Generation regimes of bidirectional hybridlymode-locked ultrashort pulse erbium-dopedall-fiber ring laser with a distributed polarizerALEXANDER A. KRYLOV,1,* DMITRIY S. CHERNYKH,2,5 NATALIA R. ARUTYUNYAN,3,4

VYACHESLAV V. GREBENYUKOV,3 ANATOLY S. POZHAROV,3 AND ELENA D. OBRAZTSOVA3,4

1Fiber Optics Research Center of the Russian Academy of Sciences, 38 Vavilov Street, 119333 Moscow, Russia2Avesta Project Ltd, 11 Fizicheskaya Street, Laboratory Building, Troitsk, 142190 Moscow, Russia3A.M. Prokhorov General Physics Institute of the Russian Academy of Sciences, 38 Vavilov Street, 119333 Moscow, Russia4National Research Nuclear University MEPhI (Moscow Engineering Physics Institute), 31 Kashirskoye shosse, 115409 Moscow, Russia5P.N. Lebedev Physical Institute of the Russian Academy of Sciences, 53 Leninskiy Prospekt, 119991 Moscow, Russia*Corresponding author: sokolak@mail.ru

Received 11 March 2016; revised 19 April 2016; accepted 19 April 2016; posted 19 April 2016 (Doc. ID 261034); published 19 May 2016

We report on the stable picosecond and femtosecond pulse generation from the bidirectional erbium-doped all-fiber ring laser hybridly mode-locked with a coaction of a single-walled carbon nanotube-based saturable absorberand nonlinear polarization evolution that was introduced through the insertion of the short-segment polarizingfiber. Depending on the total intracavity dispersion value, the laser emits conservative solitons, transform-limitedGaussian pulses, or highly chirped stretched pulses with almost 20 nm wide parabolic spectrum in both clockwise(CW) and counterclockwise (CCW) directions of the ring. Owing to the polarizing action in the cavity, we havedemonstrated for the first time, to the best of our knowledge, an efficient tuning of soliton pulse characteristics forboth CW and CCW channels via an appropriate polarization control. We believe that the bidirectional laserpresented may be highly promising for gyroscopic and other dual-channel applications. © 2016 Optical

Society of America

OCIS codes: (140.4050) Mode-locked lasers; (320.7090) Ultrafast lasers; (060.5530) Pulse propagation and temporal solitons;

(160.4236) Nanomaterials; (060.2420) Fibers, polarization-maintaining.

http://dx.doi.org/10.1364/AO.55.004201

1. INTRODUCTION

Bidirectional ultrashort pulse (USP) ring lasers may be highlyprospective for different dual-channel applications. Amongthem gyroscopy attracts much attention due to possiblelock-in effect mitigation, which is of great concern for high-precision gyro development [1]. It is quite natural to extrapo-late this idea to USP fiber lasers owing to their exceptionalefficiency, compactness, and stability compared with USPdye or solid-state lasers. However, bidirectional operation ofa mode-locked (ML) fiber ring laser was realized for the firsttime only in 2008 by Kieu and Mansuripur [2] after 41 yearssince the first demonstration of the He–Ne bidirectional MLlaser by Buholz and Chodorow [3].

Up to now several schemes of bidirectional ML fiber lasershave been successfully demonstrated [2,4–9]. Some of themexploit the pure ring cavity design [2,4–6], but the others con-tain a four-port circulator for independent control of clockwise(CW) and counterclockwise (CCW) pulses [7–9]. It should bestressed that the vast majority of these lasers generate

conservative solitons (CSs) with ∼600 fs∕1 ps duration in bothCW and CCW directions. It is quite obvious due to the excel-lent intrinsic stability against different perturbations that isinherent to CSs. More recently Yao [10] has presented a bidi-rectional stretched-pulse erbium-doped fiber ring laser bymeans of the appropriate intracavity dispersion managementthat allowed significant pulse-width shortening down to∼200 fs in each channel. However, none of the schemes dem-onstrated by now enables broad tunability of countercirculatingpulse characteristics, which, in turn, would be quite useful forgyroscopic applications.

It is of great importance that the colliding pulse mechanismof passive mode locking (so-called colliding pulse mode locking[CPML]) in bidirectional lasers implies a presence of a saturableabsorber (SA) in the cavity for initiating USP generation inboth directions of the ring [11]. Moreover, to favor CPML gen-eration, CW and CCW pulses should meet each other in theSA, thus reducing total cavity losses [2,11]. It evidently meansthat SA thickness should be significantly less than a laser pulse

Research Article Vol. 55, No. 15 / May 20 2016 / Applied Optics 4201

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length for the most stable CPML generation [2,11]. In addition,pulse fluence should be of the order of the SA saturation fluenceto promote total loss reduction in the case of the simultaneousarrival of countercirculating pulses to the SA [11]. Modernsaturable absorbers, such as semiconductor saturable absorbermirror (SESAM) [7] or carbon nanotubes [2,4,6,9,10] andgraphene [8], easily satisfy these requirements being the bestcandidates for bidirectional ML fiber laser development.

