A recent invited paper (Tang et al., 2014) reports the experimental observation of the generation of stable
pulse trains in a ring fiber laser with repetition rates varying in the range between 3 GHz and 285 GHz.
Contrary to what is stated, the theory published in that invited paper does not support the claim that the
generation mechanism of the pulse train is the cavity induced modulation instability effect

WABNITZ, Stefan

Archivio istituzionale della ricerca - Università di Brescia

Optical Fiber Technology 25 (2015) 13–14Contents lists available at ScienceDirectOptical Fiber Technologywww.elsevier .com/locate /yof teRegular ArticlesComment on ‘‘GHz pulse train generation in ﬁber lasers by cavityinduced modulation instability’’http://dx.doi.org/10.1016/j.yofte.2015.05.0131068-5200/ 2015 Elsevier Inc. All rights reserved.⇑ Fax: +39 030380014.E-mail address: stefan.wabnitz@unibs.itStefan Wabnitz ⇑Dipartimento di Ingegneria dell’Informazione, Università degli Studi di Brescia, via Branze 38, 25123 Brescia, Italya r t i c l e i n f oArticle history:Received 13 December 2014Revised 22 May 2015Available online 13 July 2015Keywords:Mode-locked lasersUltrafast ﬁber laserModulation instabilityNonlinear ﬁber opticsa b s t r a c tA recent invited paper (Tang et al., 2014) reports the experimental observation of the generation of stablepulse trains in a ring ﬁber laser with repetition rates varying in the range between 3 GHz and 285 GHz.Contrary to what is stated, the theory published in that invited paper does not support the claim that thegeneration mechanism of the pulse train is the cavity induced modulation instability effect. 2015 Elsevier Inc. All rights reserved.In a recent invited paper [1], Tang et al. describe a ﬁber ring lasercomprising an erbium doped ﬁber pumped by a 1480 nm, highpower Raman ﬁber laser, a span of standard single mode ﬁber, apolarization controller (PC) and a polarization-independentisolator. The average cavity dispersion is anomalous and equal toabout 3.3 ps/nm/km. By increasing the pump power above200 mW, and by suitably adjusting the intracavity PC, the cwmodeof operation of the laser became unstable, and break-up of the cwemission into a train of sub-picosecond pulses with repetition ratescontinuously varying in the range between 3 GHz [see Fig. 3(a) ofRef. [1]] and 32 GHz [see Fig. 4(a) of Ref. [1]], depending on thePC waveplates orientation, was observed. On the other hand, for agiven PC conﬁguration and by increasing the pump power up to2 W, the repetition rate of the generated pulse train increased upto about 285 GHz [see Fig. 5(a) of Ref. [1]]. Clearly, the particularsetting of the intracavity PC determines the net cavity birefringenceof the ﬁber laser. The cavity birefringence of their ﬁber laserwas notestimated nor measured by Tang et al.; however they have statedon page 612 of Ref. [1] that the linear birefringence of the cavityis somehow related to the cavity detuning, although this relation-ship is never expressed in explicit form. In fact, in describing theirpulse train generation experiments, Tang et al. use the term ‘‘cavitydetuning’’ as being equivalent to ‘‘cavity birefringence’’.Based on the observation that the observed pulse repetition ratedepends on ‘‘cavity birefringence’’, and on their hypothesis that‘‘cavity birefringence’’ is equivalent to ‘‘cavity detuning’’, Tanget al. claim that the explanation of their experiments is based onthe cavity modulation instability effect which was described inRefs. [2–4]. In fact, the ‘‘Theoretical description’’ section of Ref.[1] repeats the analysis of the modulational instability that isinduced by cavity boundary conditions in a cw pumped, passivenonlinear cavity that was presented in Ref. [2] (see also the originalRef. [5] for the formally identical transverse instability).However the laser cavity that was described in Ref. [2] isfundamentally different from the ﬁber ring laser presented in Ref.