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Optics Express

Optics Express

  • Editor: Michael Duncan
  • Vol. 13, Iss. 16 — Aug. 8, 2005
  • pp: 6092–6098
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Wide bandwidth slow light using a Raman fiber amplifier

Jay E. Sharping, Yoshitomo Okawachi, and Alexander L. Gaeta  »View Author Affiliations


Optics Express, Vol. 13, Issue 16, pp. 6092-6098 (2005)
http://dx.doi.org/10.1364/OPEX.13.006092


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Abstract

We demonstrate an all-optical tunable pulse delay scheme that utilizes the power-dependent variation of the refractive index that accompanies stimulated Raman scattering in an optical fiber. Using this technique, we delay 430-fs pulses by up to 85% of a pulse width. The ability to accommodate the bandwidth of pulses shorter than 1 ps in a fiber-based system makes this technique potentially viable for producing controllable delays in ultra-high bandwidth telecommunication systems.

© 2005 Optical Society of America

1. Introduction

The concepts of phase, group, information, and signal velocity have been the subject of numerous recent studies [1

1. M. D. Stenner, D. J. Gauthier, and M. A. Neifeld, “The speed of information in a ‘fast-light’ optical medium,” Nature 425, 695–698 (2003). [CrossRef] [PubMed]

,2

2. R. W. Boyd and D. J. Gauthier, “Slow and fast light,” Progress in Optics43, edited by E. Wolf, 497–529, (Elsevier, Amsterdam, 2002). [CrossRef]

]. These ideas have been explored in great detail over many decades [3

3. L. Brillouin, Wave propagation and group velocity (Academic Press, New York, 1960).

], but recent interest in this area stems from dramatic experimental demonstrations of fast and slow light [4–8

4. 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]

] and from the likelihood that these effects can be used in novel laboratory and commercial devices. Some of the proposed uses for slow light include optical buffers, continuously variable optical delays, low-power optical switching, and quantum memory. The motivation behind our research is to identify the ideal, fiber-based technique(s) for generating slow light for a variety of applications based on ease of use, wavelength agility, allowable pulse durations, conceptual simplicity and maximum total and/or relative delay [9–11

9. Y. Okawachi, M. S. Bigelow, J. E. Sharping, Z. M. 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]

].

In this paper, we report the first demonstration of slow-light using a Raman fiber amplifier. This system has the advantage of being able to accommodate the bandwidth of and to controllably delay pulses less than 1-ps duration. Specifically, we show for 430-fs input pulses that a controllable change in delay of 85% of a pulse width is possible. The system has many of the same advantages as demonstrated using stimulated Brillouin scattering [9

9. Y. Okawachi, M. S. Bigelow, J. E. Sharping, Z. M. 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]

, 12–14

12. 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,” to be published in J. Opt. Soc. Am. B (2005).

], that is, the slow-light resonance can be positioned at the desired wavelength by tuning the wavelength of the pump, the use of a highly nonlinear optical fiber permits the use of relatively low pump powers, operation is at room temperature, and it is compatible with telecommunication technology. We believe this demonstration represents the first step in the application of Raman amplifiers as controllable delay lines for ultrafast systems and in optical communication devices.

We find that in this system several mechanisms which impact the group velocity of an amplified pulse must be considered, such as gain-dependent self-phase modulation and cross-phase modulation, and wavelength-dependent gain combined with nonzero group-velocity dispersion. Indeed, an understanding of pulse propagation in Raman amplifiers is critical for developing a complete understanding of the impact of Raman in-line amplifiers in fiber communication systems [15

15. P. L. Voss and P. Kumar, “Raman-effect induced noise limits on χ(3) parametric amplifiers and wavelength converters,” J. Opt. B: Quantum Semiclass. Opt. 6, S762–S770 (2004). [CrossRef]

, 16

16. F. A. Oguama, H. Garcia, and A. M. Johnson, “Simultaneous measurement of the Raman gain coefficient and the nonlinear refractive index of optical fibers: theory and experiment,” J. Opt. Soc. Am. B 22, 426–436 (2005). [CrossRef]

]. A relevant study of the optically-induced pulse delay from a solid-state Raman amplifier based on a Ba(NO3)2 crystal is reported in Ref. [17

17. K. Lee and N. M. Lawandy, “Optically induced pulse delay in a solid-state Raman amplifier,” Appl. Phys. Lett. 78, 703–705 (2001). [CrossRef]

]. In that work, 90-ps pulses of wavelength 1.2 μm were delayed by as much as 105 ps.

