Broadband rhenium disulfide optical modulator for solid-state lasers

Rhenium disulfide (ReS2), a member of group VII transition metal dichalcogenides (TMDs), has attracted increasing attention because of its unique distorted 1T structure and electronic and optical properties, which are much different from those of group VI TMDs (MoS2, WS2, MoSe2, WSe2, etc.). It has been proved that bulk ReS2 behaves as a stack of electronically and vibrationally decoupled monolayers, which offers remarkable possibilities to prepare a monolayer ReS2 facilely and offers a novel platform to study photonic properties of TMDs. However, due to the large and layer-independent bandgap, the nonlinear optical properties of ReS2 from the visible to mid-infrared spectral range have not yet been investigated. Here, the band structure of ReS2 with the introduction of defects is simulated by the ab initio method, and the results indicate that the bandgap can be reduced from 1.38 to 0.54 eV with the introduction of defects in a suitable range. In the experiment, using a bulk ReS2 with suitable defects as the raw material, a few-layered broadband ReS2 saturable absorber (SA) is prepared by the liquid phase exfoliation method. Using the as-prepared ReS2 SA, passively Q-switched solid-state lasers at wavelengths of 0.64, 1.064, and 1.991 μm are in

1. INTRODUCTION

Recently, 2D materials, including graphene ^[1], topological insulators ( ${Bi}_{2} {Se}_{3}$ , ${Bi}_{2} {Te}_{3}$ , etc.) ^{[2–5" target="_self" style="display: inline;">–5]}, black phosphorus ^{[6–10" target="_self" style="display: inline;">–10]}, and transition metal dichalcogenides (TMDs) ( ${MoS}_{2}$ , ${WS}_{2}$ , etc.) ^[11,12], with outstanding electronic and optical properties have been widely used in energy storage devices, transistors, photodetectors, electroluminescent devices, and optical saturable absorbers for ultrafast photonics ^{[13–28" target="_self" style="display: inline;">–28]}. Among these materials, 2D TMDs are relatively easy to exfoliate, affordable, and highly reliable ^{[2931" target="_self" style="display: inline;">–31]}. Further, 2D TMDs are materials consisting of an atomic plane of a transition metal (Mo, W, Re, Ti, Zr, Hf, V, Nb, Ta, etc.) sandwiched between two chalcogen planes (S, Se, Te) ^[32,33]. Aside from the most popular TMDs of group VI ( ${MoS}_{2}$ , ${WS}_{2}$ , ${MoSe}_{2}$ , ${WSe}_{2}$ , etc.), ${ReS}_{2}$ , a representative of group VII TMDs, has recently attracted significant interest for its unusual properties in many aspects of structural, electro-optical, and chemical properties ^[34,35]. A vision has emerged that ${ReS}_{2}$ will apparently be more worthwhile over isotropic TMDs from group VI for traditional applications and beyond. Differing from the popular group VI TMDs, due to charge decoupling from an extra valence electron of Re atoms, ${ReS}_{2}$ possesses a unique distorted 1T structure with weak interlayer coupling, which offers remarkable possibilities to prepare few-layered ${ReS}_{2}$ facilely ^[36]. As a result of the distorted 1T structure, both the monolayer and bulk ${ReS}_{2}$ are direct bandgap semiconductors. Furthermore, the overall bandgap does not change significantly from monolayer to multilayer (1.35 eV for bulk and 1.43 eV for monolayer) ^[37]. Consequently, ${ReS}_{2}$ has shown layer-independent electrical, optical, and vibrational properties ^[38]. This suggests that ${ReS}_{2}$ could offer a novel platform to study mesoscopic physics of 2D systems without the limitation of obtaining monolayer-thick flakes. However, the large and layer-independent bandgap also causes a problem for applications where a particular bandgap is required. For 2D materials, it has been reported that the impurities or defects in materials can localize electronic states, which in turn can generate narrow bands, a Mott transition, and even Anderson localization ^[39]. Recently, the existence of lattice imperfections in 2D graphene-like structures has been used to tail local properties and achieve new functionality ^[40,41]. Inspired by this conclusion, in this work, we calculated the band structure with the introduction of defects by the ab initio method ^[15]. The result shows that the bandgap of ${ReS}_{2}$ reduces with the modification of S defects. We believe this work may be helpful in the design of variable bandgaps in 2D optoelectronic materials.

