
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    [CrossRef]
  4. A. Villeneuve, P. Mamyshev, J. U. Kang, G. I. Stegeman, J. S. Aitchison, and C. N. Ironside, “Efficient time-domain demultiplexing with separate signal and control wavelengths in an AlGaAs nonlinear directional coupler,” IEEE J. Quantum Electron. 31, 2165–2172 (1995).
    [CrossRef]
  5. J. M. Fini, P. L. Hagelstein, and H. A. Haus, “Multiphoton tunneling in a nonlinear interferometer,” Phys. Rev. A 64, 043813 (2001).
    [CrossRef]
  6. K. S. Chiang, “Intermodal dispersion in two-core optical fibers,” Opt. Lett. 20, 997–999 (1995).
    [CrossRef] [PubMed]
  7. J. K. Ranka, R. S. Windeler, and A. J. Stentz, “Visible continuum generation in air silica microstructure optical fibers with anomalous dispersion at 800 nm,” Opt. Lett. 25, 25–27 (2000).
    [CrossRef]
  8. G. Lenz, J. Zimmermann, T. Katsufuji, M. E. Lines, H. W. Hwang, S. Spälter, R. E. Slusher, S.-W. Cheong, J. S. Sanghera, and I. D. Aggarwal, “Large Kerr effect in bulk Se-based chalcogenide glasses,” Opt. Lett. 25, 254–256 (2000).
    [CrossRef]
  9. T. M. Monroe, K. M. Kiang, J. H. Lee, K. Frampton, Z. Yusoff, R. Moore, J. Tucknott, D. W. Hewak, H. N. Rutt, and D. J. Richardson, “High-nonlinearity, extruded, single-mode, holey optical fibers,” In Optical Fiber Communications Conference (OFC), Postconference Digest, Vol. 70 of OSA Trends in Optics and Photonics (Optical Society of America, Washington, D.C., 2002), FA1, pp. 1–3.

2001 (1)

J. M. Fini, P. L. Hagelstein, and H. A. Haus, “Multiphoton tunneling in a nonlinear interferometer,” Phys. Rev. A 64, 043813 (2001).
[CrossRef]

2000 (3)

1998 (1)

1995 (2)

K. S. Chiang, “Intermodal dispersion in two-core optical fibers,” Opt. Lett. 20, 997–999 (1995).
[CrossRef] [PubMed]

A. Villeneuve, P. Mamyshev, J. U. Kang, G. I. Stegeman, J. S. Aitchison, and C. N. Ironside, “Efficient time-domain demultiplexing with separate signal and control wavelengths in an AlGaAs nonlinear directional coupler,” IEEE J. Quantum Electron. 31, 2165–2172 (1995).
[CrossRef]

1988 (1)

Aggarwal, I. D.

Aitchison, J. S.

A. Villeneuve, P. Mamyshev, J. U. Kang, G. I. Stegeman, J. S. Aitchison, and C. N. Ironside, “Efficient time-domain demultiplexing with separate signal and control wavelengths in an AlGaAs nonlinear directional coupler,” IEEE J. Quantum Electron. 31, 2165–2172 (1995).
[CrossRef]

Attanasio, D. V.

E. L. Wooten, K. M. Kissa, A. Yi-Yan, E. J. Murphy, D. A. Lafaw, P. F. Hallemeier, D. Maack, D. V. Attanasio, D. J. Fritz, G. J. McBrien, and D. E. Bossi, “A review of lithium niobate modulators for fiber-optic communications systems,” IEEE J. Sel. Top. Quantum Electron. 6, 69–82 (2000).
[CrossRef]

Bossi, D. E.

E. L. Wooten, K. M. Kissa, A. Yi-Yan, E. J. Murphy, D. A. Lafaw, P. F. Hallemeier, D. Maack, D. V. Attanasio, D. J. Fritz, G. J. McBrien, and D. E. Bossi, “A review of lithium niobate modulators for fiber-optic communications systems,” IEEE J. Sel. Top. Quantum Electron. 6, 69–82 (2000).
[CrossRef]

Cheong, S.-W.