Though, being compared to quantum well-based SESAMs,single-walled carbon nanotube-based saturable absorbers(SWCNT-SAs) benefit frommuchmore easier and cost-effectivefabrication techniques, the possibility of beingused inboth linearand ring cavities, ultrafast carrier relaxation time [12], andsignificantly enhanced noise characteristics [13]. Furthermore,SWCNTs can be naturally dispersed in different polymer matri-ces forming high optical quality thin films that can be furtherbuilt in the laser cavitywithout breaking the all-fiber setup aswellas requiringmechanical or thermal adjustments [14–16]. UnlikeSESAMs, CNT-based saturable absorbers exhibit saturablebehavior over a much wider spectral band (up to 500 nmand more) at the expense of the inherent distribution ofSWCNTs diameters and chiralities [14,15,17], which is quitefavorable for wideband photonic-switching applications [18].

Nonetheless, despite well-elaborated SWCNT-based filmfabrication technologies, it is difficult to control such a crucialcharacteristic for laser mode locking as an absorber responsetime during the SWCNT-SA fabrication process. As a matterof fact, SWCNT-SA response time defined by a complicatedtube–tube interactions (excited-state energy is transferred tometallic NTs with further quenching) [12] strictly dependson the particular sample fabrication process [19]. Moreover,a polarization dependence of saturable absorption cannot becontrolled as well since SWCNTs orientations are randomlydistributed. All these features make SWCNT-SA characteristicsas well as corresponding ML laser performance absolutely un-predictable, thus impeding a realization of a reproducible USPgeneration especially in the bidirectional laser.

To overcome this drawback hybrid mode-locking mecha-nism may be employed which implies a coaction of a so-called“slow” SA, such as SWCNTs, and a “fast” one, such as nonlinearpolarization evolution (NPE), based on the nonlinear Kerr effectin fibers [20]. In this case SWCNT-SA not only facilitatesmode-locking start-up due to lower saturation energy but alsoprovides a nonlinear filtering and spurious CW radiation sup-pression [21], significantly improving laser performance. High-quality USP shaping, in turn, primarily occurs due to theextremely fast NPE mechanism. Commonly NPE is introducedby means of a point fiber-pigtailed polarizer embedded into acavity [21]. However, in this paper, we propose a distributedpolarizer based on the short-segment Panda-type birefringentfiber possessing a polarizing effect [20] for NPE launch inthe ring cavity, which additionally allows us to keep the all-fiberdesign of our bidirectional ML fiber ring laser. Moreover, apartfrom a strong polarization arrangement, polarizing action in thecavity is strictly favorable for providing an efficient control overCW and CCW pulse characteristics through the fine tuning ofintracavity losses.

In this work we investigate generation regimes of the bidi-rectional colliding pulse hybridly ML erbium-doped all-fiberring laser depending on the total cavity dispersion and demon-strate for the first time to the best of our knowledge fine controlover CW and CCW pulse characteristics.

2. EXPERIMENTAL SETUP

The bidirectional hybridly ML laser setup is shown in Fig. 1.The ring cavity is based on the home-made erbium-doped ac-tive fiber (Er3+-fiber) pumped with a 980 nm, 200 mW laserdiode through the 980/1550 wavelength division multiplexer.We used three single-mode step-index active fibers with strictlydifferent group velocity dispersion (GVD) values: anomalous(#1), close to zero (#2), and normal (#3). Additionally, intra-cavity dispersion was carefully managed by means of theSMF28 fiber (β2 � −21.2 ps2∕km at 1560 nm) and SMF-LS fiber (β2 � �3.3 ps2∕km at 1560 nm). Principal character-istics of Er-doped fibers employed are summarized in Table 1.

To realize CPML generation, a thin-film saturable absorberbased on single-walled carbon nanotubes (CNT module) wasplaced in the ring cavity, as shown in Fig. 1. Arc-dischargedSWCNTs were dispersed in the ≈50 μm thick carboxymetyl-cellulose polymer film [14,15] that was further sandwiched be-tween two FC/APC connectors (one or two successive units)forming common CNT module [20,22]. In this work twoSAs were used: one of them was prepared with pure CNTs[22], but the other contained boron-nitride-doped CNTs(C:BNNTs) [22,23]. Meanwhile the concentration of B andN atoms in the resulting CNT lattice was very low (it was esti-mated to be less than 5%) to modify the CNT diameter andenergy zone structure significantly. Thus, they should be con-sidered as defects in the regular CNT mesh. SWCNT diame-ters estimated from the radial breathing mode frequencypositions in corresponding Raman spectra were distributedaround 1.4 nm [24] as inherent to arc-discharged SWCNTs.

