## Abstract

A 2.5nm-thickness molybdenum diselenide (MoSe_{2}) saturable absorber (SA) is prepared by electron beam evaporation (EBE) method. Applying the prepared MoSe_{2} SA to an acousto-optic (AO) Q-switched fundamental laser, a dual-loss-modulated intra-cavity optical parametric oscillator (IOPO) has been experimentally realized. The signal-pulse train from this IOPO has 0.0053 standard deviation (SD) of pulse amplitude. When the MoSe_{2} SA is applied to IOPO, the signal pulse is compressed by maximum 68%, the peak power increases by 274%, and the nonlinear conversion increases by 12.6%. To solve the established rate equation of IOPO, the ground-state and excited-state absorption cross section of MoSe_{2} are rationally estimated to be 1.04×10^{−18}cm^{−2} and 6.25×10^{−19}cm^{−2} from the measured transmittance curve, and the excited-state lifetime is 275.6µs. The numerical solution of the equations fits the experimental data well.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

## 1. Introduction

The eye-safe coherent sources with high peak power in the near-infrared (NIR) spectral region of 1.5-1.6 µm have attracted increasing interest in recent years, which are widely used in the fields of telemetry, radar, communications, etc [1–3]. The eye-safe laser can be traditionally generated by an erbium (Er)-doped laser system, but the thermal effect in the media limits the pulse-repetition rate to only several hertz. Nonlinear frequency transformation, such as stimulated Raman scattering or optical parametric oscillator (OPO), is another approach to obtain the laser at this spectral range. Compared with Raman scattering, OPO provides high-conversion coherent light because of its nonlinearities ${\chi ^{(2)}}$ related to second-order nonlinear process [4–7]. Furthermore, by applying the OPO cavity into the fundamental-laser cavity, the nonlinear conversion of OPO can be further increased [8–10].

For intracavity OPOs (IOPOs), the Q-switched fundamental laser with higher peak power can support higher nonlinear conversion. So, the short-pulse-width and high-peak-power Q-switched laser is efficient to the operation of IOPO [11,12]. Another factor affecting the nonlinear conversion of IOPO is the stability of fundamental-pulse train. Therefore, stable operation and pulse-compression performance of Q-switches for fundamental laser are very important for IOPO. Among all the Q-switching methods, acousto-optic (AO) actively Q-switched laser can obtain controllable pulse with definite repetition rate, but the pulse width of actively Q-switched laser is usually wide. Compared with actively Q-switched ones, passively Q-switched lasers with saturable absorbers (SAs) can generate short-width pulse. Many kinds of SAs have been applied to obtain Q-switched pulses at different wavelengths so far [13–16]. Among these SAs, two-dimensional (2D) transition metal dichalcogenides (TMDCs) are regarded as promising optical modulators due to their unique properties [17–20], and some of them are combined with active Q-switch to realize dual-loss modulated laser [21–24]. Though doubly Q-switched lasers based on TMDCs are advantageous to nonlinear transformation due to their high peak power and stability, few of them have been selected to pump OPO so far [25]. As a member of the 2D TMDCs family, layered molybdenum diselenide (MoSe_{2}) with broadband saturable absorption from 400 to 2100 nm can efficiently modulate 1µm laser [26–28]. By combining the few-layer MoSe_{2} SA with AO modulator (AOM), the stable pulse trains with high peak power from the doubly Q-switched laser are expected to be excellent fundamental-light source to IOPOs [29,30]. However, as far as we know, IOPOs pumped by MoSe_{2}-SAs based passively Q-switched lasers have not been experimentally demonstrated.

Dynamical rate equations have been proved to be efficient to predict the performances of lasers or IOPOs [31,32]. For OPOs Q-switched by 2D SA, the absorption cross section and energy-state lifetime reflecting saturated absorption characteristics are necessary for establishing rate equation. Because the energy level structure of 2D TMDCs is under study, there are few reports on their saturated absorption parameters required for dynamic models [33,34]. So far, there is no research work on rate equation of laser Q-switched by MoSe_{2}, let alone the rate equation of Q-switched OPO based on MoSe_{2}.

