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Femtosecond harmonically mode-locked fiber laser with time jitter
January 15, 1995 / Vol. 20, No. 2 / OPTICS LETTERS 189 Femtosecond harmonically mode-locked fiber laserâ¨with time jitter below 1 ps S. Gray, A. B. Grudinin, W. H. Loh, and D. N. Payne Optoelectronics Research Centre, Southampton University, Southampton SOl7 1BJ, UK Received May 24, 1994 We have made an experimental study of the time jitter in a harmonic passively mode-locked fiber soliton ringâ¨laser. We demonstrate that jitter as low as 600 fs (100-550 Hz), which is less than the soliton pulse width, canâ¨be achieved at a repetition frequency of 463 MHz. The results support the suggestion that the stability of theâ¨laser is dependent on the long-range soliton interaction through the excitation of acoustic waves that is inducedâ¨by the propagating pulses. The time jitter was measured by analysis of the rfâ¨spectrum of the laser output intensity.7 Generallyâ¨this spectrum consists of a main peak sitting onâ¨a broadband pedestal. Knowing the intensity andâ¨bandwidth of the pedestal, one can deduce theâ¨time jitter of the laser.7 Figure 2 shows the jitterâ¨measured as a function of the pulse repetitionâ¨rate for a laser cavity fundamental frequency of Passively mode-locked fiber soliton lasers are attracÂ¬â¨tive optical short-pulse sources for laboratory andâ¨telecommunications applications by virtue of variousâ¨appealing properties such as their simplicity of conÂ¬â¨struction, tunability, and subpicosecond operation.â¨The energy quantization effect1 caused by the solitonâ¨regime of operation of fiber soliton lasers results inâ¨excellent stability of the duration and energy of theâ¨individual pulses, but it also leads to pulse-repetition-â¨rate instabilities that for many applications are unÂ¬â¨acceptable. One solution is to operate the laserâ¨with just a single pulse circulating inside the cavÂ¬â¨ity, but this generally leads to low repetition ratesâ¨(â5 MHz) and correspondingly low average outputâ¨powers, unless short cavities of a few meters are used.â¨Other techniques involving additional subcavities,2â¨extracavity feedback,3 or intracavity modulation4â¨have been demonstrated, permitting higher-harmonicâ¨mode locking, but these techniques would appear toâ¨be difficult to implement in a practical system. Recently we experimentally demonstrated that, unÂ¬â¨der certain conditions, stable passive harmonic modeâ¨locking occurs in a ring laser configuration,5 andâ¨it was postulated that the so-called long-range soliÂ¬â¨ton interaction effect6 is responsible for such passiveâ¨repetition-rate self-stabilization. In this Letter we present an investigation of thisâ¨effect and demonstrate that time jitter as low asâ¨600 fs (over the 100-500-Hz range) can be obtainedâ¨at a repetition rate as high as 463 MHz in a fullyâ¨passive mode-locked ring configuration. The laser configuration used in our experimentsâ¨is shown in Fig. 1 and is similar to that deÂ¬â¨scribed elsewhere.5 It consists of 4 m of Er/Ybâ¨codoped fiber, a length of standard telecom fiber,â¨a polarization-sensitive isolator, and two sets of poÂ¬â¨larization controllers. The laser was pumped by aâ¨conventional Nd:YAG laser at 1064 nm. To reduceâ¨pump power amplitude noise, we used an externalâ¨feedback loop that permitted us to keep pump powerâ¨fluctuations to below 1%. Mode locking of the laserâ¨was achieved by adjustment of the polarization conÂ¬â¨trollers, and at certain positions of the polarizationâ¨controllers a harmonic passively mode-locked regimeâ¨was observed. By changing the pump power we wereâ¨able to change the repetition rate of the laser.5 5.78 MHz and pulse width of 0.8 ps (FWHM). The figure shows a strong oscillatory