Pulse generation and propagation beyond the limit of soliton spectral resonances

Pulse generation and propagation beyond the limit of soliton spectral resonances
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  15 January 1998 Ž . Optics Communications 146 1998 241–244 Pulse generation and propagation beyond the limitof soliton spectral resonances I. Cristiani  a , P. Franco  b , M. Midrio  c , M. Romagnoli  d, ) a  Dipartimento di Elettronica, Uni Õ ersita di Pa Õ ia,  Õ ia Ferrata 1, I-27100 Pa Õ ia, Italy ` b Pirelli Ca Õ i s.p.a.,  Õ iale Sarca 222, I-20146 Milan, Italy c  Dipartimento di Elettronica e Informatica, Uni Õ ersita di Pado Õ a,  Õ ia Gradenigo 6  r  A, I-35131 Pado Õ a, Italy ` d Fondazione Ugo Bordoni,  Õ ia B. Castiglione 59, I-00142 Rome, Italy Received 2 May 1997; revised 3 September 1997; accepted 3 September 1997 Abstract We show the generation and propagation of picosecond solitons in a bidirectionally Raman-pumped fiber laser made of 25 or even 50 km of step-index fiber. As long as the loop length to soliton period ratio is greater than 8 but not a multiple of it, we demonstrate dynamical and stable propagation beyond the soliton spectral resonance limit.  q 1998 Elsevier ScienceB.V. PACS:  42.55.y; 42.55.w; 42.81.d. Keywords:  Stimulated Raman scattering; Fiber solitons; Raman lasers One of the most relevant problems in soliton lasers andin periodically amplified transmission systems arises fromthe coupling of the soliton to the continuum of radiation w x 1,2 . This mechanism, that becomes more efficient when-ever the pulse dispersion length is comparable to thelength of the periodical perturbation, leads to an extra lossin terms of dispersive waves that imposes a limit to thegeneration of ultrashort pulses in fiber lasers and enhances w x soliton–soliton interactions 3 . Since the strength of theeffect depends on the energy variation in each amplified w x span 1,4 , one way to reduce the size of this variationconsists in distributing the amplification.Raman amplification is a good practical way to dis- w x tribute the gain in each amplification stage 5,6 . Neverthe-less the Raman pump attenuation upon propagation stillcauses a small but not negligible evolution of the solitonparameters. In the bidirectional pumping configuration,that has the peculiarity to be symmetric, the adiabaticevolution of short solitons even permits the restoration of  ) Corresponding author. E-mail: romag@fub.it. both width and amplitude at the end of each amplificationstage. Contrarily to the sudden amplification occurring inthe lumped systems that deviates the pulse parametersfrom those typical of solitons, in this case the emission of radiation is uniquely due to the alternance of temporalbroadening and narrowing with the spatial period of oneamplification stage. Hereafter we are going to discuss thisexperimental configuration where the continuum generatedby the periodic energy variation does not fulfil the phasematching condition for the organization of the spectralsidebands corresponding to the soliton resonances with theamplication chain. This is achieved by selecting a loop 1  2 Ž . length, say  z  km , to soliton period  z  s  p t   r  b  a 0 o 2 2 Ž . km ratio,  Z   , small enough to rule out the phase match- a ing condition for at least the lower-order spectral side-bands. This condition can be expressed as follows8  N  y 1  -  Z   - 8  N  , 1 Ž . Ž . a Ž . where the integer  N   G 2 stands for the order of the w x spectral sidebands 2 . In this framework where the soliton 0030-4018 r 98 r $19.00 q  1998 Elsevier Science B.V. All rights reserved. Ž . PII   S0030-4018 97 00517-8  ( ) I. Cristiani et al. r Optics Communications 146 1998 241–244 242 Ž . propagation is dynamical condition 1 predicts also the Ž . allowed pulsewidths  T   s 1.763 t   margins, fwhm o2  z  b   1  T z  b   1 a 2 fwhm a 2 - -  , 2 Ž . ž / 4 p  N   1.763 4 p  N  y 1 w x generalizing then the conclusion drawn in Ref. 6 that far Ž away from the soliton resonance condition  Z   f 0 or vice a . versa  Z  ™ `  the soliton area is preserved upon propaga- a tion. Ž . In order to demonstrate the