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Intra-pulse Raman frequency shift versus conventional Stokes generation of diode laser pulses in optical fibers

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Abstract

We report experimental observations of stimulated Raman scattering in a standard fiber using a directly modulated DFB semiconductor laser amplified by two erbium-doped fibers. The laser pulse width was variably controlled on a nanosecond-scale; the laser emission was separated into two distinct regimes: an initial transient peak regime, followed by a quasi steady-state plateau regime. The transient leading part of the pump pulse containing fast amplitude modulation generated a broadband Raman-induced spectral shift through the modulation instability and subsequent intra-pulse Raman frequency shift. The plateau regime amplified the conventional Stokes shifted emission expected from the peaks of the gain distribution. The output signal spectrum at the end of a 9.13 km length of fiber for the transient part extends from 1550 nm to 1700 nm for a pump pulse peak power of 65 W. We found that the Raman-induced spectral shift is measurable about 8 W for every fiber length examined, 0.6 km, 4.46 km, and 9.13 km. All spectral components of the broadband scattering appear to be generated in the initial kilometer of the fiber span. The Stokes shifted light generation threshold was higher than the threshold for the intra-pulse Raman-induced broadened spectra. This fact enables the nonlinear spectral filtering of pulses from directly modulated semiconductor lasers.

©2005 Optical Society of America

1. Introduction

Raman scattering is a process for generating down-converted light by exciting molecular vibrations in materials, such as silica glass. It is generally weak, however, under laser pumping conditions stimulated Raman scattering has become a viable means for amplifying weak signals at a longer wavelength than the pump wavelength. The frequency shift and the gain band width are characteristics of the material, which does not require special doping or preparation. In fibers the pump laser may emit several Watts of optical power to achieve Raman amplification. Recently high power cw sources were developed as Raman amplifiers; they have potential applications in optical communications systems [1], as well as for medical imaging and for tunable sources.

The growing interest in Raman scattering is not confined to using a cw pump sources. Indeed modulated sources with pulse widths in the femto-pico- and nanosecond time regimes are also widely exploited. Directly modulated semiconductor diode lasers are a very attractive source of the pump pulses for investigation of nonlinear phenomena in optical fibers on a nanosecond scale because they are compact and relatively inexpensive. A semiconductor laser diode can be used as a master oscillator in the Master Oscillator Power Amplifier (MOPA) configuration that is now one of the most widely used schemes for high power pulse generation. The development of double cladding fiber amplifiers enables the amplification of a Master Oscillator signal up to hundreds Watts of average power.

When cw or long pulses of pump and signal are involved the features of the SRS are well understood. On the other hand when short pulses or beams modulated with high frequency are considered, the SRS spectra become much more complex and difficult to understand. Stimulated Raman scattering can be accompanied by self-steepening of the pulse, self- and cross-phase modulation, as well as many other phenomena. One of the specific features of the direct modulation of laser diodes is the relaxation oscillation appearing at the leading edge of pulses [2]. The presence of the relaxation oscillations can trigger many nonlinear effects usually considered in the context of ultrashort pulses. The Raman-induced spectral shift is one of the most intensively investigated effects for ultrashort pump pulses. It appears as a continuous transfer of energy from high-frequency components of a pulse to the lower-frequency components of the same pulse. The effect was first discovered for solitons and therefore was called the soliton self-frequency shift [3,4]. Since then the Raman-induced frequency shift has been studied extensively in context of physical studies of pulse propagation and for wavelength-tunable femtosecond soliton generation [57]. Most investigations deal with solitons, nevertheless the Raman-induced frequency shift should occur for any optical pulses. Recently a general theory of the Raman-induced spectral shift was developed [8], which applies to the long-pulse situation we consider in this paper. Generally the Stokes generation and Raman-induced frequency shift are considered separately; nevertheless a unified description is possible [9]. For very short pulses the time response of the medium also needs to be considered [10]. Pump noise also affects the Stokes generation with nanosecond pulses [11,12]. All of these effects have to be considered for SRS of the pulses generated by the directly modulated laser diode.

In this paper we present the experimental results of the investigation of stimulated Raman scattering (SRS) due to a nanosecond-scale, directly modulated DFB laser emitting at a wavelength of 1549 nm, which is amplified by two erbium-doped fibers before launching into a fiber. We found that two parallel processes occur; the leading edge of the pulse shows the effect of the Raman induced spectral shift, while the plateau shows the Stokes wave amplification at the wavelengths corresponding to the gain maximum. The leading part of the pulse can be used for simple broadband signal generation. The difference between the pump powers needed for SRS in these two regimes enables the possibility of a nonlinear filtering of the pump pulse to eliminate the transient part of pulse. This technique may be important for example in MOPA configurations where the laser diode is used as the Master Oscillator.