In this work, firstly, a 2.5nm-thickness MoSe_{2} SA is prepared by electron beam evaporation (EBE) method, whose optical characteristics are thoroughly investigated. Secondly, a signal resonant KTP IOPO pumped by a doubly Q-switched Nd^{3+}:YVO_{4} laser with the prepared few-layer MoSe_{2} SA and an AOM has been experimentally realized. AOM is utilized to control the signal-pulse-repetition rate. The MoSe_{2} SA, as the passive Q switch, is expected to compress the pulse width for high peak power. Such a doubly Q-switched IOPO based on 2D-MoSe_{2} SA could operate steadily with higher nonlinear conversion than the AO singly Q-switched IOPO. Finally, based on the nonlinear transmittance curve, methods for estimating the absorption cross section and the excited-state lifetime of 2D-MoSe_{2} SA are given. The rate equation of Q-switched IOPO based on MoSe_{2} SA is also solved by computer programming. The calculated values are in agreement with the experimental ones.

## 2. Fabrication and optical characteristics of 2D MoSe_{2} SA

Different from the commonly used liquid-phase exfoliation method, the EBE method with post selenization is employed to prepare few-layer SA, which strictly control the homogeneity and thickness of MoSe_{2} [35–37]_{.} In the preparation process, Mo film with 1nm-thickness is deposited on c-cut Al_{2}O_{3} substrate by e-beam evaporation (ATS 500, HHV). Then the deposited film with substrate is thermally annealed in selenium rich ambience at 830°C for 10 minutes. During the thermal treating, the Ar mixed H_{2} of 270/30 sccm are employed as carrier gas and reactive gas.

The characterizations of the synthesized material are detailed investigated (Fig. 1). In Fig. 1(a), photograph of 2cm-width MoSe_{2} sample shows good contract compared to the edge of Al_{2}O_{3} substrate. The optical micrograph (CX23, Olympus) with a 50 µm by 50 µm region is measured for the sample, whose color contrast gives the number of layers in general [40]. The optical micrograph in Fig. 1(b) indicates a contrast between MoSe_{2} sample and pristine transparent sapphire substrate. The 2D spectral image of the intensity of A_{1g} mode is plotted in Fig. 1(c), and little variation of the intensity in Raman mapping image shows the high homogeneity of synthetic MoSe_{2} over a large area [41]. Raman spectrum is collected by a Raman spectrometer excited by laser of 532 nm with a photon detector (Horiba LabRAM HR Evolution). As shown in Fig. 1(d), there are two characteristic peaks A_{1g} (237 cm^{−1}) and E^{1}_{2g} modes (282 cm^{−1}) observed in this experiment. The A_{1g} mode is related to an out-of-plane vibration of Se atoms, while the E^{1}_{2g} mode means the in-plane vibrations with the Se atoms and Mo atoms heading opposite directions. Compared with the Raman spectrum of the bulk MoSe_{2} with the A_{1g} mode of 242 cm^{−1}, a red shift about 5 cm^{−1} is obtained in our experiment, which verifies a few-layer structure of the sample [38,39,42]. In Fig. 1(e), scanning electron microscopy (SEM, Regulus8100, Hitachi) shows a layered structure of the MoSe_{2} sample at the edge of the piece. The thickness and morphology of MoSe_{2} are measured by atomic force microscopy (AFM, Bruker Dimension Icon) in Fig. 1(f). The thickness analyzed from the height profile is about 2.5 nm, which indicates a structure of 2-3 layers corresponding to the above-analysis results of optical micrograph and Raman spectrum [43,44].

By use of the double optical path method [45], the nonlinear transmittance of MoSe_{2}^{-}SA is shown in Fig. 2. The laser source is an AO Q-switched solid-state laser with 15 kHz repetition and 120 ns pulse-width at 1.06µm, whose average output power is 481 mW. The approximated nonsaturable loss (*α _{s}*) and initial transmittance (

*T*) are about 14% and 77.8% respectively, then the modulation depth (Δ

_{0}*T*) is calculated to be 8.2%. The saturation power density (

*I*) is fitted to be 1.998 MW/cm

_{sat}^{2}. Inset of Fig. 2 provides the linear relation between transmittance and peak-energy density for low-power density, from which the slope of 1.93 is obtained by linear fitting.

