1. Introduction
Sub-nanosecond eye-safe near-infrared (1.5 µm) and mid-infrared (3–5 µm) lasers with high pulse energy, stability, and a low repetition rate offer significant advantages for various practical applications, including atmospheric monitoring, remote sensing, and optoelectronic countermeasures [
1,
2]. The use of nonlinear optical (NLO) crystals allows for the effective generation of near-infrared and mid-infrared lasers through nonlinear frequency conversion. Among these methods, the optical parametric oscillator (OPO) stands out for its compact, simple, and robust configuration, making it a widely used tool in infrared laser applications. The continuous-wave mode-locking (CWML) technique is commonly applied to generate ultrashort pulses. However, in CWML lasers, the energy for each pulse is relatively low due to the high repetition rate. For CWML lasers, the typical pulse energy varies from pJ to tens of nJ, whereas the repetition rate is typically restricted by the cavity length and measured in tens of MHz. Additionally, the high repetition rate can lead to significant thermal lensing, resulting in heat accumulation in materials during optical nonlinearity measurements. To address this, efforts have been made to develop single passively Q-switched and mode-locked (QML) lasers. These QML lasers operate with a repetition rate primarily determined by saturable absorption. However, achieving a modulation depth close to 100% with these lasers remains a challenge, and maintaining amplitude stability beneath the Q-switched envelope is an ongoing concern.
The integration of an active modulator into a passively QML laser, termed dual-loss modulation [
3,
4], allows control over the envelope’s repetition rate. In dual-loss-modulated QML lasers, the Q-switched envelope’s repetition rate is regulated by the active modulator, while the mode-locking (ML) pulses depend on both the active modulation and the saturable absorption, leading to a 100% modulation depth. However, given the presence of multiple ML pulses within a Q-switched envelope, the average peak power for these ML pulses tends to be relatively low, typically in the range of 0.1 to tens of kW. This limitation has prompted efforts to achieve higher peak power ML lasers by reducing the number of ML pulses within a Q-switched envelope. The dual-loss-modulated QML laser, distinguished by its high peak power, sub-nanosecond pulse duration, and precise repetition rate adjustment, has emerged as an exceptional pump source for intracavity OPOs (IOPOs). Consequently, an IOPO pumped by a dual-loss-modulated QML laser has been proposed, with both theoretical simulations and experimental results demonstrating the generation of a signal beam characterized by a narrow pulse width and high average power [
5].
In recent years, a variety of one-dimensional and two-dimensional (2D) nanomaterials have emerged and developed as potential candidates for OPO systems driven by Nd-doped lasers. These materials include carbon nanotubes [
6], graphene [
7], and transition metal dichalcogenides (TMDs) [
8]. Among the TMDs, novel alloyed TMD species have gained significant interest due to their thermodynamic reliability, intriguing electrical characteristics, and layer-dependent properties [
9,
10,
11]. These alloyed TMDs offer extensive possibilities for various applications such as field-effect transistors [
12], hydrogen evolution catalysts [
13], and optoelectronic devices [
14]. For instance, it has been demonstrated that the band gap of 2D Mo
(1−x)W
xS
2 monolayer alloys can be adjusted from 1.82 eV (x = 0.2) to 1.99 eV (x = 1) by altering the elemental composition [
15]. Such enhanced freedom introduced by alloying components might significantly improve the performance of ultrashort laser pulse generation. Mo
(1−x)W
xS
2 alloys have been theoretically and experimentally proven to possess broadband saturable absorption characteristics, serving as promising saturable absorbers (SAs) [
16,
17,
18,
19]. Yan et al. reported a passively Q-switched Er:YAG laser employing multilayer Mo
0.5W
0.5S
2 (MoWS
2), generating microsecond pulses at 1645 nm [
16]. Ahmad et al. demonstrated passively Q-switched fiber lasers at various wavelengths using Mo
0.8W
0.2S
2 thin films [
17,
18]. Niu et al. presented a 2 μm doubly Q-switched mode-locked (DQML) Tm:YAP laser incorporating an electro-optic modulator and Mo
0.5W
0.5S
2 SA, achieving a pulse width of 205 ns and a peak power of 2.44 kW [
19]. However, to the best of our knowledge, there has been no associated experimental study or accompanying theoretical analysis on OPOs driven by QML Nd-doped solid-state lasers based on ternary Mo
(1−x)W
xS
2 alloys.