Fig. 1. The experimental setup used to demonstrate slow light in a Raman fiber amplifier (det, detector; FPC, fiber-polarization conroller; other abbreviations are described in the text). The reference pulse is used for the FTSI measurement of the signal delay.

ΔT=GΓ,
(1)

The experimental setup is shown in Fig. 1. Signal pulses are derived from a Ti:Sapphire-pumped optical parametric oscillator (OPO). The wavelength of the OPO is continuously tunable over the entire range of wavelengths used in this experiment (1590–1643 nm), and it emits nearly transform-limited pulses. For pulses centered at a wavelength of 1640 nm, the spectral width is 9.1 nm-FWHM corresponding to a transform-limited temporal width of 430 fs. Prior to entering the Raman amplifier, the signal propagates through several optics and 8 m of standard optical fiber (SMF-28e).

In our setup, we have chosen to use Fourier-transform spectral interferometry (FTSI) to measure the delays of the signal pulses since it provides the ability to accurately measure delays as small as tens of fs between pulses of very low peak power. By using pulses whose peak power is kept <1 mW, self-phase modulation of the signal pulses is negligible. Temporally-separated reference pulses, which are used to measure the signal delay, are generated by passing the signal pulse train through an asymmetric Michelson interferometer. The resulting temporal separation is approximately 1.7 ns. Synchronous pump pulses are created by detecting the signal pulse train on a photodiode and using that electronic signal to amplitude modulate the output of a CW tunable diode laser. The resulting 500 ps-long, 1535 nm pump pulses are optically amplified and combined synchronously with the signal via a wavelength-division multiplexer (WDM).

Fig. 2. (a) Plots of gain versus pump peak power for several different signal wavelengths. (b) Gain slope versus signal-pump frequency detuning. The measured slopes plotted on the left axis are compared with the ASE spectrum which is plotted on the right axis.

In the Raman amplifier portion of the system, signal, reference and pump pulses co-propagate through a 1-km span of highly-nonlinear dispersion-shifted fiber (HNLF). The zero-dispersion wavelength of the HNLF was measured to be 1551±2nm, with a slope of 0.04 ps/(nm2km), and a nonlinear coefficient of 11 (W-km)-1. As shown in Fig. 1, the signal and pump pulses temporally overlap resulting in amplification and induced delay of the signal pulse. The reference pulse propagates without interacting with the pump, and so it remains unamplified. The pump pulses are then spectrally filtered from the signal and reference pulses using a second WDM.

The gain characteristics of the Raman amplifier are shown in Fig. 2. Using the OSA, we measure the gain as a function of pump peak power for a fixed pump wavelength (1535 nm) and for different settings of the signal wavelength. Here, the value for the gain is determined by the increase in signal power when the pump is turned on as compared with that when the pump is off. From Fig. 2(a) we see that the relationship between gain and pump power is linear and that the gain slope increases as the signal is tuned closer to the peak of the Raman gain. Plotted in Fig. 2(b) on the left axis is the value for the gain slope as a function of signal-pump frequency detuning. The spectral dependence of the gain slope follows exactly that of the Raman amplified spontaneous emission (ASE) measured for this system, which is plotted on the right axis of Fig. 2(b). The maximum Raman gain achieved using this system (not shown) is 35 dB for a peak pump power of 2.6 W. The maximum power is an experimental limitation imposed by the power handling capability of the WDM used for combining and filtering the pump and the signal. Over this range of pump powers, we did not observe saturation of the gain.

After propagating through the Raman amplifier, the signal and reference pulses are passed through an asymmetric Mach-Zehnder interferometer (MZI) having a path difference that compensates for the temporal separation between the reference and signal pulses. Temporally, the output of the MZI consists of the following four components which traverse different arms of the interferometer: reference pulses that traverse the short arm, reference pulses that traverse the long arm, signal pulses that traverse the short arm, and signal pulses that traverse the long arm. The system is configured so that the reference pulses traversing the long arm and signal pulses from the short arm are nearly temporally coincident. When the output is measured by an optical spectrum analyzer (OSA), a spectral interferogram similar to that shown in Fig. 3(a) is observed. The OSA output can be expressed as [20

20. L. Lepetit, G. Cheriaux, 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]

]

