Investigations of 2D PtS2’s Saturable Absorption Characteristic and Its Optimization to OPO’s Operation

A 6.2 nm-thickness platinum disulfide (PtS2) film was prepared by electron beam evaporation with post vulcanization. The nonlinear transmittance was measured by power scanning method and the modulation depth is fitted to be 13%. Based on the transmittance curve, saturable absorption parameters of PtS2 are calculated with inhomogeneously broadening mechanism, including 6.4298 × 10−19 cm−2 ground-state absorption cross-section, 2.5927 × 10−19 cm−2 excited-state absorption cross-section, and 1.043 ms excited-state lifetime. The PtS2 film combined with active time management was implemented to modulate the fundamental light of optical parametric oscillator (OPO). Owing to the nonlinear absorption property of PtS2, the operation of Q-switched OPO was optimized in both the experiment and dynamical theory. In particular, the conversion efficiency was experimentally improved by 13.2%. The pump-to-signal conversion efficiency went up to 3.29%, which is the highest conversion value reported so far. The theoretical values fit the experiment well, which are from the Gaussian rate equations with PtS2’s saturable-absorption characteristic.


Introduction
As passive modulators for laser pulses, two-dimensional (2D) transition metal sulfides (TMDCs) have attracted much attention in recent years, because of the advantages of fast recovery time, high modulation depth, and low preparing cost [1,2]. As a member of the TMDCs family, the few-layer platinum disulfide (PtS 2 ) consists of S-Pt-S atoms in the plane, and there are strong covalent bonding and weak van der Waals bonding between the layers [3,4]. Few-layer PtS 2 is promising in 1µm-and-above-wavelength laser modulation, and its bandgap ranges from 0.25 eV for bulk to 1.6 eV for monolayer [5][6][7][8][9]. At present, 2D PtS 2 has been applied to fiber laser to obtain 1 µm or 1.5 µm-wavelength pulse [5,10,11]. Although 2D TMDC has been proven to have a high damage threshold and a high switching ratio, layered PtS 2 has not been reported to be used in solid-state lasers as a passive modulator [12][13][14][15].
Based on second-order nonlinear frequency conversion, optical parametric oscillator (OPO) can generate 1.5-1.6 µm coherent eye-safe light [16,17]. Compared to extracavity OPO, the high photon density of fundamental laser for the intracavity OPO (IOPO) can be fully utilized to generate signal or idler pulses with high single-pulse energy. For a Q-switched IOPO, the shorter width and higher peak fundamental laser contribute to higher conversion [18,19]. Although the lasers Q-switched by 2D TMDCs are reported a lot, few of them have been applied to OPO's fundamental lasers because of the low time-stability of pulse sequence [20][21][22][23]. If an active Q-switch is introduced to manage the action time of the saturable absorber (SA), the IOPO modulated by 2D PtS 2 is prospected. Moreover, due to PtS 2 's saturable absorption characteristic, the experimental optimization of Q-switched IOPO could be realized.
Dynamic rate equations are effective in guiding the experiments of lasers or OPOs based on PtS 2 [24,25]. Compared with the plane-wave approximation results, the theoretical calculations are better fitted to the experimental results when considering the Gaussian spatial distribution of the fundamental photon [26,27]. So far, few works have been involved in the Gaussian rate equations of IOPOs. The saturation absorption parameters of PtS 2 are needed to solve the dynamic equations, and they are also the keys to obtaining narrowpulse and high peak-power lasers. As the energy band structure of PtS 2 is still being researched, the values of SA parameters are rarely reported, including the ground-state absorption cross-section, the excited-state absorption cross-section, and the excited-state lifetime. Therefore, a dynamical investigation of lasers modulated by PtS 2 has not been reported in the literature, especially not an IOPO pumped by it.
In this work, a few-layer PtS 2 SA was prepared by the method of electron beam evaporation (EBE) method, and its optical properties were thoroughly investigated. Considering the inhomogeneously broadening mechanism, the SA parameters of PtS 2 were estimated from the measured transmittance curves. Then, the dynamic coupling rate equations under the Gaussian spatial distribution were derived and solved for a Q-switched IOPO with PtS 2 . Finally, in our experiment, a signal-resonant KTP IOPO based on the prepared PtS 2 SA was realized. The acousto-optic (AO), as an active modulator, was used to control the fundamental-pulse-repetition rate. The few-layer PtS 2 SA was used to optimize the performance of Q-switched IOPO as a passive Q-switch. The optimization of PtS 2 SA to IOPO was analyzed, including the pulse-width compression, the peak-power improvement, the pulse-sequence stability and the nonlinear-conversion-efficiency promotion. The theoretical results are in reasonable agreement with the experimental values.