In this paper, 2D MoWS2 nanosheets were synthesized through the liquid-phase exfoliation method, followed by an evaluation of their nonlinear optical response. An LD-pumped idler-resonant KTA-based IOPO driven by a dual-loss-modulated QML laser with an acousto-optic modulator (AOM) and MoWS2 SA was constructed within this research framework. Under a certain pump power, sub-nanosecond single mode-locking pulses of the signal and idler waves were obtained, respectively. Leveraging the QML pulses’ fluctuation mechanism and assuming a Gaussian spatial distribution, a set of coupled rate equations governing the diode-pumped idler-resonant IOPO, driven by a dual-loss-modulated QML laser with AOM and MoWS2 SA, were derived. Our numerical simulation results are fundamentally in agreement with the experimental values. These investigations underscore the promising potential of MoWS2 as a highly effective nanomaterial for advanced ultrafast solid-state laser systems.
3. Results and Discussion
In the experiment, the diode-pumped idler-resonant dual-loss-modulated QML YVO
4/Nd:YVO
4/KTA IOPO system operates in two distinct stages: the QML stage and the sub-nanosecond single mode-locking (ML) stage. The experimental results indicated that the primary factors influencing the OPO’s operational status were the active modulation frequency and pump power. The repetition rates of the Q-switched envelopes were controlled by the AOM. During the QML stage, the pulse width of the Q-switched envelope and the number of mode-locking pulses within the Q-switched envelope decrease with increasing pump power and decreasing AOM repetition rate. When the pulse width of the Q-switched envelope becomes shorter than the time interval between two mode-locking pulses, only one mode-locking pulse exists within a Q-switched envelope, marking the transition to the sub-nanosecond single ML stage. At this stage, the OPO output pulses are sub-nanosecond with repetition rates determined by the AOM. The threshold power required for the signal and idler waves was approximately 10.1 W.
Figure 4 depicts the average output powers of both the signal and idler waves concerning the pump powers across various modulation frequencies
. A clear trend is evident, showcasing a consistent rise in the average output powers of both waves with increasing incident pump powers and modulation frequencies. At the point where the pump power reached 21.8 W, the maximum average output powers for the signal wave, observed at modulation frequencies of 1, 2, 3, and 4 kHz, were 318, 364, 398, and 434 mW, respectively. Simultaneously, the corresponding maximum average output powers for the idler wave stood at 169, 194, 206, and 230 mW for the same frequencies.
The experimental results, depicted in
Figure 5 using scattered symbols, showcased the durations of the signal and idler waves’ Q-switched envelopes concerning various pump powers for different modulation frequencies
. For the signal wave’s single ML pulse generation, the experimentally determined threshold powers were 14.68 W for
= 1 kHz, 16.16 W for
= 2 kHz, 17.05 W for
= 3 kHz, and 18.41 W for
= 4 kHz. Concurrently, the threshold powers for the idler wave’s single ML pulse generation were 16.16 W for
= 1 kHz, 17.05 W for
= 2 kHz, 18.41 W for
= 3 kHz, and 19.4 W for
= 4 kHz. These specific pump powers represent the threshold values for the generation of single ML pulses for the signal and idler waves. It is important to note that the idler-resonant KTA IOPO driven by the dual-loss-modulated QML laser can generate sub-nanosecond single ML pulses of the signal and idler waves only when the pump powers surpass these threshold values. Notably, at equivalent modulation frequencies
, the threshold power for generating the idler wave’s single ML pulse was marginally higher than that required for the signal wave’s single ML pulse.