In the past years, there has been observed a growing interest in fundamental and applied research related to ${ReS}_{2}$ ^[36,42]. Among these achievements, the nonlinear optical properties and the corresponding applications are rarely investigated, in contrast with its electronic and chemical properties. Recently, Liu et al. and Mao et al. have found ${ReS}_{2}$ can be used in 1.5 μm fiber lasers as the saturable absorber (SA) and obtained picosecond pulse lasers ^[43,44]. In comparison with fiber lasers, solid-state lasers possess superiorities, such as high power and smooth spectral property without sidebands. Recently, our group has achieved a $Q$ -switched solid-state laser at 2.8 μm by using ${ReS}_{2}$ as a saturable absorber ^[45]. The above successful applications in ultrafast lasers make ${ReS}_{2}$ a promising optical modulator. However, the mechanism that the ${ReS}_{2}$ with a large bandgap ( $\sim 1.35 eV$ ) can be used at a wavelength beyond the theoretical response wavelength (shorter than 0.918 μm) still lacks verification in both theory and experiment. In addition, up to now, the broadband absorption properties and the applications in solid-state lasers have not been investigated systematically. In this paper, based on the theoretical analysis, by using bulk ${ReS}_{2}$ with suitable S defects as raw material, a broadband ${ReS}_{2}$ SA is constructed, and its properties are characterized systematically. Using the as-prepared ${ReS}_{2}$ SA in solid-state lasers, passively $Q$ -switched lasers at 0.64, 1.064, and 1.991 μm are demonstrated, respectively. To further study their ability to generate ultrafast pulses, their ultrafast photonics application in a femtosecond solid-state laser is realized successfully for the first time, to the best of our knowledge, and pulses as short as 323 fs were obtained at 1.06 μm with an output power of 350 mW. The above work broadens the applied spectral ranges of ${ReS}_{2}$ and experimentally identifies that ${ReS}_{2}$ with suitable S defects is a promising broadband optical modulator.

2. THEORETICAL ANALYSIS OF THE BAND STRUCTURE

Based on the reported unit-cell parameter of ${ReS}_{2}$ , the monolayer supercell with 36 Re atoms and 72 S atoms is created and optimized by using the Vienna ab initio simulation package ^[46]. The calculated band structures with different Re to S ratio (R) are shown in Fig. 1. When R is $1 ∶ 2$ , from Fig. 1(b), it can be seen that ${ReS}_{2}$ is a direct gap semiconductor with a bandgap of 1.38 eV, which is close to the experimental value of 1.37 eV ^[47]. With S atomic defects, the band structures of monolayer ${ReS}_{2}$ are calculated with R of $1 ∶ 1.972$ , $1 ∶ 1.944$ , and $1 ∶ 1.889$ , respectively, as shown in Figs. 1(c)–1(e). The results show that the bandgap of ${ReS}_{2}$ decreases with the increase of S vacancies. However, when Re vacancies are introduced, electrons are localized near the S atoms, which are close to the Re vacancies, which results in the non-negligible electronic density of states at the Fermi level. As shown in Fig. 1(a), by introducing Re vacancy with R of $1 ∶ 2.057$ , the energy band intersects with the Fermi level, which indicates that, in this case, the ${ReS}_{2}$ has no bandgap and exhibits a metallic character. The above results show that S-containing defects result in a small but noticeable reduction of the bandgap, whereas Re-containing defects work adversely, which is comparable with the results of ${WS}_{2}$ and ${MoS}_{2}$ ^[41,48]. A difference is that the creation of an Re vacancy causes the character of ${ReS}_{2}$ from semiconductor to metallic state, while ${WS}_{2}$ and ${MoS}_{2}$ retain semiconductors with a W or Mo vacancy. It appears that, due to the complex distorted 1T structure of ${ReS}_{2}$ , the electronic localization in a ${ReS}_{2}$ monolayer is more severe, as compared with the ${MoS}_{2}$ and ${WS}_{2}$ monolayer case.