behavior andâ¨a general tendency for the jitter to decrease atâ¨frequencies near 500 MHz. The lowest jitter ofâ¨1.1 ps (100-550 Hz) was observed at the frequencyâ¨of 526 MHz. A similar oscillatory dependence (withâ¨maxima at the same frequencies) was observed whenâ¨the pump power feedback loop was switched off,â¨but the lowest time jitter was then â10 ps. Noteâ¨also that we obtained the same general behaviorâ¨for several different cavity lengths as well. By changing the length of the laser cavity we wereâ¨able to study the jitter for different pulse widths and 'â¨observed that the shorter the pulses, the lower theâ¨time jitter. The lowest jitter of 600 fs (100-550 Hz)â¨was obtained for 0.7-ps pulses at a repetition rate ofâ¨463 MHz in a laser cavity with a fundamental freÂ¬â¨quency of 11.0 MHz (zc = 18 m). The third-order rfâ¨spectrum at 1388 MHz is shown in Fig. 3. The raÂ¬â¨tio of jitter to pulse separation is 3 X 10~4. Furtherâ¨reduction of the cavity length did not result in an imÂ¬â¨provement of the time jitter, but at a rather shortâ¨cavity length (zc = 8.6 m) we found that the laserâ¨tends to operate at the same harmonic frequencyâ¨of 139 MHz in a very broad range of pump power;â¨i.e., the change of pump power level simply caused Pumpâ¨stabilizationâ¨circuit _ Pumpâ¨1064nm O â QS- pc WDM Isolator/â¨polarizer Standardâ¨telecom Er/Ybâ¨codoped fiber fiber 50:50â¨coupler Â°n PCU xz Output Fig. 1. Experimental configuration. WDM, wavelength-â¨division multiplexer; PC's, polarization controllers. I 0146-9592/95/020189-03$6.00/0 Â© 1995 Optical Society of America OPTICS LETTERS / Vol. 20, No. 2 / January 15, 1995 190 20 ation. As was shown recently,6 each soliton excitesâ¨a weak transverse acoustic wave, which causes aâ¨change of the refractive index. In accordance withâ¨the theory, each 0.7 soliton in the standard teleÂ¬â¨com fiber directly perturbs the refractive index byâ¨Sraac â 10-11. In addition, however, the cylindriÂ¬â¨cal structure of the fiber can act as a resonator forâ¨acoustic waves excited at the appropriate eigenfre-â¨quencies. The relevant eigenfrequencies show up asâ¨a series of peaks in the acoustic response spectrumâ¨that are separated by ~50 MHz, with a maximumâ¨near 500 MHz.6 The refractive-index perturbationâ¨is thus considerably enhanced when the waves areâ¨periodically excited at these frequencies. The enÂ¬â¨hancement factor can be estimated from a simpleâ¨model of a resonantly driven damped harmonic osÂ¬â¨cillator and is of the order of tJT, where rd is theâ¨damping constant of the oscillator and T is the resoÂ¬â¨nant (driving) period. Since rd and T are of the orderâ¨of microseconds13 and nanoseconds, respectively, theâ¨index change is thus increased by a factor of 103 atâ¨resonant frequencies near 500 MHz. (Our recentâ¨measurements of the acoustic phase indicate thatâ¨the refractive-index change at these resonant acousÂ¬â¨tic frequencies is in the range of 10-8-10"7.) Thusâ¨the soliton stream imposes a significant phase modÂ¬â¨ulation on itself, and in the steady-state regimeâ¨each soliton is trapped by the acoustic field of itsâ¨predecessor. The oscillatory nature of the measured time jitÂ¬â¨ter in Fig. 2 fits well with the above picture. Noteâ¨that the frequency separation between minima in theâ¨time-jitter dependence is also close to 50 MHz andâ¨that the jitter is lowest near 500 MHz, indicatingâ¨that the mode-locked laser is most strongly stabilizedâ¨when the mode-locking frequency coincides with oneâ¨of the acoustic resonant frequencies, and thus the inÂ¬â¨duced phase modulation is enhanced. Variations inâ¨the 50-MHz separation may be accounted for by theâ¨excitation of different types of acoustic wave, and theâ¨decrease of jitter with pulse width, as observed previÂ¬â¨ously, is