Material Fabrication and Characterization in Experiment
PtS 2 thin film was synthesized by metal film plus post-sulfurization treatment [28]. In the first step, the Pt film was deposited on c-cut sapphire (Al 2 O 3 substrate) by using an electron beam evaporation furnace (ATS 500, HHV, West Sussex, UK). After that, the Pt-coated Al 2 O 3 substrate was thermally annealed in a sulfur-rich ambiance for 30 min. During the thermal treatment, a flow of 80 sccm H 2 S was introduced for sulfurization and the Ar/H 2 mixture of 225 sccm/75 sccm was employed as a carrier gas and reactive gas. Finally, the PtS 2 sample was removed for characterization. The PtS 2 SA is characteristically summarized in Figure 1. The Raman spectrum of the PtS 2 SA was measured by a Raman spectrometer (Horiba LabRAM HR Evolution, Kyoto, Japan), excited by a 532 nm laser. As shown in Figure 1a, the two characteristic peaks at 260 cm −1 and 336 cm −1 correspond to the in-plane E 1 2g vibrational mode and the out-of-plane A 1g vibrational mode, respectively. The frequency interval between the two peaks is 76 cm −1 . As has already been established, the E 1 2g mode is related to the in-plane vibration of the S and Pt atoms heading in opposite directions. The A 1g mode is related to the out-of-plane motion of the S atom, which reflects the coupling between layers. The A 1g peak of PtS 2 prepared in this experiment is blueshifted by 2 cm −1 compared with bulk-like PtS 2 , which implies the 2D nanostructure [12,14]. The optical micrograph (CX23, Olympus, Tokyo, Japan) measured in Figure 1b demonstrates the contrast between the PtS 2 sample and pristine transparent sapphire substrate. The color contrast of the sample indicates that the sample is a few-layer film. Figure 1c shows the atomic force microscopy (AFM, Bruker Dimension Icon, Billerica, MA, USA) where the thickness and the corresponding height diagram are given. As illustrated in the figure, the thickness of PtS 2 is approximately 6.2 nm. Considering the 5.03 Å thickness of single-layer and 3.07 Å interplanar spacing for PtS 2 [29,30], the structure of the sample is approximately 8 layers, which corresponds to the abovementioned optical micrograph and Raman spectrum analysis results. The nonlinear transmittance of PtS2 SA versus different incident peak power intensity is measured by double-optical-path method [31]. An AO Q-switched solid-state laser (1.06 μm wavelength, 120 ns pulse width, 15 kHz repetition rate) was used as the laser source. The nonlinear transmittance of the sample is shown in Figure 2a. The approximated nonsaturable loss (αs), initial transmittance (T0), and saturation transient intensity (Isat) were fitted as 9.3%, 77.0%, and 1.077 MW/cm 2 , respectively, and then the modulation depth (ΔT) was calculated to be 13%. With the increasing peak-energy density at the low power density, the material transmittance increases linearly, as shown in Figure 2b. The slope obtained by linear fitting is 1.14.

Theoretical Evaluation of IOPO with 6.2 nm-Thick PtS2′s Saturable Absorption Characteristic
In theory, Q-switching dynamics is well explained by rate equations [32]. In this section, the Gaussian assumption and PtS2′s characteristic were considered for the dynamical model of a Q-switched Nd:YVO4/KTP IOPO with AO active timemanagement.

