Quasi-coherent noise-like pulses in a mode-locked fiber laser with a 3D rotatable polarization beam splitter

Abstract

For the first time, to the best of our knowledge, we experimentally observed a novel quasi-coherent noise-like pulse (NLP) in a simplified nonlinear polarization evolution mode-locking fiber laser when appropriate polarization was maintained for the lasing light through a three-dimensional rotatable polarization beam splitter inside the cavity. The degree of first-order coherence was evaluated after an interferogram measurement. The evolution of the measured shot-to-shot spectrum revealed that the NLPs possess quasi-coherence. Self-starting ultrafast soliton pulses switching to quasi-coherent NLPs at higher pump power levels were due to the preservation of the soliton features, mainly the Kelly sidebands in the spectrum. Quasi-coherent NLPs with average power of 56.58 mW and 10.4% slope efficiency were achieved with single pulse energy of 3.22 nJ.

Full text

Letter Vol. 46, No. 6 / 15 March 2021 / Optics Letters 1305
Quasi-coherent noise-like pulses in a
mode-locked fiber laser with a 3D rotatable
polarization beam splitter
Renlai Zhou,1,2,5Qian Li,2,* H. Y. Fu,3AND K. Nakkeeran4
1Naval University of Engineering, Wuhan 430033, China
2School of Electronic and Computer Engineering, Peking University, Shenzhen 518055, China
3Tsinghua-Berkeley Shenzhen Institute (TBSI), Tsinghua University, Shenzhen 518055, China
4School of Engineering, Fraser Noble Building, University of Aberdeen, Aberdeen AB24 3UE, UK
5e-mail: zrlhit@126.com
*Corresponding author: liqian@pkusz.edu.cn
Received 26 January 2021; revised 9 February 2021; accepted 10 February 2021; posted 18 February 2021 (Doc. ID 420832);
published 8 March 2021
For the first time, to the best of our knowledge, we experi-
mentally observed a novel quasi-coherent noise-like pulse
(NLP) in a simplified nonlinear polarization evolution
mode-locking fiber laser when appropriate polarization was
maintained for the lasing light through a three-dimensional
rotatable polarization beam splitter inside the cavity. The
degree of first-order coherence was evaluated after an inter-
ferogram measurement. The evolution of the measured
shot-to-shot spectrum revealed that the NLPs possess quasi-
coherence. Self-starting ultrafast soliton pulses switching
to quasi-coherent NLPs at higher pump power levels were
due to the preservation of the soliton features, mainly the
Kelly sidebands in the spectrum. Quasi-coherent NLPs with
average power of 56.58 mW and 10.4% slope efficiency were
achieved with single pulse energy of 3.22 nJ. © 2021 Optical
Society of America
https://doi.org/10.1364/OL.420832
Special mode-locked pulses called noise-like pulses (NLPs)
were first demonstrated in an erbium-doped fiber (EDF) laser
by Horowitz et al. [1]; their study attracted interest in both
research and applications owing to its extraordinary features.
Compared to the soliton pulses (SPs), the NLPs could possess
high energy which could reach up to a level of microjoules, and
wider pulse duration which could reach hundreds of nanosec-