## 3. Experimental setup

The experimental setup for the laser diode (LD)-pumped double Q-switched laser with signal resonant IOPO is schematically demonstrated in Fig. 3. A fiber-coupled 808 nm LD with a 400µm-diameter core (PHOTECK, USA) is applied as the pump source. The 3×3×5 mm size and 0.6 at. % Nd^{3+} doped Nd:YVO_{4} is used as gain medium, whose two faces are antireflection (AR) coated at 808 nm and 1.06 µm. The 25-mm-long KTP crystal in type-II noncritical phase-matching configuration (*θ *= 90°and *ϕ *= 0°) is used along the x-axis to have both a maximum effective nonlinear coefficient and no walk-off among the fundamental, signal, and idler beams. One face of KTP is high reflection (HR) coated at 1.57 µm and high transmission coated at 1.06 µm. Another face is AR coated at the wavelength 1.57 µm and 1.06 µm. Both of the gain medium and the nonlinear crystal are wrapped with indium foil and held in a copper block which is strictly cooled at 20°C to reduce the thermal-lens effect efficiently. M_{1}, as the plane input mirror, is AR coated at 808 nm and HR coated at 1.06 µm. The plane M_{2} is used as output mirror, which is AR coated at 1.06 µm and 25% transmission coated at 1.57 µm. All the mirrors are placed on the 17MAX600 adjusting brackets (Melles Griot, USA). The distance between M_{1} and the first surface of Nd^{3+}:YVO_{4} is 10 mm. The fundamental cavity length between M_{1} to M_{2} is about 150 mm, while the physical length of OPO cavity is selected to be about 26 mm as short as possible. Then the fundamental laser oscillates in M_{1}M_{2} cavity and the signal light oscillates between M_{2} and the first face of KTP.

The crystal in AOM with an effective length of 47 mm is AR coated at 1064 nm (R < 0.2%) on both surfaces and the modulation rate of AOM could be tuned from 1 kHz to 50 kHz. In the experiment, two repetitions of AO (*f _{p}*=15 kHz and 25 kHz) are applied.

The generated laser power is measured by a MAX500AD laser power meter (Coherent Inc., U.S.A.). The signal-pulse and fundamental-pulse temporal behavior are recorded by two fast photo-electronic diodes (with response time of less than 1 ns) and a TDS620B digital oscilloscope (Tektronix, U.S.A.). The spectroscopy is recorded by a MS9710C spectrometer (Anritsu, Japan) working in wavelength range of 600-1750nm. The beam quality factor of the signal light is measured by a laser beam quality analyzer (M2MS, Thorlabs, U.S.A.) with a beam profiler (BP209-IR/M, Thorlabs, U.S.A.).

## 4. Results and discussions

#### 4.1 Experimental results

The spectra of the fundamental and signal light for MoSe_{2}+AO doubly Q-switched IOPO are showed in Fig. 4. It can be seen from this picture that the fundamental and signal wavelength are located at about 1064 nm and 1573 nm, respectively.

The temporal pulse trains in Fig. 5 indicate the stability of pulse amplitude. Figure 5(a) shows a pulse train from the MoSe_{2} passively Q-switched laser whose output mirror is 4% 1064nm-transmission coated, when the LD-pump power is selected to be higher than the threshold of IOPO. The steady operation of passive Q-switch may be affected by the thermal effect of MoSe_{2} SA owning to the high photon energy in the cavity. It can be seen that the standard deviation (SD) of pulse amplitude is 0.0808 at 6.6W pump power for the pulse train from MoSe_{2}-SA passively Q-switched laser. Up to now, the OPO pumped by MoSe_{2}-SA singly Q-switched laser has not been obtained yet. In order to obtain a sufficiently stable fundamental-pulse sequence to pump OPO based on MoSe_{2}, AO modulator is introduced to manage regular switching time. Figure 5(b) show the typical pulse trains of signal light from MoSe_{2}+AO dual-loss modulated IOPO, under the incident pumped power of 6.6 W and AO modulation of 15 kHz. It can be concluded that the pulse-repetition rate depends on AO modulation rate in MoSe_{2}+AO doubly Q-switched IOPO. The SD of signal pulse trains from doubly Q-switched IOPO is only 0.0053, which is much smaller than 0.0327 SD of AO singly Q-switched IOPO (Fig. 5(c)). In our opinion, the stable operation of OPO generally owes to that of fundamental laser. In a dual-loss Q-switched laser, the participation of passive SA can suppress the number of longitudinal modes, and then shorten the line width [24,46]. The limitation for fundamental-light longitudinal mode can contribute to the stable operation of 1064nm laser and OPO. Therefore, the application of MoSe_{2} SA can efficiently improve the stability of Q-switched IOPO.

