## Delay-tunable gap-soliton-based slow-light system

Optics Express, Vol. 14, Issue 25, pp. 11987-11996 (2006)

http://dx.doi.org/10.1364/OE.14.011987

Acrobat PDF (443 KB)

### Abstract

We numerically and analytically evaluate the delay of solitons propagating slowly, and without broadening, in an apodized Bragg grating. Simulations indicate that a 100 mm Bragg grating with Δ*n*=10^{-3} can delay sub-nanosecond pulses by nearly 20 pulse widths without any change in the output pulse width. Delay tunability is achieved by simultaneously adjusting the launch power and detuning. A simple analytic model is developed to describe the monotonic dependence of delay on Δ*n* and compared with simulations. As the intensity may be greatly enhanced due to a reduced velocity, a procedure for improving the delay while avoiding material damage is outlined.

© 2006 Optical Society of America

## 1. Introduction

1. Y. Jiang, W. Jiang, L. Gu, X. Chen, and R. T. Chenb, “80-micron Interaction Length Silicon Photonic Crystal Waveguide Modulator,” Appl. Phys. Lett. **87**, 221,105 (2005). [CrossRef]

2. R. S. Jacobsen, K. N. Andersen, P. I. Borel, J. Fage-Pedersen, L. H. Frandsen, O. Hansen, M. Kristensen, A. V. Lavrinenko, G. Moulin, H. Ou, C. Peucheret, B. Zsigri, and A. Bjarklev, “Strained Silicon as a New Electro-Optic
Material,” Nature **441**, 199–202 (2006). [CrossRef] [PubMed]

3. R. W. Boyd, D. J. Gauthier, and A. L. Gaeta, “Application of Slow Light in Telecommunications,” Opt. Photon. News **17**, 18–23 (2006). [CrossRef]

5. J. B. Khurgin, “Optical Buffers Based on Slow Light in Electromagnetically Induced Transparent Media and Coupled Resonator Structures: Comparative Analysis,” J. Opt. Soc. Am. B **22**, 1062–1074 (2005). [CrossRef]

6. G. Lenz, B. J. Eggleton, C. K. Madsen, and R. E. Slusher, “Optical Delay Lines Based on Optical Filters,” J. Quantum Electron. **37**, 525–530 (2001). [CrossRef]

7. B. J. Eggleton, R. E. Slusher, C. M. de Sterke, P. A. Krug, and J. E. Sipe, “Bragg Grating Solitons,” Phys. Rev. Lett. **76**, 1627–1630 (1996). [CrossRef] [PubMed]

8. D. Taverner, N. G. R. Broderick, D. J. Richardson, R. I. Laming, and M. Ibsen, “Nonlinear Self-Switching and Multiple Gap-Soliton Formation in a Fiber Bragg Grating,” Opt. Lett. **23**, 328–330 (1998). [CrossRef]

9. B. J. Eggleton, C. M. de Sterke, and R. E. Slusher, “Bragg Solitons in the Nonlinear Schrodinger Limit: Experiment and Theory,” J. Opt. Soc. Am. B **16**, 587–599 (1999). [CrossRef]

10. N. G. R. Broderick, D. J. Richardson, and M. Ibsen, “Nonlinear Switching in a 20-Cm-Long Fiber Bragg Grating,” Opt. Lett. **25**, 536–538 (2000). [CrossRef]

11. D. N. Christodoulides and R. I. Joseph, “Slow Bragg Solitons in Nonlinear Periodic Structures,” Phys. Rev. Lett. **62**, 1746–1749 (1989). [CrossRef] [PubMed]

12. A. Aceves and S. Wabnitz, “Self-Induced Transparency Solitons in Nonlinear Refractive Periodic Media,” Phys. Lett. A **141**, 37–42 (1989). [CrossRef]

19. J. T. Mok, C. M. de Sterke, I. C. M. Littler, and B. J. Eggleton, “Dispersionless Slow Light Using Gap Solitons,” Nature Phys. **2**, 775–780 (2006). [CrossRef]

*n*, while tunability can be achieved by varying the launch power and detuning. A simple model that relates the delay of the slow light system to Δ

*n*is proposed and compared to simulations. A way to avoid material damage due to potentially large peak intensity enhancement is also outlined.

