Vol. 5, No. 2/February 1988/J. Opt. Soc. Am. B 373

Direct measurement of nonlinear frequency chirpof Raman radiation in single-mode

optical fibers using a spectral window method

A. S. L. Gomes, V. L. da Silva, and J. R. Taylor

Optics Section, Laser Group, Imperial College of Science and Technology, London SW7 2BZ, England

Received April 16, 1987; accepted October 27, 1987

The frequency chirps of the first-Stokes Raman (1.12-,m) and fundamental (1.06-,m) picosecond (-100-psec)pulses propagated through various lengths of single-mode optical fiber have been measured. The fiber lengths werevaried from a regime in which walk-off was significant to a regime where it could be neglected. Besides being of

positive sign and substantially greater than that of the fundamental, the chirp of the Raman radiation was found tobe highly nonlinear, in good qualitative agreement with theoretical predictions.

INTRODUCTION

The enhancement of many nonlinear-optical processes inoptical fibers, which has developed over the past 10 years,provides a convenient means of generating new wavelengthranges and of manipulating pulse shapes.

1 However, insome cases, the low thresholds for the nonlinearities cancause problems through the generation of unwanted radia-tion and can set limits for useful power levels in transmis-sion. For pulses in the picosecond-femtosecond range, self-phase modulation and stimulated Raman scattering havereceived particular attention, with specific reference topulse-compression schemes2 in which the associated group-velocity dispersion of the ultrashort pulses plays an impor-tant role.

The effect of self-phase modulation (SPM) in fibers hasbeen examined in detail by Stolen and Lin.3 The intensity-dependent nonlinear refractive index gives rise to an intensi-ty-dependent phase shift, with an associated instantaneousfrequency shift that is proportional to the time derivative ofthe intensity. Hence the spectrally broadened pulses exhib-it a chirp, i.e., a time-dependent frequency. This mecha-nism forms the basis of the fiber-grating-pair pulse com-pressor, in which the chirped pulses are subsequently passedthrough a grating pair that can exhibit dispersion of the signopposite that of the fiber, and permits temporal compres-sion. Group-velocity dispersion (GVD) can contribute sig-nificantly to the process, in that it tends to linearize thechirp across the pulse.4 '5

An alternative means of generating short pulses is to applya spectral windowing technique to the self-phase-modulatedpulses. We showed previously, using this technique, thatnarrowing by a factor of -3 can be achieved when the band-width of the spectral window is narrower than the SPMpulse bandwidth (by a factor of >3), provided that all othernonlinear effects can be neglected.6 Furthermore, the spec-tral window technique has been used, in conjunction with astreak camera, to provide a direct method of measurement ofthe degree of chirp present in a pulse.6'7 The same tech-nique has been employed in this reported investigation, aswe describe below.

Stimulated Raman scattering (SRS) in glass waveguideswas first observed in 1972 by Stolen et al.,8 and the implica-tions of optical communications were soon realized. Apump pulse propagating in an optical fiber first creates aStokes pulse by spontaneous Raman scattering, which isthen amplified by the corresponding stimulated process.The critical power levels at which SRS becomes a dominantprocess in the fiber have been defined by Smith.9

SRS in fibers has been used as a means of generating newwavelengths 0 and also has served as the basis for a universalfiber-optic measurement system." More recently, weshowed that the cascaded process of SRS in fibers leads topump-pulse fragmentation and that, in the positive GVDregime, the fragments have a negative chirp that can befurther compressed in a positively dispersive delay line. Byusing this technique, pulses of -5 psec separated by 300 psecwere derived from 100-psec pump pulses at 1.06 ym.12 Onthe other hand, SRS has been shown to introduce cross talkin multiplexed fiber systems13 and also should be avoided infiber-grating compressor systems.5"14 SRS has also beensuggested as a means of amplifying solitons in all-fiber com-munication systems,15 while soliton-Raman generation hasbeen shown to be a powerful technique in the generation offrequency-tunable, femtosecond, kilowatt soliton pulses inthe near infrared, in both single-pass' 6 and fiber oscillatorconfigurations. 17,18

The results described here are concerned with the investi-gation of the chirp of the fundamental (1.06-Am) and Raman(first Stokes at 1.12-gm) pulses in optical fibers in a regimewhere -30% of the total power was converted into the first-Stokes component. Various fiber lengths were used, from-60 m, where there was little walk-off between the 100-psecfundamental and first-Stokes Raman pulses, to -240 m,where walk-off was significant. A related experimentalwork 920 was recently published that described operationwith the pump radiation in the visible (532 nm), where GVDis much larger. In addition, recent theoretical treatmentshave been published on the frequency chirp of combinedSRS and SPM pulses in regimes where walk-off is importantor can be neglected,2 22 and both are considered in our ex-perimental study.