2. Experimental setup

A Mitsubishi DFB diode laser ML976H6F with emission wavelength 1549 nm was used as a primary pulse source. The maximum average power at the fiber output of the pulsed DFB laser was 1.5 mW. The pulses were then amplified by a two stage Er-doped fiber amplifier (EDFA), see Fig. 1, to a maximum peak power as high as 70 W. We used the SRS DG535 pulse generator for direct modulation of the diode laser. The shortest pulses from the laser were approximately 3 ns in duration; this value was dictated by the current pulse duration available from the pulse generator. For pulses longer than 50 ns we observed saturation of Er-doped fiber amplifier. Therefore, we used variable pulse lengths whose duration fell in the range between 3 ns and 30 ns. Input pulses pass through a circulator to enter to a 10-m long EDF which used as a first stage in a double pass amplifier configuration. After the first-pass amplification the pulses were reflected from a fiber Bragg grating and amplified in second pass in the same fiber amplifier. The pulse then enters the circulator again to reach the second stage of the EDFA, which was comprised of a 15 m fiber span. The 980 nm pump power for the first stage was 30 mW, while for second stage we used the maximum 980 nm pump power of 80 mW. The repetition frequency of the signal pulses typically was 1 kHz. No difference in the results was found when the pulse repetition frequency was decreased to 100 Hz.

 figure: Fig. 1.

Fig. 1. Schematic of the two stage EDFA.

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The maximum amplification of the two stage EDFA was 47 dB. This corresponds to output pulses with maximum peak power of 70 W. Amplified pulses are inserted into a fiber where the stimulated Raman scattering was investigated. The signal from the fiber output was passed to a mochromator and then detected by an InGaAs photodetector whose output is amplified and monitored by an oscilloscope. The resulting bandwidth of the electrical circuit was 500 MHz, which permits the detection of nanosecond scale pulses.

Figure 2 shows the pulse shape at the EDFA output for several current pulses driving the laser diode. A current bias of 8 mA was applied in this case; the threshold current of the laser diode is 10 mA. It should be mentioned that the bias was always well below the laser threshold because even very low cw radiation at the laser output saturated the EDFA.

 figure: Fig. 2.

Fig. 2. Typical pulse shapes at the EDFA output; (a) the power measured for a range of pulse currents, (b) the first three nanoseconds of the pulse measured with a 8-GHz photodetector and a sampling oscilloscope.

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Damped oscillations with a period of approximately 5 ns appear at the leading edge of the pulse. We attribute them to an electrical oscillation in our circuit. However some faster oscillations were observed with an 8 GHz detector and a high bandwidth oscilloscope. Figure 2(b) shows the initial 3 ns of the laser pulses after the EDFA. Relaxation oscillations were observed in the first 3–5 ns time span. The relaxation oscillations gradually disappear at longer times.

 figure: Fig. 3.

Fig. 3. Pulse shapes for different wavelengths using the monochromator.

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Our experimental facilities do not allow accurate spectral measurements of pulses. Nevertheless some estimation can be made from the pulse shapes measured at slightly different wavelengths of the monochromator. Figure 3 shows the pulse shape at 1549 nm, 1548.5 nm and 1549.5 nm. We observe that the leading peak has broader spectrum than the trailing plateau regime. The estimation of the bandwidth of the leading peak shows that FWHM is around 1 nm.

3. Experimental results and discussion

To observe SRS generation we used standard single mode SMF-28 fibers; we chose three fiber lengths for the study: 9.13 km, 4.46 km and 0.6 km. When launched into the fiber the pump pulse converts to conventional SRS generation at the Raman gain maximum, and to a broadband emission due to the Raman induced frequency shift. To explore this further we measured the pulse shapes at the fiber output for the set of wavelengths in the range between 1549 nm (pump wavelength) and 1700 nm (maximum detectable wavelength for our detector). Figure 4 shows several examples of the Stokes pulse shapes at the output from the 9.13 km long fiber after passing through a monochromator, whose resolution was equal to 1 nm. For the results in Fig. 4 we launched the pump pulses into the fiber with a plateau power of 10 W, a maximum peak power of 18 W at the leading edge, and total pulse duration of 30 ns. The data in Fig. 4(a) shows a short output pulse, which appears in the spectral range from 1552 nm to 1580 nm. Its duration is approximately 5 ns, which corresponds to the duration of the leading peak of the pump pulse, see Fig. 2(a).

Figure 4(b) displays the spectrally filtered pulse shapes at the wavelengths 1650 nm, 1660 nm, and 1670 nm. The Stokes pulse with the maximum amplitude appears at 1660 nm. This wavelength corresponds to the Stokes frequency shift equal to 430 cm-1 or 12.9 THz, which is equal to the shift for the principal peak of the Raman gain in silica glass fibers. The duration of the plateau part of the Stokes pulse can be estimated as 17 ns between the minimum (t=3.6 ns) and half of maximum (t=20.6 ns). This is somewhat shorter than the 26.5-ns long plateau part of the pump pulse measured in the same manner. Some shortening of the Stokes pulse width as well as the plateau’s power increase from the beginning to the end of the pulse is expected due to the walk-off effect in the fiber. From this data we deduce that the plateau part of the pump pulse causes conventional Stokes amplification process, whereas the initial part of the pump gives a broadband spectrum.

 figure: Fig. 4.

Fig. 4. Stokes pulse shapes for different wavelengths taken from the output of the 9.13 km fiber.

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 figure: Fig. 5.

Fig. 5. Dependence of the pulse energy at the fiber output on wavelength. The peaks near 1660 nm and 1675 nm correspond to maxima for the Raman gain.

