Lead Sulfide Saturable Absorber Based Passively Mode-Locked Tm-Doped Fiber Laser

Abstract

In this paper, a passively mode-locked Tm-doped fiber laser by employing lead sulfide (PbS) nanoparticles as the saturable absorber (SA) is successfully demonstrated in the 2 μm region for the first time, to the best of our knowledge. Measured by a home-made balanced twin-detector setup at 2 μm, the PbS SA was characterized by the modulation depth of 10.69%, the non-saturable loss of 74.27%, and the saturable peak intensity of 8.62 MW/cm2, respectively. The laser delivered stable conventional soliton with a pulse duration of 1.24 ps and a repetition rate of 21.93 MHz. The center wavelength and 3 dB bandwidth are 1957.37 nm and 3.43 nm, respectively. Additionally, the second-order harmonic soliton pulses with a repetition rate of 43.86 MHz were also observed by further increasing the pump power. Our work reveals that PbS material is a reliable SA applied for pulse generation in the 2 μm spectral region.

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Lead Sulfide Saturable Absorber Based Passively Mode-locked
Tm-doped Fiber Laser
Fei Liu1, Ying Zhang2, Xiaodong Wu1, Jianfeng Li1, Senior Member, IEEE, Fei Yan1,
Xiaohui Li2, Abdul Qyyum2, Zhu Hu1, Chen Zhu3, and Yong Liu1, Senior Member, IEEE
1State Key Laboratory of Electronic Thin Films and Integrated Devices, School of Optoelectronic Science and Engineering, University of
Electronic Science and Technology of China (UESTC), Chengdu 610054, China
2School of Physics and Information Technology, Shaanxi Normal University, Xi’an 710119, China
3Science and Technology on Solid-State Laser Laboratory, Beijing 100015, China
This work is supported by National Natural Science Foundation of China under Grant 61435003, Grant 61722503, and Grant 61421002,
the Fundamental Research Funds for the Central Universities under Grant ZYGX2019Z012, the Science and Technology on
Solid-State Laser Laboratory, the Joint Fund of Ministry of Education for Equipment Pre-research under Grant 6141A02033411, and
the Field Funding for Equipment Pre-research under Grant 61404140106. Corresponding author: Jian-feng Li (e-mail:
lijianfeng@uestc.edu.cn).
Abstract: In this paper, a passively mode-locked Tm-doped fiber laser by employing lead sulfide (PbS) nanoparticles as the saturable
absorber (SA) is successfully demonstrated in the 2 μm region for the first time, to the best of our knowledge. Measured by a
home-made balanced twin-detector setup at 2 μm, the PbS SA was characterized by the modulation depth of 10.69%, the
non-saturable loss of 74.27%, and the saturable peak intensity of 8.62 MW/cm2, respectively. The laser delivered stable conventional
soliton with a pulse duration of 1.24 ps and a repetition rate of 21.93 MHz. The center wavelength and 3 dB bandwidth are 1957.37 nm
and 3.43 nm, respectively. Additionally, the second-order harmonic soliton pulses with a repetition rate of 43.86 MHz were also
observed by further increasing the pump power. Our work reveals that PbS material is a reliable SA applied for pulse generation in the
2 μm spectral region.
Index Terms: Tm-doped fiber laser, lead sulfide, saturable absorber, mode-locking.