the result of stronger refractive-index perturÂ¬â¨bation, which is proportional to the soliton energy.6 Knowing the change of the refractive index inducedâ¨by the acoustic waves, we can estimate the time jitÂ¬â¨ter by using perturbation theory for the distributedâ¨model, based on solution of the nonlinear Schrodinger 15 - T a Jjio . ! "5 5 - * 0 100 200 300 400 500 600 700 Frequency (MHz) Fig. 2. Time jitter as a function of repetition frequencyâ¨for a total cavity length of 35 m. a change in the fraction of the nonsoliton compoÂ¬â¨nent without breaking up the harmonic mode lockÂ¬â¨ing. Note, however, that for such a short cavity theâ¨. length of the codoped fiber, which has a low disperÂ¬â¨sion, is now comparable with the length of standardâ¨telecom fiber. This results in a reduction of the netâ¨intracavity dispersion and consequently in a decreaseâ¨of the pulse energy, which, as will be mentioned beÂ¬â¨low, is a key parameter for the self-stabilization. There are several sources of time jitter in mode-â¨locked lasers: pump power fluctuations, variousâ¨thermal effects, and noise of the laser gain medium.8â¨However, a harmonically mode-locked fiber laser hasâ¨an additional source of time jitter owing to unconÂ¬â¨trolled changes of adjacent pulse temporal positions,â¨and hence the jitter is significantly stronger than thatâ¨which occurs in lasers operating at the fundamentalâ¨frequency. In this sense a fiber soliton laser operatÂ¬â¨ing in the harmonically mode-locked regime is similarâ¨to a soliton transmission system; i.e., a soliton streamâ¨in a fiber laser experiences periodic gain and loss andâ¨suffers from the same sources of time jitter, includingâ¨the Gordon-Haus effect9 and soliton-soliton interÂ¬â¨action. Extensive studies of soliton transmissionâ¨systems that have been performed in the past sevÂ¬â¨eral years (see, for example, Ref. 10 and referencesâ¨therein) revealed that in order to maintain the soliÂ¬â¨ton stream intact over unlimited distances one hasâ¨to incorporate into the transmission line spectral filÂ¬â¨tering and synchronous modulation. The existenceâ¨of just one component (either filter or modulator)â¨results in only a partial reduction of instability,10â¨whereas phase modulators have been shown to beâ¨able to suppress Gordon-Haus jitter with minimalâ¨generation of dispersive wave components.11 ThereÂ¬â¨fore a stable steady-state regime of operation for aâ¨harmonically mode-locked fiber soliton laser needsâ¨spectral filtering and synchronous modulation. In the present laser configuration (see Fig. 1) it isâ¨easy to find a spectral filter; the laser gain curveâ¨acts as a natural spectral filter with a bandwidth ofâ¨â35 nm.12 The synchronous modulation action is provided byâ¨the solitons themselves through acoustic wave gener- -20 ? Â£ "40 3 | -60â¨o t -80 0. -100 - 1.388,430 1.388,431â¨Frequency (GHz) 1.388,432 Fig. 3. Third-order rf spectrum for a repetition freÂ¬â¨quency of 463 MHz and a cavity length of 18 m, indicating 600-fs (100-550-Hz) jitter. January 15, 1995 / Vol. 20, No. 2 / OPTICS LETTERS 191 For our case 0ac = 0.33 rad, = 2.3, T = 3 x 103,â¨Clf = 10, G2 = 5, and N0 = 3 X 108, which gives usâ¨or = 0.4, or 160 fs in physical units, in reasonablyâ¨good agreement with the experimental results. In conclusion, we have experimentally studied aâ¨harmonically mode-locked fiber soliton laser andâ¨demonstrated that time jitter as low as 600 fs, whichâ¨is less than the pulse width, can be obtained at a repeÂ¬â¨tition rate of 463 MHz. Time-jitter dependence withâ¨the laser repetition rate has revealed oscillatory beÂ¬â¨havior with a characteristic period of ~50 MHz and aâ¨tendency for the time jitter to decrease with the pulseâ¨width. The experimental results are consistent