0740-3224/88/020373-08$02.00 (© 1988 Optical Society of America

Gomes et al.

374 J. Opt. Soc. Am. B/Vol. 5, No. 2/February 1988 Gomes et al.

Fig. 1. Experimental scheme: RF, radio-frequency 50-MHz acousto-optic modulator; AMP, power amplifier; BS, beam splitter; L's, lenses;M, mirror. See text for details.

EXPERIMENT

Figure 1 shows a schematic of the experimental arrange-ment. A cw mode-locked Nd:YAG laser (Quantronix Model116) operated at 1.06 Atm was used as the source of funda-mental pump radiation. This laser system has been de-scribed in detail elsewhere.23 A synchroscan streak camera(extended S photocathode) was used to monitor continual-ly (with 20-psec resolution) the laser output pulses, whichwere maintained at 100-psec duration by adjustment to thelaser cavity length. The average power from the mode-locked laser was -7 W, corresponding to a peak power of-700 W at the 100-MHz pulse-repetition rate.

Single-mode fiber with a cutoff at 1 Am was used; the fiberwas also non-polarization-preserving with a 7 -Am core diam-eter, 1 dB/km loss, and 35-psec/nm km GVD at 1.06 Atm.Various lengths of fiber were examined: 60,90,120, and 240m.

A 1-m monochromator with an 1800-line/mm grating im-posed the spectral window with a minimum bandpass of 0.1nm, and the throughput radiation was monitored on thesynchroscan streak camera.

By using uncoated 20X microscope objectives a typicaloverall fiber-lens system, throughput efficiency of 50% waspossible.

RESULTS AND DISCUSSION

As is known from previous work,"' 9 24 the time delay be-tween the Stokes and pump pulses is given by

ALD(X)A(vcv

where D(A) is the dispersion in dimensionless units [D(X) =cDX, where D is the dispersion in picoseconds per nanometerkilometer], Av is the frequency separation between Stokesand pump, v is the pump frequency, and AL is the fiberlength. For our case X = 1064 m, v = 9398 cm-', Av = 440cm'1, D(X) = 0.011, and the walk-off distance for a 100-psecpulse is 60 m. The critical power for cw SRS generationdefined by Smith9 at which 50% of the pump radiation isconverted to Raman signal is given by

Pcr = kA/GLeff, (2)

where A is the core area of the fiber, Leff is the effectiveinteraction length, and G is the peak Raman gain, 9.2 X 10-12cm W-' at 1.06 m. The factor k takes into account that thepolarization is not maintained over the fiber length; hencethe gain G is replaced by the average value G2, and k candepend on several fiber parameters, including length, andoverall can lie between 16 and 20. For our fiber parameters,k 20. Stolen and Johnson19 have shown that the theoreti-cal prediction for the critical power for pulsed excitation,although not totally accurate, is relatively well described bythe above equations, agreeing with their experimentally es-tablished results. Substitution of our experimental valuesinto Eq. (2) predicts a critical power of 280 W, which for100-psec pulses corresponds in this case to an average powerof 2.8 W.

c

X:

alC:

.0Li

0ru

-4-CvL_ai

0n

1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4Pump power-average (W)

Fig. 2. Plot of conversion efficiency to Raman versus average power in the various fiber lengths.

40

30

20

10

Gomes et al.

(a)

3.2 nm

E E

E g 0 nm E

Fig. 3. Recorded spectra of (a) pump and (b) Raman (first-Stokes)radiation. The fiber length was 120 m, and the peak power was 200W.

Table 1. Spectral Width of Pump and Raman Pulsesfor the Four Different Fiber Lengths Employeda

Spectral Width (nm)Fiber Length (m) Pump (1.06 ,um) Raman (1.12 ym)

60 1.8 1390 2.4 17

120 3.2 20240 13.8 20

a Peak power was 200 W.