Fig. 1. Experimental setup of the bidirectional hybridly MLerbium-doped all-fiber ring laser. Insets: polarizing action of the PZfiber (left) and its cross-section image (right). More detailed informa-tion about PZ fiber is below in the text and [20].

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Small-signal transmittance values (T 0) are close to eachother and amount to T 0 ≈ 61% for CNT-SA (two films in-stalled) and T 0 ≈ 54% for C:BNNT-SA (one film installed)at 1560 nm wavelength, respectively [22]. However, as it isshown in Fig. 2, saturation behavior measured with a home-made 1.56 μm probe Er-doped fiber laser with ≈120 fs pulsewidth at 38.1 MHz repetition rate is strictly different for givensamples [22].

As a matter of fact, SWCNT-SAs have the ability ofpulse shaping due to their saturable absorption behavior.Experimentally obtained dependence of losses l��l � 1 − T �1 − Eout

p ∕E inp �� on the input pulse energy Ep was fitted assum-

ing a previously developed model of a slow saturable absorber[25] implying a probe laser pulse width to be much shorter thanthe absorber recovery time. In fact, this assumption is justifiedwith a quite accurate approximation of the experimental data,as it is depicted in Fig. 2. As a result, modulation depth of thefilm transmission ΔT for C:BNNT-SA (ΔT � 14.9� 0.6%)is more than 4 times (4.1) larger than that for the CNT-SA(ΔT � 3.6� 0.2%) keeping almost the same saturation en-ergy (E sat � 21� 3 pJ for C:BNNT-SA, E sat � 23� 4 pJfor CNT-SA) [22]. Taking into account mode field diameterof the SMF28 fiber (≈10.6 μm) corresponding saturation flu-ence was calculated to be F sat � 24 μJ∕cm2 for C:BNNT-SAand F sat � 26 μJ∕cm2 for CNT-SA. In addition, being acrucial characteristic for a laser mode locking, the ground-staterecovery time was indirectly estimated on the basis of carefulanalysis of the laser pulse width dependence on the pulse energyfor a corresponding SWCNT-SA ML erbium-doped all-fiberring soliton laser to be τr ∼ 700 fs for CNT-SA and τr ∼400 fs for C:BNNT-SA, respectively. The detailed informationabout this method is presented in [22].

An additional pulse shaping mechanism was realizedthrough the fast NPE implementation in the laser cavity. Infact, the key element of the NPE is a polarizer that introducesintensity-dependent losses. As in our previous work on thehybridly ML soliton fiber laser, here we apply a specially devel-oped birefringent “Panda”–type silica-glass fiber [20] also pos-sessing a polarizing effect (so-called PZ fiber) as an all-fiberintracavity polarizer. Its polarizing action is based on thecut-off wavelengths difference of the orthogonally polarizedHE11 fiber modes (slow and fast ones) owing to the anisotropicW -type refractive-index profile [20].

The ratio of output powers of these modes (extinction ratio)exceeds 20 dB in the 100 nm wide spectral band centered at1560 nm for a 0.7 m long PZ fiber inserted into the ring, as it isdemonstrated in the inset of Fig. 1. The GVD introduced bythe PZ fiber was estimated from the measured refractiveindex profile to be β2�PZF� ≈ −28.6 ps2∕km at 1560 nmwavelength.

To complete NPE setup, two polarization controllers (PCs)were embedded into the ring according to Fig. 1. It is worthnoting that the NPE setup contributes to the intracavity lossvariation as well, which is crucial for ML laser performance.

Laser radiation was put out through a 3 dB fused fibercoupler placed between the CNT module and PZ fiber.

Of course, the laser cavity is free of an isolator, which is anecessary condition for the bidirectional generation appear-ance. Meanwhile, CW and CCW outputs were supplied withisolators to prevent any parasitic reflection from a measure-ment setup.

It should be also stressed that a laser cavity itself as well as apumping scheme are not symmetrical. However, as it will beshown later, this fact is not a drawback for CW and CCW pulsecharacteristics equalization.

During experiments pulse intensity autocorrelations weremeasured with an INRAD autocorrelator, while pulse spectrawere registered with a high-resolution (0.01 nm) ANDOspectrum analyzer. CW and CCW pulse trains were simulta-neously observed by means of the fast photodetectors withbandwidths of Δf PD ≈ 5 GHz and a dual-channel 350 MHzTEKTRONIX 2465A analog oscilloscope. Radiofrequencyspectra were detected by means of the 9 kHz/3 GHzROHDE&SCHWARZ FSL3 spectrum analyzer with a300 Hz resolution bandwidth (RBW).

3. EXPERIMENTAL RESULTS

A. Conservative SolitonsAt first we realized bidirectional ML generation with 2.5 mlong Er-doped fiber #1 and CNT-SA in the ring. Taking intoaccount GVD values of different fibers composing a 6 m longring, the total intracavity GVD value was estimated to beDT ≈ −0.14 ps2. As a matter of fact, such large anomalousGVD should support a soliton-type USP generation [20].

