Access to this full-text is provided by Optica Publishing Group.
Content available from Optics Express
This content is subject to copyright. Terms and conditions apply.
Research Article Vol. 30, No. 20 / 26 Sep 2022 / Optics Express 35911
Generation of different mode-locked states in a
Yb-doped fiber laser based on nonlinear
multimode interference
PEIYUN CHEN G, MENGMENG HA N, QIANYING LI,A ND XUE WEN SH U*
Wuhan National Laboratory for Optoelectronics & School of Optical and Electronic Information,
Huazhong University of Science and Technology, Wuhan, 430074, China
*xshu@hust.edu.cn
Abstract:
We demonstrated an ultrafast Yb-doped fiber laser with a single mode fiber-graded
index multimode fiber-single mode fiber (SMF-GIMF-SMF) structure based saturable absorber.
The GIMF was placed in the groove of an in-line fiber polarization controller to adjust its
birefringence, enabling the SMF-GIMF-SMF structure to realize efficient saturable absorption
based on nonlinear multimode interference without strict length restriction. By adjusting two
intra-cavity polarization controllers, stable dissipation solitons and noise-like pulses were achieved
in the 1030 nm waveband with pulse durations of 10.67 ps and 276 fs, respectively. We also
realized Q-switched mode-locked pulses in the same fiber laser cavity. By the dispersive Fourier
transform method, the real-time spectral evolution in the buildup process of the Q-switched
mode-locked state was captured, which showed that the continuous-wave in this laser could
gradually evolved into the stable Q-switched mode-locked pulses through unstable self-pulsation,
relaxation oscillation and rogue Q-switching stage. To the best of our knowledge, our work
reveals the buildup dynamics of the Q-switched mode-locked operation in a fiber laser for the first
time. And we also studied the real-time spectral evolution of the stable Q-switched mode-locked
pulses, which exhibited periodic breathing property.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Ultrafast mode-locked fiber lasers possess great application prospects in communication, medical,
industry and military fields due to the characteristics of high peak power, ultra-short pulse
duration, cost-effective design, compact and alignment-free structure. As the key component in a
mode-locked laser, the saturable absorber (SA) has an important impact on laser performance.
Various methods have been used to achieve saturable absorption, such as nonlinear polarization
rotation, nonlinear polarization evolution, nonlinear optical loop mirror, semiconductor saturable
absorber mirrors, graphene and other two-dimensional materials [1–10]. Most SA materials are
easily deteriorated in atmospheric environments, and their damage thresholds are low. Using SAs
based on all-fiber structures can avoid the above problems. The nonlinear multimode interference
(NLMMI) technique based on single mode fiber-multimode fiber-single mode fiber (SMF-MMF-
SMF) structure has been proposed to realize mode-locked operation in all-fiber laser cavity [11].
As light is coupled from SMF into MMF, multiple high-order modes will be excited in the MMF.
The multimode interference effect between modes will leading to self-imaging phenomenon
along the MMF [12]. When the incident light intensity is high enough, the nonlinear effect such
as self-phase modulation and cross-phase modulation in the fiber cannot be ignored, which will
lead to the nonlinear multimode interference effect [11]. Under this condition, the period of
the self-imaging is related to the light intensity. Therefore, for the MMF with fixed length, the
transmission efficiencies of the light with different intensity, coupling from MMF to SMF, are
different. When the length of the MMF matches
LM=(2m+1)
Z
/
2
(m=0, 1, 2, . . .)
, where Z
is the self-imaging period under low power, the low-power light will be coupled into the fiber
#468615 https://doi.org/10.1364/OE.468615
Journal © 2022 Received 22 Jun 2022; revised 20 Aug 2022; accepted 5 Sep 2022; published 15 Sep 2022
Research Article Vol. 30, No. 20 / 26 Sep 2022 / Optics Express 35912
cladding and consumed, while most of the high-power light will be coupled into the fiber core and
remained, thus achieving saturable absorption [13–15]. Compared with traditional mode-locking
methods, the NLMMI based fiber modulator possesses simple preparation method, low cost,
long service life and high-power tolerance. Since Nazemosadat et al. proved theoretically that
the SMF-MMF-SMF structure had typical saturable absorption characteristics in 2013 [11],
the use of such all-fiber SAs in fiber lasers has aroused great interest of researchers. In recent
years, various fiber structures based on NLMMI have been reported as artificial SAs, such as
the SMF-GIMF-SMF [15–25], single mode fiber-step index multimode fiber-single mode fiber
(SMF-SIMF-SMF) [14], single mode fiber-few mode fiber-single mode fiber (SMF-FMF-SMF)
[26] and so on. In order to achieve the saturable absorption, the length of the MMF should
satisfy an odd multiple of half of the self-imaging length. However, most of the self-imaging
lengths of common MMFs are in the order of millimeters or even micrometers, which makes
the fabrication of the SMF-MMF-SMF-based SAs require high-precision preparation during the
fiber cutting and splicing steps. Since the current fiber cutting and splicing methods usually rely
on manual operation, it is difficult to obtain a SMF-MMF-SMF structure that perfectly meets the
requirements. Therefore, it is necessary to explore new fiber structure preparation methods or
optimize the NLMMI fiber structures.
