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Optics Express

Optics Express

  • Editor: Michael Duncan
  • Vol. 14, Iss. 6 — Mar. 20, 2006
  • pp: 2317–2322
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All-optical slow-light on a photonic chip

Yoshitomo Okawachi, Mark A. Foster, Jay E. Sharping, Alexander L. Gaeta, Qianfan Xu, and Michal Lipson  »View Author Affiliations


Optics Express, Vol. 14, Issue 6, pp. 2317-2322 (2006)
http://dx.doi.org/10.1364/OE.14.002317


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Abstract

We demonstrate optically tunable delays in a silicon-on-insulator planar waveguide based on slow light induced by stimulated Raman scattering (SRS). Inside an 8-mm-long nanoscale waveguide, we produce a group-index change of 0.15 and generate controllable delays as large as 4 ps for signal pulses as short as 3 ps. The scheme can be implemented at bandwidths exceeding 100 GHz for wavelengths spanning the entire low-loss fiber-optics communications window and thus represents an important step in the development of chip-scale photonics devices that process light with light.

© 2006 Optical Society of America

1. Introduction

Over the past decade, there has been great interest in controlling the group velocity of pulses of light in optical materials [1

1. R. W. Boyd and D. J. Gauthier, “‘Slow’ and ‘fast’ light,” Progress in Optics 43, edited by E. Wolf (Elsevier, Amsterdam, 2002), Chap. 6, p. 497–530. [CrossRef]

]. Many of the techniques for achieving “slow light” rely on a laser-induced transmission window within a spectral absorption line of a material [2–6

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]

] to produce a reduction in the group velocity. If devices based on slow light are developed which accommodate telecommunication data rates exceeding 10 GHz, several critical applications such as data synchronization, tunable data buffers, and pattern correlation, can be implemented [7

7. See, for example, R. Ramaswami and K. N. Sivarajan, Optical Networks: A Practical Perspective (Morgan Kaufmann, San Francisco, CA, 2002), 2nd ed., Chap. 12.

].

Development of silicon-based nanophotonic devices for photonics-on-chip technology has recently been the subject of substantial research activity. The silicon-on-insulator (SOI) platform has inherent advantages for all-optical devices due to the high index contrast between the silicon core and silica cladding, which allows for strong optical confinement, large effective optical nonlinearities, and highly compact photonic circuits [8

8. M. A. Foster, K. D. Moll, and A. L. Gaeta, “Optimal waveguide dimensions for nonlinear interactions,” Opt. Express 12, 2880–2887 (2004). [CrossRef] [PubMed]

]. Nonlinear effects in SOI waveguides have led to demonstrations of all-optical switching [9

9. V. R. Almeida, C. A. Barrios, R. R. Panepucci, and M. Lipson, “All-optical control of light in a silicon chip,” Nature 431, 1081–1084 (2004). [CrossRef] [PubMed]

], Raman amplification [10–12

10. H. Rong, A. Liu, R. Nicolaescu, M. Paniccia, O. Cohen, and D. Hak, “Raman gain and nonlinear optical absorption measurements in a low-loss silicon waveguide,” Appl. Phys. Lett. 85, 2196–2198 (2004). [CrossRef]

], and Raman lasing [13–15

13. H. Rong, R. Jones, A. Liu, O. Cohen, D. Hak, A. Fang, and M. Paniccia, “A continuous-wave Raman silicon laser,” Nature 433, 725–728 (2005). [CrossRef] [PubMed]

] in silicon nanostructures. In particular, the large Raman gain coefficient in SOI waveguides allows for appreciable amplification over sub-cm waveguide lengths with gains as high as 24 dB [16

16. V. Raghunathan, O. Boyraz, and B. Jalali, “20 dB on-off Raman amplification in silicon waveguides,” in Proceedings of CLEO ’05, paper CMU1 (2005).

]. As we discuss below, the large Raman gain coefficient (gR = 4.2 cm/GW) [17

17. Q. Xu, V. R. Almeida, and M. Lipson, “Demonstration of high Raman gain in a submicrometer-size silicon-on-insulator waveguide,” Opt. Lett. 30, 35–37 (2005). [CrossRef] [PubMed]

] and the relatively narrow linewidth of silicon represent significant advantages for producing large slow-light effects.