## 2. Device principles

*n*is the average refractive index. Thus, a weak pulse with a spectrum lying inside this bandgap, that is launched into a Bragg grating is strongly reflected, as illustrated in Fig. 1(b), showing an intensity contour plot of time vs position. In contrast, an intense pulse with intensity

*I*, through the Kerr nonlinear response of the material, can raise the refractive index according to

*n*

_{0}is the refractive index at low intensities and

*n*

_{2}, taken to be positive, is the nonlinear coefficient, thus shifting

*λ*and the bandgap to a longer wavelength, allowing the pulse to be transmitted through the grating. This is illustrated in Fig.1(c), which shows that the pulse travels at a velocity, given by the inverse slope of the contour, less than that in a uniform medium. Such a pulse, a gap soliton, can propagate, in principle, at any velocity between 0 and

_{B}*c*/

*n*, where

*c*is the speed of light in vacuum, without broadening [13]. It is the possibility of the very low gap soliton velocities that gives rise to potentially large temporal delays.

14. M. De Sario, C. Conti, and G. Assanto, “Optically Controlled Delay Lines by Pulse Self-Trapping in Parametric Waveguides with Distributed Feedback,” IEEE J. Quant. Elect. **36**, 931–943 (2000). [CrossRef]

*λ*. The launch power can be adjusted using a variable optical attenuator, while the detuning can be adjusted by either varying Λ or

_{B}*n*[15

15. M. L. Povinelli, S. G. Johnson, and J. D. Joannopoulos, “Slow-Light, Band-Edge Waveguides for Tunable Time Delays,” Opt. Express **13**, 7145–7159 (2005). [CrossRef] [PubMed]

16. V. G. Ta’eed, M. Shokooh-Saremi, L. Fu, D. J. Moss, M. Rochette, I. C. M. Littler, B. J. Eggleton, Y. Ruan, and B. Luther-Davies, “Integrated All-Optical Pulse Regenerator in Chalcogenide Waveguides,” Opt. Lett. **30**, 2900–2902 (2005). [CrossRef] [PubMed]

*n*

_{2}of the order of 10

^{-13}cm

^{2}/W and

*n*

_{0}of roughly 2.5. The large nonlinearity and the large core-cladding index difference, leading to a smaller effective mode area, substantially lower the required optical power. Fabrication of chalcogenide-based waveguide gratings via photosensitivity producing a large photo-induced Δ

*n*has also been reported [17

17. M. Shokooh-Saremi, V. G. Taeed, N. J. Baker, I. C.M. Littler, D. J. Moss, B. J. Eggleton, Y. Ruan, and B. Luther- Davies, “High-Performance Bragg Gratings in Chalcogenide Rib Waveguides Written with a Modified Sagnac Interferometer,” J. Opt. Soc. Am. B **23**, 1323–1331 (2006). [CrossRef]

## 3. Method

18. C. M. de Sterke, K. R. Jackson, and B. D. Robert, “Nonlinear Coupled Mode Equations on a Finite Interval: A Numerical Procedure,” J. Opt. Soc. Am. B **8**, 403–412 (1991). [CrossRef]

*A*

_{±}=|

*A*

_{±}(

*z*,

*t*)|

*e*(

^{iδ′}*c*/

*n*)

*t*is the complex forward and backward propagating envelops with

*δ*′=(

*ω*′-

*ω*)/(

_{B}*c*/

*n*), where

*ω*′ is the pulse frequency,

*ω*is the Bragg frequency, located in the center of the photonic bandgap,

_{B}*γ*is the nonlinear coefficient and

*κ*=

*ηπ*Δ

*n*/

*λ*is the coupling strength, where

*η*≈0.8 in silica fibers represents the mode-field grating overlap. For our simulations we focus on parameters corresponding to our recent experiment [19

19. J. T. Mok, C. M. de Sterke, I. C. M. Littler, and B. J. Eggleton, “Dispersionless Slow Light Using Gap Solitons,” Nature Phys. **2**, 775–780 (2006). [CrossRef]