The output characteristics and operation mechanisms of different mode-locked fiber lasers have
also caused extensive concern, such as conventional solitons, dissipation solitons, bound solitons,
noise-like pulses, soliton explosion and so on. As most commercial optical spectrum analyzers
can only measure the average results of ultrafast pulses accumulated over the equipment sweep
time, the dispersive Fourier transform (DFT) technique is applied to study the real-time spectral
dynamics and ultrafast transient processes of various mode-locking operations. When an ultrafast
pulse is incident into a dispersive element with a large group velocity dispersion, the pulse will
be fully stretched, and each component with a different wavelength in the pulse will be discrete
in time domain due to the different group velocities of the light components, thus achieving the
frequency-time mapping. The DFT method, as an analogy of the Fraunhofer diffraction in time
domain based on the far-field approximation, can map the frequency spectrum of an ultrafast
pulse to a stretched temporal pulse waveform with a profile similar to the spectrum [27]. As
the DFT method can stretch the ultrashort pulse to nanosecond scale, the profile details of the
pulse spectrum can be resolved by high-speed oscilloscopes and photodetectors, which enables
high-resolution real-time spectral measurements. The formation mechanisms and real-time
evolution processes of different kinds of solitons and pulsation behaviors in mode-locked fiber
lasers have become a hot topic and have been widely studied based on the DFT method [28–31].
As an incomplete mode-locked state, the Q-switched mode-locked (QSML) state has both
mode-locking and Q-switching output characteristics, which is widely reported in ultrafast fiber
lasers [5,32–34]. It has been generally observed that the QSML pulses possess periodic dynamic
oscillation characteristics in time domain. However, the dynamic characteristics of the QSML
operation in frequency domain and its real buildup process have been rarely reported due to
the limitation of the measurement equipment. With the development of the DFT technology, it
becomes possible to study the spectral dynamics and real-time buildup evolution process of the
QSML pulses, which is important for further understanding the QSML operation in fiber lasers.
In this paper, we proposed a mode-locked Yb-doped fiber laser based on a SMF-GIMF-SMF
structure. We put 10 cm GIMF in the groove of an in-line fiber polarization controller (PC) to
tune its birefringence, so that the saturable absorption effect based on NLMMI can be realized
without strict length restriction by turning the PC. By increase the pump power and adjusting the
PCs in the cavity, stable dissipation solitons and noise-like pulses were observed in the 1030
nm waveband. We also obtained QSML pulses at 1032.6 nm. Based on the DFT method, the
entire buildup process of the QSML state was studied for the first time, which comprised unstable
self-pulsation, relaxation oscillation, rogue Q-switching stage and finally stable QSML state.
Research Article Vol. 30, No. 20 / 26 Sep 2022 / Optics Express 35913
Moreover, the experimental results also show that the spectral evolution of the stable QSML
pulses possesses periodic breathing property.
2. Experimental setup
A ring Yb-doped all-fiber laser cavity based on SMF-GIMF-SMF-SA was built, as shown in
Fig. 1(a). The pump source was a 980 nm laser diode (LD) with 250 mW maximum output
power. The pump light entered the fiber cavity through a 980/1030 nm wavelength division
multiplexer (WDM). A section of 15 cm ytterbium-doped single-clad fiber (YDF) was fused
with the 1030 nm output port of the WDM, serving as the gain medium. 10% of the light was
output from the cavity for studying through a 90:10 fiber coupler (OC). A 1030 nm polarization
independent isolator (PI-ISO) in the cavity limited the unidirectional propagation of light. Two
manual paddle fiber PCs (PC1 and PC2) were used to regulate the intra-cavity birefringence to
provide appropriate cavity conditions for the formation of mode-locking. The total cavity length
was
∼
12 m, with net normal dispersion. The characteristics of the laser output were monitored
by an optical spectrum analyzer (OSA), a digital oscilloscope with a 5 GHz photodetector (PD),
a radio-frequency (RF) spectrum analyzer, and an autocorrelator.
Fig. 1.
Experimental setup of the Yb-doped fiber laser based on a SMF-GIMF-SMF SA. (a)
Schematic diagram of the fiber laser. (b) The SMF-GIMF-SMF SA structure.
The SA was prepared by splicing two sections of SMF (HI 1060) on both sides of a
∼
10
cm long GIMF (YOFC, 62.5/125
µ
m) to form a SMF-GIMF-SMF structure, as shown in the
Fig. 1(b). The self-imaging period of the GIMF is in the order of micrometers, which makes it
hard to get accurate cutting length manually. In order to relieve the strict requirement on the
GIMF length when acting as a SA, several methods have been proposed, such as offset splicing
[19,20] or introducing an inner microcavity [21] when splicing SMF and GIMF, stretching the
GIMF through a precision translation stage [15–18], or inserting a short piece of large-mode-area
fiber between SMF and GIMF [22–24]. In our experiment, we placed the GIMF in the groove of
an in-line manual fiber PC, and then adjusted the PC to mechanically compress the GIMF, which
created stress-induced birefringence within the GIMF and introduced additional nonlinear phase
shift of the light in the GIMF. Under an appropriate birefringence condition, the total phase shift
of the high-power light reached an integer multiple of 2
π
, and the light was self-focused in the
fiber core, while the low-power light was coupled into the fiber cladding. That is, the nonlinear
phase shift of the light can be flexibly adjusted by rotating the PC to make the length of the GIMF
satisfy an odd multiple of the half-beat length, thus realizing saturable absorption. This approach
was more simple, flexible and low loss than other methods.