Fig. 1. Theoretical band structure of monolayer ${ReS}_{2}$ . (a) $R = 1 ∶ 2.057$ , (b) $R = 1 ∶ 2$ , (c) $R = 1 ∶ 1.972$ , (d) $R = 1 ∶ 1.944$ , and (e) $R = 1 ∶ 1.889$ .

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Based on the calculation results, it can be concluded that, by the introduction of S defects in a suitable range, the bandgap of ${ReS}_{2}$ can be reduced from 1.38 ( $R = 1 ∶ 2$ ) to 0.56 eV ( $R = 1 ∶ 1.889$ ), and the corresponding absorption wavelength edge extends from 0.9 to 2.2 μm. Due to the layer-independent properties of ${ReS}_{2}$ , the above calculations based on a monolayer ${ReS}_{2}$ should be effective for multilayer and bulk ${ReS}_{2}$ . Considering the semiconducting properties of ${ReS}_{2}$ , when ${ReS}_{2}$ is excited by light with photon energy larger than the gap energy, electrons will be transferred from the valance band to the conduction band. Under strong excitation, the final states will be fully occupied and exhibit saturable absorption, which indicates that ${ReS}_{2}$ with S defects can be used as a broadband saturable absorber ^[41].

3. PREPARATION AND CHARACTERIZATION OF THE ReS2 SA

For ReS₂ SA preparation, the liquid phase exfoliation (LPE) is considered as a simple but effective technique to synthesize ${ReS}_{2}$ from the bulk crystals toward few-layered structures. First, the ${ReS}_{2}$ powder was prepared from bulk crystal through a grinding process. Then, we mixed the ${ReS}_{2}$ powder with alcohol and executed 4-h ultrasonic exfoliation to undertake the liquid exfoliation process. To avoid the change of the material properties under high temperature, the ultrasonic process was operated at a suitable interval. After that, the solution was centrifuged at 2000 r/min for 10 min and the supernatant was collected for standby. Finally, the extracted ${ReS}_{2}$ supernatant was transferred onto a plane substrate or mirror by spin coating at 500 r/min for 10 s and dried under an infrared oven lamp. Recent studies have shown that controllable formation of vacancies in monolayer TMDs can be realized experimentally by the methods such as pulsed laser deposition (PLD), $α$ -particle irradiation, and thermal annealing ^[41,49]. Most of the above methods control the defects by tuning the ratio of the atoms in raw materials. However, the various growth conditions, proton thermal motion, and mechanical stress also can cause lattice imperfection, which makes it difficult to control the defects of the SA precisely. In this work, based on the theoretical analysis, by characterization with energy-dispersive X-ray spectroscopy (EDS), we chose a commercially available purity ${ReS}_{2}$ bulk crystal with suitable defects as the raw material. With the EDS, the R of the bulk ${ReS}_{2}$ is characterized by point scanning and map scanning, respectively. In the point scanning, we selected 12 points randomly on the surface of ${ReS}_{2}$ sample, and the result shows that the R ranges from $1 ∶ 1.828$ to $1 ∶ 1.919$ by moving from the center to the edge of the sample. To confirm the average ratio, as shown in the inset of the Fig. 2(a), the bulk ${ReS}_{2}$ sample is placed on a piece of carbon conductive adhesive, and a $4 mm \times 3 mm$ area is measured by map scanning. Except for the C atoms and O atoms from air and the conductive adhesive, the average R is $1 ∶ 1.846$ for the bulk sample, which matches well with the ratio range measured by point scanning. After the exfoliation process, to identify the existence of vacancies in the as-prepared ReS₂ SA, we measure the average R of the few-layered ReS₂ SA based on the sapphire substrate. As shown in Fig. 2(b), except for the C, O, and Al from air and the sapphire substrate, the average R of the ${ReS}_{2}$ flakes is measured to be $1 ∶ 1.743$ . Compared with the bulk ${ReS}_{2}$ , the proportion of S atoms reduces in the few-layered ReS₂ SA. This is because, during the preparation of ReS₂ SA, especially in the process of grinding and ultrasonic exfoliation, some defects or vacancies are introduced at the Re sites and S sites under the action of external forces. In the structure of ${ReS}_{2}$ , S atoms located on the out-of-plane ^[27]. Thus, in the process of exfoliation, compared with Re atoms, more S atoms are replaced by vacancies or defects due to atomic collision. As a consequence, the R of bulk ${ReS}_{2}$ is different from that of few-layered flakes. According to the theoretical analysis, the bandgap of ${ReS}_{2}$ reduces with the S vacancies. Therefore, the sample has a bandgap less than 0.56 eV, and the corresponding maximum absorption wavelength should be greater than 2.2 μm.