On-chip delay schemes in silicon have recently been explored [18–22

18. J. E. Heebner and R. W. Boyd, “‘Slow’ and ‘fast’ light in resonator-coupled waveguides,” J. Mod. Opt. 49, 2629–2636 (2002). [CrossRef]

]. These schemes involve resonators [18

18. J. E. Heebner and R. W. Boyd, “‘Slow’ and ‘fast’ light in resonator-coupled waveguides,” J. Mod. Opt. 49, 2629–2636 (2002). [CrossRef]

], make use of the band-edge of silicon [19

19. 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]

], or utilize photonic crystal structures [20

20. H. Gersen, T. J. Karle, R. J. P. Engelen, W. Bogaerts, J. P. Korterik, N. F. van Hulst, T. F. Krauss, and L. Kuipers, “Real-space observation of ultraslow light in photonic crystal waveguides,” Phys. Rev. Lett. 94, 073903 (2005). [CrossRef] [PubMed]

], and thus typically operate within a relatively narrow range of wavelengths.

Some degree of thermal tuning of these structures, similar to that in fiber Bragg gratings [23

23. B. J. Eggleton, A. Ahuja, P. S. Westbrook, J. A. Rogers, P. Kuo, T. N. Nielsen, and B. Mikkelsen, “Integrated tunable fiber gratings for dispersion management in high-bit rate systems,” J. Lightwave Technol. 18, 1418–1432 (2000). [CrossRef]

], has been demonstrated [21

21. Y. A. Vlasov, M. O’Boyle, H. F. Hamann, and S. J. McNab, “Active control of slow light on a chip with photonic crystal waveguides,” Nature 438, 65–69 (2005). [CrossRef] [PubMed]

], but this restricts their use to those applications in which an ultrafast reconfiguration is not required. In addition, single-beam delay schemes have been realized in semiconductor waveguides [24

24. J. MØrk, R. Kjaer, M. van der Poel, and K. Yvind, “Slow light in semiconductor waveguide at gigahertz frequencies,” Opt. Express 13, 8136–8145 (2005). [CrossRef] [PubMed]

], quantum dot amplifiers [25

25. M. van der Poel, J. MØrk, and J. Hvam, “Controllable delay of ultrashort pulses in a quantum dot optical amplifier,” Opt. Express 13, 8032–8037 (2005). [CrossRef] [PubMed]

], and vertical-cavity surface-emitting laser amplifiers [26

26. X. Zhao, P. Palinginis, B. Pesala, C. Chang-Hasnain, and P. Hemmer, “Tunable ultraslow light in verticalcavity surface-emitting laser amplifier,” Opt. Express 13, 7899–7904 (2005). [CrossRef] [PubMed]

].

Here we demonstrate optically tunable delays in a robust and highly compact SOI architecture based on slow light induced by stimulated Raman scattering (SRS). Within a nanoscale waveguide, we produce group index changes as large as 0.15 and generate controllable delays greater than a full pulse width for signal pulses as short as 3 ps. Our scheme is noteworthy since it is compatible with silicon-on-insulator technology, the delay of each pulse within a pulse train can be separately controlled, tunable delays can be generated at telecommunication wavelengths and at bandwidths of up to 100 GHz, and the same waveguide can be used to produce delays at different wavelength channels across the entire telecommunication spectrum. These results thus represent a critical step in the development of chip-scale optical signal processing devices that control light with light.

2. Theory

ng(ω)=n(ω)+ωdndω.
(1)

By taking the Hilbert transform of a Lorentzian fit to the experimentally measured gain curve, we can infer the refractive index change due to this Raman contribution, and Fig. 2 shows the phase and group-index changes as functions of wavelength. At the peak of the Raman resonance the total delay ΔTD of the signal pulse in passing through the material due to the presence of the pump field is given by [24

24. J. MØrk, R. Kjaer, M. van der Poel, and K. Yvind, “Slow light in semiconductor waveguide at gigahertz frequencies,” Opt. Express 13, 8136–8145 (2005). [CrossRef] [PubMed]

]

ΔTD=GΓR,
(2)

Fig. 1. Top: Measured Raman gain (solid circles) and inferred refractive index change as a function of wavelength, which is derived via the Kramers-Kronig relations from the Lorentzian best-fit curve of the experimental points. Bottom: Plot of the inferred group index as a function of wavelength derived from the index change in the top plot.

