1. Introduction

Passively mode-locked (PML) fiber lasers are low-cost, simple and compact sources that have long been studied for the generation of a wide variety of optical pulses in stationary regimes like conservative and dissipative solitons, dispersion-managed solitons, similaritons, but also in less stationary regimes like those of noise-like pulses (NLPs), due to their significance in industry and scientific research. PML fiber lasers can be divided into two main architectures: the ring cavity design and the figure-of-eight laser (F8L) cavity. The first one uses nonlinear polarization evolution (NPE) in the cavity, yielding a power-dependent transmission through a polarizer which provides the nonlinear switching mechanism [1]. This is an efficient technique for achieving a broadband spectrum and ultrashort pulses. The second architecture presents the particularity that nonlinear switching is provided by a nonlinear optical loop mirror (NOLM) and is thus decoupled from the ring cavity section [2].

For a NOLM to provide switching, the symmetry of the Sagnac scheme has to be broken in some way. A conventional NOLM requires a power imbalance between the counter-propagating beams in the loop so that the power-dependent phase shift caused by self-phase modulation (SPM) can produce an intensity-dependent transmission. This can be done for example if an asymmetric coupler is used in the NOLM design. On the other hand, in a power-symmetric scheme, nonlinear switching can still be obtained through the polarization dependence of the nonlinear phase shift. In this case, it is necessary to create a polarization asymmetry between the counter-propagating beams by inserting for example a quarter-wave retarder (QWR) in the loop. In such a polarization-imbalanced scheme, it is important to ensure that the ellipticity of each beam is maintained along the loop. This can be done in practice by applying twist to the low-birefringence fiber to moderate the effect of the residual birefringence [3–5]. The polarization-imbalanced NOLM has been successfully implemented for a number of applications, including passive mode-locking of F8L cavities [4,6,7].

In recent years there has been an increasing interest in the study of a puzzling mode of operation of PML fiber lasers, in which NLPs are produced. First demonstrated by Horowitz et al. [8], this particular regime of fiber lasers has been drawing attention due to its potential for generating very broad spectra covering hundreds of nanometers [9–11], for achieving high energy pulses [7,12–14] and for applications requiring low temporal coherence [8]. NLPs are partially stationary pulses consisting of a bunch of extremely variable ultrashort sub-pulses conserving stable global properties like the total duration of the bunch, its average amplitude, energy and average spectrum. Typical features include a very large and smooth optical spectrum and an optical autocorrelation with a narrow coherence peak riding a wide pedestal. The duration of the central coherence peak and the pedestal reflects the average duration of the sub-pulses and of the whole packet, respectively.

It is important to stress that NLPs are not as stationary as any kind of solitons; actually they combine a (relative) global stability with a complex chaotic evolution at a local level, at the scale of their fine inner structure. In spite of the ever-growing literature on the topic, there is still no agreement on the mechanisms of formation of these pulses [8,15–18]. Moreover, many aspects of their dynamics and the dependence of pulse properties on laser parameters remain unclear. For example, some authors have reported that changing the pump power affects the energy and the width of the bunch without modifying the average peak power of the pulse or the shape of the optical spectrum [16,19,20]; others observed that, beyond certain duration, a NLP tends to split into multiple pulses as pump power is increased [7]. In terms of pulse energies, high values up to 250 nJ have been reached without pulse breaking [7,12–14].

The NLP regime is quite ubiquitous as its presence does not appear to depend critically on the laser architecture and the details of its particular design. Besides, NLPs have been observed in various spectral windows including EDF [6–11,13,16,20], YDF [21] and TDF [14,22]. Another remarkable aspect of NLPs is that they have demonstrated better efficiency than solitons in nonlinear processes such as cascaded stimulated Raman scattering [23], non-linear frequency conversion [23,24] and supercontinuum (SC) generation [25,26], among others. For all these reasons NLPs, whose regime is studied in this paper, are very attractive for several important applications including spectral interferometry [27], optical coherence tomography [28], micromachining, sensing, optical metrology and SC generation [29].