When the GIMF-SA was not inserted into the fiber cavity, no matter how to increase the
pump power or adjust the intra-cavity PCs, stable pulses cannot be obtained, indicating that other
devices in this cavity cannot provide effective saturable absorption to achieve self-mode-locking.
By inserting the GIMF-SA into the fiber cavity and carefully adjusting the in-line PC, we obtained
stable mode-locked pulses output. We studied the linear and nonlinear optical absorption
Research Article Vol. 30, No. 20 / 26 Sep 2022 / Optics Express 35914
characteristics of the GIMF-based SA at an effective status, and the results are presented in Fig. 2.
The linear transmission spectrum of this GIMF-SA from 1010 nm to 1060 nm waveband shown
in Fig. 2(a) was measured using a super-continuum broadband light source. The loss of the SA is
measured to be about -4.56 dB at 1030nm. The nonlinear transmission property of the GIMF-SA
was investigated using a home-made 1030 nm mode-locked fiber laser with a pulse duration of
∼
1
ps and a repetition rate of 12.5 MHz. Based on the balanced two-detector measurement method
[35], we obtained the nonlinear transmission curve shown in Fig. 2(b). And the experiment result
in Fig. 2(b) is fitted by the below function [36],
T=1−α0·exp(−I/Isat) − αns
where Tis the transmission,
α0
is the modulation depth, Iis the incident peak intensity,
Isat
is
the saturation intensity and
αns
is the non-saturable loss. As can be seen from the transmission
curve, the SMF-GIMF-SMF structure has typical saturable absorption properties. According
to the fitting curve, the modulation depth of the SA is
∼
8.8%, the non-saturable loss is 58.5%,
and the saturation intensity is 0.34 GW/cm
2
, which shows excellent nonlinear characteristics
comparable to real SA materials.
Fig. 2.
Optical absorption characteristics of the SMF-GIMF-SMF based SA. (a) The
transmission spectrum; (b) the nonlinear transmission curve of the GIMF-SA.
3. Results and discussion
3.1. Dissipation solitons
By adjusting the intra-cavity PC1 and PC2 appropriately, and increasing the pump power to
100 mW, stable dissipative solitons were achieved. The spectra with the central wavelength
of 1032 nm at different pump powers are presented in Fig. 3(a). The 3dB bandwidth of the
spectrum increases from 5 nm to 6.5 nm due to the self-phase modulation effect in the fiber
cavity. The spectrum has steep edges and “cat ear” structures on both sides of the spectral
profile, which are the typical characteristics of dissipative solitons in normal dispersion fiber
lasers [37,38]. The oscilloscope trace of the dissipative solitons is shown in Fig. 3(b). The
pulse interval period is measured to be ∼60 ns, which is equal to the time it takes light to travel
around the fiber cavity. And the low-amplitude parasitic peak adjacent to the main pulse is the
oscillating signal induced by the imperfect impedance matching of the oscilloscope and PD
used for measurement [42]. Figure 3(c) presents the soliton autocorrelation trace. The pulse
duration is 10.67 ps given by the sech
2
fitting. We also measured the RF spectrum of the laser
with a resolution of 3 kHz in different frequency measuring ranges, illustrated in Fig. 3(d) and
the inset. The center frequency of the RF spectrum is located at 16.67 MHz matched well with
the 12-m long cavity, demonstrating that the dissipative soliton operates at the fundamental
Research Article Vol. 30, No. 20 / 26 Sep 2022 / Optics Express 35915
frequency. The signal-to-noise ratio (SNR) is measured to be
∼
50 dB indicating good stability of
the mode-locked laser. We continuously monitored the spectrum for 2.5 hours. The result is
shown in Fig. 3(e). It can be noted that the spectral profile is nearly unchanged, which further
confirms the stable operation of the dissipative soliton.
Fig. 3.
Characteristics of the dissipative solitons. (a) Optical spectra at different pump
powers; (b) Oscilloscope trace of the soliton train; (c) Autocorrelation trace and the sech
2
fitting curve; (d) RF spectra in different frequency ranges; (e) Long-time spectrum monitoring
result.
3.2. Noise-like pulses
As the pump power was 105 mW, noise-like pulses can also be obtained in the same fiber cavity
by adjusting the PC1 and PC2 with the in-line PC state unchanged. The spectra under different
pump powers are shown in Fig. 4(a). The central wavelength is around 1030.5 nm with the 3dB
bandwidth of
∼
6 nm. With the increase of pump power, the 3dB bandwidth also increases slightly.