*λ*≈1

*µ*m, in the core of a silica fiber with typical parameters:

*γ*=6.4 /(W km) and Δ

*n*≤10

^{-3}, as appropriate for silica glass. The results can however be generalised to other materials and geometries. The grating is apodized, with Δ

*n*varying as [1-cos(

*πz*/

*l*)]/2 for 0<

_{a}*z*<

*l*and [1+cos(

_{a}*π*[

*z*-(

*L*-

*l*)]/

_{a}*l*)]/2 for

_{a}*L*-

*l*<

_{a}*z*<

*L*, with

*l*=15 mm, and Δ

_{a}*n*constant in between the two regions. We choose an apodized grating because it is the simplest design in which relatively efficient coupling can be achieved. This leaves us the following parameters: (1) index contrast Δ

*n*, (2) grating length

*L*, (3) launch power

*P*, (4) pulse detuning

*δ*′, and (5) pulse width Δ

*τ*. We note that in terms of the detuning

*δ*=(

*ω*-

*ω*)/(

_{B}*c*/

*n*), where

*ω*is frequency, the photonic bandgap extends from

*δ*=-

*κ*to

*δ*=+

*κ*. The definitions of various spectral parameters are illustrated in Fig. 2(a). Assuming a lossless grating, where the gap soliton travels at a constant velocity, the delay simply scales linearly with

*L*. We therefore fix

*L*=100 mm, a typical grating length. Since the gap solitons’ group velocity and width both vary with the launch peak power, of which the effects are illustrated in Fig. 2(b), we choose to launch at the power

*P*=

*P*that results in an output pulse having the same pulse width as the input. The timing of the output pulse under this condition is then used to evaluate the delay.

_{0}*τ*-

_{d}*τ*

_{d0}, where

*τ*is the pulse propagation delay when the device is on, and

_{d}*τ*

_{d0}is that when it is off. The device is considered to be off when the bandgap is detuned far away from the pulse frequency, in which case the pulse propagates unaffected by the grating and has a delay of

*τ*

_{d0}=

*nL*/

*c*. The device is considered on when the pulse is tuned to lie inside the bandgap. In practice, the detuning can be adjusted by varying the strain that is applied to the grating, and thus the device can be mechanically switched between the on and off states.

9. B. J. Eggleton, C. M. de Sterke, and R. E. Slusher, “Bragg Solitons in the Nonlinear Schrodinger Limit: Experiment and Theory,” J. Opt. Soc. Am. B **16**, 587–599 (1999). [CrossRef]

*δ*′ such that 1.2

*δ*<

_{p}*κ*-

*δ*′<3

*δ*, where

_{p}*δ*is the 3 dB spectral width of the pulse.

_{p}## 4. Results

19. J. T. Mok, C. M. de Sterke, I. C. M. Littler, and B. J. Eggleton, “Dispersionless Slow Light Using Gap Solitons,” Nature Phys. **2**, 775–780 (2006). [CrossRef]

*t*/

*a*

_{±}), with

*a*-=257 ps for

*t*<0 and a

_{+}=514 ps for

*t*>0, leading to a full width at half maximum (fwhm) of the intensity of Δ

*τ*=680 ps. We obtain the pulse delay and required launch peak power by adjusting the launch power until the fwhm of the output pulse matches that of the input pulse (680 ps). This is repeated for Δ

*n*from 10

^{-4}to 10

^{-3}, a typical range for silica gratings, while keeping the detuning to be at a constant value from the edge of the photonic bandgap (i.e.

*κ*-

*δ*′ is a constant). Five such detunings are chosen:

*δ*′=

*κ*-1.2

*δ*,

_{p}*κ*-1.5

*δ*,

_{p}*κ*-2.0

*δ*,

_{p}*κ*-2.5

*δ*and

_{p}*κ*-3.0

*δ*where

_{p}*δ*=14.09 m

_{p}^{-1}is the spectral fwhm of the 680 ps pulse with a constant temporal phase.