Figure 6 give the average output power and pulse width of signal light versus the 808nm-LD incident pump power for the MoSe_{2}+AO dual-loss modulated and AO singly Q-switched IOPO at two different AO modulation rate. In Fig. 6(a), the signal output average power at *f _{p}*=15 kHz is slightly higher than 25 kHz at the same pump power, whether in doubly Q-switched IOPO or in AO singly Q-switched IOPO. For MoSe

_{2}+AO doubly Q-switched IOPO (Fig. 6(c)), the maximum output power in experiment is 111.1 mW at the maximum incident-pump power of 7.6 W and AO modulation rate of 15 kHz. Because of the insertion loss from MoSe

_{2}SA, the average output power of the doubly Q-switched IOPO is generally lower than that of the singly Q-switched IOPO. The threshold pump powers for singly Q-switched and doubly Q-switched IOPO are about 5 W and 5.5W, respectively. Figures 6(b) and 6(d) show the pulse widths of the signal light versus incident pump power for two kinds of Q-switched IOPO, at pulse-repetition rate of 15 and 25 kHz, respectively. The pulse width commonly decreases with increasing pump power, but increases with increasing AO repetition rate. In experiment, the signal pulse can be compressed a lot when the few-layer 2D MoSe

_{2}SA is inserted into the fundamental cavity. The maximum compression ratio calculated from Fig. 6 is approximated to 68% from 6.78 ns (in AO Q-switched IOPO) to 2.2 ns (in MoSe

_{2}+AO Q-switched IOPO), at 7.6 W maximum pump power and

*f*=15 kHz.

_{p}Short pulse width contributes to high peak power, and the peak power of fundamental light is critical to the nonlinear conversion of Q-switched OPO. The signal peak power *P _{peak}* and the pulse energy

*E*are expressed from the Eqs. (1) and (2) [29].

_{pulse}*P*is the signal output average power. By use of Eqs. (1) and (2), the calculated pulse energy and peak power of signal light from the experimental data for two kinds of Q-switched IOPO are shown in Fig. 7.

_{average}The approximated peak powers of signal light are demonstrated in Fig. 7. The maximum pulse peak powers of singly Q-switched IOPO and doubly Q-switched IOPO are calculated to be 0.9 and 3.37 kW, respectively. When the MoSe_{2} SA is applied to AO singly Q-switched IOPO, the maximum increase radio of 274% can be available for the peak power, under the maximum incident pump power of 7.6 W and 15 kHz repetition.

To compare the nonlinear conversion efficiencies of doubly and singly Q-switched IOPO, the undepleted fundamental laser without OPO depletion is monitored as the depleted fundamental laser leaking from OPO. Figures 8(a) and 8(b) show the undepleted and depleted 1064 nm profiles from the Q-switched laser cavity, when the incident pumped power is 7.4 W and the modulating rate is 15 kHz. By use of Eq. (3) [29], the nonlinear conversion efficiencies of doubly and singly Q-switched IOPO are calculated to be 56.1% and 46.4%, respectively.

In Eq. (3),*E*represents the single pulse energy of undepleted fundamental laser, and

_{1}*E*is the single pulse energy of the depleted fundamental laser leaking from IOPO under the same condition.

_{2}The dependence of conversion efficiency on LD power in two different Q-switched IOPO is exhibited in Fig. 8(c) when *f _{p}*=15 kHz. The conversion efficiency increases by maximum 12.6% in MoSe

_{2}+AO Q-switched IOPO over that in an AO Q-switched one with the maximum experimental pump power.