The pulse energies of the signal and idler waves’ Q-switched envelopes for different
were determined based on the average output powers and the pulse repetition rates, and the results are depicted in
Figure 6 using scattered symbols. Specifically, the maximum pulse energies for the signal wave were found to be 318, 182, 132.6, and 108.5 μJ under modulation frequencies of 1, 2, 3, and 4 kHz, respectively. Similarly, for the idler wave, the maximum pulse energies were 169, 97, 68.6, and 57.5 μJ, respectively, at the corresponding frequencies. Hence, it can be inferred that lower repetition rates contribute to enhancing the energies of both the signal and idler waves’ single ML pulses. By employing the durations and energies of the single ML pulses for the signal and idler waves, the estimated peak powers for the signal wave’s single ML pulses were calculated as 441.6, 242.6, 170.1, and 132.3 kW for modulation frequencies of 1, 2, 3, and 4 kHz, respectively. Similarly, the estimated peak powers for the idler wave’s single ML pulses were calculated as 203.6, 111.5, 74.6, and 59.9 kW for the respective modulation frequencies of 1, 2, 3, and 4 kHz, as seen in
Figure 7 with scattered symbols.
Figure 8 presents the typical output spectrum of the idler-resonant dual-loss-modulated QML KTA IOPO at an incident pump power of 19.4 W and an AOM modulation rate of 1 kHz. The spectrum exhibited the fundamental and signal waves at 1064 nm and 1535 nm, respectively, while the idler wave was detected at a wavelength of 3467 nm.
In
Figure 9a, an extended temporal profile of the idler wave’s sub-nanosecond single ML pulse at
= 1 kHz for the pump power of 16.16 W is depicted. The extended oscilloscope trace enables estimation of the ML pulse width, as shown in
Figure 9a [
28,
29]. Based on this trace, the estimated single ML pulse width was approximately 830 ps, corresponding closely to
= 471 ps. Moreover, to illustrate the stability of the single ML pulse IOPO laser, a temporal idler wave’s single ML pulse train, recorded by the digital oscilloscope for
= 1 kHz at the pump power of 17.05 W, is displayed in
Figure 9b. The pulse-to-pulse amplitude fluctuation, defined as the ratio between the highest deviation and the mean pulse amplitude, measured within the 1 kHz sub-nanosecond idler wave laser pulses, was found to be less than 4%. This result underscores the high stability of the laser output.
Figure 10 and
Figure 11 show the oscilloscope traces illustrating the pulses of the signal and idler waves within the idler-resonant dual-loss-modulated QML KTA IOPO at various incident pump powers, while maintaining the AOM’s modulated frequency at 1 kHz, respectively. In particular, observations from
Figure 10a–d demonstrate a noticeable trend: The pulse widths of the signal wave’s Q-switched envelopes progressively diminish with increased incident pump power. This reduction results in a corresponding decrease in the number of ML pulses present underneath the Q-switched envelope. Specifically, at pump powers of 11.29 W, 12.52 W, and 14.01 W, there were five, three, and two ML pulses, respectively, coexisting beneath the signal wave’s Q-switched envelope. Remarkably, upon reaching 14.68 W pump power (
Figure 10d), it is evident that a single sub-nanosecond ML pulse beneath the Q-switched envelope of the signal wave was successfully achieved.
Furthermore, as showcased in
Figure 11, the pulse widths of the idler wave’s Q-switched envelopes decreased consistently with increasing incident pump power. Specifically, at pump powers of 11.29 W, 12.52 W, and 14.68 W, there were eight, six, and two ML pulses, respectively, coexisting beneath the idler wave’s Q-switched envelope. Notably, upon reaching 16.16 W pump power (
Figure 11d), it becomes apparent that a single sub-nanosecond ML pulse beneath the idler wave’s Q-switched envelope was successfully achieved.
Additionally, wavelength-tuning in our OPO setup is achieved primarily by adjusting the OPO or using a tunable pump source. In the case of our idler-resonant intracavity KTA OPO, the tuning of the output wavelength is controlled by varying the phase-matching conditions within the nonlinear KTA crystal. This can be realized mainly by temperature tuning or angle tuning. This allows for fine adjustments to the signal and idler wavelengths, thereby enabling tunability of the output wavelength. Additionally, tuning can be achieved by altering the pump power or the cavity configuration, which impacts the gain and resonant conditions of the OPO system. These methods enable broad spectral tunability while maintaining the performance of the 2D MoWS2 SA. In our experiments, we observed that the pulse widths of the signal and idler waves varied with tuning wavelength due to the wavelength-dependent nonlinear optical properties of the MoWS2 SA. As the wavelength is tuned, changes in the absorption cross-section and saturation intensity influence the mode-locking dynamics, leading to different pulse durations. Specifically, at shorter wavelengths, the stronger absorption characteristics of MoWS2 lead to shorter pulse widths due to more efficient mode-locking. Conversely, at longer wavelengths, where the absorption is weaker, the pulse width tends to increase.