Stable self-starting single-pulse ML generation in both direc-tions of the ring was obtained in a rather narrow pump powerrange from 60 to 88 mW. Figure 3 shows autocorrelation tracesand spectra of CW and CCW pulses at 76 mW pump power,which were almost fully equalized through the appropriate PCsadjustment. It should be stressed here that central wavelengths

Table 1. Characteristics of Erbium-Doped Fibers

Er-doped fiber ## #1 #2 #3

GVD at 1560 nm [ps2∕km] −24.3 �6.6 �22.2Small-signal absorption at 980 nm[dB/m]

11 43 14

Mode-field diameter at 1560 nm [μm] 10.6 4.5 5.3Cut-off wavelength [μm] 1.34 0.9 1.0

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0.50 CNT-SA Fsat=26 μμJ/cm2

C:BNNT-SA Fsat=24 μμJ/cm2

Lo

sses

Pulse energy (pJ)

Fig. 2. Saturation behavior of SWCNTs-based saturable absorbersupon 120 fs pulse excitation at 1560 nm wavelength.

Research Article Vol. 55, No. 15 / May 20 2016 / Applied Optics 4203

of countercirculating pulses were almost equal within the0.2 nm resolution band of the ANDO spectrum analyzer.Pulse widths amounted to 795 and 798 fs while output averagepowers were measured to be 1.35 and 1.21 mW for CW andCCW channels, respectively. Obviously, as seen in Fig. 3, goodapproximation of experimental data with corresponding solitonfunctions (P�ω� ∝ sech2�ω�) together with well-resolved Kellyside-peaks (in logarithmic scale) is evidence in favor of the sol-iton-type pulse generation in both directions of the ring.However, the time-bandwidth product (TBP � Δν · τp) forall pulses obtained varied from 0.36 to 0.42, slightly exceedingthe well-known TBP value of 0.315 inherent to fundamentalsolitons.

It is worth noting that during autocorrelation measurementswe observed an interesting effect: maximizing of the autocor-relation signal via input pulse polarization adjustment forone channel led to its zeroing for another and vice versa.Thus, we can expect that pulses are crossed in the SA beingalmost orthogonally polarized, which promotes destructivepulse interaction reduction [11] and improves bidirectionallaser performance.

This hypothesis possibly accounts for the outstanding tun-ability of CW and CCW pulse characteristics experimentallydemonstrated in Fig. 4. In this case fine variation of the solitonpulse width and spectrum width (the inset) was realized via PCsadjustments, i.e., intracavity loss control for CW and CCWchannels at a constant pump power of 81 mW. Obviously, lossincrease is responsible for the pulse energy reduction and, as aresult, corresponding soliton pulse width growth in accordancewith the soliton area theorem. As it was expected both curvesintersect at ECW

p ≈ ECCWp condition proving an exceptional

capability of the scheme developed to generate almost equalizedcountercirculating pulses despite essential cavity asymmetry.Taking into account this fact together with almost equal short-est pulse widths obtained for CW (524 fs) and CCW (502 fs)channels it is reasonable to expect almost equal NPE actionsfor CW and CCW channels in the CS generation regime.Furthermore, NPE action can be carefully controlled in bothchannels through appropriate PCs adjustments.

Average output power varied in this experiment from 1.09to 2.28 mW for the CCW channel and from 0.84 to 2.02 mWfor the CW one. Corresponding laser pulse width ranged from887 to 502 fs for the CCW channel and from 1.28 ps to 524 fsfor the CW one. Furthermore, it was possible to suppress anychannel (CW or CCW) significantly through the appropriatePCs adjustment resulting in the stable unidirectional genera-tion in the ring. Meanwhile, the contrast Q of laser outputsmeasured as the ratio of the highest to the lowest average outputpower (Q � Pmax∕Pmin) was equal to 18.8 dB (PCW

max �1.73 mW, PCW

min � 23 μW) for the CW channel (rightmostpoint in Fig. 4) and 32.1 dB (PCCW

max � 2.28 mW,PCCWmin � 1.4 μW) for the CCW one (leftmost point in Fig. 4)

at the constant pump power of 81 mW.We attribute the origination of these weak parasitic signals

to the pulse scattering in the thin-film SWCNT-based SA sincea discernible part of its nonsaturable losses stems from the lightscattered by randomly distributed SWCNTs [26,27] and fur-ther caught by a single-mode fiber. The seed power is likely tobe the same for both channels, although the difference inresulting signals (and measured contrasts as well) can beapparently ascribed to the nonsymmetrical cavity design.