The generation of SC refers to the massive creation of new frequencies outside the input spectrum via the combination and interaction of multiple nonlinear optical effects such as self-phase and cross-phase modulation (SPM and XPM), formation of higher-order solitons (HOS), modulation instability (MI), four-wave mixing (FWM) and stimulated Raman scattering (SRS), as it has been shown in various works published on the subject [30,31]. SC light can be generated using different methods and from different sources including continuous wave (CW) [32] or pulsed sources like short pulses [33], ultra-short pulses [34] and even NLPs [25,26,35–37].

Another significant regime in PML fiber lasers is harmonic mode-locking (HML). It consists in producing a train of periodic pulses at a repetition rate that is an integer multiple of the cavity fundamental frequency [38], which is particularly attractive for optical communications. HML is not the exclusivity of soliton lasers and several cases of HML noise-like pulsing regimes have been observed [7,39,40].

In this work we study NLPs generation from an erbium/ytterbium double-clad fiber (EYDCF) F8L including a polarization-imbalanced NOLM. The laser can be operated in either fundamental or harmonic mode-locking regimes. Pulses featuring record high energies and a broad, flat optical bandwidth are reported.

2. Experimental setup

The schematic of the fiber laser system under study is depicted in Fig. 1. This setup, with a total length of about 215 m, consists of a figure-of-eight laser formed by a ring section and a NOLM. In the ring section, a 980/1550 nm combiner was used to launch the pump power from a 976-nm laser diode (Focus Light DLS03-FCMSE55-I-25-976-5) into the active fiber. This active fiber is a piece of EYDCF of 1.6 m of length with a core diameter of 12 µm (NA = 0.20) and an inner cladding diameter (flat-to-flat) of 130 µm. This fiber has 70-dB/m core absorption at 1530 nm. A polarization-independent optical isolator (PI-ISO) is inserted to ensure unidirectional laser operation. A power-symmetric, polarization-imbalanced NOLM scheme is used as the saturable absorber (SA): it consists of a 50/50 coupler, a 10-m-long low-birefringence single-mode fiber (SMF2, D = 18 ps/nm/km) twisted at a rate of 5 turns per meter and a quarter-wave retarder (QWR) inserted asymmetrically in the loop in order to break the polarization symmetry. The switching mechanism of such a NOLM relies on the polarization dependence of the nonlinear phase shift in the twisted loop. The ring cavity also contains a section of the same single-mode fiber (SMF1) of ~200 m of length and a polarization controller (PC). The 10% output port is provided by a 90/10 coupler, with the 90% output port connected to the combiner. In order to perform two measurements simultaneously, an 80/20 coupler is spliced to the laser output. The 20% output port is connected to a 2-GHz photodetector (Thorlabs DET08CFC) and the detected signal is monitored on a 2-GHz real-time oscilloscope (Tektronix MSO5204B). The 80% port is connected to an optical spectrum analyzer (OSA, Anritsu MS9740A). Contrary to other similar schemes reported previously [6,11,41,42], in the present setup the state of polarization in the cavity is not fixed because of the absence of a polarizer.

 

Fig. 1 Passively mode-locked figure-of-eight laser setup.

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3. Results and discussions

For appropriate settings of the QWR and PC, we obtain a stable self-starting mode-locking operation. Figure 2(a) presents the scope trace of a stable train of pulses with a period of T = 1.1 µs. This means that fundamental mode locking is achieved (a single pulse circulates in the 215-m-long cavity). This result confirms that a polarizer at the input of the polarization-imbalanced NOLM is not necessary in this scheme in order to obtain the mode-locking regime, although such a polarizer was always used in previous works. This result also indicates that mode-locking is due to the saturable absorber action of the NOLM and not to the nonlinear polarization rotation (NPR) in the ring section [41]. The absence of a saturable absorber effect in the ring section is further confirmed by observing that, when we tested the setup of Fig. 1 prior to the NOLM insertion, no mode-locking operation could be obtained from this ring laser configuration.