Fig. 2. Measured position and the corresponding EDS image of (a) the raw bulk ${ReS}_{2}$ and (b) the as-prepared few-layered ${ReS}_{2}$ .

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To identify the thickness and the distribution of the flakes, an atomic force microscope (AFM) is used to study the morphology of the as-prepared ${ReS}_{2}$ SA. Figure 3(a) shows an AFM scan image of the sample in a large area, due to the weak interlayer coupling, where the distribution of flake thicknesses, as shown in Fig. 3(b), indicates good uniformity of the flake thickness. To study the detailed morphology, a smaller area is measured with high resolution, as shown in Fig. 3(c). The length and width of ${ReS}_{2}$ flakes are as large as 3–5 μm, which has potential for applications in solid-state bulk lasers, where the oscillation laser dimension is much larger than it is in fiber lasers. Compared with the samples in our previous paper, the flakes in this work have a slightly larger dimension and thickness ^[45]. That is because, in the two preparation processes, the concentration of ${ReS}_{2}$ and the ultrasonic time differ, resulting in a slight difference in thickness and dimension of the flakes. Figure 3(d) shows the typical height profiles of the section marked in Fig. 3(c). The thickness of the flakes is about 4 nm, corresponding to $\sim 6$ layers thick ^[50].

(a), (b) AFM image of the ReS2 SA with 30 μm×30 μm area and the corresponding distribution of flake thicknesses. (c), (d) High-resolution AFM image with 6 μm×6 μm area and the typical height profiles.

Fig. 3. (a), (b) AFM image of the ${ReS}_{2}$ SA with $30 μm \times 30 μm$ area and the corresponding distribution of flake thicknesses. (c), (d) High-resolution AFM image with $6 μm \times 6 μm$ area and the typical height profiles.

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The Raman spectra of the as-prepared ${ReS}_{2}$ SA and the pure sapphire substrate are measured by a Raman microscope with a 532 nm laser as the excitation source, as shown in Fig. 4(a). The Raman spectrum was acquired in the $100 - 500 {cm}^{- 1}$ wavenumber range by a lens-based spectrometer with a cooled charge-coupled device (CCD) detector. A $100 \times$ , $NA = 0.9$ objective is used to focus the beam on the flake with 1.0 μm diameter. The spectral resolution of the setup was $0.34 {cm}^{- 1}$ per CCD pixel for an 1800 grooves/mm grating. In general, there are two types of active Raman modes in 2D ${ReS}_{2}$ , intralayer vibration modes (higher frequencies) and interlayer vibration modes (lower frequencies) ^[29]. However, due to the weak lattice coupling between the layers, these low-frequency vibrational modes are usually quite challenging to be observed. Thus, Fig. 4(a) only shows the typical intra-layer vibration modes to confirm the material as ${ReS}_{2}$ . The $A_{g}$ modes located at 137.1 and $143.7 {cm}^{- 1}$ are assigned to out-of-plane vibrations of Re atoms. Among the $E_{g}$ modes, the modes located at 151.8, 162.4, 213.2, and $235.5 {cm}^{- 1}$ are caused by the in-plane vibrations of Re atoms, while the modes located at 307.1 and $310.7 {cm}^{- 1}$ are due to the in-plane vibrations of S atoms ^[51]. Except for these modes, due to the low symmetry of ${ReS}_{2}$ , there are many higher-frequency Raman modes in Fig. 4(a), which are mainly coming from the light S atoms.