In Fig. 2 the average power in the Raman first-Stokescomponent is plotted as the percentage conversion efficiencyagainst average pump power in the fiber for the various fiberlengths. No curve fitting was applied to the plots of the

experimental points, and the curves drawn were arbitrarilychosen by eye. Threshold peak powers in the 90-,120-, and240-m fibers of 130, 130, and 110 W, respectively, were re-

corded, while in the 60-m fiber a 1% conversion to Ramanwas measured at a peak power of 160 W. For the 60-m fiberat a 2.3-W pump power (the calculated critical peak powernot being achieved), conversion to Raman was 20%, while for

the other fiber lengths at an average power of 2 W (200-Wpeak) the Raman conversion lay between 30-40%, increasingslightly for the longer lengths. As has been described above

and shown by Stolen and Johnson,19 the critical power re-lates to a 50% conversion to Raman signal in the cw case.For pulsed excitation the agreement has been shown to bequite good. For the longest fiber used in this work, viz., 240m, at 2.2-W average power, efficiencies approaching 50%were achieved. For the 60-m fiber at 2.2-W average power,approximately 10% efficiency was recorded. This can beexplained in that the 60-m fiber length is of the order of one

calculated walk-off length for the fiber parameters. Sincethe peak of the Raman signal occurs at the order of two walk-off lengths,19 insufficient length was available in the 60-mfiber to permit optimum Raman conversion to be achieved.

Vol. 5, No. 2/February 1988/J. Opt. Soc. Am. B 375

The fact that 30-40% Raman conversion was possible in the90-, 120-, and 240-m fibers at 2-W average power wouldindicate that the maximum signal generated was > 1.5 timesthe calculated walk-off distance, in reasonable agreementwith the results of Stolen and Johnson.19

Figures 3(a) and 3(b) show typical recorded spectra for thefundamental and first-Stokes beams. They correspond to L- 120 m and P = 200 W peak (thus with a conversionefficiency of -32%). The spectra for all the other fiberlengths were similar, differing only in spectral width for thedifferent fiber length-peak powers employed, and the re-sults are summarized in Table 1. The main spectral fea-tures in the presence of significant Raman generation, prin-cipally the severe depletion of the frequency-downshiftedleading edge of the pump pulse, leading to a distinct asym-metry in the spectra, have been described by several au-thors.

2 12 2 ,2 5

-2 7

In order to measure the chirp across the pulses (bothRaman and fundamental), the spectrograph was used with a

Fig. 4. a, Streak-camera-recorded intensity profile of spectrallywindowed fundamental pulse after propagation through 240 m offiber. Peak power was -100 W. b, As in a, but for Raman depletedpulses at three different wavelengths: 1, 1063.5 nm; 2, 1064 nm; and3, 1064.5 nm. The fiber length was 240 m, and the peak power was200 W.

376 J. Opt. Soc. Am. B/Vol. 5, No. 2/February 1988

240 m

120m90m

20 401.0 TEMPORAL SHIFT (psec)

60

20

30

Fig. 5. Measured chirp of 1.06-ttm pump pulses for the differentfiber lengths employed. The peak power was 200 W, and the centralwavelength was defined to be 1064.5 nm.

bandpass of 0.2 nm (for the measurements near 1.12 jim).The basis for the spectral window mechanism is explained inRef. 6. For a pulse that suffers only the action of SPM(narrowing also occurs in the presence of SPM and GVDeffects), a pulse narrower than the input by a factor of 2.5Xis expected after the spectral window. In Fig. 4a this isshown to be the case for a fiber length of 240 m with a peakpower of -100 W for an input pulse width of 100 psec, wherea 40-psec pulse was recorded after the spectral window.

In the spectral windowing technique, maintaining a fixedbandpass and scanning across the spectrally broadenedpulse profile should keep the temporal width of the trans-mitted signal constant, allowing it to move only in timeaccording to the degree of chirp across the input pulse.This, however, is true only provided that no other nonlinearmechanism is present, i.e., the chirp is assumed to be linearacross the pulse.