1. Introduction
In recent years, 2 μm mode-locked Tm-doped fiber lasers have attracted much attention owing to its unique applied
advantages in mid-infrared wavelength conversion, medical diagnosis, laser LIDAR, nanoscale imaging, special material
processing and so on [1-7]. A key point for the formation of mode-locking is the saturable absorption effect, which can be
achieved using either artificial SAs based on fiber’s nonlinear Kerr effect or real SAs based on the nonlinear absorption
effect [8-10]. However, the former usually needs strong pump strength and long cavity length due to the high nonlinear
threshold of silica fiber, which inevitably leads to bulky construction and is not conducive to realize the self-starting of
mode-locking [11,12]. Therefore, the real SAs with a low response threshold are alternatively adopted to achieve
mode-locking. In the past few decades, semiconductor saturable absorber mirrors (SESAMs) [13-15] has been regarded as
one of the most important elements for mode-locking. However, it usually requires complex fabrication process and costly
systems. Nowadays, a series of low dimensional SAs including CNTs [16-18], graphene [12, 19-21], transition metal
dichalcogenides (TMDCs) (e.g., WS2, MoS2, WSe2, MoSe2 and ReS2) [22-27] and black phosphorus [28-31] have been
regarded as good substitutes for SESAMs. These SAs have been widely used to achieve mode-locking at different optical
bands. Among them, CNTs are widely adopted because of its good stability and fast response time. Especially, Liu et al.
revealed the dynamics buildup process of soliton molecules, harmonic mode-locking states, and the transition from
Q-Switching to mode-locking in a CNT SA based ultrafast fiber laser [32-34], providing the theoretical and experimental
basis for the researchers to better understand the soliton dynamics in the fiber laser. Nevertheless, the accurate control of
CNT’s diameter is required to match the desired laser wavelengths with the absorption, which restricts its broadband
tunability. Although graphene possesses an excellent broadband absorption performance as a result of its zero bandgap,
suitable modulation depth for pulse generation cannot be ensured due to the weak absorption of approximately 2.3% per
layer. Owing to the unique absorption, TMDCs have been also employed to achieve pulsed fiber laser in the visible spectral
range. But large direct bandgaps of TMDCs result in that suitable defects should be introduced to extend laser wavelengths,
which increases their fabricating complexity and limits their application in mid-infrared region. In contrast, black phosphorus
as an emerging SA in recent years, offers a layer-dependent bandgap from 0.3 (bulk) to 2 eV (monolayer), widely covering
the bandgap range of graphene and TMDCs. Unfortunately, it is easily oxidized and has a bad stability.

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Most recently, semiconductor PbS nanoparticles as the oldest light-harvesting materials for infrared detectors [35],
biomarkers [36, 37] and solar cells [38, 39], presented its great optical potential from near-infrared to mid-infrared region (1
~3.2 μm) [40, 41]. Owing to its narrow bandgap (0.41 eV), bandgap tunability and good long-term stability, PbS
nanoparticles have attracted people’s intensive attention and been regarded as an effective SA material to overcome the
shortcomings of the aforementioned materials. Lee et al. demonstrated a 1.55 μm passively Q-switched erbium-doped fiber
laser by using the film-type PbS quantum dots (QDs) material as the SA [42]. After that, based on the PbS/CdS core/shell
QDs SA, Ming et al. obtained the mode-locked Er-doped fiber laser with 54 ps pulse duration and 2.71 mW maximal output
power [43]. Then, at the same waveband, the PbS QDs in polystyrene films was fabricated to realize the Q-switched
Er-doped fiber laser by Sun et al. This fiber laser yielded stable Q-switched pulses with maximum output power of 40.19 mW
and pulse duration of 3.9 μs [44]. Due to the polymer films structure, however, these PbS QDs as SAs have low damage
threshold and consequently limits the performance of mode-locking. By employing the PbS nanoparticles without any
polymer as the SA, Zhang et al. have obtained a 1533 nm mode-locked fiber laser with good stability for more than 1 month,
which proved the potential of PbS nanomaterials in ultra-short pulse generation [45]. Furthermore, using the same PbS
nanoparticles, our research group has successfully demonstrated the Q-switched Dy3+-doped fiber laser that is tunable from
2.71 to 3.08 μm [46]. Although these works indicate that PbS material as the SA is a good candidate for the fiber lasers at
1.5 μm and 3 μm wavelength range, it has never been reported in the 2 μm region.