It can be seen that compared with the dissipative soliton, the spectrum of the noise-like pulse is
flatter, and there is no obvious sideband appearing on the spectrum. As shown in Fig. 4(b), the
pulse interval is
∼
60 ns corresponding to the cavity length of 12 m. Figure 4(c) presents the
autocorrelation trace of the pulse. It shows that the pulse profile has a very narrow spike structure
with a broad pedestal, presenting the characteristic feature of noise-like pulses [39,40]. The detail
of the spike structure with sech
2
fitting curve is shown in the inset of Fig. 4(c). The durations of
the narrow peak and the wide pedestal are 276 fs and
∼
4.9 ps, respectively. The RF spectra of the
laser measured in 15 MHz and 300 MHz spans with 3-kHz resolution are presented in Fig. 4(d)
Research Article Vol. 30, No. 20 / 26 Sep 2022 / Optics Express 35916
and the inset. The repetition frequency is 16.67 MHz. The SNR reaches
∼
40 dB, indicating a
relatively stable mode-locked state. The long-time spectrum is monitored and shown in Fig. 4(e).
The spectrum of the noise-like pulse keeps relatively stable during the 2.5-hour-long operation.
Fig. 4.
Characteristics of the noise-like pulses. (a) Optical spectra at different pump powers;
(b) Oscilloscope trace of the noise pulse train; (c) Autocorrelation trace; (d) RF spectra in
different frequency ranges; (e) Long-time spectrum monitoring result.
3.3. Q-switched mode-locked state
When rotating the intra-cavity PCs, the introduced disturbances broke the balance of gain and
loss in the laser, resulting in abrupt fluctuations of laser energy. In the meantime, the SA was not
fully saturated, the gain saturation effect in the fiber cavity did not respond in time to suppress
the sharp increase of laser energy, leading to Q-switching instability in the fiber laser [41]. And
then the QSML operation was obtain.
The pump threshold of the QSML state was 112 mW. Figure 5shows the characteristics of the
QSML pulses. The time-domain QSML pulse sequences at different pump powers are presented
in Fig. 5(a). With the pump power increasing, the interval period of the Q-switched envelope
is gradually shortened and the width of the envelope is narrowed slightly. Figure 5(b) and the
inset show the larger versions of a Q-switched envelope at different time ranges. Within the pulse
envelope, the discrete narrow pulses always keep a stable time interval of 60ns, indicating the
mode-locked operation. Figure 5(c) illustrated the spectra at different pump powers. The central
Research Article Vol. 30, No. 20 / 26 Sep 2022 / Optics Express 35917
wavelength is at 1032.6 nm, and the 3 dB bandwidth increases from 1.38 nm to 2.1 nm with the
pump power increasing from 112 mW to 200 mW. The RF spectra at the pump power of 125 mW
are shown in Fig. 5(d) and the inset. It can be seen that the center frequency is 16.67 MHz, which
is consistent with the fundamental frequency of the mode-locked state. The SNR is about 50 dB.
Furthermore, there are multiple symmetrical frequency sidebands on both sides of the central
peak, and the frequency interval between sidebands is 70 kHz. It verifies that the intensity of the
mode-locked pulse train slowly oscillates with the repetition frequency of 70 kHz, which matches
the oscillation period of the Q-switched envelop measured to be
∼
14.3
µ
s at the 125-mW pump
power shown in Fig. 5(a).
Fig. 5.
Characteristics of the QSML pulses. (a) Oscilloscope traces at different pump
powers; (b) Details of a single pulse envelope; (c) Optical spectra at different pump powers;
(d) RF spectra.
As can be seen in Fig. 5, the QSML state obviously has the periodic dynamic characteristic.
The dynamic properties in time domain can be measured using the oscilloscope, but the dynamic
changes of the QSML pulse spectra cannot be detected using the current OSA which can only
measure the average spectra of pulses over the sweep time. In order to observe the pulse spectrum
at each round trip and explore the real-time spectral dynamics of the QSML operation, the DFT
method was applied by injecting the output pulses into a 20km long SMF with a dispersion of
−
30 ps/nm/km at 1030 nm to map the real-time spectra to the stretched temporal pulse waveforms
which can be detected by high-speed real-time oscilloscopes. The stretched pulses were detected
by a 36 GHz real-time oscilloscope together with a 10 GHz high-speed PD. The resolution was
calculated to be
∼
0.167nm for the DFT measurement. The real-time oscilloscope captured the
real-time evolution process from continuous wave (CW) to QSML operation. Figure 6(a) presents
the shot-to-shot spectra from the 10000th round trip to the 25000th round trip (RT) in a time
window, which includes the spectral evolution of the whole buildup process. Each round trip
takes about 60 ns, equal to the mode-locked pulse interval period. It can be seen that from the
10000th RT to the 15000th RT, the laser presents a continuous low power output. It demonstrates
that the laser is at CW state and there is no stable pulse, so the output laser stretching can only get
Research Article Vol. 30, No. 20 / 26 Sep 2022 / Optics Express 35918
diffuse spectra without clear profiles. From the 15000th RT to the 17000th RT, the laser spectrum
exhibits an evolution process. After the 17000th RT, the laser output presents a relatively stable
QSML state. It can be calculated that the buildup process of the QSML state lasts no more than
180
µ
s. Figure 6(b) and 6(c) present the real-time spectra of the CW and the dissipative solitons
as the contrast groups. It can be seen that the real-time spectra of the CW laser exhibit a diffuse
noise state because there is no pulse to be stretched to reproduce the laser spectrum profile. The
shot-to-shot spectra of the dissipative solitons show a relatively stable state without obvious
oscillations, which is quite different from the QSML state.