At a peak power of 200 W in the 240-m fiber with 37%Raman conversion, the effect of additional nonlinearitythrough the Raman process can be seen through the spectralwindow mechanism; see Fig. 4b. The pulses were recordedat central wavelengths of 1, 1063.5 nm; 2, 1064.0 nm; and 3,1064.5 nm. Clear variations of the recorded pulse widthsindicate a nonlinear chirp. Beyond the region shown in Fig.4b, the streak-camera-recorded temporal pulse profiles inthe frequency-downshifted leading edge of the pump pulse,where Raman depletion is most severe, generally wereshorter, compared with those in the upshifted trailing edgeindicating a greater frequency chirp at the front of the pumppulse. It should be noted that, because of Raman depletionon the long-wavelength side of the induced shift resultingfrom SPM and cross-phase modulation, the correspondingtemporal profiles through the spectral window exhibitedonly two main features (as distinct from three; see Fig. 4a,where Raman generation is minimal) because of suppressionof the longer-wavelength component. By varying the wave-length of the spectral window, we recorded the chirp acrossthe pump pulse for the various fiber lengths, and this isshown in Fig. 5 for the 90-, 120-, and 240-m fibers. Thecentral wavelength was defined as 1064.5 nm, and the peakpower for all cases was fixed at 200 W. In addition, the

experimentally measured wavelength shift AX is plotted, asdistinct from the usually quoted frequency shift Av wherechirp is defined, although Av is proportional to AX.

For the 60-m fiber (the results are not shown in Fig. 5, forclarity) the recorded chirp was effectively linear, -0.02 nm/psec, and did not vary when the pump power was increasedto 230 W peak. Correspondingly, the chirp in the 90- and120-m fibers, assuming linearity, was 0.014 and 0.026 nm/psec, respectively. As can be seen, the chirp in the 240-nm-long fiber was distinctly nonlinear. In addition, it was foundthat the chirp associated with the frequency-downshiftedfront edge of the fundamental pulse exhibited a measurablylarger chirp, 0.029 and 0.048 nm/psec for the 90- and 120-mfibers, respectively. It is most likely that, since quite effi-cient Raman generation significantly modifies the frequen-cy-downshifted rising edge of the pump pulse, reshaping andcross-phase modulation will contribute to the increasedchirp on the pulse's rising edge.

For the 240-m fiber, the discontinuity in the frequency-downshifted region could not be fully resolved; however,such an intense feature has been predicted theoretically2 2 25for the pump radiation in the regime of pulse walk-off andstrong SRS generation.

A similar technique was applied to measure the associatedRaman chirp, which is displayed in Fig. 6. The peak pumppower was 200 W with the exception of the result for 60 m,where 230 W was used. Several interesting features appearthat should be noted. Primarily, the chirp for the Ramansignal is significantly larger than that of the correspondingfundamental pulse, 0.53, 0.21, 0.15, and M0.09 nm/psec (inthe initial approximately linear region) for the 60-, 90-, 120-,and 240-m lengths, respectively. Consequently the chirp ofthe Raman component in the 60-m fiber was approximately25 times that of the fundamental, with this ratio decreasing

-8.0

-6.0

I -4.0W

B- 2.0-i:

-60

0

S

0

0S

4.0

6.0

.0

Fig. 6. Measured chirp of the 1.12-gm Raman (first-Stokes) pulsesfor the different fiber lengths employed. The peak power was 200W except for 60-m fiber, for which it was 230 W. The centralwavelength was defined to be 1119 nn.

-5.0 [-4.0

-3.0

-2.0

-1.0

-60 -40

I,

z" ,

Gomes et al.

Vol. 5, No. 2/February 1988/J. Opt. Soc. Am. B 377

Fig. 7. Effect of spectral window on the Raman pulses, as recordedusing a streak camera, showing the strong nonlinearity of the chirpacross the pulse. The fiber length was 240 m, the peak power was200 W, and the central wavelengths were a, 1111 nm; b, 1120 nm; andc, 1131 nm.

with length to -7 and -3 times for the 90- and 120-m fibers.Significantly greater chirp in the Raman component wasobserved in the visible by Stolen,19 and an increase has beentheoretically predicted by Lugovoi.28 Therefore it can beseen that, in the absence of dominant GVD effects, for thecase of the 60-m fiber, which is approximately the walk-off'distance, the Raman pulse is generated with a chirp manytimes that of the fundamental pump-pulse chirp, which de-creases through propagation.