withâ¨the suggestion of a passive self-stabilization effectâ¨driven by transverse acoustic wave excitation owingâ¨to electrostriction. Theoretical estimates are in goodâ¨agreement with experimental results. The authors gratefully acknowledge the useful reÂ¬â¨marks of the anonymous referees regarding the freÂ¬â¨quency response of the self-induced acoustic phaseâ¨modulation. equation (NSE). In the case of a passively mode-â¨locked fiber laser the NSE can be written in the form + (</>ac - yr2)i/> + ia\<I)\24> + S(z) (1) where the left-hand side is the unperturbed NSE;â¨the first term in the right-hand side describes theâ¨laser gain, the second term stands for the intracav-â¨ity laser filter, and the third term describes the acÂ¬â¨tion of the acoustic phase modulation, where <f>M =â¨2tt/ ASnaczd, y = 4>ac$c2/T2, <fc = zjzd, zd is the disÂ¬â¨persion length, and T is the time interval betweenâ¨pulses normalized to the soliton pulse width. Theâ¨fourth term represents mode locking by means of aâ¨fast saturable absorber, and S(z) is the noise sourceâ¨from the laser amplifier. In the model, we haveâ¨made an assumption that the time jitter is much lessâ¨than the pulse period, and therefore we consider T asâ¨a constant parameter. Note also that, in our case,â¨the dimensionless cavity length Â£c = 2.3, and thereÂ¬â¨fore a distributed model simply gives us an estimateâ¨of the time jitter. Applying perturbation theory for the NSE14 andâ¨taking the solution of the unperturbed NSE as References 1. A. B. Grudinin, D. J. Richardson, and D. N. Payne, Electron. Lett. 28, 67 (1992). 2. E. Youshida, Y. Kimura, and M. Nakazawa, Appl.â¨Phys. Lett. 60, 932 (1992). 3. M. L. Dennis and I. N. Duling III, Electron. Lett.â¨28, 1894 (1992). i/f(z,r) = rj sech rj(r â rJexpftQr â </>], (2) we can obtain the equation for the soliton temporalâ¨position rc in the steady-state regime (17 â 1): 4. I. Y. Khrushchev, D. J. Richardson, and E. M. Dianov,â¨in Proceedings of the Nineteenth European Conferenceâ¨on Optical Communications (Convention of Nationalâ¨Societies of Electrical Engineers of Western Europe,â¨Montreux, Switzerland, 1993), p. 33. 5. A. B. Grudinin, D. J. Richardson, and D. N. Payne, d2rc(z) 4/3 drc(z)â¨dz2 3 dz + 2yrc(z) = Sn(z). (3) Here we assume that the noise impact on the solitonâ¨temporal position is driven by the soliton frequencyâ¨fluctuations. The noise correlation function is9 Electron. Lett. 29, 1860 (1993). 6. A. N. Pilipetskii, A. V. Luchnikov, and A. M. Prokhorov, Sov. Lightwave Commun. 3, 29 (1993). 7. D. von der Linde, Appl. Phys. B 39, 201 (1985). 8. H. A. Haus and A. Mecozzi, IEEE J. Quantum Elec- (G2 - 1) (Sn(z)Sn(z')> = S(z ~ z') = S(z - z')No tron. 29, 983 (1993). 9. J. P. Gordon and H. A. Haus, Opt. Lett. 11, (1986). 10. A. Mecozzi, J. D. Moores, H. A. Haus, and Y. Lai, J.â¨Opt. Soc. Am. B 9, 1350 (1992). 11. N. J. Smith, K. J. Blow, W. J. Firth, and K. Smith, in 3N0Â£c (4) where N0 â WJhu is the number of photons per unitâ¨energy and Ws is the soliton energy. Taking the Fourier transform of Eq. (3) and solvingâ¨the equation in the spatial frequency domain k, weâ¨arrive at the expression for the rms time jitter (z âÂ» Nonlinear Guided-Wave Phenomena, Vol. 15 of 1993â¨OSA Technical Digest Series (Optical Society of AmerÂ¬ ica, Washington, D.C., 1993), p. 363. 12. J. E. Townsend, W. L. Barnes, K. P. Jedrzeijewski, and S. G. Grubb, Electron. Lett. 27, 1958 (1991).â¨13. R. M. Shelby, M. D. Levenson, and P. W. Bayer, Phys.â¨Rev. B 31, 5244 (1985). 3Nn _ (G2 - i)r2iy r +90 = <|rc(,fe)|2>d& = J âx 14. A. Bondeson, M. Lisak, and D. Anderson, Phys. Scr. <tt2 20, 479 (1979). 32/V0</>acÂ£c2 ' 2/3y (5) where /3 = 2/(Cl2^c) and is the dimensionlessâ¨filter bandwidth.
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