*τ*-

_{d}*τ*

_{d0}and the required launch peak power

*P*

_{0}as a function of Δ

*n*for the different detunings. The right axis of Fig. 3(a) shows the scale corresponding to the fractional delay,

*F*=(

*τ*-

_{d}*τ*

_{d0})/Δ

*τ*, corresponding to the grating’s delay capacity. Note from Fig. 3 that as Δ

*n*increases, the delay increases sub-linearly, while the required launch power decreases. The increased delay is a result of stronger interaction between the forward and backward propagating waves, creating an effectively longer path length. The required launch power decreases with Δ

*n*as a result of intensity enhancement due to the slow light effect. Less incident power is required to maintain the intensity for the same bandgap shift to be achieved.

*n*in silica limited to ~10

^{-3}, the fractional delay for 680 ps pulses in a 100 mm grating, depending on the detuning, can be up to nearly 20 pulse widths, with the required launch power of the order of a few kW (1 kW corresponds to 3.65 GW/cm

^{2}). Since all data points in Fig. 3 represent delayed pulses of 680 ps wide, they imply delay tunability without any change in pulse width. To achieve this for a given grating, namely for a fixed Δ

*n*, the delay is tuned by varying both the detuning and the launch power appropriately. The inset in Fig. 3(b) shows the input pulse (dotted line) and output pulses (solid lines) through a Bragg grating with Δ

*n*=10

^{-3}, at launch powers and detunings indicated by the grey box in Fig. 3(b). It illustrates a continuously tunable delay from ~8 to ~12.5 ns, or group velocities ranging from 0.037 to 0.057

*c*/

*n*. This corresponds to a tuning range of approximately 7 pulse widths, with a constant output pulse width of 680 ps. Transmission of the delayed pulses ranges from 20% to 28%, as illustrated in the inset of Fig. 3(a), with the loss associated with the input (output) coupling and velocity mismatch between the incident (transmitted) pulse and the gap soliton. Transmission decreases as the delay increases because of an increased velocity mismatch. For the same Δn, the delay increases with decreasing detuning, at the expense of increasing required launch power.

*P*

_{0}. Recall that

*P*

_{0}is the required launch power so that the output pulse width equals that of the input pulse. Since in the simulation we only have control over the launch power and not the output pulse width, the pulse widths are matched by trying different values of

*P*

_{0}. Similarly, since pulse delay is a function of launch power, the same iterative process of finding P0 gives us a range that contains the delay

*τ*. It is found that the output pulse delay can be sensitive to launch power. Generally, obtaining the accuracy in

_{d}*τ*shown by the error bars requires

_{d}*P*

_{0}to be accurate to within′ 0.1%, which is the reason why the error bars in

*P*

_{0}in Fig. 3(b) are virtually invisible on the scale of the plots. This fact also makes comparison of delay between experiments and simulations difficult, since uncertainties in power measurements are usually large (≳10%). A better grating design may be able to lower the sensitivity of delay on launch power.

*n*of 0.01 [17

17. M. Shokooh-Saremi, V. G. Taeed, N. J. Baker, I. C.M. Littler, D. J. Moss, B. J. Eggleton, Y. Ruan, and B. Luther- Davies, “High-Performance Bragg Gratings in Chalcogenide Rib Waveguides Written with a Modified Sagnac Interferometer,” J. Opt. Soc. Am. B **23**, 1323–1331 (2006). [CrossRef]

*n*means that the maximum delay can be greatly improved. With

*n*

_{2}of chalcogenide up to ~1000× higher than that of silica [20

20. R. E. Slusher, G. Lenz, J. Hodelin, J. Sanghera, L. B. Shawand, and I. D. Aggarwal, “Large Raman Gain and Nonlinear Phase Shifts in High-Purity As2Se3 Chalcogenide Fibers,” J. Opt. Soc. Am. B **21**, 1146–1155 (2004). [CrossRef]

*n*=10

^{-3}and

*δ*′=

*κ*-1.5

*δ*, the pulse slows down by a factor of 19 while the total internal peak intensity of the forward and backward waves reaches 12 times that of the incident pulse. Generally, the enhancement increases with the slow down factor since a slowed pulse is spatially compressed, though the exact degree of enhancement partly depends on the amount of incident pulse energy coupled into the grating, which is determined by the pulse shape and velocity mismatches between the incident pulse and the gap soliton. In the next section, we develop and verify an analytic model to predict the delay, particularly in chalcogenide-based gratings, then look at how the internal intensity varies with

_{p}*δ*′ and

*κ*, and suggest on a way avoid material damage.