This behavior can most likely be explained simply interms of GVD. From Table 1 it can be seen that the width ofthe Raman spectra has practically been established at 90 mand that little further broadening takes place and SPMbroadening is not so dominant. Assuming a GVD of -30psec/nm km for a -100-psec Raman pulse for the 240-mfiber gives an approximate broadening to -245 psec for the20-nm spectrally wide pulse. Hence, assuming a totallylinear chirp over the full pulse width, an approximate chirpof -0.08 nm/psec is calculated. Similarly, values for the120- and 90-m fibers are 0.11 and 0.12 nm/psec, respectively,in fair agreement with the experimental values of 0.09, 0.15,and 0.21 nm/psec for the 240-, 120-, and 90-m fibers.

Fig. 8. Streak-camera records of the effect of the GVD on the arrival time of Raman pulses (right-hand side) with respect to the pump pulse(center) for different fiber lengths: a, 60 m; b, 90 m; c, 120 m; and d, 240 m.

Gomes et al.

378 J. Opt. Soc. Am. B/Vol. 5, No. 2/February 1988

It should be noted that the Raman chirp in the 60-m fiberwas measured only over the central 30 psec of the pulse.Theoretical treatments have shown that high gradient chirpfeatures are present in this regime,21 2225 which will decreaseand linearize owing to GVD.

A measurably higher chirp was present on the frequency-downshifted leading edge of the Raman pulses, and in ourregion of detection this was linear for the 60- and 90-mfibers. For the 120- and 240-m fibers deviation from linear-ity was clearly apparent, and this was associated with thedetection of the cascade generation of the second-Stokescomponent at -1.18 m, which tends to deplete the leadingedge of the first-Stokes pump pulse.

The highly nonlinear nature of the first-Stokes Ramanchirp in the presence of GVD effects for the 240-m fiber isapparent from the synchroscan streak-camera recordsshown in Fig. 7, recorded at a peak pump power of 200 W.For a perfectly linear chirp, the spectral window techniqueshould generate pulses of equal duration at different wave-lengths. The measured pulse widths of (Fig. 7a) 101 psec,(Fig. 7b) 64 psec, and (Fig. 7c) 46 psec at 1111, 1120, and 1131nm, respectively, also indicates that the chirp was decreasingwith decreased wavelength.

The spectral windowing technique was also used to mea-sure the temporal separation of the central wavelengths ofthe fundamental and first-Stokes Raman pulses and,through the use of Eq. (1), to estimate the source of theStokes pulse. This was done by a double-exposure methodon the streak camera. First the monochromator was cen-tered at 1064.0 nm and the fundamental pump pulse wasstored. The monochromator was then centered at 1119 nmand the streak stored on top of the original image; hencepump and Raman beams could be temporally displayed si-multaneously.

Figure 8 shows the recorded images for the fiber lengthsexamined. It should be noted that time increases to the lefton the figure. The pulses to the extreme right are the Ra-man pulses, those to the center the central peak of the pumppulse, and those to the left an artifact of the spectral win-dowing, i.e., the trailing-edge component.6 7 Since all pulsesrecorded under different conditions, the time scan of thecamera was not the same for all measurements. The calcu-lated time delays for the fiber parameters are 103, 154, 206,and 412 psec for the 60-, 90-, 120-, and 240-m lengths, re-spectively, and those measured experimentally were 75, 150,212, and 406 psec. Similar to the results of Stolen andJohnson,' 9 these values would indicate [if Eq. (1) were used]that the source of the Raman pulse is just inside the fiberinput face, apart from the case of the 60-m fiber, where it wasmeasured to be about 15 m inside. However, error in thedetermination of the central wavelength of one pulse mayhave led to the discrepancy between the theoretical andexperimental values.

CONCLUSION

Using the spectral windowing technique in association witha synchroscan streak camera, we have measured the associ-ated chirp of the fundamental and Stokes pulses in variouslengths of single-mode optical fiber, covering one to fourwalk-off distances. All pulses exhibited larger chirps ontheir frequency-downshifted leading edges, and deep modu-

lation of the chirp was observed on the fundamental for thelongest fiber lengths. Clear variations of the rate of changeof chirp on the leading edge of the fundamental and first-Stokes pulses for the longer fiber lengths were most likelydue to the generation of the first-Stokes and second-Stokessignals, respectively.