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Figure 5 shows the dependence of the energy of output pulses versus the wavelength for pump pulses with the leading peak power of 26 W and the plateau power of 15 W. This plateau power is closed to the threshold power of second Stokes generation. For higher powers the first Stokes is depleted. We observe two maxima in the spectrum at 1660 nm (430 cm-1 or 12.9 THz frequency shift) and at 1675 nm (480 cm-1 or 14.4 THz frequency shift). The two maxima coincide well with the Raman gain maxima for silica glass fibers. We also observe a strong, broadband signal extending from 1550 nm to 1700 nm. The increase of the input power causes further widening of the broadband part of the spectrum.

When 3 ns pulses were used for pumping only the broadband part of the spectrum appears; Some results are summarized in Fig. 6. The spectra were scaled to have maxima equal to unity. For the 9.13 km fiber length the spectral bandwidth was measured to 1700 nm. It probably extends beyond this, but our photodetector no longer responds after 1700 nm. The detectable spectrum depends both on fiber length and input power. For the 0.6 km long fiber the longest detectable wavelength is 1580 nm. Launching a peak input power of 50 W into the 9.13 km fiber length the output spectrum falls faster than for the 70-W peak input power experiments (Fig. 6). Similar dependencies were observed for 4.43 km long fiber. No maxima were found at the Stokes wavelength for 3-ns pump pulses at any input power and any fiber length.

 figure: Fig. 6.

Fig. 6. Output spectra for 3-ns laser diode pump pulse.

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It is interesting to note that all spectral components of the broadband spectrum were apparently initiated at the beginning of the fiber. To prove this we have measured the time delay between the pulses at the fiber output for different wavelengths. Figure 7 shows the result obtained for the 9.13 km fiber length and 70 W of the pump peak power. The linear dependence fits very well the experimentally measured time delays. The slope of the dependence shows the fiber dispersion equals 19.7 ps/nm-km. This value is the same as the published dispersion value for SMF-28 fiber. The results of the delay-time measurements may be reasonably understood only when all spectral components start near the beginning of the fiber. Otherwise a deviation of the experimental points from the straight line would be observed. For example if the longest wavelengths would appear in the second kilometer of the fiber, the delay for these wavelength would be 10% down from the straight line. Experimental points on the graphic allow the conclusion that the statistical error is less than 10%, and therefore all wavelengths appear at the beginning of the fiber with the length no longer than 1 km. At the same time Fig. 6 shows that the power for the long wavelength part of the spectrum growths strongly for the 9.13 km long fiber as compared with the 0.6 km long fiber. Summarizing these results we conclude that spectral components have to be generated near the beginning of the fiber and the rest of the fiber amplifies the power of each spectral component.

 figure: Fig. 7.

Fig. 7. Pulse delay at the fiber output.

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We also measured the output pulse energy at the pump wavelength when the 3 ns long pulses were applied. Figure 8 shows the results obtained for the 9.13 km, 4.46 km, and 0.6 km fiber lengths. This results shows that the pump depletion process for the leading segment of the pulse begins at approximately the same power, which we determined was 8 W for every fiber length. As expected, the output energy drops more sharply with input power for longer fibers. For about 15 W of input power the output energy drops to about 10 % of its input value.

 figure: Fig. 8.

Fig. 8. The ratio between the output pump peak power and the input pump peak power. The output was filtered through a monochromator to extract the energy at the pump wavelength.

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As a first approximation the experimental results can be described by the model including the modulation instability (MI) and the Raman induced spectral shift. The modulation instability leads to an exponential growth of small perturbations of the power. It occurs in the anomalous dispersion regime [1]. It was shown theoretically, that MI can break a pulse into multiple solitons [13, 14]. This mechanism was used for wavelength conversion [15] and was discussed also in the context of super-continuum generation [16].

In our experiments MI causes the breakup of the transient part of pump pulse to a set of short pulses with different durations. The subsequent Raman induced frequency shift results in the broadband output signal. The MI can be initiated by self-phase modulation (SPM) and injected noise which in our case can be amplified spontaneous emission (ASE) from the EDFA. The two effects are distinct because ASE affects both the leading edge and the plateau, while SPM is dominant for the leading edge representing fast oscillations in the intensity. The experimental results are consistent with the absence of MI in the plateau regime, so ASE does not play important role in our experiments. Numerical calculations including SPM and the Raman induced spectral shift show that the formation of a set of solitons from pulse with duration of 100 ps (half width at 1/e level) begins at power equal to 20 W for the 1 km long fiber. The pulse duration is reasonably close to the characteristic time of relaxation oscillations in semiconductor lasers; and the 20 W power threshold is also reasonably close to our measured power. At the same time the plateau is sufficiently smooth to be free of these solitonic processes and thus promotes conventional Stokes generation.