3. Experiment

By exploiting the larger Raman gain coefficient, narrower Raman linewidth, and highly confining geometries of silicon waveguides as compared to glass fibers, we generate large slow-light effects on chip. The source for our signal pulses is an optical parametric oscillator (OPO) with the central wavelength tuned to 1686.14 nm. The pulse bandwidth is 1.47 nm FWHM, which corresponds to a transform-limited pulsewidth of 2.67 ps. In order to generate the synchronous pump pulses, the OPO signal is detected using a fast photodiode and the photocurrent pulse is used to amplitude modulate a CW laser at 1549.97 nm to produce a pump pulse 50 ps in duration. This pump pulse is then amplified using an erbium-doped fiber amplifier (EDFA), and the signal and pump pulses are combined using a wavelength-division multiplexer (WDM) and coupled into the Si waveguide using an inverse nanotaper structure (see Fig. 2) [30

30. V. R. Almeida, R. R. Panepucci, and M. Lipson, “Nanotapers for compact mode conversion,” Opt. Lett. 28, 1302–1304 (2003). [CrossRef] [PubMed]

]. The wavelengths of the pulses are adjusted such that the signal wavelength is at the peak of the Raman resonance. The waveguide sample consists of an 8-mm-long embedded waveguide with a silicon core cross section of 250 nm by 450 nm and a SiO2 cladding. To measure the delay, we compare the signal pulse to a reference pulse (which does not interact with the pump) using Fourier transform spectral interferometry (FTSI) [29

29. J. E. Sharping, Y. Okawachi, and A. L. Gaeta, “Wide bandwidth slow light using a Raman fiber amplifier,” Opt. Express 13, 6092–6098 (2005). [CrossRef] [PubMed]

,31

31. L. Lepetit, G. Chériaux, and M. Joffre, “Linear techniques of phase measurement by femtosecond spectral interferometry for applications in spectroscopy,” J. Opt. Soc. Am. B 12, 2467–2474 (1995). [CrossRef]

], which in our scheme allows for measurement of delays as small as 10 fs. A Michelson interferometer is used to generate signal and reference pulses. After both pulses go through the waveguide, they are recombined using a Mach-Zehnder interferometer to be nearly overlapped in time. A spectral interferogram is measured and the fringe spacing yields the inverse of the delay between the pulses.

We observe continuously tunable delays by simply varying the pump power. Typical results are illustrated in Fig. 3, which shows a plot of total delay as a function of the gain parameter G. A linear relationship between the total delay and the gain parameter is observed, as expected from Eq. (2). The slope of the delay versus G plot and the theoretically predicted relation between delay and gain (Eq. (1)) implies a Raman linewidth of 300 GHz. This value is larger than the Raman linewidth measured experimentally, and we conclude that this discrepancy results from the assumption of narrow pulse bandwidths compared to the Raman gain linewidth in the theory [32

32. Z. Zhu, D. J. Gauthier, Y. Okawachi, J. E. Sharping, A. L. Gaeta, R. W. Boyd, and A. E. Willner, “Numerical study of all-optical slow-light delays via stimulated Brillouin scattering in an optical fiber,” J. Opt. Soc. Am. B 22, 2378–2384 (2005). [CrossRef]

]. Since the bandwidth of the signal pulse is comparable to the linewidth of the Raman resonance, the spectral components near the edges of the pulse experience smaller induced delays than the central spectral components, which results in a reduced net pulse delay. Additionally, the gain in this case is limited by the bandwidth of the RF components used.

Fig. 2. Left: Experimental setup for coupling into the SOI planar waveguide. Right: Schematic configuration for generating and measuring delay. The signal and pump pulses are overlapped in time going into the waveguide.
Fig. 3. Total measured delay as a function of the measured Raman gain parameter (dashed line represents the best fit to the data). Continuous tuning of the delay is generated between 0 and 282 fs. We observe the theoretically predicted linear relationship between the delay and the gain parameter.