onds. NLPs with various pulse shapes were also demonstrated
in fiber lasers [2], which includes Gaussian-, rectangular-, and
trapezoidal-shaped pulses, and bunched pulses. Due to these
versatile properties, NLPs found potential applications in the
fields of micromachining [3], supercontinuum generation [4],
and low spectral coherence interferometry [5].
Generally, NLPs have a compact wave packet profile that
contains a bunch of ultrashort pulses with random intensity and
duration in the time domain, and a smooth and broad spectrum
in the frequency domain. Due to the random tiny pulses within
its wave packet, there was no measurable phase coherence in
the NLPs that were generated in different configurations of
mode-locked fiber lasers that were reported so far in the litera-
ture. Runge et al. [6] measured the pulse-to-pulse fluctuations
in the NLPs by monitoring the single-shot spectrum, and found
that the fringe visibility showed no phase coherence in the NLP
regime. However, Kwon et al. [7] observed a weak spectral inter-
ference pattern between two consecutive NLPs, and reported
the feasibility of partially coherent NLPs. The same research
group, theoretically studied the shot-to-shot coherence of laser
pulses in different quasi-mode-locking regimes, and reported
that both the laser cavity configuration and the net-cavity dis-
persion play critical roles in the generation of partially coherent
NLPs [8]. To the best of our knowledge, until now, no experi-
mental demonstration of the generation of NLPs with a high
amount of partial phase coherence (quasi-coherence) has been
observed.
In this Letter, to the best of our knowledge, we report the first
experimental observation of a novel quasi-coherent NLP with
a Kelly sideband spectrum in a simplified mode-locked fiber
laser setup with a three-dimensional (3D) rotatable polarization
beam splitter (PBS) within its cavity. The output characteristics
of the NLPs were investigated for different pump powers, which
assisted in the understanding of the dynamics of the proposed
mode-locked fiber laser that can be switched from the SP regime
to a stable quasi-coherent NLP regime. The measured interfer-
ogram indicated that the first-order coherence of the generated
NLP was greatly improved due to the preservation of the soliton
features, mainly the Kelly sidebands in its spectrum.
Different from other nonlinear polarization evolution (NPE)
mode-locked lasers, the bulk optical devices such as half-wave
and quarter-wave plates were not included. Instead, a 3D rotat-
able PBS was deployed on a horizontal surface within the cavity.
A schematic of the fiber laser setup is shown in Fig. 1. The polari-
zation states of the optical signal lasing in the laser cavity could
be fine-tuned by 3D maneuvering of the PBS position. The
gain was provided by a 1 m long EDF (EDFL-980-HP, Nufern),
which was pumped by a 976 nm laser diode (LD) through
a 980/1550 nm wavelength-division multiplexer (WDM).
An in-line polarization controller (PC) was included to enhance
0146-9592/21/061305-04 Journal © 2021 Optical Society of America