Additionally, by using the beam quality analysis system without power attenuation, the beam profile of the signal light from the doubly Q-switched IOPO with MoSe_{2} SA and AOM are measured under incident pumped power of 7.4 W and modulation rate of 15 kHz, as is shown in Fig. 9. The beam quality factors *M ^{2}* of the signal light are measured as

*M*and

_{x}^{2}*M*of 2.96 and 2.51.

_{y}^{2}#### 4.2 Theoretical evaluation

The rate equations are efficient tools to analyze the Q-switched dynamics. In this section, a LD-pumped doubly Q-switched Nd:YVO_{4}/KTP IOPO with an AOM and a 2.5nm-thickness MoSe_{2} SA is considered. By neglecting the spatial variation of the photon densities, the rate equations with saturated absorption characteristics of MoSe_{2} SA for the IOPO can be obtained based on our previous work [29].

*E*(

_{j}(t)*j*=

*p*,

*s*,

*i*) is electrical field of the fundamental light, the signal light and the idler light, respectively;

*n(t)*is the population inversion intensity of the fundamental-laser medium;

*n*and

_{y0}*n*(

_{y1}*t*) are the ground-state and the excited-state population density for the SA;

*δ*is the diffractive loss caused by the thermal effect in the gain medium;

_{T}*l*,

*l*and

_{g}, l_{KTP}, l_{OPO}*l*represent the physical length of the laser cavity, the gain medium, the KTP crystal, the OPO cavity and SA, respectively;

_{y}*σ*and

*τ*are the stimulated-emission cross section and the stimulated-radiation lifetime of laser gain medium;

*t*is the round-trip time of the fundamental light;

_{r}*L*is the round trip loss including the intrinsic loss of the laser cavity;

*ω*(

_{j}*j*=

*p*,

*s*,

*i*) is the frequency of the three lights;

*ɛ*(

_{j}*j*=

*s*,

*i*) denotes the dielectric constant and

*τ*(

_{j}*j*=

*s*,

*i*) is the OPO cavity lifetime of the signal (idler);

*δ*=

*ɛ*, where

_{0}d_{eff}*d*is the effective nonlinear coefficient of the OPO crystal, and

_{eff}*ɛ*is the dielectric constant of the vacuum. If we assume the perfect phase matching,

_{0}*I*= 1;

*δ*(

_{a}*t*) is the loss function describing a gradual AOM due to the exponential time delay when the AO switch turns on, which can be written as ${\delta _a}(t )= {\delta _a}\exp \left[ { - {{\left( {\frac{t}{{{t_{AO}}}}} \right)}^2}} \right]$ [47].

In Eq. (4) and (8), *σ _{g}* and

*σ*are the ground-state and the excited-state absorption cross section, which are the key parameters for saturable absorption properties of SA.

_{e}*σ*and

_{g}*σ*satisfy the relation between peak-energy density

_{e}*E*and transmission distance

*z*(Eq. (9)). [48,49]

*T*) at low power density and the maximum transmittance at high power density (

_{0}*T*), Eq. (10) and (11) can be derived from Eq. (9) [34,50,51].

_{max}*T*,

_{0}*T*and

_{max}*k*can be obtained from Fig. 2. Then

*σ*and

_{g}*σ*of 2.5nm-thickness MoSe

_{e}_{2}SA can be estimated to be 1.16×10

^{−18}cm

^{−2}and 7×10

^{−19}cm

^{−2}by Eqs. (10) and (11). Although there are no reported values of absorption cross sections for MoSe

_{2}SA, the values we calculated above correspond to the typical values of another TMDC SA [34,52]. In Eq. (8),

*τ*is the excited-state lifetime of SA. As the energy-band structure of TMDC is complex [52], there is no report on the excited-state lifetime of 2D-MoSe

_{y}_{2}as a laser modulator, to our best knowledge. Here, we estimate the saturable-absorption excited-state lifetime of MoSe

_{2}SA based on the measured non-linear transmittance data and spectral broadening mechanism.

According to the relation between absorption cross section and state lifetime (Eq. (12)), *τ _{y}* (

*=*1

*/A*

_{21}) can be approximated [53].