Figure 5 shows weak signal spectra together with corre-sponding USP ones. First of all, well-resolved Kelly side-peaksfurther prove soliton-type USP generation in the ring.Moreover, intracavity GVD calculated on the basis of side-peaks positions in the spectra of both CW and CCW pulses(DT � −0.12 ps2) [20] is very close to that one estimated usingGVD of fibers composing the ring (DT ≈ −0.14 ps2).Obviously, as seen in Fig. 5, both central wavelengths andside-peaks positions almost coincide for USP and the corre-sponding weak signal (especially for CW channel suppressed),which is evidence in favor of the scattering nature of weak para-sitic signals. Of course, during its propagation along the ringweak radiation undergoes some evolution giving rise, in par-ticular, to the Lorentzian spectra shapes, as it is demonstratedin Fig. 5(b).

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Fig. 3. Autocorrelation traces and spectra of the equalized CW andCCW pulses at 76 mW pump power.

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Fig. 4. Pulse width and spectrum width (the inset) tuning forCW and CCW pulses depending on the normalized CW outputpulse energy ECW

p ∕�ECWp � ECCW

p � at the constant pump power of81 mW.

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As a matter of fact, parasitic radiation in one channel doesnot prevent the laser from a stable USP generation in the other.However, USP scattering in a SA can be a reason for the mutualinfluence of CW and CCW channels. Moreover, different con-trasts of the bidirectional laser outputs can indicate unequalinfluence of CW and CCW channels on each other arisingfrom the cavity asymmetry. To verify this assumption we inde-pendently recorded radiofrequency spectra of both CW andCCW pulse trains (without mixing them) in the case of almostequal outputs (PCW

out � 1.1 mW, PCCWout � 0.9 mW at 60 mW

pump power). As it is depicted in Fig. 6, there are low-intensityleft-side-peaks near the fundamental repetition rate frequencyof f rep � 33.56 MHz (equal for both CW and CCW pulsetrains) in the countercirculating channels’ spectra. Ofcourse, there are right-side-peaks located the same distance(f bn ≈ 600 kHz) apart from the fundamental frequency peak.Undoubtedly, spectra observed can be considered as beat notesof the countercirculating pulses with weak parasitic radiationscattered by CNT-SA. Indeed, being naturally overlappeddue to the colliding pulse ML mechanism, the weak scatteredlight and USP interact during their copropagation along thering leading to the possible frequency pulling and, as a result,lock-in effect appearance, which could be a significant draw-back for a dead-band free gyro development. Obviously, beatnotes are naturally unstable resulting in some evolution of thebeat note frequency f bn in time, as seen in Fig. 6. Moreover,

the side-peak in the CW channel spectrum is more intense(at ≈12 dB), which is in consistency with our previous mea-surements of output contrast.

Taking into account corresponding power spectrum values[S�f �] it is possible to estimate beat note modulation depth (m)for each channel according to the following expression:

m � 2ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiS�f bn�∕S�f rep�

q. Modulation depth appears to be

m ≈ 0.75% for the CCW channel and m ≈ 3.1% for theCW one. Furthermore, output contrasts (Q) for CW andCCW channels determined as a corresponding ratio of thelaser power (PLR

av ) to the parasitic radiation power (PPRav )

can be derived from the following relationship: m ≈2

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiPLRav · PPR

av

p∕�PLR

av � PPRav � giving Q ≈ 4∕m2 � S�f rep�∕

S�f bn�. Retrieved from Fig. 6, Q amounts to ≈49 dB forthe CCW channel and ≈36 dB for the CW one, respectively.Output contrasts in this case sufficiently exceed those of theunidirectional generation reported above. It is quite evidentsince laser generation in this case occurs in both channels.Thus, results obtained undoubtedly indicate the unequal mu-tual influence of CW and CCW channels that resulted fromthe cavity asymmetry.

Further we examined hybrid mode-locking features. To dothis we collected the data for both CW and CCW pulse widthsτp from Fig. 4 and plotted them with respect to the correspond-ing pulse energies Ep, as it is depicted in Fig. 7. It turns out thatwhole data obtained for both CW and CCW pulses can becarefully approximated with one decaying exponential functionτp � τ0 � A · exp�−Ep∕E0� with an asymptote τ0 �470� 35 fs. It should be stressed that both τ0 and the shortestpulse width τmin (τmin � 502 fs for the CCW channel andτmin � 524 fs for the CW one) are close to the pulse widthτp retrieved from a purely unidirectional hybridly ML solitonring laser (with isolator embedded) built from the same ele-ments and at the same pump power of 81 mW (τp � 490 fs,Pav � 3.3 mW, Ep � 75.6 pJ) [20]. Moreover, they are suf-ficiently smaller than a pulse width (τp � 795 fs) measuredin the unidirectional laser without NPE action (the PZ fiberis substituted with the SMF28 one) at the same pump

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ΔΔλλ= 2.91 nm, Pout=23 μμW

CW max, ΔΔλλ= 6.02 nm, Pout=1.73 mW

Po

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Fig. 5. Spectra of CW and CCW pulses in the unidirectional gen-eration regime (a) and their fitting (b).