Although the Raman component exhibits a nonlinearchirp, an approximate linearity extends over significantranges, and it may be possible through spectral selection andcompensation with a conventional grating pair to achievepulse compression of spectral regions of the Raman pulses.However, in subsequent measurements we have so far failedto achieve any significant compression.

For the shortest fiber length, for which dispersion was lesssignificant, the Raman pulse was generated with a chirpmany times that of the fundamental pulse, which recenttheoretical considerations 22 25 have shown to be associatedwith pump depletion and GVD.

ACKNOWLEDGMENTS

Funding for this research from the Science and EngineeringResearch Council and British Telecom Research Laborato-ries is gratefully acknowledged. V. L. da Silva wishes tothank the Conselho Nacional de Desenvolvimento e Pes-quisa (Brazilian Agency) for financial support. The au-thors wish to thank D. Schadt, of the Institute of OpticalResearch, Sweden, for making available the preprint of Ref.22.

REFERENCES

1. R. H. Stolen, "Nonlinear properties of optical fibers," in OpticalFiber Telecommunications, S. E. Miller and A. G. Chynoweth,eds. (Academic, New York, 1979), Chap. 5.

2. A. S. L. Gomes, "Picosecond pulse compression and nonlinearprocesses in single mode optical fibres," Ph.D. dissertation(University of London, London, 1986).

3. R. H. Stolen and C. Lin, "Self phase modulation in silica opticalfibers," Phys. Rev. A. 17, 1448-1453 (1978).

4. D. Grischkowsky and A. C. Balant, "Optical pulse compressionbased on enhanced frequency chirp," Appl. Phys. Lett. 41, 1-3(1982).

5. W. J. Tomlinson, R. H. Stolen, and C. V. Shank, "Compressionof optical pulses chirped by self-phase modulation in fibers," J.Opt. Soc. Am. B 1, 139-149 (1984).

6. A. S. L. Gomes, A. S. Gouveia-Neto, J. R. Taylor, H. Avramo-poulos, and G. H. C. New, "Optical pulse narrowing by thespectral windowing of self-phase modulated picosecond pul-ses," Opt. Commun. 59, 399-404 (1986).

7. A. S. L. Gomes, A. S. Gouveia-Neto, and J. R. Taylor, "Directmeasurement of chirped optical pulses with picosecond resolu-tion," Electron. Lett. 22, 41-42 (1986).

8. R. H. Stolen, E. P. Ippen, and A. R. Tynes, "Raman oscillationin glass optical waveguides," Appl. Phys. Lett. 20, 62-64 (1972).

9. R. G. Smith, "Optical power handling capacity of low loss opti-cal fibers as determined by stimulated Raman and Brillouinscattering," Appl. Opt. 11, 2489-2494 (1972).

10. C. Lin, L. G. Cohen, R. H. Stolen, G. W. Tasker, and W. G.French, "New infrared sources in the 1-3.3 ,um region by effi-cient stimulated Raman emission in glass fibers," Opt. Com-mun. 20, 426-428 (1977).

11. L. G. Cohen and C. Lin, "A universal fiber optic (UFO) mea-surement system based on a near-IR fiber Raman laser," IEEEJ. Quantum Electron. QE-14, 855-859 (1978).

12. P. M. W. French, A. S. L. Gonies, A. S. Gouveia-Neto, and J. R.Taylor, "Picosecond stimulated Raman generation, pump pulsefragmentation and fragment compression in single mode opticalfibers," IEEE J. Quantum Electron. QE-22, 2230-2235 (1986).

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13. A. Tomita, "Cross talk caused by stimulated Raman scatteringin single-mode wavelength-division multiplexed systems," Opt.Lett. 8, 412-414 (1983).

14. A. S. L. Gomes, U. Osterberg, W. Sibbett, and J. R. Taylor, "Anexperimental study of the primary parameters that determinethe temporal compression of cw Nd:YAG laser pulses," Opt.Commun. 54, 377-382 (1985).

15. A. Hasegawa, "Amplification and reshaping of optical solitonsin a glass fiber-IV: Use of the stimulated Raman process,"Opt. Lett. 8, 650-652 (1983).

