1. Introduction

Recently, new types of saturable absorbers based on single-walled carbon nanotubes (SWCNTs) have been intensively investigated for the fiber and solid-state laser mode-locking. SWCNT-based saturable absorbers benefit from rather simple manufacturing process in comparison with SESAMs, sub-picosecond recovery times, broad absorption spectra, and acceptable nonlinear modulation depths. These advantages together with merits of the thulium-doped fiber give rise to possible application of mode-locked thulium-doped lasers in the atmosphere spectroscopy [1], micromachining, medicine [2], LIDARs and others. Different schemes incorporating SWCNT saturable absorbers have been reported lately for thulium-doped mode-locked fiber lasers [3–5]. At first, SWCNTs were positioned as a thin polymer film between two optical connectors into the ring laser cavity [3]. In [4], a linear cavity configuration based on a fiber taper embedded in an SWCNT/polymer composite was employed. The usage of the simple dry-transfer contact press method of SWCNTs deposition onto a highly reflective Au-mirror was also presented for linear cavity configuration [5]. Ultrashort pulse generation achieved in the above-mentioned lasers resulted in the shortest pulses ranging from several picoseconds down to 750 fs [4].

A nonlinear amplifying loop mirror (NALM) application as an additional saturable absorber provides efficient self-switching, pedestal suppression and pulse shaping. The gain incorporation as well as unequal splitting ratio breaks the symmetry in the loop. As an active fiber is placed asymmetrically inside the loop, the gain immediately amplifies one pulse while the counter-propagating pulse is also eventually amplified in the end of its transmission around the loop. Thus, the nonlinear Kerr effect in the fiber causes an intensity-dependent difference in the optical path lengths and phase delay for counter-propagating pulses [6]. This leads to the intensity dependent loop mirror reflectivity, providing an efficient pulse shortening mechanism by appropriate linear phase delay adjustment in the loop, which can be realized through the polarization control implementation adjusting also a generation wavelength.

In contrast to the CW lasing, GVD management inside the loop substantially promotes the NALM operation properties for the short pulse generation by significant CW signal suppression. Due to strictly different evolution of counter-propagating pulses transmitted inside the dispersion-imbalanced loop, there occurs an additional intensity-dependent phase shift [7]. As a result, generated pulses can be switched out of the NALM while any CW background signal is reflected by dispersion-imbalanced loop. Furthermore, NALM pulse cubing impact results in the effective background wave suppression and, therefore, pulse interactions reduction [8].

We report for the first time to the best of our knowledge on the NALM-based thulium-doped all-fiber laser mode-locked by means of a polymer film incorporating SWCNTs. Dispersion-imbalanced NALM acts as an additional fast saturable absorber providing an efficient pulse shortening along with background signal suppression. The SWCNTs and NALM used together form a hybrid mechanism for mode-locking initiation that provides self-switching, spectral sidebands suppression and generation of high-qualify femtosecond pulses.

2. Experimental scheme

The experimental setup of the laser is presented in Fig. 1(a) . The laser cavity is formed by linear and nonlinear fiber loop mirrors. The linear one (FLM) has estimated reflection of 88% at 1.9 μm. The other mirror is a NALM based on a 20:80 fiber coupler. Here a 0.7 m-long segment of a step-index (Δn = 0.012) thulium-doped aluminum-silica (0.8 wt% thulium, 3.6 wt% aluminum) glass fiber (TDF) is positioned asymmetrically inside a loop. The TDF dispersion, measured by low-coherent interferometric technique, varied monotonically in the 1.2-2.1 µm wavelength range giving β₂ = −76 ps²/km at 1.9 µm. The active fiber possesses 10 μm core diameter with λ_c ≈2.2 µm cutoff wavelength, and 60 dB/m non-saturated absorption at 1.56 μm. Pump radiation of 1 W max power from a CW erbium-ytterbium co-doped fiber laser was coupled into the NALM in a clockwise direction through the 1.56/1.9 µm wavelength division multiplexer (WDM).

 

Fig. 1 a) Schematic sketch of the Tm-doped ML fiber laser. Insert: pulse train; b) transmission spectra of the CMC films

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A short segment of a low-loss normal dispersion highly nonlinear (β₂ = + 280 ps²/km, Δn≈0.11, d_eff ≈3.4 µm, γ ≈15 W^–1·km^–1 at 1890 nm) germanium-silica fiber (GeO₂/SiO₂) is incorporated into the fiber loop to manage the overall net cavity dispersion. Germanium oxide concentration in the fiber core was estimated to be 75 mol% [9]. The length of the GeO₂/SiO₂ fiber was varied during experiments through a cutback method. A squeezing hand-made polarization controller (PC) inserted into the loop provides both an efficient lasing wavelength tuning and appropriate adjustment of NALM operation regime.