## 5. Prediction of the delay

*q*=

*k*-

*k*, where

_{B}*k*is the wave number and

*k*=

_{B}*π*/

*d*is the wave number at the Bragg condition. The group velocity

*V*, ignoring end effects, can then be found from the dispersion relation, and can be shown to be [21

_{g}21. P. S. J. Russell, “Bloch Wave Analysis of Dispersion and Pulse Propagation in Pure Distributed Feedback Structures,” J. Mod. Opt. **38**, 1599–1619 (1991). [CrossRef]

*τ*-

_{d}*τ*

_{d0}of a pulse is thus

*apparent*detuning

*δ*′+Δ

*δ*with Δ

*δ*>

*κ*-

*δ*′ the bandgap shift induced by the positive Kerr nonlinearity. The delay

*τ*is then given by the linear dispersion relation of the Bragg grating at the apparent detuning, with

_{d}*δ*=

*δ*′+Δ

*δ*in Eq. (5) where Δ

*δ*can be found by fitting the numerical results. The dashed lines in Fig. 3(a) are fitted in such a way.

*δ*. Fig. 3(a) indicates that Δ

*δ*does not depend on the individual values of

*κ*(i.e. Δ

*n*) or

*δ*′, but depends on their difference

*κ*-

*δ*′. The fitted values of Δ

*δ*for each detuning are summarised in Table 1. Using this model, we estimate that the maximum delay achievable in chalcogenide gratings, which has a reported Δ

*n*≈0.01 [17

17. M. Shokooh-Saremi, V. G. Taeed, N. J. Baker, I. C.M. Littler, D. J. Moss, B. J. Eggleton, Y. Ruan, and B. Luther- Davies, “High-Performance Bragg Gratings in Chalcogenide Rib Waveguides Written with a Modified Sagnac Interferometer,” J. Opt. Soc. Am. B **23**, 1323–1331 (2006). [CrossRef]

## 6. Intensity enhancement and avoidance of material damage

*τ*

_{GS}together with known values of

*δ*′ and

*κ*, one can then solve numerically for

*δ*and

*v*using Eqs. (7) and (8), and thus determine the peak intensities of the forward- and backward-propagating waves

*I*

_{±}comprising the gap soliton given by

^{4}=(1-

*v*)/(1+

*v*).

*τ*

_{GS}to 680 ps, and calculate the the total peak intensity

*I*

_{tot}=

*I*

_{+}+

*I*

_{-}of the gap soliton inside the grating as function of Δ

*n*for the five different detunings. The result indicates that for each detuning

*I*

_{tot}does stay almost constant (within ±0.5%) for the range 10

^{-4}<Δ

*n*<10

^{-2}, and appears to approach an asymptotic value at large Δ

*n*. The asymptotic value of

*I*

_{tot}for each detuning is shown in the last column of Table 1, which shows that

*I*

_{tot}increases with decreasing detuning, since a larger bandgap shift is required (

*c.f.*Fig. 2(b)). Therefore, while the required launch power

*P*

_{0}decreases with

*κ*(c.f. Fig. 3(b)), the field enhancement due to the slow light effect ensures that the gap soliton propagating inside the grating has nearly the same intensity regardless of the value of

*κ*. This calculation confirms that the bandgap shift is expected to be weakly dependent on

*κ*if

*κ*-

*δ*′ is unchanged, and thus validates the analytic model.

*n*using the normalised velocity

*v*obtained above and Eq. (6) with

*L*=100 mm. The result is plotted in Fig. 4(a), which shows the same trend in the delay as a function of Δ

*n*and

*δ*′ as the simulation results in Fig. 3(a). Discrepancy exists between the two figures because the model does not take into account apodization or any effects of coupling in general.