S(ω)=E0(ω)+Ea(ω)2
=E0(ω)2+Ea(ω)2+2E0(ω)Ea(ω)cos(ϕaϕ0),
(2)

where E 0 and Ea are the reference and Raman-amplified electric fields, respectively, ω is the frequency of the field, and ϕa and ϕ 0 are the phases of the Raman-amplified and reference fields, respectively. The final term in Eq. (2) is critical because it contains the spectral modulation due to the interference between the temporally separated Raman-amplified and reference fields. The phase difference in Eq. (2) must account for gain-induced spectral shift of the amplified field as well as for cross-phase modulation between the pump and the signal. Pulse delays resulting from gain-induced spectral shifts can be included by adding a temporal component according to ∆TSS = D∆λℓ/c, where D is the group-velocity dispersion coefficient given in units of [ps/(nm km)], ∆λ is the gain-induced spectral shift, and ℓ is the fiber length. In practice, most of the contribution to ∆TSS occurs in the standard fiber in between the Raman amplifier and the OSA. The phase shift due to cross-phase modulation between the quasi-CW pump and signal arises within the Raman amplifier and is given by ϕXPM = 2γPpL, where L is the length of the HNLF.

Measurements of slow light in this Raman amplifier are shown in Fig. 4 where the signal wavelength is 1637 nm, which is very close to the peak of the Raman gain profile. The gain parameter (left axis) and signal time delay (right axis) are plotted as functions of pump peak power. We see for moderate and high pump powers that both the gain and delay vary linearly with respect to pump power. The slight nonlinearity in the curves at low pump powers is due to the difficulty in measuring the gain at these small values. The slope of the delay curve with respect to G is 15 fs which, according to the approximate relation given in Eq. (1), corresponds to a gain bandwidth of 8 THz. This derived value for the gain bandwidth is larger than the 4-THz width of the linear portion of the real part of the nonlinear coefficient as plotted by Voss, et. al. [15

15. P. L. Voss and P. Kumar, “Raman-effect induced noise limits on χ(3) parametric amplifiers and wavelength converters,” J. Opt. B: Quantum Semiclass. Opt. 6, S762–S770 (2004). [CrossRef]

] and by Stolen, et. al [19

19. R. H. Stolen, J. P. Gordon, W. J. Tomlinson, and H. A. Haus, “Raman response function of silica-core fibers,” J. Opt. Soc. Am. B 6, 1159–1166 (1989). [CrossRef]

]. The origin of this discrepancy is likely the result of the fact that data in Fig. 4 was recorded as a part of the sequence of measurements for several different wavelengths (see Fig. 2) and that the Raman gain spectrum is not a Lorentzian as assumed in deriving Eq. (1). Optimization of the gain and delay were not performed prior to recording data for each signal wavelength. If the polarization overlap of the pump and signal is not optimal, the output signal pulse will be broadened temporally due to gain-induced polarization mode dispersion, and the measured delay for a given gain will be reduced. The maximum delay achieved for the data depicted in Fig. 4 is 140 fs, which is 40% of the transform-limited pulse width.

Figure 5 shows three delayed signal pulses in the Fourier-transformed, time-domain representation where the system was adjusted to obtain as large a delay as possible prior to each measurement. For these pulses, the relative signal delay was varied from 0 to 370±30 fs, which at the maximum is 85% of a transform-limited pulse duration. The measured gain for the case of maximum delay was G = 7, which implies a Raman gain bandwidth of 3 THz extrapolated from Eq. (1). Note that the peak positions read from the plot do not correspond to the actual Raman group delay. To obtain the delay, corrections due to cross-phase modulation (50 fs less delay for the 370 fs case) and wavelength shift (82 fs greater delay for the 370 fs case) must be applied. As inferred from Fig. 5, we observe that the spectral width of the pulses does not change from the zero-delay case as the delay is varied.

Fig. 3. (a) Spectral interferograms along with the (b) Fourier-transformed pulse position.
Fig. 4. Plots of gain and delay vs. pump power.
Fig. 5. Amplitude of the transformed interferograms for pulse delay changes of 0 fs, 135 fs and 370 fs. The delay of 370 fs is the maximum delay achieved with our setup.