Chiang, K. S.

Fini, J. M.

J. M. Fini, P. L. Hagelstein, and H. A. Haus, “Multiphoton tunneling in a nonlinear interferometer,” Phys. Rev. A 64, 043813 (2001).
[CrossRef]

Friberg, S. R.

Fritz, D. J.

E. L. Wooten, K. M. Kissa, A. Yi-Yan, E. J. Murphy, D. A. Lafaw, P. F. Hallemeier, D. Maack, D. V. Attanasio, D. J. Fritz, G. J. McBrien, and D. E. Bossi, “A review of lithium niobate modulators for fiber-optic communications systems,” IEEE J. Sel. Top. Quantum Electron. 6, 69–82 (2000).
[CrossRef]

Hagelstein, P. L.

J. M. Fini, P. L. Hagelstein, and H. A. Haus, “Multiphoton tunneling in a nonlinear interferometer,” Phys. Rev. A 64, 043813 (2001).
[CrossRef]

Hall, K. L.

Hallemeier, P. F.

E. L. Wooten, K. M. Kissa, A. Yi-Yan, E. J. Murphy, D. A. Lafaw, P. F. Hallemeier, D. Maack, D. V. Attanasio, D. J. Fritz, G. J. McBrien, and D. E. Bossi, “A review of lithium niobate modulators for fiber-optic communications systems,” IEEE J. Sel. Top. Quantum Electron. 6, 69–82 (2000).
[CrossRef]

Haus, H. A.

J. M. Fini, P. L. Hagelstein, and H. A. Haus, “Multiphoton tunneling in a nonlinear interferometer,” Phys. Rev. A 64, 043813 (2001).
[CrossRef]

Hwang, H. W.

Ironside, C. N.

A. Villeneuve, P. Mamyshev, J. U. Kang, G. I. Stegeman, J. S. Aitchison, and C. N. Ironside, “Efficient time-domain demultiplexing with separate signal and control wavelengths in an AlGaAs nonlinear directional coupler,” IEEE J. Quantum Electron. 31, 2165–2172 (1995).
[CrossRef]

Kang, J. U.

A. Villeneuve, P. Mamyshev, J. U. Kang, G. I. Stegeman, J. S. Aitchison, and C. N. Ironside, “Efficient time-domain demultiplexing with separate signal and control wavelengths in an AlGaAs nonlinear directional coupler,” IEEE J. Quantum Electron. 31, 2165–2172 (1995).
[CrossRef]

Katsufuji, T.

Kissa, K. M.

E. L. Wooten, K. M. Kissa, A. Yi-Yan, E. J. Murphy, D. A. Lafaw, P. F. Hallemeier, D. Maack, D. V. Attanasio, D. J. Fritz, G. J. McBrien, and D. E. Bossi, “A review of lithium niobate modulators for fiber-optic communications systems,” IEEE J. Sel. Top. Quantum Electron. 6, 69–82 (2000).
[CrossRef]

Lafaw, D. A.

E. L. Wooten, K. M. Kissa, A. Yi-Yan, E. J. Murphy, D. A. Lafaw, P. F. Hallemeier, D. Maack, D. V. Attanasio, D. J. Fritz, G. J. McBrien, and D. E. Bossi, “A review of lithium niobate modulators for fiber-optic communications systems,” IEEE J. Sel. Top. Quantum Electron. 6, 69–82 (2000).
[CrossRef]

Lenz, G.

Lines, M. E.

Maack, D.

E. L. Wooten, K. M. Kissa, A. Yi-Yan, E. J. Murphy, D. A. Lafaw, P. F. Hallemeier, D. Maack, D. V. Attanasio, D. J. Fritz, G. J. McBrien, and D. E. Bossi, “A review of lithium niobate modulators for fiber-optic communications systems,” IEEE J. Sel. Top. Quantum Electron. 6, 69–82 (2000).
[CrossRef]

Mamyshev, P.