 

Fig. 2 Noise-like pulses fundamental mode locking: (a) oscilloscope trace of pulse train; (b) time-domain envelope in single-shot mode; (c) optical spectra in mode-locking and CW regimes; (d) intensity autocorrelation trace of pulse (inset: close-up on central spur).

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The pulse measured in the time-domain using the 2-GHz photodetector and oscilloscope is shown in Fig. 2(b). Here in single-shot acquisition mode, we can appreciate a NLP envelope that is nearly stationary with a full width at half maximum (FWHM) duration of ~13 ns. Also, the optical spectrum is depicted in Fig. 2(c). A very broad and flat SC spectrum extending over 200 nm is obtained (solid red line), whose measurement is unfortunately limited on the right side by the range of the OSA. The spectral maximum appears at 1566.54 nm in the region of erbium emission. Besides, a pair of peaks appears close to 1536 nm and 1543 nm, which are attributed to residual CW emission. This spectrum also presents a significant red-shifted component that decays smoothly by 15 dB over 150 nm, from 1600 nm to the upper limit of the OSA, 1750 nm. The 3-dB bandwidth of this spectrum is 18 nm (corresponding to the peak of erbium emission), however it reaches 75 nm at 10 dB and 145 nm at 15 dB from the peak. It is evident that when there is no mode-locking operation, the spectrum (dotted black line) is much narrower and only presents a few peaks in the erbium emission band at the mentioned wavelengths, illustrated in Fig. 2(c). Finally, in order to further confirm the NLP regime, the autocorrelation trace is obtained using an autocorrelator (FR-103XL) and the mentioned scope. A typical NLP autocorrelation trace was obtained, with a narrow coherence peak riding a wide and smooth pedestal that extends beyond 200 ps, limited by the range of the autocorrelator as can be observed in Fig. 2(d). In spite of this, the pedestal presents a marked slope that allows estimating its extension to a few hundreds of ps (much narrower than the duration of the whole bunch), which is consistent with the existence of sub-ns substructures within the NLPs, as discussed in [41]. The peak-to-pedestal ratio is ~5:1. The inset of Fig. 2(d) shows a close-up on the central spur, with a FWHM bandwidth of about 1 ps. Also, a maximal average output power of 275.25 mW was measured in the fundamental mode-locking regime with a maximal pump power of 25 W. This corresponds to a laser efficiency slightly lower than 1%. The single pulse energy in this mentioned case, when the NLP regime is sufficiently stationary, is estimated to be 302.8 nJ.

To obtain mode-locking at low pump power, a mechanical stimulation was necessary. Nonetheless, it is noteworthy that mode-locking is self-starting in all cases if the pump power is higher than 7 W, remaining stable for hours. Once this regime is achieved, stable single-pulse operation is maintained although pump power is increased, even if the pump power is tuned to the highest level (25 W), unlike results reported in other references where the main packet splits into several NLPs if pump power is increased beyond some point [7,39]. On the other hand, at high pump power, starting from stable fundamental mode-locking operation, slight QWR adjustments allow observing a transition to multiple pulsing operation in the form of stable harmonic mode-locking up to the 6th order, as shown in Fig. 3. However, it can be seen how the pulse train is affected by amplitude fluctuations when the harmonic order increases.

 

Fig. 3 Scope traces of harmonic mode-locking.

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Starting again from the stable waveform presented in Fig. 2(b), PC adjustments allow in some cases to observe some less stationary NLP regimes, as can be seen in Fig. 4. In the first three planes of this figure we can see different captures of the waveform in single-shot acquisition mode, where the presence of sub-pulses (sub-units) with an average duration on the order of ~1 ns is clearly visible. On the left side of the NLP, towards shorter times, the waveform is compact and displays a steep slope, whereas on the right, the waveform tends to break into multiple sub-pulses with random temporal distribution; their amplitudes decline smoothly from left to right, until they disappear completely on the scope. This smooth decay at the right side of the waveform is also visible in the fourth plane of Fig. 4, where 10000 traces are averaged. The quasi-stationary regime observed is similar to the dynamics reported in [41], where sub-structures at sub-ns scale were found to be released from a NLP, drifting away from the main packet on the right side and decaying progressively with increasing distance. For this regime the optical spectrum and the autocorrelation trace are very similar to those of Fig. 2.