Gaussian Rate Equations of IOPO
The Gaussian transversal distribution and longitudinal distribution of the photon density in the cavity are considered in the rate equations, as well as the thermal effect of the gain medium. The average intracavity photon density ( , ) r t φ of the TEM00 mode can be represented by The nonlinear transmittance of PtS 2 SA versus different incident peak power intensity is measured by double-optical-path method [31]. An AO Q-switched solid-state laser (1.06 µm wavelength, 120 ns pulse width, 15 kHz repetition rate) was used as the laser source. The nonlinear transmittance of the sample is shown in Figure 2a. The approximated nonsaturable loss (α s ), initial transmittance (T 0 ), and saturation transient intensity (I sat ) were fitted as 9.3%, 77.0%, and 1.077 MW/cm 2 , respectively, and then the modulation depth (∆T) was calculated to be 13%. With the increasing peak-energy density at the low power density, the material transmittance increases linearly, as shown in Figure 2b. The slope obtained by linear fitting is 1.14. The nonlinear transmittance of PtS2 SA versus different incident peak power intensity is measured by double-optical-path method [31]. An AO Q-switched solid-state laser (1.06 μm wavelength, 120 ns pulse width, 15 kHz repetition rate) was used as the laser source. The nonlinear transmittance of the sample is shown in Figure 2a. The approximated nonsaturable loss (αs), initial transmittance (T0), and saturation transient intensity (Isat) were fitted as 9.3%, 77.0%, and 1.077 MW/cm 2 , respectively, and then the modulation depth (ΔT) was calculated to be 13%. With the increasing peak-energy density at the low power density, the material transmittance increases linearly, as shown in Figure 2b. The slope obtained by linear fitting is 1.14.

Theoretical Evaluation of IOPO with 6.2 nm-Thick PtS2′s Saturable Absorption Characteristic
In theory, Q-switching dynamics is well explained by rate equations [32]. In this section, the Gaussian assumption and PtS2′s characteristic were considered for the dynamical model of a Q-switched Nd:YVO4/KTP IOPO with AO active timemanagement.

Gaussian Rate Equations of IOPO
The Gaussian transversal distribution and longitudinal distribution of the photon density in the cavity are considered in the rate equations, as well as the thermal effect of the gain medium. The average intracavity photon density ( , ) r t φ of the TEM00 mode can be represented by

Theoretical Evaluation of IOPO with 6.2 nm-Thick PtS 2 's Saturable Absorption Characteristic
In theory, Q-switching dynamics is well explained by rate equations [32]. In this section, the Gaussian assumption and PtS 2 's characteristic were considered for the dynamical model of a Q-switched Nd:YVO 4 /KTP IOPO with AO active time-management.

Gaussian Rate Equations of IOPO
The Gaussian transversal distribution and longitudinal distribution of the photon density in the cavity are considered in the rate equations, as well as the thermal effect of the gain medium. The average intracavity photon density φ(r, t) of the TEM 00 mode can be represented by In this formula, w l is the average beam radius of the fundamental light.
where φ j (0, t)(j = s, i) represents the intracavity photon densities of the signal light and idler light; φ j (0, t)(j = g, a, y) represents the fundamental light intracavity photon densities at the positions of Nd: YVO 4 crystal, AO crystal, and PtS 2 SA, respectively [33]; w j (j = g, a, y) represents the radius of the TEM 00 mode in the abovementioned three positions. The relationship between the photon densities and the electric field is represented by φ(r, t) = εE 2 (r, t)/4hω. Considering the transverse Gaussian distribution of beam energy, is the electrical field of the fundamental light, the signal light and the idler light on the laser axis.
Under Gaussian assumption, the excited-state population densities n y1 (r, t) of the saturable absorber can be expressed as The IOPO rate equation with the saturable absorption characteristic of PtS 2 SA is obtained by referring to the previous research work [26,27,32,33]. (8) Equation (4) describes the loss of fundamental-light photons by thermal effect, AO crystal and nonlinear transformation of the KTP crystal. In the equation, − σ g − σ e l y n y1 (r, t)φ y (r, t) + σ e l y n y0 φ y (r, t) represents the loss of fundamental-light photons by PtS 2 SA. The gain of signal-light and idler-light photons with time can be described by Equations (5) and (6). Equation (7) shows the loss of the population inversion in the laser medium. In the equations, t r is the round-trip time of the fundamental light. l, l g , l KTP and l OPO are the physical lengths of the laser cavity, the gain medium, KTP crystal, and OPO cavity. ε j (j = p, s, i) is the dielectric constant and the frequency of the three lights. In Equation (4), δ T is the diffractive loss caused by the gain medium's thermal effect. δ a (t) can be written as [32], where t AO and δ a are the turn-off time and the intrinsic diffraction loss of the AO Q-switch. δ a (t) is used to describe the loss function of the gradual AO modulator (AOM) caused by the exponential time delay. The basic parameters for calculating the rate equation refer to previous work [32][33][34][35].