In our work, we experimentally demonstrated a stable 2 μm passively mode-locked Tm-doped fiber laser using PbS
nanomaterials as the SA. The nonlinear characteristics of PbS were measured by a 2 μm home-made mode-locked fiber
laser. The fiber laser mode-locked by PbS SA delivered stable conventional soliton pulses operating at fundamental
repetition rate state. When further increasing pump power, a second-order harmonic mode-locking was also obtained.
2. Preparation and Characterization of PbS SA
In our experiment, the PbS sample was prepared by using the sol-gel method and mixing PbS powder with acetone solvent
in a volume ratio of 1:3. Stable PbS nanoparticles dispersion was collected from the supernatant after centrifugation to
separating large agglomerations for 30 minutes at 2000 rpm in a vortex mixer (Langyue SK-1, China). For the PbS
nanoparticles dispersion, the scanning electron microscopy (SEM: Hitachi SU8220, Japan) images with different scales (2
μm and 500 nm) are shown in Figs. 1(a) and 1(b). It is seen that PbS nanoparticles obviously present irregular
microstructure, mainly existing in the forms of stereo-structure and polygon. Feng et al. explained the reason why the
irregular shapes of PbS nanoparticles formed [47]. In Fig. 1(c), the transmission electron microscopy (TEM: JEOL JEM-2100,
Japan) image provides that the lateral size of PbS nanoparticles is in the range of 75-200 nm. The measured average size
of individual PbS nanoparticle is approximately 80 nm. Note that some of the larger and the darker nanoparticles were
generated by the agglomeration of smaller particles [48, 49]. Thus, the size distribution of PbS nanoparticles is not as broad
as we can see. Figure 1(d) presents a high resolution TEM (HRTEM: JEOL JEM-2100, Japan) image with 10 nm lateral size.
The observed spacing of lattice fringes is approximately 0.33 nm. A clear cladding was formed by acetone attached solution
during the fabrication process of PbS nanoparticles dispersion, which reveals a signal of good dispersibility. As illustrated in
Fig. 1(e), the energy dispersive spectroscopy (EDS) analysis of PbS nanoparticles was also executed. It is seen that the
chemical composition of the sample corresponds well to the atomic structure of PbS, except for Si and Al derived from the
sample placement stations. To further confirm the pulse generation performance of PbS nanoparticles dispersion, it was
deposited on the end face of fiber jumper (shown in the inset of Fig. 1(f)) and then was fabricated as a fiber-compatible SA.
Fig. 1. Characterization of PbS nanoparticles dispersion. (a) The SEM image with 2 μm scale. (b) The SEM image
with 500 nm scale. (c) The TEM image with 200 nm scale. (d) The HRTEM (high-resolution TEM) image with 10 nm
scale. (e) The EDS analysis. (f) Photograph of PbS nanoparticles dispersion and the fiber-compatible PbS-SA device.

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Additionally, we designed a typical balanced twin-detector setup to investigate the nonlinear transmission characteristics
of PbS SA in the experiment, as depicted in Fig. 2(a). The home-made 2 μm all-fiber pulse laser source consists of a
picosecond Tm-doped fiber laser seed and a Tm-doped fiber amplifier. For the amplified picosecond pulse with a maximum
average power of 39.6 mW, its repetition rate, pulse duration, and signal-to-noise ratio (SNR) are 10.27 MHz, 21 ps, and
60.5 dB, respectively. The laser output was divided into a reference path and a measurement path using a 3-dB optical
coupler. To minimize the measuring errors, the average output powers of two optical paths were detected using the same
model power meters with the measurement accuracy of microwatt level. Figure 2(b) presents the nonlinear transmission
curve of PbS SA by fitting the measured data with the following formula [23]:
T (I) =1-ΔT×exp (-I/Isat)-αns, (1)
where T (I) is the transmittance and I is the incident peak intensity. ΔT, αns and Isat represent the modulation depth, the
non-saturable loss and the saturable peak intensity of PbS SA, which are calculated to be 10.69%, 74.27%, and 8.62
MW/cm2, respectively.
Fig. 2. (a) The experimental setup for the nonlinear transmission measurement of PbS SA. (b) Measured nonlinear transmission curves.