 

Fig. 4 Temporal profiles showing a less stationary regime than in Fig. 2(b), obtained by slight adjustments of the QWR.

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Finally, at the 80% laser output, a spool of 100 m of length of highly nonlinear fiber (HNLF, nonlinear coefficient γ = 10.8/W/km, 1550-nm zero-dispersion wavelength) with a very low dispersion slope of 0.006 ps/(nm²∙km) was spliced in an attempt to enhance the spectral broadening of the NLP. A taper ensured minimal loss between the fibers having very different values of mode area. For this measurement, the laser was set in a stable fundamental NLP regime, such as the one depicted in Fig. 2. A stable train of pulses was still obtained at the HNLF output, same as in Fig. 2(a). By measuring the optical spectrum on the OSA, an extended and very flat SC spectrum was observed, covering 450 nm, from below 1300 nm to 1750 nm, as can be seen in Fig. 5. Because of the prominence of the peak of erbium emission in the 1550 nm region, the 3-dB bandwidth is only of 30 nm, however the bandwidth is as large as 260 nm at 10 dB and 375 nm at 15 dB from the peak. The use of the HNLF at the laser output results in a widening of the spectrum in the order of hundreds of nm towards shorter wavelengths with respect to the spectrum measured directly at the laser output (Fig. 2(c)). It can be appreciated that there are a pair of peaks (shoulders) on either sides of the spectral maximum at 1536 nm, around 1400 nm and 1700 nm. We conclude that these peaks are due to degenerate FWM because the HNLF has zero second-order dispersion at 1550 nm, which favors phase-matching, and these lateral peaks are equidistant from the central peak in terms of frequency: Δν₁ = 18.96 THz and Δν₂ = 18.83 THz (see Fig. 5). Besides, according to the asymmetric shape of the spectrum we conclude that intrapulse Raman scattering (self-frequency shift) also plays a part; in contrast, no SRS peak is observed at 1650 nm, which is consistent with the fact that the SRS threshold is higher than the FWM threshold under phase-matching conditions [43].

 

Fig. 5 Extended SC spectrum of fundamental mode-locking with a 100-m-long HNLF at the laser output.

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In this work, using a F8L scheme including a polarization-imbalanced NOLM without polarization control, NLPs with quite remarkable properties were produced. Firstly, in spite of the low laser efficiency, stable single-pulse energies as high as 300 nJ were obtained, which is to the best of our knowledge the highest NLP energy directly at the laser output reported to date [7,12–14]. In particular, splitting into multiple pulses, which usually restricts maximal NLP energy as pump power is raised in polarization-controlled schemes [7], was not found to be a limiting factor in this case. Although harmonic mode-locking was evidenced, the low order values reported in this work (only up to 6, which contrasts with more than 1000 in [7,39]) are consistent with the reduced tendency of the NLP to split into multiple pulses in the present scheme. The low value of laser efficiency (~1%) can be attributed mainly to the location of the output coupler in the scheme in Fig. 1, and to its coupling ratio. Inserting this coupler after the EYDCF, at the point where intracavity power is the highest, would improve the output power and the efficiency, which is currently affected by the PI-ISO insertion loss (~2 dB) and the nonlinear loss introduced by the NOLM. Besides, the output power (and the efficiency) of the laser could be maximized by optimizing the coupling ratio of the output coupler. For example, Fig. 2(b) in [9] illustrates how the laser output power strongly depends on the output coupling ratio. Finally, optimizing the EYDCF length, reducing splice losses between EYDCF and SMF-28 fibers (caused by mode field diameter mismatch) can also contribute to further increase the efficiency. After such an optimization process, we believe that single NLP energies of 1 μJ or beyond could be reached. Secondly, the broad and smooth optical spectrum, extending over more than 200 nm is at least comparable with those obtained in previous studies [9–11,35,36], and can be readily extended and further flattened using a HNLF at the laser output. In terms of 3-dB bandwidth, much larger values, exceeding 100 nm, have been obtained in [9,40] (where a HNLF is also used, although inserted in the cavity). However it should be stressed that, in many cases, this measurement offers a very incomplete picture of the observed spectra. For example, in [10], the 3-dB bandwidths of the reported spectra are around 10-20 nm in the 1550 nm region; however these values do not reflect the very broad extension of these spectra, which actually expand (and sometimes are quite flat) over ~200 nm. In this work, we observed that 10-dB and 15-dB bandwidths account more accurately for the actual expansion of our spectra. In this case, the corresponding values compare with (and even exceed) those obtained in [9,10,40]. It has to be stressed also that, at the HNLF output, spectral broadening does not only take place to the right, as it usually occurs, but is also observed towards shorter wavelengths (down to 1300-1400 nm, see Fig. 5). Finally, starting from moderate values of pump power, mode locking is self-starting, which is not a common characteristic of the F8L with polarization-imbalanced NOLM (an exception can be found in [42]).