PtS 2 SA Parameters Derivation by Inhomogeneously Broadening Mechanism
For PtS 2 SA, the change of the population inversion density is shown in Equation (8). σ g and σ e are the ground-state and excited-state absorption cross-sections of SA, which are Nanomaterials 2022, 12, 1670 5 of 11 essential parameters to characterize saturable-absorption properties of SA. By using the information in reference [33], we can obtain the relationship between them.
The values of small-signal transmittance (T 0 ) at a low power density, maximum transmittance (T max ) at a high power density, and slope k were obtained, as shown in Figure 2. Then, the values of σ g and σ e for the 6.2 nm-thickness PtS 2 SA can be estimated to be 6.4298 × 10 −19 cm −2 and 2.5927 × 10 −19 cm −2 . Considering the inhomogeneously broadening mechanism, the excited-state lifetime of PtS 2 is calculated to be 1.043 ms [33]. Table 1 demonstrates the calculated key parameters of PtS 2 SA. These parameters can be substituted into Equations (4)- (8), which are solved by computer programming. In addition, Equations (4), (7), and (8) could dynamically model a PtS 2 SA passively Q-switched laser.

Experimental Setup
The experimental setup for doubly Q-switched Nd 3+ : YVO 4 IOPO with AO modulator (AOM) and PtS 2 SA is shown in Figure 3. A commercial LD with 400 µm beam diameter is used as the pump source, and the 808 nm-wavelength laser from LD is focused by the 1:0.5 coupled lens. The gain medium used in the experiment is a Nd:YVO 4 laser crystal with a 3 × 3 × 5 mm 3 size and 0.6 at.% Nd 3+ dope. The two faces of the crystal were antireflection (AR)-coated at both 808 nm and 1064 nm wavelengths. The 5 × 5 × 20 mm 3 KTP crystal with type II non-critical phase-matching configuration (θ = 90 • , ϕ = 0 • ) along X-axis is applied to obtain a maximum effective nonlinear coefficient. The fundamental cavity length is about 125 mm, which is from mirror M 1 to M 2 . The OPO cavity length is about 28 mm, and the signal light oscillates between M 2 and the first side of KTP. The repetitions of AO were 15 kHz and 25 kHz, respectively. Nanomaterials 2022, 12, x FOR PEER REVIEW 6 of 11 antireflection (AR)-coated at both 808 nm and 1064 nm wavelengths. The 5 × 5 × 20 mm 3 KTP crystal with type II non-critical phase-matching configuration (θ = 90°,ϕ = 0°) along X-axis is applied to obtain a maximum effective nonlinear coefficient. The fundamental cavity length is about 125 mm, which is from mirror M1 to M2. The OPO cavity length is about 28 mm, and the signal light oscillates between M2 and the first side of KTP. The repetitions of AO were 15 kHz and 25 kHz, respectively. A laser power meter (MAX500AD, Coherent Inc., Santa Clara, CA, USA) was employed to measure the laser average output power. Two fast photo-electronic diodes (with a rising time of 1 ns) and a digital oscilloscope (TDS620B, Tektronix, Beaverton, OR, USA) were used to measure the fundamental-pulse and the signal-pulse temporal characteristics of the output, respectively. A spectrometer (MS9710C, Anritsu, Atsugi, Japan), working in the wavelength range of 600-1750 nm, was employed to record the laser spectrum. A laser power meter (MAX500AD, Coherent Inc., Santa Clara, CA, USA) was employed to measure the laser average output power. Two fast photo-electronic diodes (with a rising time of 1 ns) and a digital oscilloscope (TDS620B, Tektronix, Beaverton, OR, USA) were used to measure the fundamental-pulse and the signal-pulse temporal characteristics of the output, respectively. A spectrometer (MS9710C, Anritsu, Atsugi, Japan), working in the wavelength range of 600-1750 nm, was employed to record the laser spectrum.