1306 Vol. 46, No. 6 / 15 March 2021 / Optics Letters Letter
Fig. 1. Schematic of a simplified NPE mode-locked fiber laser.
OSA, optical spectrum analyzer; OC1, OC2, and OC3, 3 dB optical
couplers.
the mode locking. Two fiber collimators were used for position-
ing and coupling of the light signal, with a coupling efficiency
of about 75%. A polarization-insensitive isolator (PI-ISO) was
added for unidirectional light propagation in the laser cavity.
The total cavity length was ∼11.64 m with a net-cavity disper-
sion of −0.338 ps2, indicating that the mode locking operated
in the anomalous dispersion regime. The output spectrum
and pulse train were monitored by an optical spectrum ana-
lyzer (OSA, AQ6370D, Yokogawa, resolution 0.02 nm) and
a real-time 59 GHz bandwidth oscilloscope (DPO-75902SX,
Tektronix) connected via an ultrafast response InGaAs pho-
todiode detector (UPD-15-IR2-FC, >25 GHz bandwidth).
The RF of laser operation was monitored by a signal analyzer
(N9030B, Agilent) which has a bandwidth of 3 Hz–50 GHz.
In this proposed NPE mode-locked fiber laser, the polariza-
tion states of the transmitted beam from the PBS were regulated
by maneuvering the PBS along the zaxis [9]. The SPs were
generated in the fiber laser when the PBS was steered about
4.5 deg clockwise. Mode-locked multi-pulse state SPs were
self-started when the pump power was raised to 135 mW. Then
the pump power was lowered to 100 mW for the cavity to mode-
lock single a stable SP. When the pump power was reduced to
70 mW, the cavity went out of mode locking. Measured output
spectra are depicted in Fig. 2(a), where the red and blue curves
represent the continuous-wave (CW) signal and SP, respectively.
On the SP spectrum, Kelly sidebands were observed, and the
3 dB spectral bandwidth was measured as 6.84 nm. The mea-
sured pulse train and RF spectrum are shown in Figs. 2(b) and
2(c). The output pulse train was monitored within 90 min,
and it showed a high stability. The measured SP period was
∼56.95 ns which coincides with the fundamental repetition
rate of 17.55882 MHz. The signal-to-noise ratio (SNR) mea-
sured above 90 dB indicating a highly stable SP operation in this
cavity. A wideband RF spectrum up to 1.5 GHz presented in
the Fig. 2(c) inset disclosed that the SP operation was very sta-
ble. The corresponding intensity autocorrelation (AC) trace is
shown in Fig. 2(d). The full width at half-maximum (FWHM)
pulse duration was ∼460.1 fs, which was calculated through
a sech2profile fit for the measured pulse. The time-bandwidth
product calculated as 0.4 was nearly the transform-limited value
0.315 of a chirp-free Sech2-shaped pulse.
When the pump power was further increased to 225 mW,
the soliton state switched to a different stable pulsating mode-
locked state in the cavity. The measured spectral and temporal
characteristics of the new state are depicted in Figs. 2(e)–2(h).
In the frequency domain, compared to the SP state, the new
state possessed a broadband spectrum and increased intensity,
as shown in Fig. 2(e) and, more interestingly, a series of spikes
were observed. The spectral spikes were related to the Kelly side-
bands. The phase-matching condition of the Kelly sidebands
can be calculated as 2πN=D/2×(ω2+1/τ 2), where Nis
the order of the sidebands with an angular frequency offset of ω
from the central frequency ω0. 1.763τis the FWHM of the SP
duration, and D=4π / (ω2
2−ω2
1)is the net dispersion of the
cavity, with ω1,2being the frequency offset of the two adjacent
spikes from the central frequency [10]. The measured central
frequency ω0= ∼ 836.911 THz, and the computed right and
left frequency locations of the spikes shown in Fig. 2(e) were
R1=0.936, R2=1.936, R3=2.953, R4=4.04, R5=5.049,
R6=6.061, L1=0.966, L2=2.044, L3=3.022, and
L4=4.078. As expected, the calculated frequency locations of
the spikes coincided with the OSA recorded spectrum, revealing
that the spikes on the spectrum belonged to Kelly sidebands that
met the phase-matching conditions. The measured output pulse
train is shown in Fig. 2(f), in which the adjacent pulses temporal
Fig. 2. Output features of (a)–(d) the SP and (e)–(h) the NLP: (a), (e) output spectrum; (b), (f ) pulse train; (c), (g) RF spectrum; (d), (h) intensity
AC trace.