*κ*, but increases with

*κ*-

*δ*′. Given the maximum non-destructive intensity of the structure for a particular pulse width, one could first make sure the detuning is sufficiently large to prevent the peak intensity from reaching the damage threshold. Meanwhile, one can safely use materials exhibiting a large maximum index contrast, and thus large

*κ*, to improve the delay without worrying about excessive intensity enhancement causing damage. This is so because the required launch power is lowered accordingly to maintain a relatively constant gap soliton intensity regardless of

*κ*. The upper limit of delay is only restricted by

*κ*(see Fig. 3(b) or Fig. 4(a)), and ultimately by loss [22

22. R. S. Tucker, P.-C. Ku, and C. J. Chang-Hasnain, “Slow-Light Optical Buffers: Capabilities and Fundamental Limitations,” J. Lightwave Technol. **23**, 4046–4066 (2005). [CrossRef]

**2**, 775–780 (2006). [CrossRef]

*κ*, the delay is the limited by the damage threshold. Figure 4(b) shows the calculated delay and total peak intensity as a function of detuning from the bandedge (

*κ*-

*δ*′) for Δ

*n*=10

^{-3}(

*κ*=23.6 cm

^{-1}). It can seen from Fig. 4(b) that both

*I*

_{tot}and the delay increases with

*κ*-

*δ*′, indicating a trade-off between delay and high internal intensity that may cause material damage.

## 7. Conclusion

*n*, simultaneous tuning of launch power and detuning leads to tunable delay without any change in the pulse width. Analysis on the gap soliton solution reveals that while the pulse intensity within the grating increases with the parameter

*κ*-

*δ*′, is independent of

*κ*. To avoid material damage, a sufficiently large detuning should be chosen. Meanwhile, the delay can be safely improved by using materials with large maximum index contrast.

## References and links

1. | Y. Jiang, W. Jiang, L. Gu, X. Chen, and R. T. Chenb, “80-micron Interaction Length Silicon Photonic Crystal Waveguide Modulator,” Appl. Phys. Lett. |

2. | R. S. Jacobsen, K. N. Andersen, P. I. Borel, J. Fage-Pedersen, L. H. Frandsen, O. Hansen, M. Kristensen, A. V. Lavrinenko, G. Moulin, H. Ou, C. Peucheret, B. Zsigri, and A. Bjarklev, “Strained Silicon as a New Electro-Optic
Material,” Nature |

3. | R. W. Boyd, D. J. Gauthier, and A. L. Gaeta, “Application of Slow Light in Telecommunications,” Opt. Photon. News |

4. | R. Boyd and D. Gauthier, “Slow and Fast Light,” in |

5. | J. B. Khurgin, “Optical Buffers Based on Slow Light in Electromagnetically Induced Transparent Media and Coupled Resonator Structures: Comparative Analysis,” J. Opt. Soc. Am. B |

6. | G. Lenz, B. J. Eggleton, C. K. Madsen, and R. E. Slusher, “Optical Delay Lines Based on Optical Filters,” J. Quantum Electron. |

7. | B. J. Eggleton, R. E. Slusher, C. M. de Sterke, P. A. Krug, and J. E. Sipe, “Bragg Grating Solitons,” Phys. Rev. Lett. |

8. | D. Taverner, N. G. R. Broderick, D. J. Richardson, R. I. Laming, and M. Ibsen, “Nonlinear Self-Switching and Multiple Gap-Soliton Formation in a Fiber Bragg Grating,” Opt. Lett. |

9. | B. J. Eggleton, C. M. de Sterke, and R. E. Slusher, “Bragg Solitons in the Nonlinear Schrodinger Limit: Experiment and Theory,” J. Opt. Soc. Am. B |

10. | N. G. R. Broderick, D. J. Richardson, and M. Ibsen, “Nonlinear Switching in a 20-Cm-Long Fiber Bragg Grating,” Opt. Lett. |

11. | D. N. Christodoulides and R. I. Joseph, “Slow Bragg Solitons in Nonlinear Periodic Structures,” Phys. Rev. Lett. |