condition 1 we built thefiber loop schematically shown in Fig. 1. The main part of the loop was alternatively a span of 25 or 50 km long Ž  2 . step-index fiber  b   sy 20 ps  r km . The 0.25 dB r km 2 loss of the fiber was compensated for by bidirectionalRaman amplification. We pumped the long span of step-in-dex fiber with a pair of polarization multiplexed diodelasers on both sides. The cavity coupled power of eachsource was 100 mW and the emission wavelength 1480nm. The Raman gain achieved at 1565 nm was 6 or 8 dBdepending on which span of step-index fiber we used. Thefiber laser has been either actively or passively mode-locked. The active modulation was performed by a I-OMach-Zhender modulator with an insertion loss of 5 dB,whereas the passive modulation was achieved with anall-fiber polarization splitter with 1 dB of insertion loss.The mechanism of passive mode-locking relies on theprocess of nonlinear polarization rotation occurring duringpulse propagation in the loop followed by the polarizationanalysis performed at the end of the round trip by thepolarization beam splitter. Since the gain provided by theRaman pumps was barely sufficient to compensate for thelosses of the long span of step-index fiber, the lumpedlosses introduced by both the 3 dB output couplers and bythe other intracavity components were compensated for by Ž . an erbium-doped fiber amplifier EDFA with low outputsaturated power. An important aspect of the long loopunder investigation is that the cold cavity losses lead to acoherence length that is shorter than the loop length itself.This is confirmed by the few beat notes observed at the rf  Fig. 1. Experimental set-up of the bidirectionally Raman-pumpedsoliton fiber laser. Ž . Fig. 2. Single scan second harmonic SH autocorrelation trace of the generated pulse. In this figure the average over many round-trips demonstrates the regular repetition of the soliton propagatingin the long loop. The real time window of our autocorrelator was5 ms, the transit time in the loop was 0.125 ms. The 40 regularperiods of modulation shown for each time scan prove the stabil-ity upon propagation of 1 Mm. Longer observations show that thesame autocorrelator trace is regular for several minutes. spectrum analyzer. Nevertheless, whenever the radiationcirculating in the loop was modulated, we observed in thetime domain either a sinusoidal background that gave riseto the rf beat notes and a spike superimposed on it. Thespike corresponded to the optical soliton traveling insidethe loop. The time position of the spike was checked withan optical sampling oscilloscope with a sampling intervalof 2.5 ps. This observation evidenced a large timingfluctuation of the short pulse that on one hand permitted toexplain the lack of beat notes in the rf spectrum, and onthe other hand demonstrated that in such long loops thefree propagation prevails over the usual organization of theintracavity radiation in longitudinal modes. A direct conse-quence of this is that the observed short pulses are notstationary states of the system, i.e. in this condition and asexpected from the lack of rf beat notes the pulses couldgrow and disappear in a short as in a long time period. Wetherefore checked the stability of the short pulse propaga-tion. This was done on the pulse generated by an activelymode-locked loop 25 km long. In this experimental setupthe loop transit time was 0.125 ms, and we verified on thesingle scan autocorrelation trace a regular periodicity cor-responding to the transit time. This measurement is re-ported in Fig. 2, where the recorded 40 equal intervalscorrespond to 1 Mm of stable propagation of the soliton. Ingeneral this regular behaviour was observed for severalminutes, so we may claim that although this loop is aquasi-laser, the generated dynamical soliton persists overthousands of round trips.The autocorrelation trace and spectrum of the solitongenerated in the actively mode-locked setup are reported in  ( ) I. Cristiani et al. r Optics Communications 146 1998 241–244  243 Ž . Fig. 3. Autocorrelation trace and spectrum of the generated soliton of 6 ps  Z   s 55 generated by the actively mode-locked loop 50 km long a Ž . Ž . Ž . a , and 2.8 ps  Z   s 126.2 in the passively mode-locked loop 25 km long b . a Fig. 3a. Here the loop was 50 km long and the observed Ž pulsewidth 6 ps corresponding to  N  s 7 or 48 -  Z   - 56 a Ž .. in Eq. 1 . With the same setup we also observed 8.8 ps Ž Ž ..  