Letter Vol. 46, No. 6 / 15 March 2021 / Optics Letters 1307
separation was same as that of the SP, but intensity fluctuations
were observed in the profile of the pulse train, which implied
that the single pulse energy of this state was not steady. The
pulse fundamental repetition rate was 17.55898 MHz which
possessed the highest value in the reported NLP regime [2], as
presented in Fig. 2(g); it was about 160 Hz frequency shifted
compared with that of the SP. The SNR measured as 55 dB indi-
cated that this novel mode locking can operate reliably, but the
stability was less than the soliton state. The finer details of the
laser pulse are presented in Fig. 2(h). A double-scale structure
with a narrow pulse peak (∼499.1 fs) riding on top of a broad
pedestal was observed, which is a typical feature of NLPs. Hence
this mode-locked operation is classified as the NLP regime.
However, different from the previous reported results [2,6–8],
the intensity of the measured narrow pulse peak was much
higher than its pedestal, and the intensity ratio between the
narrow pulse peak and the pedestal was about 14. This feature
implies that the soliton characteristics were preserved in the
observed NLP that played a dominant role in the dynamics of
this state. Mainly, the Kelly sidebands occurred as spikes on
the NLP spectrum confirming the soliton feature in this state,
which has never been observed, to the best of our knowledge, in
NLPs generated in mode-locked fiber lasers.
To investigate other characteristics of the SP and NLP lasing
in the cavity at different pump power levels, average laser output
powers were measured. As depicted in Fig. 3(a), the entire mode-
locking operation can be divided into three regimes: the SP
regime, unstable regime, and NLP regime. In the SP regime with
the self-starting threshold pump power of 135 mW, the mode-
locked pulse(s) average power linearly increased with a slope
efficiency of 11.67% for increasing pump power. The maxi-
mum output power reached was 19.45 mW at a pump power of
180 mW. Stable single SPs were lased for the pump power range
of 70–100 mW and between 100–180 mW; stable multi-pulse
SPs were lased. In the pump power range of 180–225 mW,
the switching between the SP and NLP regimes happened
randomly, and hence is termed as an unstable regime. Stable
NLP lasing started from a pump power amount of 225 mW. In
the NLP regime, the output power grew linearly with a slope
efficiency of 10.4%, and an average power of 56.58 mW was
achieved at a maximum achievable pump power of 540 mW
of the source used. Within the saturation limit of the available
pump source, the measured pulse energy of the NLPs at a fun-
damental repetition rate linearly increased from 1.36–3.22 nJ.
Higher energy NLPs beyond this range may be feasible in the
proposed fiber laser with a high powered pump source. Various
regimes that output signal spectra at different pump powers
are presented in Fig. 3(b). The measured spectral profiles of the
SP and NLP regimes were different. Their respective spectral
intensity value increased with increasing pump power, without
causing any changes in their spectral profile or bandwidth.
Fig. 3. Pump power versus average (a) output power and (b) spectra.
In a mode-locking soliton spectrum, Kelly sidebands are
formed because of the interference superposition between the
SPs and dispersive waves, when their relative phase changes
by an integer multiple of 2πper cavity roundtrip time. Thus,
the presence of Kelly sidebands is a strong evidence for the
coherence of the mode-locked pulses. In order to evaluate the
first-order phase coherence of the cavity signal, a fiber Michelson
interferometer was constructed to measure the cross-coherence
of adjacent pulses, as shown in Fig. 1. Using single-mode fiber,
one arm of the interferometer was constructed to be longer
than the other by exactly one-half of the cavity roundtrip time.
The signals in the respective arms were collimated and 100%
reflected by two separate gold-coated mirrors. For the finer
adjustments of the temporal overlap between the two signals at
the interferometer output, one of the mirrors was mounted on
a precise translation stage. An in-line PC was used to maintain
the same polarization states between the interfering signals from
both arms. The spectral interference fringes were measured
through the OSA, which recorded every sweep with an ensemble
average of >3×106interference events from which the first-
order coherence g(1)
12 between adjacent pulses was calculated
with [11]