In summary, we have demonstrated an ultrafast all-optical controllable delay in an optical fiber that utilizes the real part of the nonlinear coefficient that accompanies stimulated Raman scattering. Using this device, we have delayed a 430-fs pulse by 85% of its pulse width. This approach shows that short pulses of light with wide spectral bandwidths can be delayed using slow-light processes similar to those used in past demonstrations with relatively long pulses of light. The technique has the additional advantage of being sufficiently fast that it can be used to generate an independent delay for each consecutive pulse in a pulse train, owing to the ultrafast response of the Raman effect in silica glass.

The authors would like to thank Pablo Londero, Dan Gauthier, Zhaoming Zhu, Paul Voss, Bob Boyd, Alan Willner and Yan Wang for useful discussions. Thanks also to Chris Xu for providing HNLF and numerous instruments. The authors would also like to acknowledge financial support from the DARPA DSO Slow-Light Program and from the Center for Nanoscale Systems, supported by the NSF under grant No. EEC-0117770.

References and links

1.

M. D. Stenner, D. J. Gauthier, and M. A. Neifeld, “The speed of information in a ‘fast-light’ optical medium,” Nature 425, 695–698 (2003). [CrossRef] [PubMed]

2.

R. W. Boyd and D. J. Gauthier, “Slow and fast light,” Progress in Optics43, edited by E. Wolf, 497–529, (Elsevier, Amsterdam, 2002). [CrossRef]

3.

L. Brillouin, Wave propagation and group velocity (Academic Press, New York, 1960).

4.

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]

5.

M. M. Kash, V. A. Sautenkov, A. S. Zibrov, 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]

6.

C. Liu, Z. Dutton, C. H. Behroozi, and L. V. Hau, “Observation of coherent optical information storage in an atomic medium using halted light pulses,” Nature 409, 490–493 (2001). [CrossRef] [PubMed]

7.

L. J. Wang, A. Kuzmich, and A. Dogariu, “Gain-assisted superluminal light propagation,” Nature 406, 277–279 (2000). [CrossRef] [PubMed]

8.

M. S. Bigelow MS, N. N. Lepeshkin, and R. W. Boyd, “Superluminal and slow light propagation in a room-temperature solid,” Science 301, 200–202 (2003). [CrossRef] [PubMed]

9.

Y. Okawachi, M. S. Bigelow, J. E. Sharping, Z. M. 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]

10.

S. Ghosh, J. E. Sharping, D. G. Ouzounov, and A. L. Gaeta, “Resonant optical interactions with molecules confined in photonic band-gap fibers,” Phys. Rev. Lett. 94, 093902 (2005). [CrossRef] [PubMed]

11.

J. E. Sharping, Y. Okawachi, J. van Howe, C. Xu, and A. L. Gaeta, “All-optical tunable, nanosecond delay using wavelength conversion and fiber dispersion,” in proceedings of CLEO’05, paper CTuT1 (2005).

12.

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,” to be published in J. Opt. Soc. Am. B (2005).

13.

K. Y. Song, M. G. Herráez, and L. Thévenaz, “Observation of pulse delaying and advancement in optical fibers using stimulated Brillouin scattering,” Opt. Express 13, 82–88 (2005). [CrossRef] [PubMed]

14.

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

15.

P. L. Voss and P. Kumar, “Raman-effect induced noise limits on χ(3) parametric amplifiers and wavelength converters,” J. Opt. B: Quantum Semiclass. Opt. 6, S762–S770 (2004). [CrossRef]

16.

F. A. Oguama, H. Garcia, and A. M. Johnson, “Simultaneous measurement of the Raman gain coefficient and the nonlinear refractive index of optical fibers: theory and experiment,” J. Opt. Soc. Am. B 22, 426–436 (2005). [CrossRef]

17.

K. Lee and N. M. Lawandy, “Optically induced pulse delay in a solid-state Raman amplifier,” Appl. Phys. Lett. 78, 703–705 (2001). [CrossRef]

18.

R. W. Boyd, D. J. Gauthier, A. L. Gaeta, and A. E. Willner, “Maximum time delay achievable on propagation through a slow-light medium,” Phys. Rev. A 71, 023801 (2005). [CrossRef]

19.

R. H. Stolen, J. P. Gordon, W. J. Tomlinson, and H. A. Haus, “Raman response function of silica-core fibers,” J. Opt. Soc. Am. B 6, 1159–1166 (1989). [CrossRef]

20.