[1]. As a matter of fact, Ref. [2] describes a passive ﬁber ring cavitypumped by an external cw laser beam. In that situation, the cw ﬁeldbuilds up in the cavity (of length L and with linear refractive indexn, possibly including an intensity dependent contribution) at thesame frequency of the external pump laser, say, x0, until a steadyintracavity power level is reached. Remarkably, the pump laserfrequencyx0 does not need to exactlymatch a particular resonanceor longitudinal mode of the passive ﬁber cavity, say, xR [2–4]. Thisleads to a nonzero cavity detuning d = (xR x0)tR between thelinear phase delay at the pump laser frequencyx0tR =x0nL/c (equalto w0 in the notation of Ref. [1], see Eq. (2)], and the linear phasedelay at a nearby cavity resonance frequency xR, namelyxRtR = 2 mp, with integer m. To the contrary, in a ﬁber ring laserwith no externally injected pump beam, such as the laser that isdiscussed in Ref. [1], the cw ﬁeld is necessarily locked at a givencavity frequencyxR, as it is well known from basic laser theory [6].Therefore the linear phase delay w0 in the case of the laserdescribed in Ref. [1] is a ﬁxed quantity, and not a free parameterthat can be arbitrarily varied as in the examples provided inFig. 1 of Ref. [1]. Indeed, no control of the cavity phase detuningis possible in the laser of Ref. [1], contrary to the claims by itsAuthors.14 S. Wabnitz / Optical Fiber Technology 25 (2015) 13–14Coming back to the other claim by the Authors of Ref. [1],namely that the cavity detuning of their laser can be controlledby varying the cavity birefringence, it is well known that byvarying the net cavity birefringence one may shift the cavity reso-nance, but it is not possible to drive the cw laser out of resonance.As far as the possible explanation of the wide range of variationof the observed modulational instability frequency as a function ofthe cavity birefringence, we may suggest the modulationalpolarization instability effect [7], which is known to have a gainthat extends all the way down to zero modulation frequenciesfor sufﬁciently low net birefringence, and whenever the fast axisof the ﬁber is pumped. Moreover, it is well known thatself-pulsations and mode-locking may occur in ring ﬁber lasersvia the mechanism of dissipative four-wave mixing [8],independently of the presence (or lack thereof) of modulationinstability [9]. Therefore, for a proper interpretation of theexperimental results of Ref. [1], it might be suitable to develop avector theory of dissipative four-wave mixing, including the actionof cavity birefringence.References[1] D.Y. Tang, J. Guo, Y.F. Song, L. Li, L.M. Zhao, D.Y. Shen, GHz pulse train generationin ﬁber lasers by cavity induced modulation instability, Opt. Fiber Technol. 20(2014) 610–614.[2] S. Coen, M. Haelterman, Modulational instability induced by cavity boundaryconditions in a normally dispersive optical ﬁber, Phys. Rev. Lett. 79 (1997)4139–4142.[3] M. Haelterman, S. Trillo, S. Wabnitz, Dissipative modulation instability in anonlinear dispersive ring cavity, Opt. Commun. 91 (1992) 401–407.[4] M. Haelterman, S. Trillo, S. Wabnitz, Additive-modulation-instability ring laserin the normal dispersion regime of a ﬁber, Opt. Lett. 17 (1992) 745–747.[5] D.W. McLaughlin, J.V. Moloney, A.C. Newell, New class of instabilities in passiveoptical cavities, Phys. Rev. Lett. 54 (1985) 681–684.[6] A. Yariv, Quantum Electronics, third ed., J. Wiley, New York, 1989, p. 187.[7] S. Wabnitz, Modulational polarization instability of light in a nonlinearbirefringent dispersive medium, Phys. Rev. A 38 (1988) 2018–2021.[8] M. Quiroga-Teixeiro, C. Balslev Clausen, M.P. Sørensen, P.L. Christiansen, P.A.Andrekson, Passive mode locking by dissipative four-wave mixing, J. Opt. Soc.Am. B 15 (1998) 1315–1321.[9] T. Sylvestre, S. Coen, P. Emplit, M. Haelterman, Self-induced modulationalinstability laser revisited: normal dispersion and dark-pulse train generation,Opt. Lett. 27 (2002) 482–484.

Comment on GHz pulse train generation in fiber lasers by cavity induced modulation instability

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