g(1)
12 (λ)

=[I1(λ) +I2(λ)]V(λ)
2[I1(λ)I2(λ)]1/2,(1)
where I1,2(λ) represent the measured spectral intensities
from two arms. The fringe visibility V(λ) is computed using
the measured maximum and minimum fringe intensities as
V(λ) = [Imax (λ) −Imin(λ)]/[Imax(λ) +Imin(λ)]. Before
the spectral interference measurements were made, precise
adjustments were carried out for the temporal overlapping
between adjacent pulses to select adequate fringe spacing.
Figure 4(a) depicts the spectral interference pattern and first-
order coherence of the SP. Nearly 100% spectral modulation
depth suggested a high degree of phase coherence in the SP
regime, and the calculated first-order coherence g(1)
12 is ∼0.945
over the major portion of the spectrum. With an increase in
pump power, switching happened from the SP to the NLP for
the spectral interference pattern and first-order coherence to
Fig. 4. Measured spectral interference pattern and calculated first-
order coherence: (a) SP regime and (b) NLP regime.

1308 Vol. 46, No. 6 / 15 March 2021 / Optics Letters Letter
be transformed as shown in Fig. 4(b). In contrast to the earlier
report [9], the interference pattern was still present in almost the
entire spectrum of the NLP. However, the modulation depth
was less than that in the SP regime, indicating the degradation of
pulse-to-pulse phase coherence in the NLP regime. Noticeable
fluctuations were observed in the first-order coherence, and
high coherence values were found at the locations where Kelly
sidebands were present. The zoomed-in snapshots of spectral
regions at 1528–1533 nm and 1548–1553 nm are shown in
Figs. 4(c) and 4(d), and the corresponding average first-order
coherence values were calculated as ∼0.462 and ∼0.652,
respectively. Though the phase coherence of the NLP under-
went some degradation compared to the SP, the first-order
coherence value throughout the spectrum was found to be above
∼0.408. The presence of Kelly sidebands acknowledges the
coherence of the mode-locked signal, and the strength of the
first-order coherence determines the quality of the coherence.
Even though, shot-to-shot coherence properties in a quasi-
mode-locked regime were already theoretically investigated [8],
spectra obtained through simulations were different from the
measured NLP spectra. Due to the short cavity length of around
12 m, the dynamics of collapse of solitons and interactions
between sub-pulses within a packet were evaded [12,13]. This
resulted in the lasing of relatively more regular SPs, even during
the NLP regime, which maintained the coherence of the NLP.
Besides every pulse of the NLP, a weak sub-pulse was observed. A
peak power ratio of ∼0.05 was maintained between sub-pulses
to the main pulse for various pump powers. These sub-pulses
were the coherent part (SP) of the NLP that did not collapse
or completely merge with the main pulse and provided the
quasi-coherency for the NLP. The main pulse and the sub-pulse
were coupled and simultaneously mode-locked in the fiber laser
cavity at the same wavelength.
A single-shot spectrum measurement was carried out through
a time-stretch dispersive Fourier transform technique (TS-
DFT) [14,15] in a 1 km long dispersion-compensating fiber
(DCF) with a dispersion of ∼178.4 ps2, corresponding to
a spectral resolution of ∼0.11 nm. The real-time spectral
profiles of 1000 consecutive roundtrips were obtained in a
single-shot capture, and the reconstructed sequence of the
spectral evolution is shown in Fig. 5. It is evident that the soliton
single-shot spectrum almost replicated the OSA measured
spectrum shown in Fig. 5(a). The single-shot soliton spectra
were indistinguishable from each another, resulting in a stable
output spectrum with good phase correlation. In contrast to the
almost invariable soliton spectrum, the NLP spectrum exhibits
fluctuations [Fig. 5(b)]. Despite the good profile exhibited in
each single-shot spectrum, the spectral intensity distribution
was quite different from the earlier reported incoherent NLP
[2,6]. Most of the NLP spectral energy was confined in and
around the central wavelength with no incoherent sidebands
in the shot-to-shot spectra measured by TS-DFT [16], which
is a familiar characteristic of soliton spectrum. This is further
evidence, apart from the appearance of Kelly sidebands (spikes)
on the NLP spectrum, to confirm that the NLP possessed more
SP characteristics, including the phase coherence.
To conclude, in a simplified NPE fiber laser with a 3D rotat-
able PBS, we experimentally demonstrated the mode locking of
a quasi-coherent NLP with Kelly sidebands in its spectrum.
Fig. 5. Single-shot spectral evolution for the (a) SP and (b) NLP
regime. (Top) The blue solid curve shows the OSA spectrum, and the
red dashed curve shows an arbitrarily picked single spectrum.
By adjusting the pump power, the self-starting pulses can
switch from soliton state to the NLP state that maintained
most features of solitons. To the best of our knowledge, this is
the first experimental observation of high-energy noise-like
ultrafast laser pulses with a high amount of coherence due to
preservation of soliton properties. We believe that the reported
results introduce a novel nonlinear operation regime of mode-
locked ultrafast fiber lasers that can provide useful insights
into the quasi-coherent NLP ultrafast fiber laser designs and
applications.
Funding. National Natural Science Foundation of China (61805281);
Natural Science Foundation of Guangdong Province (2019A1515010732).
Disclosures. The authors declare no conflicts of interest.
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