N  s 4 or 24 -  Z   - 32 in Eq. 1 . These results demon- a strate that the fiber laser, in order to operate, sponta-neously selects a soliton period to amplifier spacing ratioto rule out the lower-order spectral sidebands. We per-formed several other experiments with the span of 25 kmlong step-index fiber either in the active or passive mode-locking configuration. An example of autocorrelation traceand optical spectrum is reported in Fig. 3b. Here the loopwas passively mode-locked and the resulting pulsewidth Ž Ž .. was 2.8 ps  N  s 16 or 120 -  Z   - 128 in Eq. 1 . a The measured pulsewidths,  T   , obtained in our ex- fwhm periments are summarized in Fig. 4. Here the number of  Ž soliton periods within one loop length  Z   in the left-hand a . Ž axis and eight times the soliton sideband order  N   see . right-hand axis are plotted against the pulsewidths,  T   , fwhm the horizontal lines indicate the condition for exact match-ing of the soliton phase with the spatial periodicity of thepropagation system. This figure shows that, independentlyof the length of the loop or of the mode-locking scheme,the generated pulses always rule out the phase matchingcondition for the generation of the first set of sidebands Ž .  N  s 1 , and also demonstrates that soliton propagationmay occur in between two adjacent soliton resonances, in Fig. 4. Plot of the number of soliton periods within one looplength compared to eight times the soliton sideband order  N  , bothas a function of the measured pulsewidths.  ( ) I. Cristiani et al. r Optics Communications 146 1998 241–244 244Fig. 5. Simulation of the propagation in the bidirectionally Raman pumped laser. The parameters of the amplified span are the same as those Ž . Ž . Ž . Ž . of the experiment, the input soliton widths are: a  T   s 17.6 ps  Z   s 20 r p  , b  T   s 12.5 ps  Z   s 40 r p  . fwhm a fwhm a Ž . agreement with condition 1 . As also expected, we can ' note in Fig. 4 a 2 reduction factor in the measured Ž . pulsewidth from the 25 km long loop left curve incomparison to the configuration where the loop was twice Ž . longer right curve .In order to clarify the improvement obtained by rulingout the spectral sideband we show in Fig. 5 the unstablepropagation over amplified spans 50 km long of a soliton Ž . T   s 17.6 ps,  Z   s 20 r p  , undergoing a spectral reso- fwhm a Ž nance, compared to the stable one  T   s 12.5 ps,  Z   s fwhm a . Ž . 40 r p  satisfying condition 1 for  N  s 2. In the specificcase of bidirectional Raman amplification the most strikingeffect is obtained when at least the lowest-order sidebandsare ruled out. This advantage exists whenever the gain andloss functions are distributed, because the lowest-ordersinusoidal component of the Fourier expansion largelyprevails over the others.As shown by the experimental results and confirmed bythe simulations, we draw the conclusion that the stabilityof the soliton upon propagation dramatically improves assoon as the width rules out the phase matching for thegrowth of the spectral sidebands. This demonstration has astraightforward application in the design of ultra highcapacity transmission systems. Acknowledgements The work of MR was carried under in the framework of the agreement between the Italian Post and Telecommuni-cations Administration and Fondazione Ugo Bordoni. References w x  Ž . 1 J.P. Gordon, J. Opt. Soc. Am. B 9 1992 91. w x  Ž . 2 S.M. Kelly, Electron. Lett. 28 1992 806. w x 3 H.A. Haus, F.I. Kathri, W.S. Wong, E.P. Ippen, J. Quantum Ž . Electron. QE-32 1996 917. w x 4 M. Midrio, M. Romagnoli, S. Wabnitz, P. Franco, Optics Lett. Ž . 21 1996 1351. w x  Ž . 5 A. Hasegawa, Appl. Optics 23 1984 3302. w x 6 L.F. Mollenauer, J.P. Gordon, M.N. Islam, IEEE J. Quantum Ž . Electron. QE-22 1986 157.

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