Experimental Results and Discussion
The output spectrum of doubly Q-switched IOPO is shown in Figure 4a,b. The fundamental and signal light wavelengths are found to locate at 1064 nm and 1570 nm, respectively. Japan), working in the wavelength range of 600-1750 nm, was employed to record the laser spectrum.

Experimental Results and Discussion
The output spectrum of doubly Q-switched IOPO is shown in Figure 4a,b. The fundamental and signal light wavelengths are found to locate at 1064 nm and 1570 nm, respectively. Figure 4c,d display the typical pulse trains of signal light from two kinds of IOPO, under the AOM repetition rate of 15 kHz and incident pumped power of 5.0 W. The root means square error (RMS) of peak-to-peak jitter for signal light output from the doubly Q-switched IOPO is only 0.0156 value was much smaller than the 0.0667 RMS of AO singly Q-switched IOPO. As shown in Figure 4, it was concluded that the application of PtS2 SA effectively improves the peak-to-peak pulse stability of Q-switched IOPO.    Figure 4, it was concluded that the application of PtS 2 SA effectively improves the peak-to-peak pulse stability of Q-switched IOPO.
The laser characteristics of AO active Q-switched IOPO and PtS 2 + AO dual-loss modulated Q-switched IOPO at two different AO modulation rates, as shown in Figure 5. Figure 5a,c show the average output powers of these two kinds of modulation versus the incident pump powers. The 1570 nm-wavelength average output power of the singly lossmodulated IOPO was indeed higher than the dual-loss-modulated IOPO. This is attributed to the insert loss of PtS 2 SA. Compared to 3.0 W threshold of AO Q-switched IOPO, the threshold pump power of the dual-loss Q-switched operation increased to 3.6 W.
The pulse width of signal light with different pulse repetitions is shown in Figure 5b,d, which commonly declines with increasing pump power but increases with a rising AO repetition rate. In a dual-loss Q-switched laser, the number of longitudinal modes could be suppressed by the participation of SA, and then the pulse width could be cut down. Therefore, in Figure 5b,d, the signal-light pulse from IOPO pumped by a PtS 2 + AO doubly Q-switched laser was shorter than that from IOPO pumped by AO singly Q-switched laser. Because of PtS 2 's saturable absorption to fundamental laser, the signal-light pulse width is 64.3% compressed from 6.102 ns to 2.178 ns at 15 kHz pulse-repetition rate and 5.2 W pump power.
With the average output power and the repetition frequency of the pulse, the pulse energy of the signal light could be calculated by E pulse = P average /f p , which is shown in Figure 5e,g. Then, the peak power was calculated by P peak = E pulse /W, where W is the full width at half maximum (FWHM) of the signal pulse [32], shown in Figure 5f,h. Owing to the pulse compression of PtS 2 SA, the peak power of dual-loss Q-switched IOPO increased 131% from 1.815 kW in single Q-switched IOPO to 4.193 kW in doubly Q-switched one at 5.2 W pump power. could be suppressed by the participation of SA, and then the pulse width could be cut down. Therefore, in Figure 5b,d, the signal-light pulse from IOPO pumped by a PtS2 + AO doubly Q-switched laser was shorter than that from IOPO pumped by AO singly Qswitched laser. Because of PtS2′s saturable absorption to fundamental laser, the signallight pulse width is 64.3% compressed from 6.102 ns to 2.178 ns at 15 kHz pulse-repetition rate and 5.2 W pump power. With the average output power and the repetition frequency of the pulse, the pulse energy of the signal light could be calculated by Epulse = Paverage /fp, which is shown in Figure  5e,g. Then, the peak power was calculated by Ppeak = Epulse /W, where W is the full width at half maximum (FWHM) of the signal pulse [32], shown in Figure 5f,h. Owing to the pulse The temporal pulse profiles of fundamental and signal waves are shown in Figure 6a-d for two IOPOs at the incident pump power of 5.2 W and AO modulation rate of 15 kHz. In Figure 6a, the 1064 nm fundamental-pulse profile