A. Villeneuve, P. Mamyshev, J. U. Kang, G. I. Stegeman, J. S. Aitchison, and C. N. Ironside, “Efficient time-domain demultiplexing with separate signal and control wavelengths in an AlGaAs nonlinear directional coupler,” IEEE J. Quantum Electron. 31, 2165–2172 (1995).
[CrossRef]

McBrien, G. J.

E. L. Wooten, K. M. Kissa, A. Yi-Yan, E. J. Murphy, D. A. Lafaw, P. F. Hallemeier, D. Maack, D. V. Attanasio, D. J. Fritz, G. J. McBrien, and D. E. Bossi, “A review of lithium niobate modulators for fiber-optic communications systems,” IEEE J. Sel. Top. Quantum Electron. 6, 69–82 (2000).
[CrossRef]

Murphy, E. J.

E. L. Wooten, K. M. Kissa, A. Yi-Yan, E. J. Murphy, D. A. Lafaw, P. F. Hallemeier, D. Maack, D. V. Attanasio, D. J. Fritz, G. J. McBrien, and D. E. Bossi, “A review of lithium niobate modulators for fiber-optic communications systems,” IEEE J. Sel. Top. Quantum Electron. 6, 69–82 (2000).
[CrossRef]

Patel, N. S.

Ranka, J. K.

Rauschenbach, K. A.

Sanghera, J. S.

Sfez, B. G.

Silberberg, Y.

Slusher, R. E.

Smith, P. S.

Spälter, S.

Stegeman, G. I.

A. Villeneuve, P. Mamyshev, J. U. Kang, G. I. Stegeman, J. S. Aitchison, and C. N. Ironside, “Efficient time-domain demultiplexing with separate signal and control wavelengths in an AlGaAs nonlinear directional coupler,” IEEE J. Quantum Electron. 31, 2165–2172 (1995).
[CrossRef]

Stentz, A. J.

Villeneuve, A.

A. Villeneuve, P. Mamyshev, J. U. Kang, G. I. Stegeman, J. S. Aitchison, and C. N. Ironside, “Efficient time-domain demultiplexing with separate signal and control wavelengths in an AlGaAs nonlinear directional coupler,” IEEE J. Quantum Electron. 31, 2165–2172 (1995).
[CrossRef]

Weiner, A. M.

Windeler, R. S.

Wooten, E. L.

E. L. Wooten, K. M. Kissa, A. Yi-Yan, E. J. Murphy, D. A. Lafaw, P. F. Hallemeier, D. Maack, D. V. Attanasio, D. J. Fritz, G. J. McBrien, and D. E. Bossi, “A review of lithium niobate modulators for fiber-optic communications systems,” IEEE J. Sel. Top. Quantum Electron. 6, 69–82 (2000).
[CrossRef]

Yi-Yan, A.

E. L. Wooten, K. M. Kissa, A. Yi-Yan, E. J. Murphy, D. A. Lafaw, P. F. Hallemeier, D. Maack, D. V. Attanasio, D. J. Fritz, G. J. McBrien, and D. E. Bossi, “A review of lithium niobate modulators for fiber-optic communications systems,” IEEE J. Sel. Top. Quantum Electron. 6, 69–82 (2000).
[CrossRef]

Zimmermann, J.