3. Experiment Setup
The experimental ring configuration of the Tm-doped fiber laser is presented in Fig. 3. With a (2+1) ×1 pump combiner (ITF,
Canada), a commercial multimode 793 nm laser diode (BWT, China) was utilized as pump source to supply outside energy
for the laser oscillator. A 1.1 m Tm-doped double-cladding fiber (Coractive-DCF-TM-10/128) was served as the gain fiber.
Tm-doped fiber is characterized by an octagonal shaped inner cladding with 0.45 numerical aperture (NA) and the circular
fiber core with 0.22 NA. A polarization-independent isolator (Advanced Photonics, USA) ensured laser’s unidirectional
operation. 10% of a 9:1 optical coupler (OC) (AdValue Photonics, USA) was utilized to output the laser. A polarization
controller (PC) was used to optimize the performance of mode-locking. PbS SA was positioned between the OC and PC.
The total laser cavity length is 9.43 m, including 1.1 m TDF and 8.33 m SMF28e tail fibers of the intra-cavity fiber
components. The anomalous dispersion values of these two fibers at 1.993 µm ware about −84 ps2/km and −80 ps2/km,
respectively [50]. The estimated value of net cavity dispersion is -0.75 ps2. In order to obtain the laser signal, an optical
spectrum analyzer (Yokogawa AQ6375, Japan) with a high resolution of 0.05 nm and an interference autocorrelator (APE
Pulsecheck, Germany) were respectively applied for the real-time measurement of optical spectrum and pulse duration. In
addition, a 2-μm InGaAs photodetector (EOT ET-5000F, USA) with a bandwidth of 12.5 GHz and a response time of 28 ps
was employed to detect the radio-frequency (RF) spectrum and oscilloscope trace.
Fig. 3. Setup of passively mode-locked Tm-doped fiber laser based on PbS SA.

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4. Experiment Results and Discussion
In the experiment, once the PC’s position was properly set, stable mode-locking was self-started by simply increasing the
pump power. Figure 4(a) presents the relationship between pump power and output power, as well as the operation state of
the passively mode-locked Tm-doped fiber oscillator. Continuous wave (CW) with the output power of 0.66 mW firstly
appeared at the pump power of 0.88 W. When the pump power was increased to 1.01 W, the laser switched into the
mode-locking regime. Conventional soliton with a maximum output power of 6.34 mW was obtained at the pump power of
1.54 W. A segment of double-cladding single-mode Thulium-doped fiber (DC-SM-TDF) was adopted in our work is the
reason why the pump threshold of the mode-locking is up to ~1 W. We can further improve the output power by optimizing
the parameter performance of PbS SA (such as the deposition thickness and the size of nanoparticles), and decreasing the
intra-cavity loss. Additionally, using a linear cavity mode-locking structure based on PbS SA is also a good method to realize
the higher power ultrashort pulse laser output. Figure 4(b) shows the corresponding optical spectrum of conventional soliton.
Its center wavelength and 3 dB bandwidth are 1957.37 nm and 3.43 nm, respectively. A series of Kelly sidebands
symmetrically distributed around the main peak is a good indication of the conventional soliton operation, which is caused by
the spectral interference of dispersive waves. Some sub-sidebands caused by the four-wave mixing (FWM) between the
orthogonal soliton components in the fiber laser [51], also can be observed on the mode-locked spectrum. Figure 4(c) shows
the measured interference and intensity autocorrelation trace with a 7-ps scanning range. Autocorrelation signal with a full
width at half maximum (FWHM) of 1.91 ps was fitted by using the sech2 function, corresponding to a pulse duration of 1.24
ps. Thus, the calculated time-bandwidth product (TBP) of 0.335 indicates that the mode-locking is almost transform-limited.