To generate larger gain and, hence, larger delays, we take advantage of the dual wavelength output of the OPO in fs-mode. The OPO generates a short-wavelength pulse train having a broad spectrum ranging from 1540-1580 nm which can be spectrally filtered to obtain 7-ps pump pulses centered at 1549.97 nm. The long-wavelength pulse train has a spectrum ranging from 1660-1690 nm which is filtered to obtain signal pulses centered at 1686 nm. The pump pulses are amplified using an EDFA and are combined with the signal pulses using a second WDM. By using the shorter pump pulses, we achieve larger peak pump powers and observe signal delays as large as 4 ps (Fig. 4), which implies a Raman gain of 32 dB. The measured signal pulse bandwidth is 1.35 nm, which corresponds to a pulse duration of 3.1 ps, assuming it is transform-limited. Thus, we achieve a delay of 1.3 times the input pulse width. The estimated change Δngr in the group index due to the Raman process is Δngr = c ΔTD/L = 0.15, which is approximately 6 orders of magnitude larger than that previously achieved in Raman experiments in silica fiber [26

26. X. Zhao, P. Palinginis, B. Pesala, C. Chang-Hasnain, and P. Hemmer, “Tunable ultraslow light in verticalcavity surface-emitting laser amplifier,” Opt. Express 13, 7899–7904 (2005). [CrossRef] [PubMed]

]. Ultimately, the largest fractional delay that can be achieved in a single-stage stimulated scattering system is limited to approximately 3, due to the occurrence of spontaneous scattering processes that deplete the pump wave [27

27. Y. Okawachi, M. S. Bigelow, J. E. Sharping, Z Zhu, A. Schweinsberg, D. J. Gauthier, R. W. Boyd, and A. L. Gaeta, “Tunable all-optical delays via Brillouin slow light in an optical fiber,” Phys. Rev. Lett. 94, 153902 (2005). [CrossRef] [PubMed]

] for very large values (>25) of G. However, this limitation can be overcome by using cascaded stages between which an absorber is placed to prevent the build-up of a spontaneously generated Stokes signal [28

28. K. Y. Song, M. G. Herráez, and L. Thévenaz, “Long optically controlled delays in optical fibers,” Opt. Lett. 30, 1782–1784 (2005). [CrossRef] [PubMed]

]. In such a cascaded configuration, additional care must be taken to ensure that the signal and pump pulses are synchronized when entering each amplification stage.

Fig. 4. Amplitude of the Fourier transformed interferograms with no pump pulse and with a pump pulse for which the total delay is 4 ps.

4. Conclusion

We have demonstrated tunable all-optical delays in a SOI waveguide with picosecond pulses, which represents the first step towards creating optically tunable dispersion on chip. The delay can be generated at any wavelength below the bandgap of silicon and is widely tunable since it is not constrained to a material or cavity resonance. Furthermore, the Raman linewidth in silicon makes it possible to support bandwidths associated with telecommunication pulses. Lastly, the short interaction length and pump-power dependent delay provide this scheme the advantage of having a fast reconfiguration time on the order of 70 GHz. This allows for tailored delay of individual pulses within a signal pulse train, provided that the pump pulse does not overlap with the subsequent pulse.

Acknowledgments

We gratefully acknowledge support from the Center for Nanoscale Systems, supported by the NSF under grant No. EEC-0117770 and Y.O., M.A.F., J.E.S., and A.L.G. gratefully acknowledge support from the DARPA DSO Slow-Light Program.

References and links

1.

R. W. Boyd and D. J. Gauthier, “‘Slow’ and ‘fast’ light,” Progress in Optics 43, edited by E. Wolf (Elsevier, Amsterdam, 2002), Chap. 6, p. 497–530. [CrossRef]

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]

3.