L. Lepetit, G. Cheriaux, 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]

OCIS Codes
(060.2320) Fiber optics and optical communications : Fiber optics amplifiers and oscillators
(190.5650) Nonlinear optics : Raman effect
(190.5890) Nonlinear optics : Scattering, stimulated

ToC Category:
Research Papers

History
Original Manuscript: July 20, 2005
Revised Manuscript: July 26, 2005
Published: August 8, 2005

Citation
Jay Sharping, Yoshitomo Okawachi, and Alexander Gaeta, "Wide bandwidth slow light using a Raman fiber amplifier," Opt. Express 13, 6092-6098 (2005)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-13-16-6092


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References

  1. M. D. Stenner, D. J. Gauthier, and M. A. Neifeld, �??The speed of information in a �??fast-light�?? optical medium,�?? Nature 425, 695�??698 (2003). [CrossRef] [PubMed]
  2. R.W. Boyd and D. J. Gauthier, �??Slow and fast light,�?? Progress in Optics 43, edited by E.Wolf, 497�??529, (Elsevier, Amsterdam, 2002). [CrossRef]
  3. 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]
  4. M. M. Kash, V. A. Sautenkov, A. S. Zibrov, 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]
  5. C. Liu, Z. Dutton, C. H. Behroozi, and L. V. Hau, �??Observation of coherent optical information storage in an atomic medium using halted light pulses,�?? Nature 409, 490�??493 (2001). [CrossRef] [PubMed]
  6. L. J. Wang, A. Kuzmich, A. Dogariu, �??Gain-assisted superluminal light propagation,�?? Nature 406, 277�??279 (2000). [CrossRef] [PubMed]
  7. M. S. Bigelow MS, N. N. Lepeshkin, R. W. Boyd, �??Superluminal and slow light propagation in a room-temperature solid,�?? Science 301, 200�??202 (2003). [CrossRef] [PubMed]
  8. Y. Okawachi, M. S. Bigelow, J. E. Sharping, Z. M. 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]
  9. S. Ghosh, J. E. Sharping, D. G. Ouzounov, and A. L. Gaeta, �??Resonant optical interactions with molecules confined in photonic band-gap fibers,�?? Phys. Rev. Lett. 94, 093902 (2005). [CrossRef] [PubMed]
  10. J. E. Sharping, Y. Okawachi, J. van Howe, C. Xu and A. L. Gaeta, �??All-optical tunable, nanosecond delay using wavelength conversion and fiber dispersion,�?? in proceedings of CLEO�??05, paper CTuT1 (2005).
  11. 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,�?? to be published in J. Opt. Soc. Am. B (2005).
  12. K. Y. Song, M. G. Herráez, L. Thévenaz, �??Observation of pulse delaying and advancement in optical fibers using stimulated Brillouin scattering,�?? Opt. Express 13, 82�??88 (2005). [CrossRef] [PubMed]
  13. K. Y. Song, M. G. Herráez, L. Thévenaz, �??Long optically controlled delays in optical fibers,�?? Opt. Lett. 30, 1782�??1784 (2005). [CrossRef] [PubMed]
  14. P. L. Voss and P. Kumar, �??Raman-effect induced noise limits on �?(3) parametric amplifiers and wavelength converters,�?? J. Opt. B: Quantum Semiclass. Opt. 6, S762�??S770 (2004). [CrossRef]
  15. F. A. Oguama, H. Garcia, and A. M. Johnson, �??Simultaneous measurement of the Raman gain coefficient and the nonlinear refractive index of optical fibers: theory and experiment,�?? J. Opt. Soc. Am. B 22, 426�??436 (2005). [CrossRef]
  16. K. Lee and N. M. Lawandy, �??Optically induced pulse delay in a solid-state Raman amplifier,�?? Appl. Phys. Lett. 78, 703�??705 (2001). [CrossRef]
  17. R.W. Boyd, D. J. Gauthier, A. L. Gaeta, A. E.Willner, �??Maximum time delay achievable on propagation through a slow-light medium,�?? Phys. Rev. A 71, 023801 (2005). [CrossRef]
  18. R. H. Stolen, J. P. Gordon, W. J. Tomlinson, and H. A. Haus, �??Raman response function of silica-core fibers,�?? J. Opt. Soc. Am. B 6, 1159�??1166 (1989). [CrossRef]
  19. L. Lepetit, G. Cheriaux, 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]
  20. L. Brillouin, Wave propagation and group velocity (Academic Press, New York, 1960).

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