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Fundamental repetition rate frequency

frep= 33.56 MHz

Beat-note peaks

fbn

32800000 33000000 33200000 33400000 33600000

Fig. 6. Radiofrequency spectra of CW and CCW channels recordedseparately (without mixing them). RBW � 300 Hz, acquisitiontime � 5 s.

Research Article Vol. 55, No. 15 / May 20 2016 / Applied Optics 4205

power [22] and corresponding CNT-SA used. Thus, NPE playsa significant role in the pulse shaping process in both channelsproving the hybrid nature of the ML generation in the givenbidirectional fiber laser. In general, the operation regime real-ized should be considered as colliding pulse hybrid mode lock-ing (CPHML).

We have made a successful attempt to realize ML generationwith C:BNNT-SA in the cavity and obtained the pulses’ charac-teristics together with their tuning behavior being very close tothose observed in the laser withCNT-SA,which also confirms anexceptional role of the hybrid mode-locking mechanism in thesoliton generation regime of the bidirectional laser developed.

B. Gaussian PulsesFurther we have investigated bidirectional laser performancewith 1 m long Er-doped fiber #2 in the ring. It should be notedthat stable ML generation in this case was realized only with theCNT-SA used. Total intracavity GVD was calculated to beDT ≈ −0.072 ps2 on the basis of GVD of fibers composinga 4.4 m long ring.

Figure 8 shows autocorrelation traces and spectra of CWand CCW pulses measured at the pump power of 54 mW(PCW

out � 0.36 mW, PCCWout � 0.48 mW). There are some

noteworthy features arising from this data. First of all, despitenoticeable anomalous intracavity GVD, there are no Kelly side-peaks in smooth pulse spectra depicted (compare them withspectra shown in Fig. 3). Moreover, pulse spectra also withautocorrelation traces for both CW and CCW pulses were care-fully approximated with Gaussian functions rather than solitonones. In addition, taking into account appropriate spectraFWHM and laser pulse widths, time-bandwidth products(TBP � Δν · τp) for CW and CCW pulses were calculatedto be 0.49 and 0.46, respectively, being much closer to the fun-damental Gaussian-pulse TBP value of 0.441 rather than sol-iton one (0.315). Thus, we claim the generation of almostbandwidth-limited Gaussian pulses in both CW and CCWdirections of the ring. Since pulse spectra are quite narrowas compared to the spectra of common dispersion-managedstretched-pulse lasers [10] we should not expect significantpulse breathing in the cavity. On the contrary, pulses propagatealong the cavity nearly keeping their widths.

Possibly, low intracavity peak power leading to the insuffi-cient nonlinearity (self-phase modulation) action preventsCS pulse formation inside a cavity despite anomalous intracav-ity dispersion. Indeed, corresponding soliton order N �N �ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

LD∕LNL

p� estimated for CW and CCW pulses amounts to

NCW ≈ 0.33 and NCCW ≈ 0.43, respectively, being suffi-ciently less than characteristic CS order (NCS ≈ 1). Moreover,being rather low for even soliton pulse formation, peak powersof both CW and CCW pulses are likely to be insufficient fordiscernible NPE action in both channels. Thus, the laser pulsewidth is primarily determined by CNT-SA performance(τp ∼ τr) in the colliding pulse ML setup.

In contrast to the CS generation regime, we were not able torealize pulse characteristics tuning via intracavity PCs adjust-ments. Furthermore, we were unable to fully suppress anychannel through PCs adjustments, which might show evidencein favor of some polarization locking for CW and CCW pulsesinside a cavity [28].

C. Stretched PulsesThe next step was using 3 m long Er-doped fiber #3 introduc-ing significantly positive dispersion. Hence, to realize stable MLgeneration we had to use a C:BNNT saturable absorber andinsert a 4 m long SMF-LS fiber for additional dispersionand nonlinearity management, which gave us slightly positivetotal 10.4 m long cavity GVD of DT ≈ �0.001 ps2.

Autocorrelation traces and spectra of CW and CCW pulsesretrieved from the cavity at 45 mW pump power are depictedin Fig. 9. Obviously, such broad spectra with ≈20 nm width (at−10 dB level) expect ∼200 fs USP generation. Thus, output2.2 ps pulses are sufficiently chirped and could be consequentlycompressed. It is worth noting that measured spectra stronglydiffer from Gaussian ones and are closer to parabola. In addi-tion, almost equal output spectra of the same shape (related tothe same compressed pulse widths) imply almost equal NPEactions in CW and CCW channels.

Recently we have published research on the hybridly MLdispersion-managed unidirectional laser with distributed polar-izer that was made from the same components [29]. We ob-served ∼100 fs stretched pulse generation with the same broad

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Pu

lse-

wid

th (

fs)

Pulse energy (pJ)

Fig. 7. Combined dependence of CW and CCW pulse widths onthe corresponding output pulse energies Ep (data from Fig. 4).