M. M. Kash, V. A. Sautenkov, A. S. Zibriv, L. Hollberg, G. R. Welch, M. D. Lukin, Y. Rostovtsev, E. S. Fry, and M. O. Scully, “Ultraslow group velocity and enhanced nonlinear optical effects in a coherently driven hot atomic gas,” Phys. Rev. Lett. 82, 5229–5232 (1999). [CrossRef]

4.

A. V. Turukhin, V. S. Sudarshanam, M. S. Shahriar, J. A. Musser, B. S. Ham, and P. R. Hemmer, “Observation of ultraslow and stored light pulses in a solid,” Phys. Rev. Lett. 88, 023602 (2002). [CrossRef] [PubMed]

5.

M. S. Bigelow, N. N. Lepeshkin, and R. W. Boyd, “Observation of ultraslow light propagation in a ruby crystal at room temperature,” Phys. Rev. Lett. 90, 113903 (2003). [CrossRef] [PubMed]

6.

P. Ku, F. Sedgwick, C. J. Chang-Hasnain, P. Palinginis, T. Li, H. Wang, S. Chang, and S. Chuang, “Slow light in semiconductor quantum wells,” Opt. Lett. 29, 2291–2293 (2004). [CrossRef] [PubMed]

7.

See, for example, R. Ramaswami and K. N. Sivarajan, Optical Networks: A Practical Perspective (Morgan Kaufmann, San Francisco, CA, 2002), 2nd ed., Chap. 12.

8.

M. A. Foster, K. D. Moll, and A. L. Gaeta, “Optimal waveguide dimensions for nonlinear interactions,” Opt. Express 12, 2880–2887 (2004). [CrossRef] [PubMed]

9.

V. R. Almeida, C. A. Barrios, R. R. Panepucci, and M. Lipson, “All-optical control of light in a silicon chip,” Nature 431, 1081–1084 (2004). [CrossRef] [PubMed]

10.

H. Rong, A. Liu, R. Nicolaescu, M. Paniccia, O. Cohen, and D. Hak, “Raman gain and nonlinear optical absorption measurements in a low-loss silicon waveguide,” Appl. Phys. Lett. 85, 2196–2198 (2004). [CrossRef]

11.

R. Claps, D. Dimitropoulos, V. Raghunathan, Y. Han, and B. Jalali, “Observation of stimulated Raman amplification in silicon waveguides,” Opt. Express 11, 1731–1739 (2003). [CrossRef] [PubMed]

12.

R. L. Espinola, J. I. Dadap, R. M. Osgood, S. J. McNab, and Y. A. Vlasov, “Raman amplification in ultrasmall silicon-on-insulator wire waveguides,” Opt. Express 12, 3713–3718 (2004). [CrossRef] [PubMed]

13.

H. Rong, R. Jones, A. Liu, O. Cohen, D. Hak, A. Fang, and M. Paniccia, “A continuous-wave Raman silicon laser,” Nature 433, 725–728 (2005). [CrossRef] [PubMed]

14.

O. Boyraz and B. Jalali, “Demonstration of a silicon Raman laser,” Opt. Express 12, 5269–5273 (2004). [CrossRef] [PubMed]

15.

H. Rong, A. Liu, R. Jones, O. Cohen, D. Hak, R. Nicolaescu, A. Fang, and M. Paniccia, “An all-silicon Raman laser,” Nature 433, 292–294 (2005). [CrossRef] [PubMed]

16.

V. Raghunathan, O. Boyraz, and B. Jalali, “20 dB on-off Raman amplification in silicon waveguides,” in Proceedings of CLEO ’05, paper CMU1 (2005).

17.

Q. Xu, V. R. Almeida, and M. Lipson, “Demonstration of high Raman gain in a submicrometer-size silicon-on-insulator waveguide,” Opt. Lett. 30, 35–37 (2005). [CrossRef] [PubMed]

18.

J. E. Heebner and R. W. Boyd, “‘Slow’ and ‘fast’ light in resonator-coupled waveguides,” J. Mod. Opt. 49, 2629–2636 (2002). [CrossRef]

19.

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]

20.

H. Gersen, T. J. Karle, R. J. P. Engelen, W. Bogaerts, J. P. Korterik, N. F. van Hulst, T. F. Krauss, and L. Kuipers, “Real-space observation of ultraslow light in photonic crystal waveguides,” Phys. Rev. Lett. 94, 073903 (2005). [CrossRef] [PubMed]

21.