Fig. 6.
Shot-to-shot spectra of (a) the buildup process of the QSML state captured by the
DFT method, (b) the CW state and (c) the dissipative solitons.
We extracted the transition process from the 13000th to the 17000th RT, as shown in Fig. 7(a).
The corresponding oscilloscope trace of the laser output from 780
µ
s to 1020
µ
s is plotted in
Fig. 7(b). The experimental results reveal that the whole buildup process can be divided into
four stages, which are unstable self-pulsation stage (A), relaxation oscillation stage (B), rogue
Q-switching stage (C), and finally stable QSML stage (D). The laser oscillates at a low peak power
at the beginning. Under the background noise, a dominant noise is selected as the main pulse with
relatively high intensity. Because of the nonlinear effect in the fiber laser, the spectrum gradually
broadens and the pulse intensity increases, which manifests as an initial unstable self-pulsation
state. It can be seen from Fig. 7(c) that the self-pulse is similar to the mode-locked pulse with
60 ns pulse interval period, but the pulse intensity is low and unstable. We analyze that the
self-pulse is achieved due to the longitudinal mode beating and the self-phase modulation in the
fiber cavity [43,44]. The whole self-pulsation stage lasts for
∼
160
µ
s. Because of the unbalance
between the gain, loss and nonlinear effect in the fiber cavity, the growing self-pulse state cannot
be maintained for a long time, and then the laser relaxation oscillation occurs. The time interval
between two laser oscillation spikes shown in the Fig. 7(b) is
∼
11
µ
s. And there are three spikes
with successively increasing peak powers. With the increase of the pulse intensity during the
oscillation stage, the saturable absorption effect in the cavity is triggered, and the spectrum is
rapidly broadened in C stage. It shows that there are twice severe fluctuations in C stage, which
Research Article Vol. 30, No. 20 / 26 Sep 2022 / Optics Express 35919
are similar to the final QSML pulses but have higher envelope peaks and wider variation ranges
of spectral bandwidth. Figure 7(d) shows the expanded view of one rogue Q-switching envelop
in Fig. 7(a). The maximum 3dB bandwidth of the spectrum reaches 3.84 nm. At this stage,
the pulse intensity is greatly improved due to the bleaching of the saturable absorber and the
reduced intra-cavity loss. However, because of the high pulse intensity, the gain saturation effect
is induced, and the population inversion in the laser is greatly consumed, which leads to the
sharp weakening of the gain in the cavity. Under this condition, it is impossible to maintain
such high-power pulse operation, resulting in the Q-switching instability, which is manifested
as a rapid decrease of the intensity and bandwidth of the spectrum. At a certain moment after
going through the above process twice, the gain, loss, dispersion, saturable absorption and other
nonlinear effects in the laser reach a balance state, and then the stable QSML operation is realized,
as shown in the D stage in Fig. 7(a).
Fig. 7.
(a) Real-time spectra evolution process from CW to QSML state measured by
the DFT method; (b) the corresponding real-time temporal pulse evolution; (c) the detail
oscilloscope trace of the self-pulse; (d) a larger version of one fluctuation period of the
spectra in C stage.
When the pump power is 125 mW, shot-to-shot spectral evolution of the stable QSML pulses
is shown in Fig. 8(a). The averaged spectrum over 4165 RTs and the spectrum measured by an
OSA in linear scale are presented in Fig. 8(b). It can be seen that these two spectra have almost
the same profile, indicating that the DFT methods can map the spectrum of the pulse to the
stretched temporal pulse waveform perfectly. We can also get from Fig. 8(a) that the real-time
spectra show regular breathing process with the period of 238 RTs. The average breathing period
is calculated to be
∼
14.3
µ
s and the corresponding repetition frequency is 70 kHz, which is
consistent with the period of the Q-switched envelop. Due to the long gain recovery time for
the population inversion to be fully accumulated to balance the cavity loss, the QSML pulses
were at extremely low power level for about 8
∼
9
µ
s during each Q-switching oscillation period
at the pump power of 125 mW, as shown in Fig. 5(a). Because of the low power of the pulses,
the shot-to-shot spectra obtained by stretching the pulses based on the DFT method overlapped
with the noise signals and were difficult to be resolved effectively, showing a noise gap in each
Q-switching period for about 130
∼
150 RTs. Figure 8(c) and the inset show the details of the
Research Article Vol. 30, No. 20 / 26 Sep 2022 / Optics Express 35920
spectral evolution in a breathing period. We can observe that the spectral intensity increases
first and then decreases, which is the same as the evolution process of the mode-locked pulses
intensity in the Q-switched envelop. Furthermore, the 3dB bandwidth of the spectrum is widen
first and then compressed, shown in Fig. 8(d). We briefly discuss the physical mechanism of
the periodic breathing process. Due to the massive accumulation of the population inversion in
the cavity, the pulse energy gradually increases under the effect of the strong gain and the low
saturable absorption loss. The pulse power reaches the maximum when the population inversion
is consumed in large quantities and strong gain saturation effect is excited. In this process, with
the increase of the pulse energy, the self-phase modulation effect in the cavity is also enhanced,
which leads to the spectral broadening. Then, during the recovery time of the gain, the pulse
energy gradually decreases due to the strong spectral filtering effect and the enhanced loss of
the SA when the pulse energy is lower than the absorber saturation energy. The pulse power
reaches the minimum when the population inversion is fully accumulated and the gain is strong
enough to balance the whole cavity loss. During the decrease of the pulse energy, the self-phase
modulation effect is weakened, and the broadened spectrum experiences strong spectral filtering
effect, which makes the pulse spectrum gradually narrowed.