In Fig. 4(d), the RF spectrum with a resolution bandwidth of 3 kHz and a scanning range of 2 MHz shows a high signal-noise
ratio of 61.2 dB, which suggests the good uniformity of the pulse train. The measured repetition rate of 21.93 MHz is in
agreement with the theoretical cavity length dependent value, implying that single pulse was obtained per round trip. The
pulse train with the amplitude fluctuation of less than 0.8% is illustrated in the inset of Fig. 4(d), which exhibits the good
stability of the passive mode-locked fiber laser based on PbS SA.
Fig. 4. (a) Output power as a function of pump power. (b) Soliton optical spectrum. (c) Pulse autocorrelation with sech2 fitting.
(d) RF spectrum with the resolution bandwidth of 3 kHz and the scanning range of 2 MHz, inset: Oscilloscope trace.
The above single soliton state maintained at the pump range from 1.01 W to 1.54 W. When pump power exceeded 1.54
W, the multi-pulses appeared. By appropriately adjusting the pump power and the PC’s position, the multi-pulses operated
at the 2nd-order harmonic state. Figure 5 shows an example of this state at the pump power of 1.77 W. The spectrum is
presented in Fig. 5(a), showing a 3-dB bandwidth of 4.22 nm visibly wider than previous fundamental frequency soliton. It is
seen from the inset of Fig. 5(b) that the spectrum peak intensity monotonously decreases with increased order of the RF
spectrum component, and the separation between two adjacent spectrum components always keeps constant, suggesting
the high uniformity of the 2nd harmonic pulse train. The high signal noise ratio of 60.26 dB also indicates its good stability for

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pulse generation. Moreover, the RF spectrum with a scanning range of 1 MHz and a resolution bandwidth of 3 kHz was
measured to investigate the quality of the 2nd harmonic soliton pulses. In Fig. 5(c), the measured oscilloscope trace shows
that a stable pulse train uniformly exists with constant pulse separation of 22.8 ns, corresponding to the pulse repetition rate
of 43.86 MHz. This is twice of the fundamental repetition rate of the laser cavity, indicating the 2nd-order harmonic operation.
Figure 5(d) shows the measured autocorrelation trace with sech2 fitting in a 5-ps scan range. According to the FWHM of
1.682 ps when sech2-pulse fit is assumed, the pulse duration of harmonic mode-locking (HML) pulse is estimated to be 1.09
ps. The calculated TBP of 0.36 implies that the pulse is slightly chirped. The average output power is 9.06 mW
corresponding to the pulse energy of 206.8 pJ. Note that it is difficult to further increase the harmonic order in our
experiment, due to the high soliton splitting threshold in the large anomalous dispersion region determined by the soliton
area theorem [52, 53]. By reducing the net anomalous cavity dispersion or inducing high-nonlinear component to reduce the
soliton splitting threshold inside the laser cavity, the higher order harmonic or noise-like pulse could be realized. Until the
maximum pump power of 1.77 W, the mode-locking is still observed, suggesting that PbS SA is undamaged. According to
the intra-cavity laser intensity of 90.6 mW at stable mode-locking operation, the peak power density in the fiber laser is
estimated to be 360 MW/cm2, revealing that the PbS SA has a damage threshold higher than this value. In addition, the
mode-locked fiber laser could stably operate for more than half a month without any deterioration, which shows its good
long-term stability. Note that no Q-switching was observed due to low intra-cavity energy loss and a modulation depth
(10.69%) capable of achieving mode-locking. Many similar phenomena have been reported in graphene, carbon-nanotube,
or alcohol based pulse fiber lasers [54-58]. A key factor to realize the Q-switching operation is controlling the loss of the
oscillator. Thus, the Q-switched pulse can be achieved by adjusting the parameters of PbS SA or changing the operating
condition of this oscillator. For the SA material, we can prepare the PbS SA with a higher modulation depth and saturable
peak intensity to increase the pump threshold of fiber laser. Meanwhile, by changing the splitting ratio of optical coupler from
9/1 to 5/5, the Q-switched state can also be generated in the PbS SA based Tm-doped fiber laser due to the higher
intra-cavity loss. To indicate the unique advantages of PbS SA based mode-locking fiber laser, the mode-locked fiber lasers
with PbS SA and other different SAs were compared in Table 1. It can be seen that PbS SA has a higher modulation depth
appropriate for the mode-locking pulse generation. Moreover, the temporal pulse width of our fiber laser is almost
comparable to those from the lasers using graphene and TMDCs, and it is shorter than the laser output using CNT or
SESAM. The results suggest that PbS nanoparticles dispersion can be regarded as an effective saturable absorber for
ultra-short pulse generation in the Tm-doped fiber laser. This also provides us for a reliable ultra-short pulse source to
realize the nonlinear mid-infrared light generation in the future work.