The soliton self frequency shift measured in GHz can be written as, see p.186 in Ref. [1]:

ΔωR(z)=8β2TRz(15T04)

Where β2 is group velocity dispersion which is -20 ps2/km for standard fibers; TR is the first moment of the SRS response function that typically is taken as 3 fs; T0 is soliton duration determined as half width at 1/e of maximum and measured in ps; The parameter, z, is the fiber length measured in km. As discussed earlier, Fig. 7 demonstrates that all spectral components appear at the beginning of the fiber within a length no longer that 1 km. The maximum wavelength shift was detected to be equal to 145 nm or 140 THz. Eq. (1) shows that T0 has to be equal to 0.1 ps to provide the 140-THz frequency shift at the 1-km distance. On the other hand in Fig. 8 we observed that the pump power for the 9.13 km long fiber dropped to a level which was almost undetectable. The solitons with the longest pulse width must be shifted by at least by 0.5 nm (spectral resolution of our monochromator) or 0.5 THz. From Eq. (1) we deduce that the duration of the solitons must be shorter than 1 ps in order to provide the dependencies similar to that shown in Figs.7 and 9. The pulse evolution spawns a set of many solitons with durations in the range between 0.1 ps and 1 ps.

One intriguing consequence of our results is the possibility of nonlinear filtering for elimination of the transient part of pulses. The principle of the nonlinear filtering is as follows. The pump pulse first passes through the fiber where the transient peak is broken apart by the modulation instability to generate solitons, which are shifted to longer wavelengths by a Raman induced frequency shift. Then output pulses are filtered by a narrow spectral filter and the pulse plateau continues to propagate through the fiber system. The procedure can be successful since the threshold for Stokes generation is lower than that for intra-pulse Raman scattering.

We calculated the threshold for cw pump using an effective core area equaled to 81 µm2, the Raman gain equaled to 0.31×10-11 cm/W for completely depolarized light [17,18], fiber loss equaled to 0.2 dB/km. For these conditions we found the thresholds to be equal to 7.4 W for 9.13 km fiber length (an effective length is 7.4 km), 10 W for the 4.46 km fiber (effective length is 4.03 km), and 65 W for the 0.6 km fiber. The power of the plateau at which some pulse depletion actually appears was measured to be equal to 10 W for the 9.13 km fiber length and 15 W for the 4.46 km fiber. This threshold value is reasonably close to the calculated values of the SRS threshold. Note that for the 10 W plateau power the peak power is 13 W; and for the 15 W plateau power the peak power is 20 W. So the Raman threshold at which the plateau depletion appears is essentially higher than the threshold for Raman induced frequency shift. We observe that at the power for which the plateau depletion appears, the oscillating part drops by approximately 10 times for the 9.13 km fiber length and by 6 times for the 4.46 km fiber. The maximum drop of the oscillating part for the 0.6 km fiber length was 10 times; the SRS threshold was not reached for this fiber.

 figure: Fig. 9.

Fig. 9. Pulse shapes at the fiber output at the pump wavelength; a) the 4.46-km long fiber; b) the 9.13-km long fiber.

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To explore the efficacy of nonlinear filtering we measured the pump pulse shape at the fiber output at different input powers. Figure 9 shows the results for the 4.46 km long fiber (a) and for the 9.13 km long fiber (b). For low input power the output pulse shape is the same as the input one with the first peak significantly higher than the plateau. As the input peak power is increased there is a resulting decrease of the output power at the transient peak as compared with the plateau regime. The leading transient peak is completely suppressed for a 17 W input power launched into the 9.13 km long fiber, and the output pulse has a squared shape. For higher power the conventional SRS begins and some depletion of the plateau can be seen in Fig. 8(b), i.e. for the 22 W input launched into the 9.13 km fiber length.

4. Conclusions

In conclusion we have performed a detailed experimental study of the stimulated Raman scattering in a standard fiber with anomalous dispersion pumped by a directly modulated DFB semiconductor laser amplified by erbium-doped fibers. We found that the leading part of the pump pulse containing relaxation oscillations initiates the Raman induced continuous spectral shift, while the plateau provides conventional Stokes gain generating Stokes shifted wavelengths. The threshold of Stokes generation by the plateau was found to be higher that the threshold of the Raman induced spectral shift. The difference between thresholds allows the nonlinear filtering of the pulses that was experimentally examined.

Acknowledgments

JWH was supported by NSF grant INT-0226945, EK was supported by CONACYT grant 39553 and CONACYT-NSF bilateral project.

References

1. G. P. Agrawal, Nonlinear Fiber Optics, 3d ed. (Academic, San Diego, California, 2001).

2. G. P. Agrawal and N. K. Dutta, Semiconductor Lasers, Second Edition, International Thompson Publishing, 1993.

3. F. M. Mitschke and L F. Molenauer, “Discovery of the soliton self-frequency shift,”; Opt. Lett. 11,.659–661 (1986). [CrossRef]   [PubMed]  

4. J. P. Gordon, “Theory of the soliton self-frequency shift,” Opt. Lett. 11, 662–664 (1986). [CrossRef]   [PubMed]  

5. N. Nishizawa and T. Goto, “Compact System of Wavelength-Tunable Femtosecond Soliton Pulses Generation Using Optical Fiber,” IEEE Photonics Tech. Lett. 11, 325–327 (1999). [CrossRef]  

6. D. A. Chestnut and J. R. Taylor, “Soliton self-frequency shift in highly nonlinear fiber with extension by external Raman pumping,” Opt. Lett. 28, 2512–2514 (2003). [CrossRef]   [PubMed]  