16. A. S. Gouveia-Neto, A. S. L. Gomes, and J. R. Taylor, "High-efficiency single-pass solitonlike compression of Raman radia-tion in an optical fiber near 1.4 ,um," Opt. Lett. 12, 1035-1037(1987).

17. A. S. Gouveia-Neto, A. S. L. Gomes, and J. R. Taylor, "A femto-second soliton Raman ring laser," Electron. Lett. 23, 537-538(1987).

18. J. D. Kafka and T. Baer, "Fiber Raman soliton laser pumped bya Nd:YAG laser," Opt. Lett. 12, 181-183 (1987).

19. R. H. Stolen and A. M. Johnson, "The effects of pulse walk-offon stimulated Raman scattering in fibers," IEEE J. QuantumElectron. QE-22, 2154-2160 (1986).

20. A. M. Johnson, R. H. Stolen, and W. M. Simpson, "The observa-tion of chirped stimulated Raman scattered light in fibers," inUltrafast Phenomena V, G. R. Fleming and A..E. Siegman, eds.,Vol. 46 of Springer Series in Chemical Physics (Springer-Ver-lag, Berlin, 1986), pp. 160-163.

21. D. Schadt, B. Jaskorzynska, and U. Osterberg, "Numerical

study on combined stimulated Raman scattering and self-phasemodulation in optical fibers influenced by walk-off betweenpump and Stokes pulses," J. Opt. Soc. Am. B 3, 1257-1262(1986).

22. D. Schadt and B. Jaskorzynska, "Frequency chirp and spectradue to self-phase modulation and stimulated Raman scatteringinfluenced by pulse walk-off in optical fibers," J. Opt. Soc. Am.B (to be published).

23. M. D. Dawson, A. S. L. Gomes, W. Sibbett, and J. R. Taylor,"Characterisation of the output from a Q-switched/mode lockedcw Nd:YAG laser," Opt. Commun. 52, 295-300 (1984).

24. D. Gloge, "Dispersion in weakly guiding fibers," Appl. Opt. 10,2442-2445 (1971).

25. E. M. Dianov, A. Ya. Karasik, P. G. Mamyshev, A. M. Prok-horov, and V. N. Serkin, "Generation of ultrashort pulses byspectral filtering during stimulated Raman scattering in an op-tical fiber," Sov. Phys. JETP 62, 448-455 (1985).

26. A. S. L. Gomes, W. Sibbett, and J. R. Taylor, "Spectral andtemporal study of picosecond-pulse propagation in a singlemode optical fiber," Appl. Phys. B 39, 43-46 (1986).

27. A. M. Weiner, J. P. Heritage, and R. H. Stolen, "Effect ofstimulated Raman scattering and pulse walk off on self phasemodulation in fibers," in Digest of Conference on Lasers andElectro-Optics (Optical Society of America, Washington, D.C.,1986), paper ThC4.

28. V. N. Lugovoi, "Stimulated Raman emission and frequencyscanning in an optical waveguide," Sov. Phys. JETP 44,683-689(1976).

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380 J. Opt. Soc. Am. B/Vol. 5, No. 2/February 1988

V. L. da SilvaA. S. L. Gomes was born in Recife, Bra-zil, on December 2, 1956. He receivedthe B.Sc. degree in physics from the Uni-

ml a versidade Federal de Pernambuco, Bra--. zil, in 1978. He received the M.Sc. de-

gree in physics in 1982 after working onlaser-induced energy transfer in solids

, and gases using N2- and Nd:YAG-'i pumped dye lasers. In 1986 he obtained

the Ph.D. degree from Imperial College,London, working on picosecond pulsecompression and nonlinearities in opti-cal fibers. In 1987 he conducted re-

search in picosecond/femtosecond studies of nonlinearities in opti-cal fibers, including soliton propagation, while still at Imperial Col-lege. He is now a visiting professor in the physics department of theUniversidade Federal de Pernambuco, where he is working on coop-erative effects between ions in solids and glasses and applications ofultrashort pulses in solid-state spectroscopy and nonlinear effects inoptical fibers. Dr. Gomes is a member of the Optical Society ofAmerica.

J. R. Taylor

..I.7