0.0

0.2

0.4

0.6

0.8

1.0

1.2

No

rmal

ized

po

wer

Wavelength (nm)1550 1555 1560 1565 1570 1575

1530 1545 1560 1575-70

-60

-50

-40

-30

Po

wer

(d

Bm

)

Wavelength (nm)

-2.5 -2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0

0.2

0.4

0.6

0.8

1.0

1.2CW

ττp= 0.84 ps, ΔΔλλ= 4.7 nm

CCW

ττp= 1.05 ps, ΔΔλλ= 3.5 nm

Gaussian fit

No

rm. I

nte

nsi

ty

Delay (ps)

Fig. 8. Autocorrelation traces and spectra of CW and CCW pulsesobtained from the laser with Er-doped fiber #2.

4206 Vol. 55, No. 15 / May 20 2016 / Applied Optics Research Article

parabolic-type spectrum implying some aspects of the self-similar pulse evolution in the positive dispersion Er-dopedactive fiber. Meanwhile, we experimentally proved pulsebreathing behavior finding a “focus” point position inside anegative dispersion segment of the ring cavity with slightly pos-itive total GVD of �0.018 ps2 [29]. Moreover, we proposedthe “focus” point to coincide with a C:BNNT-SA position inthe ring providing additional stabilization of the USP genera-tion. In the case of colliding pulse ML operation thisassumption is also quite reasonable since C:BNNT-SA is dis-posed in the vicinity of the center of the negative dispersioncavity segment [10,29]. It is well known that slightly positivetotal GVD favors broadband stretched-pulse generation inthe dispersion-managed laser cavity, which has been realizedin the given bidirectional Er-doped all-fiber laser. Un-fortunately, the stability and reproducibility of the generationregime realized are insufficient for its further use in gyroscopicor other dual-channel applications. Moreover, as in the case ofGaussian pulses we were unable to realize pulse characteristicstuning due to a strictly narrow interval of possible PCs adjust-ments and pump powers responsible for stable USP generation.

D. Temporal and Spectral Characteristics of the CWand CCW Pulse TrainsFinally, we have analyzed temporal and spectral features of CWand CCW pulse trains by means of the analog oscilloscope andradiofrequency spectrum analyzer with 300 Hz resolutionbandwidth. Obviously, Fig. 10(a) confirms highly stableCW ML generation in both channels. Further analysis in ashorter time interval of 100 ns revealed mutual synchronizationof CW and CCW pulse trains. Indeed, as seen in Fig. 10(b), theoscilloscope was triggered by the CW pulse train (up), but theCCW pulse train (down) appeared to be also synchronized(both pulse trains stayed on screen still). Evidently this factimplies equal pulse repetition rate frequencies f rep for bothCW and CCW channels. To prove this assumption we furtherexplored the radiofrequency spectrum of mixed CW and CCWtrains with the highest available resolution of 300 Hz. As itundoubtedly follows from Fig. 10(c), repetition rate frequen-cies coincide within the 300 Hz resolution band.

As it is expected, the main reason for Δf rep origination isintracavity GVD influence [6,10]. Indeed, Δf rep that can besimply expressed as Δf rep � ΔλjDT j�2πcf 2

rep∕λ20� is directlyproportional to the wavelengths difference Δλ of countercircu-lating pulses and total intracavity dispersion DT . The typicalbeat note signal of superimposed by an external delay lineCW and CCW pulses is shown in Fig. 10(d) while its radio-frequency spectrum depicted in Fig. 10(e) displays character-istic side-peaks located 1.07 MHz (beat note frequency f bn)apart from the fundamental repetition rate frequency of43.6 MHz. Evidently, f bn should be considered as a differencein spectrum positions of CW and CCW pulses in frequencydomain, i.e., f bn � Δλ · �c∕λ20�. It is of great importance thatno beat note signal was observed unless CW and CCW pulseswere superimposed again. Moreover, using an external delayline for CW and CCW pulse superposition, we experimentallyfound the pulses’ crossing points inside a cavity; one of themappears to coincide with a CNT-SA position, which is an ab-solutely predictable result taking into account the collidingpulse ML mechanism responsible for stable bidirectional laseroperation. The second one is located inside the erbium-dopedactive fiber.

According to the data from Fig. 10(e), the central wave-lengths’ difference of CW and CCW pulses was estimated tobe Δλ ∼ 10−7 nm (at λ0 ≈ 1560 nm and DT � −0.12 ps2,

-70

-60

-50

-40

-30 CW, Pout= 0.8 mW

CCW, Pout= 0.9 mW

Po

wer

(d

Bm

)

Wavelength (nm)1520 1530 1540 1550 1560 1570 1580 1590

-10 -8 -6 -4 -2 0 2 4 6 8 10

0.0

0.2

0.4

0.6

0.8

1.0

1.2

Lorentzian fit

No

rm. I

nte

nsi

ty

Delay (ps)

Fig. 9. Autocorrelation traces and spectra of CW and CCW pulsesretrieved from the laser with Er-doped fiber #3.