(a) Raman spectra of the ReS2 SA and the sapphire substrate. (b) Absorption spectra of the ReS2 SA and the sapphire substrate, respectively. (c)–(e) Open aperture Z-scan curves of the ReS2 SA at 0.73, 1.06 and 1.94 μm, respectively.

Fig. 4. (a) Raman spectra of the ${ReS}_{2}$ SA and the sapphire substrate. (b) Absorption spectra of the ${ReS}_{2}$ SA and the sapphire substrate, respectively. (c)–(e) Open aperture Z-scan curves of the ${ReS}_{2}$ SA at 0.73, 1.06 and 1.94 μm, respectively.

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As shown in Fig. 4(b), the absorbance spectra of the ${ReS}_{2}$ SA and the pure sapphire substrate are measured using a U-3500 Hitachi UV/VIS/NIR spectrophotometer. It clearly shows that the ${ReS}_{2}$ sample has smooth absorption in the ultraviolet to mid-infrared wavelength bands, which demonstrates that the ${ReS}_{2}$ SA might be a promising broadband optical material. The Z-scan technique is used to investigate the nonlinear optical response of the as-prepared few-layered ${ReS}_{2}$ ^[52]. The experiment setup has been widely described in a previous report ^[25]. For the pump source, three stable mode-locked lasers at 0.73 μm (pulse duration: 120 fs; repetition rate: 79.7 MHz), 1.06 μm (pulse duration: 15 ps; repetition rate: 41.54 MHz), and 1.94 μm (pulse duration: 1.8 ps; repetition rate: 87.73 MHz) were used, respectively. Due to the limitation of the experiment conditions, the wavelengths of the pump sources do not match the laser output wavelengths, but the results still can show the broadband SA properties of the sample from the visible to infrared band. Figures 4(c)–4(e) show the measured open aperture Z-scan curves of the ${ReS}_{2}$ SA at 0.73, 1.06, and 1.94 μm, respectively. The normalized transmittance gradually increases when the ${ReS}_{2}$ sample moves toward the focus point ( $Z = 0$ ), indicating that the absorption of few-layered ${ReS}_{2}$ flakes becomes saturated with the increase of the incident pump intensity. This process is well-known as the typical saturable absorption behavior. The saturable absorption process could be studied by the analysis model of a two-level saturable absorber, and the intensity-dependent transmission formula is described as ^[25] where $T$ is the normalized transmittance of the sample, $L$ is the sample length, $α_{0} L$ is the modulation depth of the sample, $I_{0}$ is the peak intensity, $Z_{0}$ is the diffraction length of the beam, and $I_{s}$ is the saturation intensity. Using Eq. (1) to fit the measured data, for 0.73, 1.06, and 1.94 μm, the saturable intensities are determined to be 58.2, 21.5, and $2.7 μJ / {cm}^{2}$ , and the modulation depths are 3%, 5.2%, and 2.9%, respectively. Combined with the broadband absorption spectrum in Fig. 4(b), the existence of saturable absorption further makes the as-prepared ${ReS}_{2}$ SA as a broadband optical modulator possible.