Radiation emerging from the NALM enters the linear part of the cavity, consisting of SWCNT-module, additional polarization controller (PC) and FLM terminated the cavity. A polymer film with dispersed SWCNTs is fixed between two angle-polished ferrules of optical APC-connectors. An additional commercially available polarization controller positioned herein assists in achieving a stable mode-locking.

A fiber isolator (ISO) is spliced to the laser output to prevent laser radiation transmitting back to the laser cavity, while a fiber-pigtailed collimator (GRIN) ensures low-divergent output beam necessary for further pulse measurements.

The SWCNTs were synthesized by the arc discharge method in the helium atmosphere with the means of the Ni – Y₂O₃ catalyst in the C:Ni:Y₂O₃ 2:1:1 mixture filling a graphite anode. Carbon nanotubes synthesized by the arc-discharge method have an optical-absorption band shifted to the IR range compared to the absorption bands of nanotubes synthesized by the laser ablation, CVD, HiPCO or other methods [10]. Stable suspensions of individual SWCNTs in 1 wt% aqueous solution of the carboxymetylcellulose (CMC) have been prepared by ultrasonification followed by ultracentrifugation (acceleration of 150000 g) and a slow evaporation of the solvent [11]. The cellulose is simultaneously an efficient surfactant and the matrix material. Due to this fact, the only two components (cellulose and SWNTs) are needed to compose the suspension in order to create high-optical quality films. The cellulose is high flexible polymer and thus can form thin films with a thickness down to 4 or 6 μm [12]. A SWCNT diameter was estimated by Raman spectroscopy to be about 1.4 nm. To vary the amount of non-saturated losses in SWCNT-module we inserted CMC films with different nanotubes concentration. The thickness of films used in the experiments was ~10 µm. Transmission spectrum of the appropriate CMC film with dispersed SWCNTs is presented in Fig. 1(b) (blue trace). The most stable mode-locking regime was provided by simultaneous usage of two serial films in one saturable absorber module giving the total transmission value of 57.6% at 1.9 μm wavelength (Fig. 1(b); red trace).

For appropriate output pulse compression, an external dispersion delay line was realized by insertion of a short segment of the same GeO₂/SiO₂ fiber spliced at the NALM output. The most suitable length of the normal dispersion GeO₂/SiO₂ fiber (~0.31 m) corresponds to external GVD value of ~-0.031 ps² providing the generation of near transform-limited high-quality ultra-short pulses.

Through an accurate PCs adjustments, we have observed self-starting single-pulse mode-locking in the Tm-doped fiber laser. Once a mode-locking was initiated the laser has been operating in single-pulse regime for a long time without any perturbations.

3. Experimental results

While the GeO₂/SiO₂ fiber length was cut back from 80 cm, the overall net cavity dispersion varied from −0.044 to −0.131 ps². The pulse repetition period ranged from 25 to 22 ns corresponding to the pulse repetition frequency changing from 40 to 45.5 MHz. Figure 2 presents the evolution of the pulse intensity autocorrelation trace full-width at half maximum (FWHM), spectrum bandwidth and time-bandwidth product through the intracavity GVD variation. Pump power during these experiments was adjusted at a constant level of 310 mW.

 

Fig. 2 Evolution of laser pulse characteristics by varying the intracavity dispersion

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As it is seen in Fig. 2, pulse intensity autocorrelation trace FWHM varied from 1.69 ps down to 700 fs, while spectrum FWHM ranged in this case from 4.7 up to 15.8 nm giving time-bandwidth product variation from 0.32 to 0.6. The laser average output power slightly oscillated around 6.3 mW. Figure 3 presents autocorrelation traces and corresponding spectra measured at different values of the net cavity dispersion.

 

Fig. 3 Output pulse characteristics: a) autocorrelation traces; b) spectra

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Autocorrelation traces and spectra in the case of near zero intracavity dispersion (D₂ = −0.044 ps²) could be accurately approximated by the Gaussian-function (Fig. 3(a); red trace). Thus, the pulse duration was estimated to be 1.2 ps. At a given spectral bandwidth of 4.7 nm, time bandwidth product value reached as much as 0.48. It is slightly larger than a well-known value of 0.441 inherent to Gaussian transform-limited pulses, suggesting a generation of slightly chirped laser pulses.