*v*is light velocity in MoSe

_{2}and ${\nu _0}$ represents the center frequency. Because of the solid state of SA, only the contribution of Doppler broadening to linewidth $\Delta \nu$ is considered. Equation (13) can interpret the Doppler linewidth of MoSe

_{2}, where

*k*is Boltzmann constant and

_{b}*m*is the atomic mass of MoSe

_{2}[54]. By substituting the Doppler linewidth of MoSe

_{2}($\Delta \nu$≈2.2×10

^{8}Hz) into the Eq. (12), we can calculate that

*τ*275.6 µs which is in the same order of magnitude as that of WSe

_{y}=_{2}which is also selenide [24].

_{2}SA and Table 2 show the values of other parameters used in rate Eqs. (4)–(8).

*n*and

_{1}*n*are the refractive indices of the fundamental light in Nd:YVO

_{2}_{4}gain medium and AO crystal.

*n*(

_{j}*j = p, s, i*) is the refractive index of the three beams in the KTP crystal.

The last item of Eq. (4), $\frac{{\delta {\omega _p}I{l_{KTP}}}}{{4{\varepsilon _p}l}}{E_s}(t ){E_i}(t)$, explicates the nonlinear conversion to fundamental light by OPO, which is combined and Eq. (5)–(6) to show the dynamical evolution of three lights. By numerically solving Eq. (4)–(8) on a computer with the corresponding parameters shown in Table 1 and Table 2, the relation between *E _{j}*(

*t*) (

*j*=

*p*,

*s*,

*i*) and

*t*can be obtained. According to the equation $\phi (t )= \varepsilon {E^2}(t )/4\hbar \omega$, we can take the temporal variations of the intracavity photon densities $\phi (t )$. Then the temporal waveforms of three lights can be calculated. Furthermore, without $\frac{{\delta {\omega _p}I{l_{KTP}}}}{{4{\varepsilon _p}l}}{E_s}(t ){E_i}(t)$ and ${\delta _a}(t)$, Eq. (4), (7), and (8) are considered as the rate equation of MoSe

_{2}passively Q-switched laser.

Figures 10(a) and 10(b) demonstrate the experimental and calculated temporal-pulse profiles of the fundamental and signal light for the doubly Q-switched IOPO based on MoSe_{2} SA at *f _{p}*=15 kHz and

*Pump*= 7W. Two pulses are shown in Fig. 10(c), which are from MoSe

_{2}SA passively Q-switched laser at 6.6W pump power. It can be seen that the pulse width is about 282.59 ns and the pulse-repetition period is 6µs. The theoretical values fit the experimental data well.

## 5. Conclusions

A 2.5nm-thick MoSe_{2} SA was prepared by EBE with post selenization. Then, an intracavity KTP OPO pumped by a doubly Q-switched fundamental laser with AOM and the prepared MoSe_{2} SA was experimentally realized. In comparison with AO singly Q-switched IOPO, the doubly Q-switched IOPO with MoSe_{2} SA could generate much more stable pulse train with only 0.0053 SD. Furthermore, the signal-pulse width decreased by 68% and the peak power increased by 274%, when the few-layer 2D MoSe_{2} SA was inserted into the fundamental cavity. Owing to the pulse compression and peak-power improvement in doubly Q-switched IOPO, the nonlinear conversion efficiency of IOPO was basically raised by 12.6% with the use of few-layer MoSe_{2} SA. The experimental results indicate that the pulse-train stability, pulse compression, peak power and conversion efficiency can be efficiently improved when the 2D-MoSe_{2} is applied to AO singly Q-switched IOPOs. Lastly, based on the nonlinear transmittance curve of 2D-MoSe_{2} SA, *σ _{g}* and

*σ*were rationally estimated to be 1.04×10

_{e}^{−18}cm

^{−2}and 6.25×10

^{−19}cm

^{−2}, and

*τ*was 275.6 µs considering Doppler broadening. The rate equation was solved by computer programming and the calculated value fitted the experimental value well.

_{y}## Funding

National Natural Science Foundation of China (51307012, 61308057); Key Technology Research and Development Program of Shandong (2017CXGC0416, 2017GGX50114).

## Disclosures

The authors declare no conflicts of interest.

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