4. VISIBLE, NEAR-INFRARED, AND MID-INFRARED Q-SWITCHED LASERS WITH A ReS2 SA

With a compact 3 cm long two-mirror resonator, passively $Q$ -switched solid-state lasers based on the as-prepared ${ReS}_{2}$ SA around 0.64, 1.064, and 1.991 μm bands are investigated with Pr:YLF, Nd:YAG, and Tm:YAP as gain media, respectively. The transmittance of the three output couplers (OCs) were 1%, 10%, and 5% for 0.64, 1.064, and 1.991 μm, respectively. For 0.64 μm, the input mirror (IM) was plane and the OC had a radius of curvature of 100 mm. For 1.064 μm, the IM and OC were both plane mirrors. For the 1.991 μm laser, the IM had a radius of curvature of 1000 mm and the OC was plane. By continuously increasing the pump power and finely tilting the ${ReS}_{2}$ SA, a nicely $Q$ -switched pulse laser can be easily achieved. The average output power, peak power, pulse duration, and repetition rate versus the absorbed pump power at 0.64, 1.064, and 1.991 μm are shown in Figs. 5(a)–5(f), respectively. From the figure, we can see the output power and repetition rate increase with the absorbed pump power, while the pulse duration decreases, which are typical results of passively $Q$ -switched lasers. We stopped increasing the pump power when the output pulse trains became unstable. Under the maximum absorbed pump power, the pulse trains and the corresponding output spectra at the wavelengths of 0.64, 1.064, and 1.991 μm are shown in Figs. 6(a)–6(f), respectively. Limited to our experimental conditions, the optical spectrum analyzer (AvaSpec-NIR256) with the resolution of 3.7 nm is the only equipment that can measure the laser spectra ranging from the visible to mid-infrared band. Due to the low resolution of 3.7 nm, the spectra look smooth and cannot show the precise full width at half-maximum (FWHM). Thus, the laser output spectra cursorily measured in Fig. 6 are only to characterize the laser output wavelength. The detailed output parameters under the maximum absorbed pump power are shown in Table 1. The shortest pulse durations at 0.64, 1.064, and 1.991 μm are 160, 139, and 415 ns, respectively, which are fairly nice results for 2D-materials-based $Q$ -switched lasers. The instabilities (output power, rms) for 0.64, 1.064, and 1.991 μm are measured to be 1.529%, 2.477%, and 2.318% at 0.5 h, respectively. For passively $Q$ -switched lasers, many factors contribute to the instability of the pulse, such as the spatial hole burning affected by the crystal length, cavity length, and the crystal position in laser cavity, the absorption cross-section of the saturable absorber, and the gain cross-section of the gain medium. In our $Q$ -switching experiments, the gain media, the radii of the input mirrors and output mirrors, the transmittance of the mirrors, and the initial transmissions of SA for different wavelengths are all different, which causes the different stabilities of the three lasers. Compared with the 1.064 and 1.991 μm lasers, the smaller laser mode radius on the SA, larger reflectivity of the output mirror, and higher absorbance of SA in the visible laser are conducive to the result that the pulse train of the visible $Q$ -switched laser is more uniform than those of the other two ^[53].

ReS2Q-switched laser characteristics. (a)–(c) Average output power and peak power versus the absorbed pump power at 0.64, 1.064, and 1.991 μm, respectively. (d)–(f) Pulse duration and repetition rate versus the absorbed pump power at 0.64, 1.064, and 1.991 μm, respectively.

Fig. 5. ${ReS}_{2}$ $Q$ -switched laser characteristics. (a)–(c) Average output power and peak power versus the absorbed pump power at 0.64, 1.064, and 1.991 μm, respectively. (d)–(f) Pulse duration and repetition rate versus the absorbed pump power at 0.64, 1.064, and 1.991 μm, respectively.

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(a)–(c) Recorded pulses trains of the ReS2-based Q-switched lasers at 0.64, 1.064, and 1.991 μm, respectively. (d)–(f) Measured output spectra of the ReS2-based Q-switched lasers at 0.64, 1.064, and 1.991 μm, respectively.

Fig. 6. (a)–(c) Recorded pulses trains of the ${ReS}_{2}$ -based $Q$ -switched lasers at 0.64, 1.064, and 1.991 μm, respectively. (d)–(f) Measured output spectra of the ${ReS}_{2}$ -based $Q$ -switched lasers at 0.64, 1.064, and 1.991 μm, respectively.