In ring cavity designs, where mode locking relies on NPE, a polarizer is used in order to provide the switching characteristic. Similarly, in previous studies of the F8L based on a polarization-imbalanced NOLM [6,11,41,42,44], a polarizer is included in the ring section of the laser, in order to control the polarization at the NOLM input. Controlling input polarization allows controlling the switching characteristic of the NOLM, in particular the switching power [45,46], and thus the mode locking operation and pulse properties [6]. Without polarizer, the polarization is no longer controlled. Even so, for most input polarization states, there is still polarization asymmetry created by the QWR in the NOLM, thus switching still occurs, however the switching power is not properly defined. The absence of a polarizer in the present work may be connected with the enhanced NLP properties, because the state of polarization along the cavity is no longer restricted. This means that the laser radiation has greater freedom to self-adjust, adapting its polarization and thereby selecting the NOLM switching power, in order to optimize the mode locking operation. This automatic adjustment faculty may have an incidence on the self-starting characteristic of the laser and the properties of the generated pulses. Actually, different components of the NLP may adopt different polarization states, corresponding to different switching powers. More generally stated, by allowing polarization to adjust freely, the absence of a polarizer in the present scheme adds an additional degree of freedom to the already complex nature of NLPs, and this may constitute a key ingredient to overcome the limitations imposed by the laser cavity on the pulse energy and bandwidth.

The idea that the absence of a polarizing element may improve the NLP characteristics, in particular their spectral bandwidth and energy, is to some degree supported by the literature, in particular in the limit of long (>100 m) cavities. Increasing the cavity length is a well known strategy to increase the pulse energy; however, NLP splitting may set an upper limit to this energy. Such splitting has been observed in ring cavities with a polarizer, including km-long designs [7,39], but also a much shorter setup [40], even though the pump powers were much lower than in this work. On the other hand, previous record-high NLP energies were obtained using long figure-eight lasers without polarizing element; no pulse breaking or multiple pulsing was observed with these schemes [13,14]. In terms of bandwidth, although light propagation through km-long cavities should favor spectral broadening through nonlinear processes such as stimulated Raman scattering, record-low NLP bandwidths of a few nm were reported in [7,39], which include a polarizer. Unfortunately, polarization is an aspect that is seldom discussed in the frame of the study of NLPs (one exception can be found in [47]), and further work will be required to clarify its influence on the mode locking operation of such lasers and on the properties of the generated pulses.

4. Conclusions

We studied a F8L including a polarization-imbalanced NOLM and no polarizer. NLPs with duration of ~13 ns, a coherence time of 1.02 ps and 302.8 nJ pulse energy have been reached with a very broad and flat SC spectrum over 200 nm, from ~1520 nm to 1750 nm (the upper limit of the OSA). In addition to fundamental mode-locking operation, harmonic mode-locking to the 6th order is achieved. Finally, we were able to further extend the SC spectrum mainly towards shorter wavelengths, reaching a bandwidth of more than 450 nm, by inserting a 100-m-long HNLF at the laser output. The enhanced features of the NLPs compared to previous studies could be related to the particular cavity design in which the state of polarization is not restricted.