Y. A. Vlasov, M. O’Boyle, H. F. Hamann, and S. J. McNab, “Active control of slow light on a chip with photonic crystal waveguides,” Nature 438, 65–69 (2005). [CrossRef] [PubMed]

22.

M. Yanik, W. Suh, Z. Wang, and S. Fan, “Stopping light in a waveguide with an all-optical analog of electromagnetically induced transparency,” Phys. Rev. Lett. 93, 233903 (2004). [CrossRef] [PubMed]

23.

B. J. Eggleton, A. Ahuja, P. S. Westbrook, J. A. Rogers, P. Kuo, T. N. Nielsen, and B. Mikkelsen, “Integrated tunable fiber gratings for dispersion management in high-bit rate systems,” J. Lightwave Technol. 18, 1418–1432 (2000). [CrossRef]

24.

J. MØrk, R. Kjaer, M. van der Poel, and K. Yvind, “Slow light in semiconductor waveguide at gigahertz frequencies,” Opt. Express 13, 8136–8145 (2005). [CrossRef] [PubMed]

25.

M. van der Poel, J. MØrk, and J. Hvam, “Controllable delay of ultrashort pulses in a quantum dot optical amplifier,” Opt. Express 13, 8032–8037 (2005). [CrossRef] [PubMed]

26.

X. Zhao, P. Palinginis, B. Pesala, C. Chang-Hasnain, and P. Hemmer, “Tunable ultraslow light in verticalcavity surface-emitting laser amplifier,” Opt. Express 13, 7899–7904 (2005). [CrossRef] [PubMed]

27.

Y. Okawachi, M. S. Bigelow, J. E. Sharping, Z Zhu, A. Schweinsberg, D. J. Gauthier, R. W. Boyd, and A. L. Gaeta, “Tunable all-optical delays via Brillouin slow light in an optical fiber,” Phys. Rev. Lett. 94, 153902 (2005). [CrossRef] [PubMed]

28.

K. Y. Song, M. G. Herráez, and L. Thévenaz, “Long optically controlled delays in optical fibers,” Opt. Lett. 30, 1782–1784 (2005). [CrossRef] [PubMed]

29.

J. E. Sharping, Y. Okawachi, and A. L. Gaeta, “Wide bandwidth slow light using a Raman fiber amplifier,” Opt. Express 13, 6092–6098 (2005). [CrossRef] [PubMed]

30.

V. R. Almeida, R. R. Panepucci, and M. Lipson, “Nanotapers for compact mode conversion,” Opt. Lett. 28, 1302–1304 (2003). [CrossRef] [PubMed]

31.

L. Lepetit, G. Chériaux, and M. Joffre, “Linear techniques of phase measurement by femtosecond spectral interferometry for applications in spectroscopy,” J. Opt. Soc. Am. B 12, 2467–2474 (1995). [CrossRef]

32.

Z. Zhu, D. J. Gauthier, Y. Okawachi, J. E. Sharping, A. L. Gaeta, R. W. Boyd, and A. E. Willner, “Numerical study of all-optical slow-light delays via stimulated Brillouin scattering in an optical fiber,” J. Opt. Soc. Am. B 22, 2378–2384 (2005). [CrossRef]

OCIS Codes
(190.5650) Nonlinear optics : Raman effect
(230.1150) Optical devices : All-optical devices

ToC Category:
Optical Devices

History
Original Manuscript: January 27, 2006
Revised Manuscript: March 7, 2006
Manuscript Accepted: March 7, 2006
Published: March 20, 2006

Citation
Yoshitomo Okawachi, Mark Foster, Jay Sharping, Alexander Gaeta, Qianfan Xu, and Michal Lipson, "All-optical slow-light on a photonic chip," Opt. Express 14, 2317-2322 (2006)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-14-6-2317