Fig. 5. The second-order harmonic mode-locking pulse at the pump power of 1.77 W. (a) The optical spectrum. (b) RF spectrum
with the 3 kHz resolution bandwidth and 2 MHz scanning range, inset: RF spectrum with a scanning range of 1.0 GHz. (c)
Oscilloscope trace. (d) Pulse autocorrelation with sech2 fitting in a 5-ps scan range.

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Table 1. The comparison of 2 μm Tm-doped fiber lasers mode-locked with different SA materials
Saturable
Absoption
Materials
Modulation
Depth
@ 2 μm
Non-saturable
Loss
@ 2 μm
Pulse
Wavelength
(nm)
Output Spectral
Bandwidth
(nm)
Output Pulse
Width
(ps)
References
SWCNT
-
-
1944
0.45
10
[59]
graphene
-
-
1940
2.1
3.6
[20]
graphene
-
-
1901.6
1.5
0.37
[60]
graphene
-
-
1944
3.9
0.933
[61]
graphene
＜0.8%
-
1884
4
1.2
[62]
graphene
~2.7%
-
1912-1918
0.26@1908nm
6500
[63]
graphene
-
-
1953
2.2
2.1
[64]
SESAM
-
-
1980
92
1.5
[13]
SESAM
20%
16%
1962
0.37
18
[14]
SESAM
26%
-
1978
2
815
[15]
SESAM
20%
16%
1945
6.1
0.7
[65]
WS2
~10.9%
38.4%
1925
5.6
~1.3
[66]
MoS2
13.6
16.7%
1940
~17.3
843
[23]
MoS2
12.5%
27.2%
1927
2.86
1.51
[67]
MoSe2
4.4%
45.5%
1912.6
4.62
0.92
[68]
WSe2
1.83%
87%
1863.96
3.19
1.16
[69]
MoTe2
5.7%
70%
1930.22
4.45
0.952
[70]
PbS
10.69%
74.27%
1957.37
1961.2
3.43
4.22
1.24
1.09
This work
5. Conclusions
In summary, PbS nanoparticles dispersion was successfully employed as SA to achieve a passively mode-locked Tm-doped
fiber laser. Nonlinear saturable absorption properties of the PbS nanoparticles dispersion were also measured in the 2 μm
spectral region, by using the homemade measurement setup in our experiment. PbS SA has the measured modulation
depth of 10.69%, non-saturable loss of 74.27% and saturation peak intensity of 8.62 MW/cm2. When the laser operated at
the stable fundamental frequency mode-locked state, the pulse duration was measured to be 1.24 ps. In addition, by further
increasing the pump power, the mode-locking switches into the second-order harmonic regime with the repetition rate of
43.86 MHz and the SNR of 60.26 dB. These results suggest that PbS nanoparticles dispersion could be developed as an
effective SA material for 2 μm mode-locking generation.
Acknowledgements to author contribution
F. Liu designed the experiment, prepared the paper and discussed with J. F. Li. Y. Zhang, Abdul Qyyum and X. H. Li
fabricated PbS nanoparticles dispersion and provided the characterizations for PbS samples. X. D. Wu, F. Yan and Z. Hu
built up the system and finished the measurements with F. Liu. C. Zhu presented some good suggestion for the paper
writing. Y. Liu supervised the project.
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