Fig. 8.
(a) Shot-to-shot spectra for the stable QSML state measured by the DFT method; (b)
the averaged spectra measured by DFT and an OSA; (c) and the inset are the enlargement of
the spectral evolution process and the spectra at different RTs in a breathing period; (d) the
3 dB bandwidth of the spectra at different RTs.
4. Conclusion
In summary, we have built an Yb-doped all-fiber laser based on a SMF-GIMF-SMF SA. We
placed the GIMF in the groove of an in-line manual PC, and adjusted the PC to change the
fiber birefringence, which can relieve the strict length requirement of the GIMF as SA. In the
experiment, stable dissipation solitons and noise-like pulses were achieved with good stability
by rotating the intra-cavity PCs carefully. The central wavelengths were 1032 nm and 1030.5
nm with the pulse durations of 10.67 ps and 276 fs, respectively. By slightly adjusting the PCs,
QSML pulses can be obtained at 1032.6 nm. The amplitude of the 16.67 MHz mode-locked
Research Article Vol. 30, No. 20 / 26 Sep 2022 / Optics Express 35921
pulse was periodically modulated and the Q-switched envelops formed. Moreover, the real-time
spectral evolution process from CW to QSML operation was captured by the DFT method for the
first time, to the best of our knowledge. It demonstrates that the whole buildup process includes
four stages, which are unstable self-pulsation, relaxation oscillation, rogue Q-switching and
finally stable QSML stage. And the spectra of the pulses in one Q-switched envelop displayed
a periodic breathing process, resulting from the self-phase modulation effect and the spectral
filtering effect in the cavity. This experiment confirms that the SMF-GIMF-SMF structure is a
promising SA in ultrafast fiber systems. And the results obtained by the DFT method deepen the
understanding of the transient dynamics of the QSML operation.
Funding.
National Key Research and Development Program of China (2018YFE0117400); National Natural Science
Foundation of China (61775074).
Disclosures. The authors declare no conflicts of interest.
Data availability.
Data underlying the results presented in this paper are not publicly available at this time but may
be obtained from the authors upon reasonable request.
References
1.
Y. Mashiko, E. Fujita, and M. Tokurakawa, “Tunable noise-like pulse generation in mode-locked Tm fiber laser with
a SESAM,” Opt. Express 24(23), 26515–26520 (2016).
2.
Q. L. Bao, H. Zhang, Y. Wang, Z. H. Ni, Y. L. Yan, Z. X. Shen, K. P. Loh, and D. Y. Tang, “Atomic-layer graphene
as a saturable absorber for ultrafast pulsed lasers,” Adv. Funct. Mater. 19(19), 3077–3083 (2009).
3.
B. Guo, Q. L. Xiao, S. H. Wang, and H. Zhang, “2D Layered Materials: Synthesis, Nonlinear Optical Properties, and
Device Applications,” Laser Photonics Rev. 13(12), 1800327 (2019).
4.
J. S. He, L. L. Tao, H. Zhang, B. Zhou, and J. B. Li, “Emerging 2D materials beyond graphene for ultrashort pulse
generation in fiber lasers,” Nanoscale 11(6), 2577–2593 (2019).
5.
P. Y. Cheng, Y. Q. Du, M. M. Han, and X. W. Shu, “Mode-locked and Q-switched mode-locked fiber laser based on
ferroferric-oxide nanoparticles saturable absorber,” Opt. Express 28(9), 13177–13186 (2020).
6.
Y. Q. Du, Z. W. Xu, and X. W. Shu, “Spatio-spectral dynamics of the pulsating dissipative solitons in a normal-
dispersion fiber laser,” Opt. Lett. 43(15), 3602–3605 (2018).
7.
Y. Q. Du, X. W. Shu, and Z. W. Xu, “All-fiber passively mode-locked laser based on a chiral fiber grating,” Opt. Lett.
41(2), 360–363 (2016).
8.