-120

-100

-80

-60

-40

Po

wer

(d

Bm

)

Frequency (Hz)

CW+CCW

frep= 33.56 MHz

(c)

0.00

0.05

0.10

0.15

0.20

Inte

nsi

ty (

arb

. un

its)

Time (μs)

(d)

33550000 33555000 33560000 33565000 -1.0 -0.5 0.0 0.5 1.0 1.5

40000000 42000000 44000000 46000000-120

-100

-80

-60

Po

wer

(d

Bm

)

Frequency (Hz)

frep

fbn

frep= 43.6 MHz

fbn= 1.07 MHz

(e)

(a) (b) CW

CCW

CW

CCW

Tbn= 0.9 μs

Fig. 10. (a),(b) Typical CW (up) and CCW (down) pulse trains;(c) radiofrequency spectrum of mixed CW and CCW channels re-corded with 300 RBW; typical beat note signal (d) of superposedCW and CCW pulse trains and its spectrum (e) observed in theCPHML laser with 2 m long Er-doped fiber #1.

Research Article Vol. 55, No. 15 / May 20 2016 / Applied Optics 4207

f bn � 1.07 MHz) giving rise to the Δf rep ∼ 10−5 Hz, whichis significantly less than the lowest f rep instability(στ�f rep�∕hf repi ∼ 10−7∕10−9 at the averaging time intervalτ ∼ 10−3∕102 s) measured for common free-running USP laser[30]. Thus, we claim the coincidence of repetition rates of CWand CCW pulse trains that is a necessary condition for theirsuperposition and, as a result, beat note signal observation.Moreover, it is evident that both f rep exhibit the same evolu-tion under a thermal or vibration influence, for instance, pro-viding highly stable overlapping of CW and CCW pulses.Meanwhile, it should be stressed that temporal synchronizationof CW and CCW pulses is based on the colliding pulsemechanism of laser mode locking. Indeed, ∼1 ps pulse with∼200 μm spatial length is longer (in space) than a thin-filmsaturable absorber, which stabilizes the cross-point positionof CW and CCW pulses inside a cavity assuring strictly reliableCW and CCW pulses’ synchronization.

4. CONCLUSIONS

In conclusion, we have elaborately explored generation regimesof the bidirectional erbium-doped all-fiber ring laser hybridlymode-locked (ML) with a coaction of single-walled carbonnanotube-based saturable absorber and nonlinear polarizationevolution that was introduced through the insertion of theshort-segment polarizing fiber.

In the case of negative intracavity GVD of −0.12 ps2, wehave observed stable CS generation in both CW and CCWchannels with ≈500 fs∕1.4 ps pulse width and∼1 mW outputaverage power. Moreover, due to the polarizing action in thecavity we have demonstrated for the first time to the best ofour knowledge an efficient tuning of CS characteristics (pulsewidth and spectrum width) for both CW and CCW channelsvia an appropriate intracavity loss control. In addition, we ex-perimentally observed mutual influence of CW and CCWpulses originated from parasitic light scattering in theCNT-based saturable absorber.

An increase of intracavity GVD up to −0.07 ps2 throughpositive dispersion Er-doped fiber insertion resulted in the gen-eration of almost transform-limited Gaussian pulses withdurations strictly determined by CNT-SA performance inthe colliding pulse mode-locking setup.

Near zero cavity dispersion (�0.001 ps2) we have realizedstretched-pulse generation with almost 20 nm wide parabolicspectrum in both clockwise and counterclockwise directions ofthe ring.

Finally, we have experimentally proved that an equality ofthe CW and CCW pulse repetition rates together with the mu-tual synchronization of countercirculating pulse trains is crucialfor beat note signal observation and, as a result, gyroscopiceffects investigation. Thus, the difference in repetition ratesof CW and CCW pulse trains was estimated to be Δf rep ∼10−5 Hz on the basis of experimental beat note signal analysis,which is significantly less than f rep instability measured forcommon free-running USP lasers.

We believe that the colliding pulse hybridly ML bidirec-tional laser presented may be highly promising for future gyro-scopic and other dual-channel applications.

Funding. Russian Science Foundation (RSF) (14-22-00-243).

Acknowledgment. The authors are grateful to M. M.Bubnov and M. E. Likhachev from FORC RAS for fibersprovision. The authors also thank A. K. Senatorov for fiberGVD measurements also with A. A. Ogleznev, B. L.Davydov from IRE RAS, A. E. Levchenko from FORCRAS, and V. A. Popok for technical support.

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