7. A. Efimov, A. J. Taylor, F. G. Omenetto, and E. Vanin, “Adaptive control of femtosecond soliton self-frequency shift in fibers,” Opt. Lett. 29, 271–273 (2004). [CrossRef]   [PubMed]  

8. J. Santhanam and G. P. Agrawal, “Raman-induced spectral shifts in optical fibers: general theory based on the moment method,” Opt. Commun. 222, 413–420 (2003). [CrossRef]  

9. C. Headley III and G. P. Agrawal, “Unified description of ultrafast stimulated Raman scattering in optical fibers,” J. Opt. Soc. Am. B 13, 2170–2177 (1996). [CrossRef]  

10. A. Picozzi, C. Montes, J. Botineau, and E. Picholle, “Inertial model for stimulated Raman scattering including chaotic dynamics,” J. Opt. Soc. Am. B 15, 1309–1314 (1998). [CrossRef]  

11. L. Garcia, J. Jenkins, Y. Lee, N. Poole, K. Salit, P. Sidereas, C. G. Goedde, and J. R. Thompson, “Influence of classical pump noise on long-pulse multi-order stimulated Raman scattering in optical fiber,” J. Opt. Soc. Am. B 19, 2727–2736 (2002). [CrossRef]  

12. L. Garcia, A. Jalili, Y. Lee, N. Poole, K. Salit, P. Sidereas, C. G. Goedde, and J.R. Thompson, “Effect of pump pulse temporal structure on long-pulse multi-order stimulated Raman scattering in optical fiber,” Opt. Commun. 193, 289–300 (2001). [CrossRef]  

13. P. K. Shukla and J. J. Rasmussen, “Modulation instability of short pulses in long optical fibers,” Opt. Lett. 11, 171–173 (1986). [CrossRef]   [PubMed]  

14. P. V. Mamyshev, S. V. Chernikov, E. M. Dianov, and A. M. Prokhorov, “Generation of a high-repetition-rate train of practically noninteracting solitons by using the induced modulation instability and Raman self-scattering effects,” Opt. Lett. 15, 1365–1367 (1990). [CrossRef]   [PubMed]  

15. G. A. Nowak, Y. H. Kao, T. J. Xia, and M. N. Islam, “Low power high-efficiency wavelength conversion based on modulation instability in high-nonlinearity fiber,” Opt. Lett. 23, 936–938 (1998). [CrossRef]  

16. A. K. Abeeluck and C. Headley, “Continuous-wave pumping in the anomalous- and normal-dispersion regimes of nonlinear fibers for supercontinuum generation,” Opt. Lett. 30, 61–63 (2005). [CrossRef]   [PubMed]  

17. B. Crosignani, P. Di Porto, and S. Solimento, “Influence of guiding structures on spontaneous and stimulated emission: Raman scattering in optical fibers.” Phys. Rev. A. 21, 594–598 (1980). [CrossRef]  

18. D. Mahgerefteh, D. L. Butler, J. Goldhar, B. Rosenberg, and G. L. Burdge, “Technique for measurement of the Raman gain coefficient in optical fibers,” Opt. Lett. 21, 2026–2028 (1996). [CrossRef]   [PubMed]  

References

  • View by:

  1. G. P. Agrawal, Nonlinear Fiber Optics, 3d ed. (Academic, San Diego, California, 2001).
  2. G. P. Agrawal and N. K. Dutta, Semiconductor Lasers, Second Edition, International Thompson Publishing, 1993.
  3. F. M. Mitschke and L F. Molenauer, “Discovery of the soliton self-frequency shift,”; Opt. Lett. 11,.659–661 (1986).
    [Crossref] [PubMed]
  4. J. P. Gordon, “Theory of the soliton self-frequency shift,” Opt. Lett. 11, 662–664 (1986).
    [Crossref] [PubMed]
  5. N. Nishizawa and T. Goto, “Compact System of Wavelength-Tunable Femtosecond Soliton Pulses Generation Using Optical Fiber,” IEEE Photonics Tech. Lett. 11, 325–327 (1999).
    [Crossref]
  6. D. A. Chestnut and J. R. Taylor, “Soliton self-frequency shift in highly nonlinear fiber with extension by external Raman pumping,” Opt. Lett. 28, 2512–2514 (2003).
    [Crossref] [PubMed]
  7. A. Efimov, A. J. Taylor, F. G. Omenetto, and E. Vanin, “Adaptive control of femtosecond soliton self-frequency shift in fibers,” Opt. Lett. 29, 271–273 (2004).
    [Crossref] [PubMed]
  8. J. Santhanam and G. P. Agrawal, “Raman-induced spectral shifts in optical fibers: general theory based on the moment method,” Opt. Commun. 222, 413–420 (2003).
    [Crossref]
  9. C. Headley III and G. P. Agrawal, “Unified description of ultrafast stimulated Raman scattering in optical fibers,” J. Opt. Soc. Am. B 13, 2170–2177 (1996).
    [Crossref]
  10. A. Picozzi, C. Montes, J. Botineau, and E. Picholle, “Inertial model for stimulated Raman scattering including chaotic dynamics,” J. Opt. Soc. Am. B 15, 1309–1314 (1998).
    [Crossref]
  11. L. Garcia, J. Jenkins, Y. Lee, N. Poole, K. Salit, P. Sidereas, C. G. Goedde, and J. R. Thompson, “Influence of classical pump noise on long-pulse multi-order stimulated Raman scattering in optical fiber,” J. Opt. Soc. Am. B 19, 2727–2736 (2002).
    [Crossref]
  12. L. Garcia, A. Jalili, Y. Lee, N. Poole, K. Salit, P. Sidereas, C. G. Goedde, and J.R. Thompson, “Effect of pump pulse temporal structure on long-pulse multi-order stimulated Raman scattering in optical fiber,” Opt. Commun. 193, 289–300 (2001).
    [Crossref]
  13. P. K. Shukla and J. J. Rasmussen, “Modulation instability of short pulses in long optical fibers,” Opt. Lett. 11, 171–173 (1986).
    [Crossref] [PubMed]
  14. P. V. Mamyshev, S. V. Chernikov, E. M. Dianov, and A. M. Prokhorov, “Generation of a high-repetition-rate train of practically noninteracting solitons by using the induced modulation instability and Raman self-scattering effects,” Opt. Lett. 15, 1365–1367 (1990).
    [Crossref] [PubMed]
  15. G. A. Nowak, Y. H. Kao, T. J. Xia, and M. N. Islam, “Low power high-efficiency wavelength conversion based on modulation instability in high-nonlinearity fiber,” Opt. Lett. 23, 936–938 (1998).
    [Crossref]
  16. A. K. Abeeluck and C. Headley, “Continuous-wave pumping in the anomalous- and normal-dispersion regimes of nonlinear fibers for supercontinuum generation,” Opt. Lett. 30, 61–63 (2005).
    [Crossref] [PubMed]
  17. B. Crosignani, P. Di Porto, and S. Solimento, “Influence of guiding structures on spontaneous and stimulated emission: Raman scattering in optical fibers.” Phys. Rev. A. 21, 594–598 (1980).
    [Crossref]
  18. D. Mahgerefteh, D. L. Butler, J. Goldhar, B. Rosenberg, and G. L. Burdge, “Technique for measurement of the Raman gain coefficient in optical fibers,” Opt. Lett. 21, 2026–2028 (1996).
    [Crossref] [PubMed]

2005 (1)

2004 (1)

2003 (2)

J. Santhanam and G. P. Agrawal, “Raman-induced spectral shifts in optical fibers: general theory based on the moment method,” Opt. Commun. 222, 413–420 (2003).
[Crossref]

D. A. Chestnut and J. R. Taylor, “Soliton self-frequency shift in highly nonlinear fiber with extension by external Raman pumping,” Opt. Lett. 28, 2512–2514 (2003).
[Crossref] [PubMed]

2002 (1)

2001 (1)

L. Garcia, A. Jalili, Y. Lee, N. Poole, K. Salit, P. Sidereas, C. G. Goedde, and J.R. Thompson, “Effect of pump pulse temporal structure on long-pulse multi-order stimulated Raman scattering in optical fiber,” Opt. Commun. 193, 289–300 (2001).
[Crossref]

1999 (1)

N. Nishizawa and T. Goto, “Compact System of Wavelength-Tunable Femtosecond Soliton Pulses Generation Using Optical Fiber,” IEEE Photonics Tech. Lett. 11, 325–327 (1999).
[Crossref]

1998 (2)

1996 (2)

1990 (1)

1986 (3)

1980 (1)

B. Crosignani, P. Di Porto, and S. Solimento, “Influence of guiding structures on spontaneous and stimulated emission: Raman scattering in optical fibers.” Phys. Rev. A. 21, 594–598 (1980).
[Crossref]

Abeeluck, A. K.

Agrawal, G. P.

J. Santhanam and G. P. Agrawal, “Raman-induced spectral shifts in optical fibers: general theory based on the moment method,” Opt. Commun. 222, 413–420 (2003).
[Crossref]

C. Headley III and G. P. Agrawal, “Unified description of ultrafast stimulated Raman scattering in optical fibers,” J. Opt. Soc. Am. B 13, 2170–2177 (1996).
[Crossref]

G. P. Agrawal, Nonlinear Fiber Optics, 3d ed. (Academic, San Diego, California, 2001).

G. P. Agrawal and N. K. Dutta, Semiconductor Lasers, Second Edition, International Thompson Publishing, 1993.

Botineau, J.

Burdge, G. L.

Butler, D. L.

Chernikov, S. V.

Chestnut, D. A.

Crosignani, B.

B. Crosignani, P. Di Porto, and S. Solimento, “Influence of guiding structures on spontaneous and stimulated emission: Raman scattering in optical fibers.” Phys. Rev. A. 21, 594–598 (1980).
[Crossref]

Di Porto, P.

B. Crosignani, P. Di Porto, and S. Solimento, “Influence of guiding structures on spontaneous and stimulated emission: Raman scattering in optical fibers.” Phys. Rev. A. 21, 594–598 (1980).
[Crossref]

Dianov, E. M.

Dutta, N. K.