12. | A. Aceves and S. Wabnitz, “Self-Induced Transparency Solitons in Nonlinear Refractive Periodic Media,” Phys. Lett. A |

13. | C. M. de Sterke and J. E. Sipe, “Gap Solitons,” in |

14. | M. De Sario, C. Conti, and G. Assanto, “Optically Controlled Delay Lines by Pulse Self-Trapping in Parametric Waveguides with Distributed Feedback,” IEEE J. Quant. Elect. |

15. | M. L. Povinelli, S. G. Johnson, and J. D. Joannopoulos, “Slow-Light, Band-Edge Waveguides for Tunable Time Delays,” Opt. Express |

16. | V. G. Ta’eed, M. Shokooh-Saremi, L. Fu, D. J. Moss, M. Rochette, I. C. M. Littler, B. J. Eggleton, Y. Ruan, and B. Luther-Davies, “Integrated All-Optical Pulse Regenerator in Chalcogenide Waveguides,” Opt. Lett. |

17. | M. Shokooh-Saremi, V. G. Taeed, N. J. Baker, I. C.M. Littler, D. J. Moss, B. J. Eggleton, Y. Ruan, and B. Luther- Davies, “High-Performance Bragg Gratings in Chalcogenide Rib Waveguides Written with a Modified Sagnac Interferometer,” J. Opt. Soc. Am. B |

18. | C. M. de Sterke, K. R. Jackson, and B. D. Robert, “Nonlinear Coupled Mode Equations on a Finite Interval: A Numerical Procedure,” J. Opt. Soc. Am. B |

19. | J. T. Mok, C. M. de Sterke, I. C. M. Littler, and B. J. Eggleton, “Dispersionless Slow Light Using Gap Solitons,” Nature Phys. |

20. | R. E. Slusher, G. Lenz, J. Hodelin, J. Sanghera, L. B. Shawand, and I. D. Aggarwal, “Large Raman Gain and Nonlinear Phase Shifts in High-Purity As2Se3 Chalcogenide Fibers,” J. Opt. Soc. Am. B |

21. | P. S. J. Russell, “Bloch Wave Analysis of Dispersion and Pulse Propagation in Pure Distributed Feedback Structures,” J. Mod. Opt. |

22. | R. S. Tucker, P.-C. Ku, and C. J. Chang-Hasnain, “Slow-Light Optical Buffers: Capabilities and Fundamental Limitations,” J. Lightwave Technol. |

**OCIS Codes**

(060.4370) Fiber optics and optical communications : Nonlinear optics, fibers

(060.5530) Fiber optics and optical communications : Pulse propagation and temporal solitons

**ToC Category:**

Fiber Optics and Optical Communications

**History**

Original Manuscript: September 26, 2006

Revised Manuscript: November 27, 2006

Manuscript Accepted: November 29, 2006

Published: December 11, 2006

**Citation**

Joe T. Mok, C. Martijn de Sterke, and Benjamin J. Eggleton, "Delay-tunable gap-soliton-based slow-light system," Opt. Express **14**, 11987-11996 (2006)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-14-25-11987

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### References

- Y. Jiang, W. Jiang, L. Gu, X. Chen, and R. T. Chenb, "80-micron Interaction Length Silicon Photonic Crystal Waveguide Modulator," Appl. Phys. Lett. 87, 221,105 (2005). [CrossRef]
- R. S. Jacobsen, K. N. Andersen, P. I. Borel, J. Fage-Pedersen, L. H. Frandsen, O. Hansen, M. Kristensen, A. V. Lavrinenko, G. Moulin, H. Ou, C. Peucheret, B. Zsigri, and A. Bjarklev, "Strained Silicon as a New Electro-Optic Material," Nature 441, 199-202 (2006). [CrossRef] [PubMed]
- R. W. Boyd, D. J. Gauthier, and A. L. Gaeta, "Application of Slow Light in Telecommunications," Opt. Photon. News 17, 18-23 (2006). [CrossRef]
- R. Boyd and D. Gauthier, "Slow and Fast Light," in Prog. in Optics, E.Wolf, ed., vol. 43, pp. 497-530 (Elsevier, Amsterdam, 2002).
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