Q-switching and mode-locking technologies, as two main methods to realize pulsed output in laser cavities, have been widely concerned in recent years^1-3. However, the preferred application fields of the two are a little bit different. Specifically, mode-locked fiber lasers (MLFL) could achieve femtosecond pulses, the peak power and repetition rate of which are relatively high, therefore they are often used in devices with large resolution and fineness, but their pulse energy is low, generally in the order of pJ^4-5. Q-switched fiber lasers (QSFL) can achieve pulse energy in the order of nJ or even higher due to the kHz repetition rate and high output power⁶. Therefore, they are commonly used in laser marking, carving, welding and cutting, etc. Although both active and passive methods can be used as effective ways to achieve Q-switching, passive one is usually preferred because of its obvious advantages, such as robustness, compact structure, as well as the unnecessity of complex electronic devices, which makes the passive method show an economic and effective application prospect⁷.

With the development and expansion of some materials in recent years, the use of saturable absorbers (SAs) to achieve QSFLs has become the general trend^8-9. As a more preferred option for SAs, semiconductor saturable absorption mirrors (SESAMs) were initially the focus of research¹⁰. However, the shortcomings of SESAMs, such as the preparation complexity, narrow bandwidth, and high cost force scientists to find other feasible alternatives, especially those that can further improve the overall efficiency and compactness while ensuring high optical nonlinearity of the device¹¹. The discovery of graphene solved the urgent development demand of QSFLs, and further pushed the development of SA to a new climax¹². Soon, a lot of latterly developed materials with similar properties are explored to be the possible choices of SAs, including graphene analogues such as transition metal dichalcogenides (TMDs), topological insulators (TIs), and exotic materials such as black phosphorus (BP), nanowires^13-17.

Most recently, the investigation of TMDs has become a research hotspot. After going through sufficient research on WS₂ and MoS₂^18-19, another TMD, tin disulfide (SnS₂), has begun to attract widespread attention²⁰. On the one hand, SnS₂ shows good oxidation resistance, which is of great benefit in improving system stability and robustness²¹. On the other hand, SnS₂ has the advantages of low cost, environmental friendliness, and sufficient global reserves, which allows it to meet the application needs of industrial and scientific full-scale production²². SnS₂ has a wider band gap than most TMDs, which is more suitable in some electronic applications^23-24. In addition, its application potential in the fields of energy storage, photocatalysts, and field emission devices cannot be underestimated²⁵. Meanwhile, the exceptional saturation absorption capabilities of SnS₂ prompts it to be widely studied in fiber laser applications^26-29. However, most of the current implementations are mode-locked pulses, and there is only one report on QSFL³⁰. Obviously, there is a lack of more systematic research on the impact of SnS₂ SA on QSFLs.

In this paper, the thickness-sensitive nonlinear characteristics of SnS₂ and the performance of lasers based on the corresponding SnS₂ SA are investigated. Three SnS₂ SAs with different thicknesses are prepared by the chemical vapor transport (CVT) technique combined with physical transfer method. The thickness information of those are characterized by atomic force microscope (AFM). The traditional balanced twin detector technique is applied to measure the nonlinear optical properties of SnS₂ SAs. Under the consistent experimental conditions, those SAs are applied to the laser respectively, and the experimental results are compared and analyzed. Our results explore the internal influence of material thickness on optical nonlinearity, which provide guidance for choosing a suitable SnS₂ SA to implement the QSFL with specific requirements, and also provide a good reference for the future research of nonlinear optical characteristics of similar TMD.

Here, the CVT technique is chosen as the preparation method to ensure the high quality of SnS₂ materials. Before the experiment, the required precursors, such as Sn and S powders with a purity of up to 99% purchased from Sigma-Aldrich, and the transport agent iodine, were placed in the reaction chamber. Due to the temperature gradient settings of different parts of the reaction chamber, the gaseous raw materials with high-temperature were deposited on the substrate surface in the low-temperature region with carrier gas, forming SnS₂ crystal with high purity. The prepared SnS₂ crystal was then peeled into thin flakes with different thickness by mechanical exfoliation (ME). The combination of CVT and ME plays a dual role in ensuring the quality of SnS₂. The obtained flakes with a certain thickness were further transferred to the fiber ceramic head by the PMMA (poly methyl methacrylate) transfer method. The steps of transfer are as follows: firstly, PMMA solution was spin coated on the flakes at a speed of 3000 rpm. Then, the spin-coated material was heated at 150 °C for 30 minutes. Finally, the substrate with the attached SnS₂-PMMA was submerged in a NaOH solution at the temperature of 80 °C, and the SnS₂-PMMA were easily removed. Later, acetone was used as solvent to remove useless PMMA and avoid unnecessary heat accumulation. During the transfer process, the microscope ensures that each SnS₂ flake was placed in the center of the ceramic head, completely covering the light passing holes on it.