4. Theoretical Analysis
In an effort to analyze the dynamic mechanism of the diode-pumped idler-resonant KTA IOPO driven by a doubly QML YVO
4/Nd:YVO
4 laser with AOM and MoWS
2 SA, the coupled rate equations can be utilized to obtain the corresponding characteristics. Based on the fluctuation mechanism [
30,
31], it is observed that the ML pulse shape remains stable after multiple round-trips within the laser cavity. Employing the assumption of Gaussian spatial distribution, the intracavity photon density corresponding to the TEM
00 mode of the fundamental wave can be mathematically described as per [
32]:
where
represents the photon density along the laser axis, with
being the average radius of the TEM
00 mode oscillating laser within the cavity. Here,
r stands for the radial coordinate,
t refers to time, and
denotes the relative amplitude of the ML pulses during the
kth roundtrip. Additionally,
signifies the onset of ML pulses evolving from noise. In relation to the resonator round-trip transit time
tr,
is assumed to be a sharp pulse centered at
t = 0, exhibiting a rapid decay within a short duration. In this context,
stands for the round-trip time within the fundamental cavity, where
,
,
, and
denote the refractive indices of the gain medium, MoWS
2 SA, AOM crystal, and KTA crystal, respectively. The variables
,
,
, and
represent the lengths of the gain medium, MoWS
2 SA, AOM crystal, and KTA crystal, while
denotes the physical length of the fundamental wave cavity.
stands for the speed of light in vacuum, and
correlates to the FWHM of the ML pulse duration at the fundamental wavelength through the equation
.
Therefore, the temporal photon intensity at different positions within the cavity during the
kth roundtrip can be described as follows:
where
symbolizes the average beam radii of the TEM
00 mode positioned at the gain medium, MoWS
2 SA, AOM crystal, and KTA crystal, respectively. These values can be computed utilizing the ABCD matrix theory.
4.1. Influence of AOM
As an active modulator, an AOM serves to mitigate its intrinsic statistical nature during the initial stages of pulse generation while retaining the nonlinear attributes of the saturable absorber and the Q-switch during the later stages of pulse compression. In each laser shot, the statistical noise pulse, which eventually becomes the ML pulse, undergoes modulation by the active modulator, resulting in an improved stability of pulse energy from shot to shot. The loss function of the AOM can be denoted as , where represents the inherent diffraction loss of the AOM, and signifies the turnoff time of the AOM.
Given that the repetition rate of the Q-switched envelopes is reliant on the modulation frequency of the AOM, the initial population inversion density of the laser crystal can be derived. Preceding the onset of a laser pulse, the initial population density at the lower laser level is assumed to be zero for a four-level gain medium. Thus, considering the Boltzmann distribution coefficient
fa in the upper level, the initial population inversion density is expressed as follows [
32]:
where
denotes the modulation frequency of the AOM and
represents the lifetime of the upper laser level of the laser medium. Additionally,
signifies the pump rate, where
is the pump power,
denotes the single-photon energy of the pump light,
represents the average radius of the pump beam, and
signifies the absorption coefficient of the gain medium.
4.2. Signal Wave’s Photon Density
In our idler-resonant IOPO, it functions as a pure singly-resonant oscillator (SRO) where the output coupler remains perfectly transparent for the signal wave. This signifies that the signal wave does not undergo the cavity. Similarly, in the context of most second harmonic generation (SHG) processes, the frequency-doubled laser also experiences no cavity, akin to the behavior of the signal wave in our IOPO. Hence, the dynamic process governing the signal wave generation in the idler-resonant IOPO is applicable when considering the SHG process of the frequency-doubling laser. Under these analogous scenarios, the photon density of the signal wave can be formulated as follows [
33]:
where
denotes the permeability of vacuum, while
represent the circular frequencies corresponding to the fundamental, signal, and idler waves, respectively. The effective nonlinear coefficient is symbolized as
deff, whereas
stand for the refractive indices of the fundamental and idler waves in the KTA medium, respectively.