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References

  1. R. W. Boyd and D. J. Gauthier, "‘Slow’ and ‘fast’ light," Progress in Optics43, edited by E. Wolf (Elsevier, Amsterdam, 2002), Chap. 6, p. 497-530. [CrossRef]
  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]
  3. M. M. Kash, V. A. Sautenkov, A. S. Zibriv, L. Hollberg, G. R. Welch, M. D. Lukin, Y. Rostovtsev, E. S. Fry, and M. O. Scully, "Ultraslow group velocity and enhanced nonlinear optical effects in a coherently driven hot atomic gas," Phys. Rev. Lett. 82, 5229-5232 (1999). [CrossRef]
  4. A. V. Turukhin, V. S. Sudarshanam, M. S. Shahriar, J. A. Musser, B. S. Ham, and P. R. Hemmer, "Observation of ultraslow and stored light pulses in a solid," Phys. Rev. Lett. 88, 023602 (2002). [CrossRef] [PubMed]
  5. M. S. Bigelow, N. N. Lepeshkin, and R. W. Boyd, "Observation of ultraslow light propagation in a ruby crystal at room temperature," Phys. Rev. Lett. 90, 113903 (2003). [CrossRef] [PubMed]
  6. P. Ku, F. Sedgwick, C. J. Chang-Hasnain, P. Palinginis, T. Li, H. Wang, S. Chang, and S. Chuang, "Slow light in semiconductor quantum wells," Opt. Lett. 29, 2291-2293 (2004). [CrossRef] [PubMed]
  7. See, for example, R. Ramaswami and K. N. Sivarajan, Optical Networks: A Practical Perspective (Morgan Kaufmann, San Francisco, CA, 2002), 2nd ed., Chap. 12.
  8. M. A. Foster, K. D. Moll, and A. L. Gaeta, "Optimal waveguide dimensions for nonlinear interactions," Opt. Express 12,2880-2887 (2004). [CrossRef] [PubMed]
  9. V. R. Almeida, C. A. Barrios, R. R. Panepucci, and M. Lipson, "All-optical control of light in a silicon chip," Nature 431, 1081-1084 (2004). [CrossRef] [PubMed]
  10. H. Rong, A. Liu, R. Nicolaescu, M. Paniccia, O. Cohen, D. Hak, "Raman gain and nonlinear optical absorption measurements in a low-loss silicon waveguide," Appl. Phys. Lett. 85, 2196-2198 (2004). [CrossRef]
  11. R. Claps, D. Dimitropoulos, V. Raghunathan, Y. Han, and B. Jalali, "Observation of stimulated Raman amplification in silicon waveguides," Opt. Express 11, 1731-1739 (2003). [CrossRef] [PubMed]
  12. R. L. Espinola, J. I. Dadap, R. M. Osgood, S. J. McNab, Y. A. Vlasov, "Raman amplification in ultrasmall silicon-on-insulator wire waveguides," Opt. Express 12, 3713-3718 (2004). [CrossRef] [PubMed]
  13. H. Rong, R. Jones, A. Liu, O. Cohen, D. Hak, A. Fang, M. Paniccia, "A continuous-wave Raman silicon laser," Nature 433, 725-728 (2005). [CrossRef] [PubMed]
  14. O. Boyraz and B. Jalali, "Demonstration of a silicon Raman laser," Opt. Express 12, 5269-5273 (2004). [CrossRef] [PubMed]
  15. H. Rong, A. Liu, R. Jones, O. Cohen, D. Hak, R. Nicolaescu, A. Fang, and M. Paniccia, "An all-silicon Raman laser," Nature 433, 292-294 (2005). [CrossRef] [PubMed]
  16. V. Raghunathan, O. Boyraz, and B. Jalali, "20 dB on-off Raman amplification in silicon waveguides," in Proceedings of CLEO ’05, paper CMU1 (2005).
  17. Q. Xu, V. R. Almeida, and M. Lipson, "Demonstration of high Raman gain in a submicrometer-size silicon-on-insulator waveguide," Opt. Lett. 30, 35-37 (2005). [CrossRef] [PubMed]
  18. J. E. Heebner and R. W. Boyd, "‘Slow’ and ‘fast’ light in resonator-coupled waveguides," J. Mod. Opt. 49, 2629-2636 (2002). [CrossRef]
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