The X-ray diffraction patterns, high-resolution TEM image and X-ray photoelectron spectroscopy of SnS₂ samples are given in our previous research²⁹, which further confirmed that the synthesized SnS₂ owns high quality crystal structure. A lot of materials were tried in the experiment. After removing the data that could not be ruled out whether it was an experimental error, three sets of data with obvious characteristics that may indicate regularity were screened for display. The selected materials with obvious data changes have a large thickness span, which may be caused by the inhomogeneity of the related properties of SnS₂³¹. The specific morphology and thickness were characterized by AFM. The thickness of thicker SnS₂ was measured as 107 nm as revealed in Fig. 1(a) and 1(d). Similarly, the thicknesses of medium and thinner flakes are 7.7 nm (Fig. 1(b) and 1(e)) and 4 nm (Fig. 1(c) and 1(f)).

SAs generally exhibit traditional intensity-related light transmittance. In detail, most of low-intensity lights are absorbed, while high-intensity lights pass through with low loss. This light intensity-dependent absorption characteristic can be theoretically described by the following formula,

$ \alpha = {\alpha _{{\rm{ns}}}} + \frac{{{\alpha _{\rm{s}}}}}{{1 + I/{I_{{\rm{sat}}}}}}\;. $ (1)

where α exhibits the total absorption of material, α_ns is non-saturable loss, α_s is modulation depth, I is light intensity, I_sat is saturation intensity. The insertion loss (IL) of SA is able to be calculated by α_ns. In the experiment, the traditional balanced twin detector technique is applied to measure the saturated absorption of materials. Using a MLFL whose pulse duration is 200 fs and repetition rate is 110 MHz at 1550 nm as a seed source, the stable illuminant for measurement is obtained. The mode-locked pulses are divided into two channels of light with synchronous and adjustable intensity through a variable optical attenuator and a 3 dB coupler, which are used as test light and reference light respectively. The reference light can be directly measured by an optical power meter, while the test light is measured after passing through the sample. The blue dots in Fig. 1(g) is the data collected from 107 nm-SnS₂ SA. After theoretical fitting with formula (1) through red line, the exact values of various nonlinear parameters in formula (1) are determined. From Fig. 1(g), the I_sat, α_s and α_ns of 107 nm-SnS₂ SA are 0.68 MW/cm², 40.5% and 15%. Similarly, the I_sat, α_s and α_ns of 7.7 nm- and 4 nm-SnS₂ SAs are 1.3 MW/cm², 36.9%, 4.3% (Fig. 1(h)) and 0.52 MW/cm², 31.5%, 26% (Fig. 1(i)).

The components of the experimental device are shown in Fig. 2, including a 980 nm laser diode (LD), erbium-doped fiber (EDF), a SnS₂ SA, a 980/1550 wavelength division multiplexer (WDM), isolator (ISO), a polarization controller (PC) and a 80/20 optical coupler (OC). LD provides pump light for the entire system, its maximum output power is 630 mW. WDM is used to synthesize a bunch of 980 nm pump light and 1550 nm light running in the cavity on a single fiber. After the excitation of pump light with high power density, 40 cm-EDF achieves the sufficient particle number reversal state, generating oscillating laser. The SnS₂ SA is the key optical modulation device in the cavity, fine tuning the PC to alter the polarization state of the laser and improve the laser quality. The ISO is used to ensure the consistency of the propagation direction of the ring laser. The OC delivers 20% of the intra-cavity laser to the outside of the cavity for real-time observation of the laser performance. The instruments used to measure the properties of QSFL are spectrometer (Yokogawa AQ6370C), spectrum analyzer (Agilent E4402B), and oscilloscope (Tektronix DPO3054).