4.3. Rate Equations
The interaction between the fundamental and idler waves exclusively took place within the OPO cavity. To reflect this, we introduced a gate function that altered the coupled rate equations:
Simultaneously, considering the transmission surpassing 99.3% at the signal wave by the output coupler (M
5), it effectively arrested the evolutionary process of the signal wave field within the idler-resonant IOPO. Given this aspect, the coupled rate equations governing the idler-resonant IOPO are formulated by amalgamating the rate equations characterizing the diode-pumped dual-loss-modulated QML laser involving AOM and MoWS
2 SA [
31] with the equations relevant to the IOPOs [
34]:
where
denotes the average population-inversion density, while
represents the stimulated emission cross-section of the gain medium. Additionally,
and
stand for the cross-sections related to the GSA and ESA of the MoWS
2 SA. Moreover,
and
signify the population densities pertaining to the ground-state and the excited-state of the MoWS
2 SA. The variables
(
i =
g,
s,
a,
k) indicate the photon densities located at the positions of the gain medium, MoWS
2 SA, AOM crystal, and KTA crystal, respectively, obtainable through the utilization of Equation (7). Furthermore,
symbolizes the idler wave photon density, whereas
represents the parametric gain coefficient, with
being the frequencies of the fundamental, signal, and idler waves, respectively. Moreover,
denotes the refractive index of the signal wave in the KTA crystal.
represents the intrinsic loss for the fundamental wave, while
stands for the stimulated-radiation lifetime of the gain medium. Additionally,
and
correspond to the excited-state lifetime of the MoWS
2 SA and the round-trip time of the idler wave, respectively. Furthermore,
denotes the intrinsic loss of the idler wave, and
stands for the reflectivity at the idler wave of the output coupler.
To simplify, we make the assumption that the modes of the fundamental and idler waves inside the KTA crystal exhibit significant overlap, i.e.,
. Under this particular condition, at the
kth round-trip time
, the rate equations can be further articulated as:
where
represents the pump beam radius. To define the initial conditions:
By numerically solving Equations (9) and (15)–(20), the resulting output pulse energies for both the idler and signal waves can be derived as follows:
4.4. Numerical Simulation Results
In the numerical simulation,
holds a significant role as it correlates with the ML pulse duration
. Given the fluctuation mechanism’s assumption that the ML pulse width
remains constant [
32],
can be treated as a constant value throughout the simulation. The numerically simulated value of
is basically in agreement with the experimental duration. It is noteworthy that in the numerical simulation, the pulse width of the ML pulse underneath the Q-switched envelope remained constant, consistent with the fluctuation mechanism’s theoretical explanation. However, in the experimental setup, the pulse width of the ML pulse underneath the Q-switched envelope marginally decreased with increasing pump power. This reduction in pulse width continued as the single ML pulse was generated. In the simulation, the pulse width of the single ML pulse was provided at the threshold pump power to verify the experimental results.
Table 2 outlines the values of the other pertinent parameters employed in the numerical simulation. By using the parameters outlined in
Table 1 and
Table 2, we can ascertain
with a specified initial value of
via the numerical solution of Equations (6)–(20). Subsequently, the output pulse energies of the idler and signal waves can be determined using Equations (21) and (22), respectively. Since the average output power within a Q-switched envelope accounts for the summation of the output powers of all the ML pulses under the Q-switched envelope, the pulse width of the Q-switched envelope can be inferred from the shape of
P(t). Given that the time interval between two neighboring ML pulses matches the cavity round-trip time, acquiring a single ML pulse beneath a Q-switched envelope necessitates that the pulse width of the Q-switched envelope is shorter than the cavity round-trip time.
The plotted curves in
Figure 5 and
Figure 6 depict the theoretically calculated data for the widths of the Q-switched envelopes and the pulse energies of the signal and idler waves concerning various pump powers corresponding to different repetition rates of the AOM.