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Table 1. Results of the Passively Q-Switched Lasers Based on the ReS2 SA

	Visible	Near-Infrared	Mid-Infrared
Wavelength (nm)	640	1064	1991
Average output power (mW)	52	120	245
Repetition rate (kHz)	520	644	677
Pulse duration (ns)	160	139	415
Peak power (W)	0.625	1.34	8.72

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With the relationship between intracavity power and the output power, the intracavity energy intensity $I$ on the SA can be calculated by the following formula: where ${\bar{P}}_{out}$ is the average output power, $f$ is the repetition rate, $R_{oc}$ is the reflection of the output mirror, and $r$ is the radius of the oscillating laser mode on the SA. Based on the ABCD matrix, the $r$ in the lasers at 0.64, 1.064, and 1.991 μm are 90, 130, and 170 μm, respectively. Thus, the corresponding maximum intracavity energy intensities on the ${ReS}_{2}$ are 78.3, 6.7, and $15.6 mJ / {cm}^{2}$ , respectively. In the experiments, no optical damage or degradation of laser performance is observed, even at the highest available fluence. Additionally, because the optical damage threshold is relative to the pulse width and in direct proportion to wavelength, the optical damage threshold of ${ReS}_{2}$ should be larger than $78.3 mJ / {cm}^{2}$ for the nanosecond pulsed lasers at the wavelengths longer than 0.64 μm.

5. ULTRAFAST LASER WITH A ReS2 SAM

To further study the saturable absorption of ${ReS}_{2}$ and investigate its ability to generate ultrafast pulses, its application in a mode-locked solid-state laser is studied. We choose Yb:CALGO as a gain medium for its excellent properties, such as the wide and smooth emission spectrum and high thermal conductivity ^[54]. Based on the ABCD propagation matrix method, the ${ReS}_{2}$ -based mode-locked laser is built in a 2.96 m long z-type resonator, as shown in Fig. 7. The laser modes radii are calculated as 50 μm and 60 μm on Yb:CALGO and ${ReS}_{2}$ , respectively. To precisely control the oscillating spot size on the ${ReS}_{2}$ in the mode-locked laser, here, the as-prepared ${ReS}_{2}$ supernatant is directly spin-coated on a mirror with high-reflection (HR) coating at 1020–1100 nm as the ${ReS}_{2}$ saturable absorption mirror (SAM).

Fig. 7. Experimental setup of the ${ReS}_{2}$ -based mode-locked laser.

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With the ${ReS}_{2}$ SAM used in the cavity, after careful adjustment, the laser runs into a continuous wave mode-locked (CWML) regime when the absorbed pump power exceeds 5.13 W. Figure 8(a) shows the dependence of average output power versus the absorbed pump power. Under the absorbed pump power of 6.47 W, a maximum average output power of 350 mW is obtained, which is hundreds of times higher than those from ${ReS}_{2}$ -based fiber lasers ^[43,44]. The instabilities (output power, rms) are measured to be less than 2% at 1 h. Figure 8(b) shows the pulse trains in 500 ns and 100 μs time scale at the maximum output power. As shown in Figs. 9(a) and 9(b), the pulse duration is measured to be 323 fs by ${sech}^{2}$ pulse shape fitting, and the spectrum is centered at 1060 nm with an FWHM of 4.23 nm, corresponding to the time bandwidth product of 0.365. In addition, the recorded radio frequency spectrum is shown in Fig. 9(c), with a fundamental beat note near 50.7 MHz and the corresponding signal-to-noise ratio of 60 dB, which is measured by a spectrum analyzer (Agilent N9000A) with resolution bandwidth (RBW) of 10 kHz. Figure 9(d) is recorded in a wide span of 1 GHz with RBW of 1.0 MHz, and the absence of any spurious modulation proves clean CWML operation of ${ReS}_{2}$ mode-locked laser.

(a) Average output power versus the absorbed pump power of the ReS2-based mode-locked laser. (b) Recorded CWML pulse trains under the maximum pump power.

Fig. 8. (a) Average output power versus the absorbed pump power of the ${ReS}_{2}$ -based mode-locked laser. (b) Recorded CWML pulse trains under the maximum pump power.