G. P. Agrawal and N. K. Dutta, Semiconductor Lasers, Second Edition, International Thompson Publishing, 1993.

Efimov, A.

Garcia, L.

L. Garcia, J. Jenkins, Y. Lee, N. Poole, K. Salit, P. Sidereas, C. G. Goedde, and J. R. Thompson, “Influence of classical pump noise on long-pulse multi-order stimulated Raman scattering in optical fiber,” J. Opt. Soc. Am. B 19, 2727–2736 (2002).
[Crossref]

L. Garcia, A. Jalili, Y. Lee, N. Poole, K. Salit, P. Sidereas, C. G. Goedde, and J.R. Thompson, “Effect of pump pulse temporal structure on long-pulse multi-order stimulated Raman scattering in optical fiber,” Opt. Commun. 193, 289–300 (2001).
[Crossref]

Goedde, C. G.

L. Garcia, J. Jenkins, Y. Lee, N. Poole, K. Salit, P. Sidereas, C. G. Goedde, and J. R. Thompson, “Influence of classical pump noise on long-pulse multi-order stimulated Raman scattering in optical fiber,” J. Opt. Soc. Am. B 19, 2727–2736 (2002).
[Crossref]

L. Garcia, A. Jalili, Y. Lee, N. Poole, K. Salit, P. Sidereas, C. G. Goedde, and J.R. Thompson, “Effect of pump pulse temporal structure on long-pulse multi-order stimulated Raman scattering in optical fiber,” Opt. Commun. 193, 289–300 (2001).
[Crossref]

Goldhar, J.

Gordon, J. P.

Goto, T.

N. Nishizawa and T. Goto, “Compact System of Wavelength-Tunable Femtosecond Soliton Pulses Generation Using Optical Fiber,” IEEE Photonics Tech. Lett. 11, 325–327 (1999).
[Crossref]

Headley, C.

Headley III, C.

Islam, M. N.

Jalili, A.

L. Garcia, A. Jalili, Y. Lee, N. Poole, K. Salit, P. Sidereas, C. G. Goedde, and J.R. Thompson, “Effect of pump pulse temporal structure on long-pulse multi-order stimulated Raman scattering in optical fiber,” Opt. Commun. 193, 289–300 (2001).
[Crossref]

Jenkins, J.

Kao, Y. H.

Lee, Y.

L. Garcia, J. Jenkins, Y. Lee, N. Poole, K. Salit, P. Sidereas, C. G. Goedde, and J. R. Thompson, “Influence of classical pump noise on long-pulse multi-order stimulated Raman scattering in optical fiber,” J. Opt. Soc. Am. B 19, 2727–2736 (2002).
[Crossref]

L. Garcia, A. Jalili, Y. Lee, N. Poole, K. Salit, P. Sidereas, C. G. Goedde, and J.R. Thompson, “Effect of pump pulse temporal structure on long-pulse multi-order stimulated Raman scattering in optical fiber,” Opt. Commun. 193, 289–300 (2001).
[Crossref]

Mahgerefteh, D.

Mamyshev, P. V.

Mitschke, F. M.

Molenauer, L F.

Montes, C.

Nishizawa, N.

N. Nishizawa and T. Goto, “Compact System of Wavelength-Tunable Femtosecond Soliton Pulses Generation Using Optical Fiber,” IEEE Photonics Tech. Lett. 11, 325–327 (1999).
[Crossref]

Nowak, G. A.

Omenetto, F. G.

Picholle, E.

Picozzi, A.

Poole, N.

L. Garcia, J. Jenkins, Y. Lee, N. Poole, K. Salit, P. Sidereas, C. G. Goedde, and J. R. Thompson, “Influence of classical pump noise on long-pulse multi-order stimulated Raman scattering in optical fiber,” J. Opt. Soc. Am. B 19, 2727–2736 (2002).
[Crossref]

L. Garcia, A. Jalili, Y. Lee, N. Poole, K. Salit, P. Sidereas, C. G. Goedde, and J.R. Thompson, “Effect of pump pulse temporal structure on long-pulse multi-order stimulated Raman scattering in optical fiber,” Opt. Commun. 193, 289–300 (2001).
[Crossref]

Prokhorov, A. M.

Rasmussen, J. J.

Rosenberg, B.

Salit, K.

L. Garcia, J. Jenkins, Y. Lee, N. Poole, K. Salit, P. Sidereas, C. G. Goedde, and J. R. Thompson, “Influence of classical pump noise on long-pulse multi-order stimulated Raman scattering in optical fiber,” J. Opt. Soc. Am. B 19, 2727–2736 (2002).
[Crossref]

L. Garcia, A. Jalili, Y. Lee, N. Poole, K. Salit, P. Sidereas, C. G. Goedde, and J.R. Thompson, “Effect of pump pulse temporal structure on long-pulse multi-order stimulated Raman scattering in optical fiber,” Opt. Commun. 193, 289–300 (2001).
[Crossref]

Santhanam, J.

J. Santhanam and G. P. Agrawal, “Raman-induced spectral shifts in optical fibers: general theory based on the moment method,” Opt. Commun. 222, 413–420 (2003).
[Crossref]

Shukla, P. K.

Sidereas, P.