Figure 5 specifically showcases the variations in the pulse widths of the signal and idler waves’ Q-switched envelopes in relation to pump powers for various values of
, represented by different curves. The figure reveals two distinct operational stages of the idler-resonant KTA IOPO driven by a dual-loss-modulated QML laser: the initial QML stage and the final sub-nanosecond single ML stage. During the QML stage, it is evident that the pulse widths of both the signal and idler waves’ Q-switched envelopes decrease as the pump power increases while decreasing
, indicating that lower repetition rates of the AOM lead to shorter pulse durations. At specific pump powers of 14.9 W for
= 1 kHz, 16.5 W for
= 2 kHz, 17.6 W for
= 3 kHz, and 18.7 W for
= 4 kHz, the pulse widths of the signal wave’s Q-switched envelopes became shorter than the cavity round-trip time, resulting in the generation of a signal wave’s single ML pulse per envelope. Concurrently, when reaching pump powers of 15.9 W for
= 1 kHz, 17.5 W for
= 2 kHz, 18.6 W for
= 3 kHz, and 19.5 W for
= 4 kHz, the idler wave’s single ML pulse per envelope was achieved. These theoretical calculations were largely consistent with the experimental findings above. However, a minor discrepancy between the experimental and simulation results was observed. Specifically, the experimental threshold powers for achieving the sub-nanosecond single ML pulses of the signal and idler waves were slightly lower than those values by the numerical simulation.
When
= 1 kHz, the variations in the number of ML pulses for both the signal and idler waves within a Q-switched envelope at different pump powers are depicted in
Figure 12. From
Figure 12a–d, it is evident that the ML pulse count for both the signal and idler waves within a Q-switched envelope decreases with increasing pump power. Notably, when
Pin = 16 W, as shown in
Figure 12d, there is only a single ML pulse present for both the signal and idler waves beneath the Q-switched envelope. From the results shown in
Figure 10,
Figure 11 and
Figure 12, it can be seen that the theoretical simulation results are consistent with the experimental results, which verifies the correctness of the theoretical simulation.
The simulated pulse energies and peak powers of the signal and idler waves’ Q-switched envelopes for different
are depicted in
Figure 6 and
Figure 7 using curves, respectively. The trend shows that the pulse energies of both the signal and idler waves’ Q-switched envelopes exhibit an approximate linear increase in relation to the pump powers. However, it is notable that as
increases, there is a decrease observed in the pulse energies and peak powers of both the signal and idler waves’ Q-switched envelopes. This suggests that a lower repetition rate tends to enhance the pulse energies and peak powers of the signal and idler waves’ QML pulses.
The performance of 2D nanomaterial-based intracavity OPOs driven by dual-loss-modulated QML lasers at 1 μm wavebands is summarized in
Table 3. In comparison to the other 2D nanomaterial-based SAs, the idler wave’s pulse width of the idler-resonant intracavity KTA OPO with MoWS
2 SA is comparatively shorter, resulting in a relatively high peak power.
The 2D MoWS2 SA offers a broad and tunable spectral window, making it highly versatile for various laser applications. In our study, the MoWS2 SA demonstrates strong nonlinear optical absorption over a wide wavelength range. By tuning the phase-matching conditions in the intracavity KTA OPO, we can achieve efficient wavelength tunability. This flexibility enables the SA to operate effectively in both the signal and idler wavelengths, showcasing its adaptability for different laser systems. We observed that the MoWS2 SA can function across a broad spectral window, from the near-infrared to mid-infrared region, with stable pulse generation. This wideband operation highlights its suitability for wavelength-tunable laser systems. The tunable response, in combination with its high damage threshold, makes the MoWS2 SA an ideal candidate for high-power and tunable laser applications. However, stability is critical for practical laser applications, especially in high-power scenarios. Our experimental tests demonstrated that the MoWS2 SA maintains consistent performance over extended periods of operation without degradation. The 2D nanomaterial’s robustness under both thermal and optical stress contributes to its long-term stability, even at high power levels. We conducted long-term operation tests and observed no significant changes in the material’s nonlinear properties or damage under high-intensity laser illumination.