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Recorded results of ReS2-based mode-locked laser. (a), (b) Autocorrelation trace for 323 fs duration and the corresponding spectrum. (c), (d) Recorded frequency spectrum with a narrow and a wide span, respectively.

Fig. 9. Recorded results of ${ReS}_{2}$ -based mode-locked laser. (a), (b) Autocorrelation trace for 323 fs duration and the corresponding spectrum. (c), (d) Recorded frequency spectrum with a narrow and a wide span, respectively.

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A mode-locked laser requires harsh conditions, so, besides mode matching on the gain material, a suitable energy intensity relative to the saturation fluence of the SA is a key factor. It is worth noting that, during the experiment, only a partial region of the ${ReS}_{2}$ SAM is available to support the mode-locking generation. One of the reasons is that, prepared by the simple LPE method, the ${ReS}_{2}$ flakes cannot distribute uniformly on the surface of the mirror. As a result, the sample shows a low surface-finish quality. In addition, based on the EDS analysis of the few-layered ${ReS}_{2}$ , the ${ReS}_{2}$ flakes showed various bandgap as the probe location on the ${ReS}_{2}$ sample changed. For a mode-locked laser with a complex cavity, the above factors are of great importance to the establishment and stabilization of the mode-locked laser.

For laser pulses longer than a few tens of picoseconds, the intense radiation brings heat deposition in the lattice, which finally causes dielectric breakdown and thermal damage. However, for ultrafast pulses shorter than 10 ps, the extremely high peak power directly breaks chemical bonds of the materials. Therefore, the damage threshold for femtosecond lasers should be evaluated with peak power intensity rather than energy intensity. In the CWML operation, the maximum peak power intensity on the SA is $18.7 GW / {cm}^{2}$ , and there is no damage observed, which indicates the damage threshold of ${ReS}_{2}$ for femtosecond laser should be larger than $18.7 GW / {cm}^{2}$ . However, until the laser turned into CWML, the laser operated in an unstable $Q$ -switched mode-locking regime when some damage occurred due to the abruptly jumped pulses with extremely high peak power.

6. CONCLUSION

We calculate the band structure of ${ReS}_{2}$ with different ratios of Re and S by Vienna ab initio simulations and find that the bandgap reduces with the S defects. In experiments, we prepared a broadband few-layered ${ReS}_{2}$ SA with the LPE method, and the characterizations indicated its broadband saturable absorption properties from the visible to mid-infrared wavelengths. Using the as-prepared ${ReS}_{2}$ SA, passively $Q$ -switched lasers at 0.64, 1.064, and 1.991 μm were realized, respectively. To further study the saturable absorption and its application in ultrafast photonics, a femtosecond solid-state laser based on few-layered ${ReS}_{2}$ was achieved successfully for the first time, and pulses as short as 323 fs were obtained at 1.06 μm with an output power of 350 mW. Our results highlight that ${ReS}_{2}$ with suitable S defects is a promising alternative for a rare broadband optical modulator and indicate the potential of ${ReS}_{2}$ in generating $Q$ -switched and mode-locked pulsed lasers. Recent studies have shown that controllable formation of vacancies in monolayer TMDs can be realized experimentally by pulsed laser deposition, $α$ -particle irradiation, and thermal annealing. Combining with these techniques, we believe that our work will be helpful for the design of ${ReS}_{2}$ optoelectronic devices with variable bandgaps.

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1. INTRODUCTION

2. THEORETICAL ANALYSIS OF THE BAND STRUCTURE

3. PREPARATION AND CHARACTERIZATION OF THE ReS2 SA

4. VISIBLE, NEAR-INFRARED, AND MID-INFRARED Q-SWITCHED LASERS WITH A ReS2 SA

5. ULTRAFAST LASER WITH A ReS2 SAM

6. CONCLUSION

Xiancui Su, Baitao Zhang, Yiran Wang, Guanbai He, Guoru Li, Na Lin, Kejian Yang, Jingliang He, Shande Liu. Broadband rhenium disulfide optical modulator for solid-state lasers[J]. Photonics Research, 2018, 6(6): 06000498.