L. Garcia, J. Jenkins, Y. Lee, N. Poole, K. Salit, P. Sidereas, C. G. Goedde, and J. R. Thompson, “Influence of classical pump noise on long-pulse multi-order stimulated Raman scattering in optical fiber,” J. Opt. Soc. Am. B 19, 2727–2736 (2002).
[Crossref]

L. Garcia, A. Jalili, Y. Lee, N. Poole, K. Salit, P. Sidereas, C. G. Goedde, and J.R. Thompson, “Effect of pump pulse temporal structure on long-pulse multi-order stimulated Raman scattering in optical fiber,” Opt. Commun. 193, 289–300 (2001).
[Crossref]

Solimento, S.

B. Crosignani, P. Di Porto, and S. Solimento, “Influence of guiding structures on spontaneous and stimulated emission: Raman scattering in optical fibers.” Phys. Rev. A. 21, 594–598 (1980).
[Crossref]

Taylor, A. J.

Taylor, J. R.

Thompson, J. R.

Thompson, J.R.

L. Garcia, A. Jalili, Y. Lee, N. Poole, K. Salit, P. Sidereas, C. G. Goedde, and J.R. Thompson, “Effect of pump pulse temporal structure on long-pulse multi-order stimulated Raman scattering in optical fiber,” Opt. Commun. 193, 289–300 (2001).
[Crossref]

Vanin, E.

Xia, T. J.

IEEE Photonics Tech. Lett. (1)

N. Nishizawa and T. Goto, “Compact System of Wavelength-Tunable Femtosecond Soliton Pulses Generation Using Optical Fiber,” IEEE Photonics Tech. Lett. 11, 325–327 (1999).
[Crossref]

J. Opt. Soc. Am. B (3)

Opt. Commun. (2)

L. Garcia, A. Jalili, Y. Lee, N. Poole, K. Salit, P. Sidereas, C. G. Goedde, and J.R. Thompson, “Effect of pump pulse temporal structure on long-pulse multi-order stimulated Raman scattering in optical fiber,” Opt. Commun. 193, 289–300 (2001).
[Crossref]

J. Santhanam and G. P. Agrawal, “Raman-induced spectral shifts in optical fibers: general theory based on the moment method,” Opt. Commun. 222, 413–420 (2003).
[Crossref]

Opt. Lett. (9)

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[Crossref] [PubMed]

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F. M. Mitschke and L F. Molenauer, “Discovery of the soliton self-frequency shift,”; Opt. Lett. 11,.659–661 (1986).
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J. P. Gordon, “Theory of the soliton self-frequency shift,” Opt. Lett. 11, 662–664 (1986).
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P. K. Shukla and J. J. Rasmussen, “Modulation instability of short pulses in long optical fibers,” Opt. Lett. 11, 171–173 (1986).
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P. V. Mamyshev, S. V. Chernikov, E. M. Dianov, and A. M. Prokhorov, “Generation of a high-repetition-rate train of practically noninteracting solitons by using the induced modulation instability and Raman self-scattering effects,” Opt. Lett. 15, 1365–1367 (1990).
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G. A. Nowak, Y. H. Kao, T. J. Xia, and M. N. Islam, “Low power high-efficiency wavelength conversion based on modulation instability in high-nonlinearity fiber,” Opt. Lett. 23, 936–938 (1998).
[Crossref]

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Phys. Rev. A. (1)

B. Crosignani, P. Di Porto, and S. Solimento, “Influence of guiding structures on spontaneous and stimulated emission: Raman scattering in optical fibers.” Phys. Rev. A. 21, 594–598 (1980).
[Crossref]

Other (2)

G. P. Agrawal, Nonlinear Fiber Optics, 3d ed. (Academic, San Diego, California, 2001).

G. P. Agrawal and N. K. Dutta, Semiconductor Lasers, Second Edition, International Thompson Publishing, 1993.

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Figures (9)

Fig. 1.
Fig. 1. Schematic of the two stage EDFA.
Fig. 2.
Fig. 2. Typical pulse shapes at the EDFA output; (a) the power measured for a range of pulse currents, (b) the first three nanoseconds of the pulse measured with a 8-GHz photodetector and a sampling oscilloscope.
Fig. 3.
Fig. 3. Pulse shapes for different wavelengths using the monochromator.
Fig. 4.
Fig. 4. Stokes pulse shapes for different wavelengths taken from the output of the 9.13 km fiber.
Fig. 5.
Fig. 5. Dependence of the pulse energy at the fiber output on wavelength. The peaks near 1660 nm and 1675 nm correspond to maxima for the Raman gain.
Fig. 6.
Fig. 6. Output spectra for 3-ns laser diode pump pulse.
Fig. 7.
Fig. 7. Pulse delay at the fiber output.
Fig. 8.
Fig. 8. The ratio between the output pump peak power and the input pump peak power. The output was filtered through a monochromator to extract the energy at the pump wavelength.
Fig. 9.
Fig. 9. Pulse shapes at the fiber output at the pump wavelength; a) the 4.46-km long fiber; b) the 9.13-km long fiber.

Equations (1)

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Δ ω R ( z ) = 8 β 2 T R z ( 15 T 0 4 )

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