S. Liu, F. P. Yan, Y. Li, L. N. Zhang, Z. Y. Bai, H. Zhou, and Y. F. Hou, “Noise-like pulse generation from a
thulium-doped fiber laser using nonlinear polarization rotation with different net anomalous dispersion,” Photonics
Res. 4(6), 318–321 (2016).
9.
Y. Q. Huang, Z. A. Hu, H. Cui, Z. C. Luo, A. P. Luo, and W. C. Xu, “Coexistence of harmonic soliton molecules and
rectangular noise-like pulses in a figure-eight fiber laser,” Opt. Lett. 41(17), 4056–4059 (2016).
10.
J. Q. Zhao, L. Li, L. M. Zhao, D. Y. Tang, and D. Y. Shen, “Cavity-birefringence-dependent h-shaped pulse generation
in a thulium-holmium-doped fiber laser,” Opt. Lett. 43(2), 247–250 (2018).
11.
E. Nazemosadat and A. Mafi, “Nonlinear multimodal interference and saturable absorption using a short graded-index
multimode optical fiber,” J. Opt. Soc. Am. B 30(5), 1357–1367 (2013).
12.
S. W. Allison and G. T. Gillies, “Observations of and applications for self-imaging in optical fibers,” Appl. Opt.
33(10), 1802–1805 (1994).
13.
S. J. Fu, Q. Sheng, X. S. Zhu, W. Shi, J. Q. Yao, G. N. Shi, R. A. Norwood, and N. Peyghambarian, “Passive
Q-switching of an all-fiber laser induced by the Kerr effect of multimode interference,” Opt. Express
23
(13),
17255–17262 (2015).
14.
T. Chen, Q. L. Zhang, Y. P. Zhang, X. Li, H. K. Zhang, and W. Xia, “All-fiber passively mode-locked laser using
nonlinear multimode interference of step-index multimode fiber,” Photonics Res. 6(11), 1033–1039 (2018).
15.
G. W. Chen, W. L. Li, G. M. Wang, W. F. Zhang, C. Zeng, and W. Zhao, “Generation of coexisting high-energy
pulses in a mode-locked all-fiber laser with a nonlinear multimodal interference technique,” Photonics Res.
7
(2),
187–192 (2019).
16.
Z. K. Wang, D. N. Wang, F. Yang, L. J. Li, C.-L. Zhao, B. Xu, S. Z. Jin, S.-Y. Cao, and Z.-J. Fang, “Stretched
graded-index multimode optical fiber as a saturable absorber for erbium-doped fiber laser mode locking,” Opt. Lett.
43(9), 2078–2081 (2018).
17.
H. H. Li, F. M. Hu, Y. Tian, P. T. Wang, J. J. Zhang, and S. Q. Xu, “Continuously wavelength-tunable mode- locked
Tm fiber laser using stretched SMF-GIMF-SMF structure as both saturable absorber and filter,” Opt. Express
27
(10),
14437–14446 (2019).
18.
Z. K. Wang, J. K. Chen, T. Y. Zhu, D. N. Wang, and F. Gao, “Graded index fiber as an all-fiber saturable absorber for
large energy conventional soliton and dissipative soliton generation,” Photonics Res. 7(11), 1214–1220 (2019).
19.
Z. P. Dong, J. Q. Lin, H. X. Li, S. J. Li, R. X. Tao, C. Gu, P. J. Yao, and X. L. Xu, “Generation of mode-locked
square-shaped and chair-like pulse based on reverse saturable absorption effect of nonlinear multimode interference,”
Opt. Express 27(20), 27610–27617 (2019).
Research Article Vol. 30, No. 20 / 26 Sep 2022 / Optics Express 35922
20.
W. Pan, L. Jin, J. Z. Wang, R. Y. Wang, H. Zhang, Y. T. Xu, X. Zhao, Y. Li, and X. H. Ma, “All-normal-dispersion
dissipative soliton fiber laser using an offset-splicing graded-index-multimode-fiber-based saturable absorber,” Appl.
Opt. 60(4), 923–928 (2021).
21.
F. Yang, D. N. Wang, Z. K. Wang, L. J. Li, C.-L. Zhao, B. Xu, S. Z. Jin, S.-Y. Cao, and Z.-J. Fang, “Saturable absorber
based on a single mode fiber-graded index fiber-single mode fiber structure with inner micro-cavity,” Opt. Express
26(2), 927–934 (2018).
22.
H. H. Li, Z. K. Wang, C. Li, J. J. Zhang, and S. Q. Xu, “Mode-locked Tm fiber laser using SMF-SIMF-GIMF-SMF
fiber structure as a saturable absorber,” Opt. Express 25(22), 26546–26553 (2017).
23.
Z. K. Wang, L. J. Li, D. N. Wang, Z. C. Le, S. Q. Zhang, S. Y. Cao, and Z. J. Fang, “Generation of pulse-width
controllable dissipative solitons and bound solitons by using an all fiber saturable absorber,” Opt. Lett.
44
(3), 570–573
(2019).
24.
T. Y. Zhu, Z. K. Wang, D. N. Wang, F. Yang, and L. J. Li, “Observation of controllable tightly and loosely bound
solitons with an all-fiber saturable absorber,” Photonics Res. 7(1), 61–68 (2019).