leaking from IOPO is shown, and so is the undepleted 1064 nm pulse profile from the AO Q-switched laser without IOPO. For comparison, the depleted and undepleted 1064 nm-pulse temporal profiles from the PtS 2 -based IOPO and laser are shown in Figure 6c. Because of PtS 2 's saturable absorption, the consumption of fundamental-light energy is larger in doubly Q-switched IOPO than that in AO Q-switched IOPO. In Figure 6e, the fundamental-to-signal conversion efficiency is calculated with the consumption of 1064 nm laser demonstrated in Figure 6a,c. Under incident pump powers of 5.2 W and f p = 15 kHz, the nonlinear conversion efficiency of doubly Q-switched IOPO is 39.9%, which increased 13.2% compared to IOPO without PtS 2 . The energy conversion from 808 nm-pump laser to 1570 nm-signal light is up to 3.29%.
By numerically solving the above-derived rate Equations (4)-(8), the temporal pulse from IOPO or laser could be calculated with PtS 2 's SA parameters in Table 1. Figure 7a,b show the theoretical and experimental pulse profiles of the fundamental light and signal light at 5.2 W pump power and 15 kHz AO-modulating rate. Figure 7c provides the calculated 1064 nm-wavelength pulse train of the PtS 2 singly Q-switched laser. It can be seen that the theoretical values from Gaussian rate equations fit the experimental data well. in Figure 6a,c. Under incident pump powers of 5.2 W and fp = 15 kHz, the conversion efficiency of doubly Q-switched IOPO is 39.9%, which increas compared to IOPO without PtS2. The energy conversion from 808 nm-pump las nm-signal light is up to 3.29%.  Several SAs have been used to improve the performance of IOPO. In Table 2, the output characteristics of doubly Q-switched IOPO with AOM and different SA are reviewed. Compared to other SAs, the 6.2 nm-thickness PtS 2 used in this work could optimize IOPO's operation at lower incident pump power (≤5.2 W). Meanwhile, doubly Q-switched IOPO based on PtS 2 attains 3.6 W, the lowest threshold, and 3.29%, the highest pump-to-signal conversion efficiency.
from IOPO or laser could be calculated with PtS2′s SA parameters in Table 1. Figure 7a,b show the theoretical and experimental pulse profiles of the fundamental light and signal light at 5.2 W pump power and 15 kHz AO-modulating rate. Figure 7c provides the calculated 1064 nm-wavelength pulse train of the PtS2 singly Q-switched laser. It can be seen that the theoretical values from Gaussian rate equations fit the experimental data well. Several SAs have been used to improve the performance of IOPO. In Table 2, the output characteristics of doubly Q-switched IOPO with AOM and different SA are reviewed. Compared to other SAs, the 6.2 nm-thickness PtS2 used in this work could optimize IOPO's operation at lower incident pump power (≤5.2 W). Meanwhile, doubly Q-switched IOPO based on PtS2 attains 3.6 W, the lowest threshold, and 3.29%, the highest pump-to-signal conversion efficiency.

Conclusions
In conclusion, a 6.2 nm-thickness PtS 2 SA was prepared using the method of EBE combined with post-sulfurization. Based on the measured nonlinear transmittance, the ground-state and the excited-state absorption cross-sections of PtS 2 SA were estimated to be 6.4298 × 10 −19 cm −2 and 2.5927 × 10 −19 cm −2 , and the excited-state lifetime was approximately 1.043 ms. In the experiment, a KTP IOPO pumped by an active-passive Q-switched fundamental laser with AOM + PtS 2 was realized. With the application of PtS 2 SA, the peak-to-peak stability of Q-switched IOPO improved by 76.6%. The pulse width of signal light was 64.3% compressed, and the peak power improved 131%. In particular, due to PtS 2 -SA's optimization, the conversion efficiency of IOPO improved by 13.2%. To the best of our knowledge, the 3.29% pump-to-signal conversion efficiency is the highest value to date for the doubly Q-switched IOPO with AOM. In theory, the rate equations under Gaussian assumption are derived and numerically solved with PtS 2 's SA parameters. The theoretical values fit the experiment ones well.