Despite the fact that dispersion map was created in the laser cavity, the autocorrelation trace kept near soliton-like envelope for larger values of anomalous GVD (Fig. 4 ). The soliton-type function [13] fitted output autocorrelation trace profiles more accurately than Gaussian one, giving rise to the pulse-length variation from 450 to 620 fs. For example, in the case of a −0.124 ps² intracavity GVD value, 520 fs soliton pulses (∆ν·∆τ = 0.32) with a 3-dB spectral bandwidth of 7.33 nm were generated.

 

Fig. 4 Autocorrelation trace approximation in the case of net cavity dispersion D₂ = −0.093 ps²

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The shortest pulse duration of slightly less than 450 fs was obtained at the intracavity dispersion value of −0.093 ps². Corresponding spectrum bandwidth reached 15.8 nm, giving time-bandwidth product value of 0.6 (Fig. 3; light blue plots). However as it is seen in Fig. 3 and Fig. 4, autocorrelation traces contain uncompressed wings along with a low-intensity pedestal, spreading over 20 ps, which may arise from a slightly inappropriate external GVD value also with insufficient pulse formation by the NALM based on a non 3-dB fiber coupler.

An increase of pump power up to 560 mW results in the preserving a single-pulse operation regime, giving 18 mW average power and 0.4 nJ pulse energy respectively in the case of −0.086 ps² net cavity GVD. Pulse intensity autocorrelation trace and spectrum depicted in Fig. 5 are quite smooth and does not contain any distortions proving high-quality ultra-short pulse generation. Given pulse duration was estimated to be 640 fs with a spectrum FWHM of 7.6 nm, which corresponds to 0.41 time-bandwidth product value and ~625 W peak power. It should be noticed that further pump power increase was limited by damage threshold of CMC polymer films.

 

Fig. 5 Output pulse characteristics: a) autocorrelation trace; b) spectrum at high average power

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It is worth noting that due to the background dispersive wave suppression by the NALM, the laser spectrum was almost free of characteristic soliton sharp Kelly-sidebands if the intracavity dispersion was slightly less than zero. Nevertheless, after the negative dispersion was increased up to −0.1 ps² its impact on a pulse formation became more evident providing well-resolved Kelly side bands generation (Fig. 3; black plot). To approve a soliton pulse generation too, an amount of the net cavity dispersion D₂ was estimated according to n-order Kelly side bands position Δλ with respect to the central wavelength λ_c [14]:

The net cavity dispersion has been found to be equal to −0.124 ps² for n = 2 in the case of 23-cm-long GeO₂/SiO₂ fiber (Fig. 3; black curve). It is in exact agreement with aforementioned GVD value.

Transmission of the NALM for pulses with a peak power P(t) could be estimated as [15]:

Here ρ is the bar port transmission of the coupler, G – the active fiber total gain, and L_NALM is the loop length. In addition, if the next condition is fulfilled:

Obviously, it is quite difficult to calculate the real transmission of the NALM for presented laser setup, because we are not aware of parameters of the pulses launched into the NALM. However, it may be fairly interesting to estimate NALM operation peculiarities using output pulse parameters together with given laser characteristics. As it is seen in Fig. 6(a) , the NALM transmission dependence possesses two maxima corresponding to significantly different pulse powers, which is in good agreement with a NALM operation theory [16]. It should be noticed that one maximum corresponds to the shortest pulse, while the other – to the longest one.

 

Fig. 6 NALM transmission dependence on a) pulse peak power; b) GVD inside the loop

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Figure 6(b) gives an understanding of how the total GVD inside the NALM influences on its transmission value. It is obviously seen in Fig. 6(b) that in the case of near zero dispersion inside the loop the NALM transmission reaches its maximum regardless of the input pulse parameters such as pulse length and peak power. It is worth noting that the same result was observed in the NALM-based laser mode-locked by the SESAM [17]. Thus, we may suggest that to realize a generation of shortest pulses with widest spectrum by a NALM based mode-locked laser, the total dispersion inside the loop has to be close to zero. It is quite different from the well-known stretched-pulse lasers, whose total intracavity dispersion must be near zero for the shortest pulse generation.

4. Conclusion

In conclusion, we have demonstrated for the first time to the best of our knowledge the thulium-doped entirely all-fiber sigma-cavity laser with a nonlinear amplifying loop mirror inside. The laser was mode-locked by the co-action of CMC polymer films incorporating SWCNTs and the NALM as an additional fast modulator. We quite accurately investigated an evolution of laser pulse characteristics through the intracavity dispersion variation. By careful intracavity and external dispersion management, the laser generated as short as 450 fs soliton-like pulses at 1870 nm with 45.5 MHz repetition rate. We observed that for shortest pulse generation the total dispersion inside a NALM has to be close to zero. The maximum pulse energy was achieved to be 0.4 nJ corresponding to the laser peak power of 625 W.