25.
H. Jiang, H. H. Li, F. M. Hu, X. H. Ren, C. Li, and S. Q. Xu, “Mode-Locked Tm Fiber Laser with a Tapered GIMF
SA Based on Nonlinear Multimode Interference Effect,” IEEE Photonics Technol. Lett. 32(9), 503–506 (2020).
26.
S. Thulasi and S. Sivabalan, “All-Fiber Femtosecond Mode-Locked Yb-Laser with Few-Mode Fiber as a Saturable
Absorber,” IEEE Photonics Technol. Lett. 33(5), 223–226 (2021).
27.
K. Goda and B. Jalali, “Dispersive Fourier transformation for fast continuous single-shot measurements,” Nat.
Photonics 7(2), 102–112 (2013).
28.
A. F. Runge, C. Aguergaray, N. G. Broderick, and M. Erkintalo, “Coherence and shot-to-shot spectral fluctuations in
noise-like ultrafast fiber lasers,” Opt. Lett. 38(21), 4327–4330 (2013).
29.
A. F. J. Runge, N. G. R. Broderick, and M. Erkintalo, “Observation of soliton explosions in a passively mode-locked
fiber laser,” Optica 2(1), 36–39 (2015).
30.
G. Herink, B. Jalali, C. Ropers, and D. R. Solli, “Resolving the build-up of femtosecond mode-locking with single-shot
spectroscopy at 90 MHz frame rate,” Nat. Photonics 10(5), 321–326 (2016).
31.
X. M. Liu, X. K. Yao, and Y. D. Cui, “Real-Time Observation of the Buildup of Soliton Molecules,” Phys. Rev. Lett.
121(2), 023905 (2018).
32.
J. Lee, J. Koo, Y. M. Chang, P. Debnath, Y. W. Song, and J. H. Lee, “Experimental investigation on a Q-switched,
mode-locked fiber laser based on the combination of active mode locking and passive Q switching,” J. Opt. Soc. Am.
B29(6), 1479–1485 (2012).
33. W. Z. Ma, T. S. Wang, Q. C. Su, F. R. Wang, J. Zhang, C. B. Wang, and H. L. Jiang, “1.9 (m square-wave passively
Q-witched mode-locked fiber laser,” Opt. Express 26(10), 12514–12521 (2018).
34.
L. Gao, W. Huang, J. D. Zhang, T. Zhu, H. Zhang, C. J. Zhao, W. Zhang, and H. Zhang, “Q-switched mode-locked
erbium-doped fiber laser based on topological insulator Bi2Se3 deposited fiber taper,” Appl. Opt.
53
(23), 5117–5122
(2014).
35.
J. Du, Q. K. Wang, G. B. Jiang, C. W. Xu, C. J. Zhao, Y. J. Xiang, Y. Chen, S. C. Wen, and H. Zhang, “Ytterbium-doped
fiber laser passively mode locked by few-layer Molybdenum Disulfide (MoS2) saturable absorber functioned with
evanescent field interaction,” Sci. Rep. 4(1), 6346 (2015).
36.
J. F. Li, H. Y. Luo, L. L. Wang, C. J. Zhao, H. Zhang, H. P. Li, and Y. Liu, “3-(m mid-infrared pulse generation using
topological insulator as the saturable absorber,” Opt. Lett. 40(15), 3659–3662 (2015).
37. P. Grelu and N. Akhmediev, “Dissipative solitons for mode-locked lasers,” Nat. Photonics 6(2), 84–92 (2012).
38.
W. H. Renninger, A. Chong, and F. W. Wise, “Dissipative solitons in normal-dispersion fiber lasers,” Phys. Rev. A
77(2), 023814 (2008).
39.
S. Kobtsev, S. Kukarin, S. Smirnov, S. Turitsyn, and A. Latkin, “Generation of double-scale femto/pico-second
optical lumps in mode-locked fiber lasers,” Opt. Express 17(23), 20707–20713 (2009).
40.
Y. Jeong, L. A. Vazquez-Zuniga, S. Lee, and Y. Kwon, “On the formation of noise-like pulses in fiber ring cavity
configurations,” Opt. Fiber Technol. 20(6), 575–592 (2014).
41.
C. Honninger, R. Paschotta, F. Morier-Genoud, M. Moser, and U. Keller, “Q-switching stability limits of continuous-
wave passive mode locking,” J. Opt. Soc. Am. B 16(1), 46–56 (1999).
42.
J. C. Wang, J. He, C. R. Liao, and Y. P. Wang, “Low-amplitude, drifting sub-pulses hiding in background of noise-like
pulse generated in fiber laser,” Opt. Express 27(21), 29606–29619 (2019).
43.
H. J. Baker and T. A. King, “Mode-beating in gain-switched iodine photodissociation laser pulse,” J. Phys. D: Appl.
Phys. 8(2), L31–L34 (1975).
44.
P. Myslinski, J. Chrostowski, J. A. K. Koningstein, and J. R. Simpson, “Self-mode locking in a Q-switched
erbium-doped fiber laser,” Appl. Opt. 32(3), 286–290 (1993).