Appl. Opt. (1)

IEEE J. Quantum Electron. (1)

A. Villeneuve, P. Mamyshev, J. U. Kang, G. I. Stegeman, J. S. Aitchison, and C. N. Ironside, “Efficient time-domain demultiplexing with separate signal and control wavelengths in an AlGaAs nonlinear directional coupler,” IEEE J. Quantum Electron. 31, 2165–2172 (1995).
[CrossRef]

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

E. L. Wooten, K. M. Kissa, A. Yi-Yan, E. J. Murphy, D. A. Lafaw, P. F. Hallemeier, D. Maack, D. V. Attanasio, D. J. Fritz, G. J. McBrien, and D. E. Bossi, “A review of lithium niobate modulators for fiber-optic communications systems,” IEEE J. Sel. Top. Quantum Electron. 6, 69–82 (2000).
[CrossRef]

Opt. Lett. (4)

Phys. Rev. A (1)

J. M. Fini, P. L. Hagelstein, and H. A. Haus, “Multiphoton tunneling in a nonlinear interferometer,” Phys. Rev. A 64, 043813 (2001).
[CrossRef]

Other (1)

T. M. Monroe, K. M. Kiang, J. H. Lee, K. Frampton, Z. Yusoff, R. Moore, J. Tucknott, D. W. Hewak, H. N. Rutt, and D. J. Richardson, “High-nonlinearity, extruded, single-mode, holey optical fibers,” In Optical Fiber Communications Conference (OFC), Postconference Digest, Vol. 70 of OSA Trends in Optics and Photonics (Optical Society of America, Washington, D.C., 2002), FA1, pp. 1–3.

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Figures (8)

Fig. 1
Fig. 1

Conventional Mach–Zehnder modulator (a) and Kerr-enhanced modulator (b) generate intensity variation in response to a drive-voltage signal Vrf. The conventional devices generate full intensity modulation when the relative phase between the arms swings by π, from constructive to destructive interference. The Kerr-enhanced device incorporating a nonlinear direction coupler can fully modulate the intensity in response to much smaller induced phases.

Fig. 2
Fig. 2

Basic coupler dynamics are described by the two-mode model. Amplitudes u and v describe modes localized at each waveguide. The modes evolve along the fiber length z according to linear coupling γ and the Kerr effect κ.

Fig. 3
Fig. 3

Stokes trajectories are circular at low power, representing harmonic oscillations between the waveguides. At the critical level of power (or nonlinearity) κ|s|/γ=2, trajectories demonstrate trapping of light in one or the other waveguide.

Fig. 4
Fig. 4

Principle of switching with enhanced sensitivity to phase shifts is depicted. A small initial phase shift ±θ puts the state on one of two diverging trajectories. For an ideal coupler design the resulting output states show perfect amplitude modulation, with all power in one or the other waveguide.

Fig. 5
Fig. 5

Electro-optic response of three KEM designs is shown as a function of normalized drive voltage. The linear modulator response κ=0 is given for comparison. Greater enhancement factors are obtained as the critical value is approached, as seen by the reduced voltage required to swing the response from 0 to 1.

Fig. 6
Fig. 6

Response versus phase for the 8×-enhanced KEM is plotted again, along with response curves incorporating input power drift of ±10%.

Fig. 7
Fig. 7

Sensitivity of the optical response to perturbations in the linear coupling and waveguide symmetry is moderate according to simulations.

Fig. 8
Fig. 8

Eye diagrams obtained from our simple dispersive model show that KEM performance is robust to moderate amounts of dispersion in the device waveguides. The top diagram has 2γL=Tbit/10, the middle has βL=0.02Tbit2, and the bottom has combined chromatic and intermodal dispersion.

Equations (8)

Equations on this page are rendered with MathJax. Learn more.

i dudz=γv+κ|u|2u,
i dvdz=γu+κ|v|2v.
TotalPower|s|=12 (|u|2+|v|2),
PowerSplittingsz=12 (|u|2-|v|2),
RelativePhaseθ=arg(u/v).
i dudz=-βd2dτ2 u+γ0-iγddτ-γd2dτ2v+κ|u|2u,
i dvdz=-βd2dτ2 v+γ0-iγddτ-γd2dτ2u+κ|v|2v.
κPL=3for8×enhancement.

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