When 107 nm-SnS₂ SA is applied to the system, the performance of the QSFL is summarized in Fig. 3. At this time, the pump power (P_pump) of the laser is adjusted to the maximum, which is 630 mW. The pulse duration (τ) of a single pulse displayed on the oscilloscope is 484.7 ns as shown in Fig. 3(a). From the RF spectrum in Fig. 3(b), the fundamental frequency (F_rep) of pulse is ~240 kHz, the signal-to-noise ratio (SNR) is up to 50 dB. RF spectrum within a bandwidth of 2 MHz in illustration indicates that the QSFL works well. The spectrum of QSFL in Fig. 3(c) reveals that the wavelength is centered at 1530.6 nm. The standard deviation of output power (P_out) monitoring within 8 hours in Fig. 3(d) is 0.493 mW, which emphasized the constancy of the laser. When the P_pump is regulated, the traditional change trends of corresponding τ, F_rep, P_out and pulse energy (E_p) are respectively shown in Fig. 3(e) and 3(f). It is found that the threshold value of laser is 212 mW. The adjustment ranges of τ and F_rep are 0.485–1.4 μs and 141–241 kHz. The maximum of P_out is 12.7 mW, and the corresponding E_p is 52.6 nJ.

Next, the other two kinds of materials are also used to realize the Q-switched pulse under the same experimental conditions. For the Q-switched pulse under the same experimental conditions. For the QSFL using 7.7 nm-SnS₂ SA, the τ is 492.6 ns at the same pump power as shown in Fig. 4(a), which is slightly inferior to the laser based on 107 nm-SnS₂ SA. The standard deviation of P_out monitoring within 8 hours in Fig. 4(b) is 0.52 mW. From Fig. 4(c), the threshold value of laser is 276 mW, the τ and F_rep are adjustable in the range of 0.493–0.844 μs and 162–240 kHz respectively. From Fig. 4(d), the maximum P_out and E_p are 14.3 mW and 59 nJ.

Similarly, the performances of QSFL employing 4 nm-SnS₂ SA are recorded in Fig. 5. The τ of the laser at the P_pump of 630 mW is 503.3 ns as shown in Fig. 5(a). The standard deviation of P_out within 8 hours is acknowledged in Fig. 5(b) as 0.543 mW. In Fig. 5(c), the adjustment range of τ and F_rep are revealed as 0.503–1.25 μs and 123–248 kHz. The boot threshold of laser is 180 mW. As show in Fig. 5(d), the maximum of P_out and E_p are obtained when the P_pump takes the maximum value of 630 mW, which are 11.3 mW and 45.7 nJ. In addition, each material has been repeatedly tested, eliminating the possibility of experimental error within our capabilities.

The performance of three different QSFLs adopting distinct SAs are summarized in Table 1. First of all, it is found that the nonlinear behavior of materials with different thickness is distinct. In terms of modulation depth, the 107 nm-SnS₂ owns the best performance. This may be related to the relaxation time. Generally, the material with larger relaxation time is beneficial to the enhancement of the modulation depth. Due to the large specific surface area and/or the presence of multiple edges shortening the lifetime of free carriers³², the thin material tends to show a shorter relaxation time, so thicker materials show the maximum modulation depth in our experiments. The difference in the initial transmittance of the three materials may be the result of the combined effect of scattering loss and carrier relaxation. With the change of thickness, the scattering loss and carrier relaxation have opposite effects on the transmittance, which leads to the existence of an optimal value to maximize the transmittance. The material with medium thickness (7.7 nm) exhibits the highest transmittance (~60%), which means that the material is closest to the equilibrium point among the three materials. The difference in the I_sat of three SAs may be due to the distinction in light utilization. Under the same initial light intensity, the light transmittance of 7.7 nm SnS₂ is the highest, which means that a lot of light goes directly through the material without being absorbed. If the material absorbs the same amount of light energy, the excitation intensity needs to be greater, so the 7.7 nm SnS₂ shows the largest saturation intensity.

The effect of SA with different nonlinearity on the performance of corresponding lasers is also obvious. The experimental results show that the output power based on SA with 40.5% modulation depth is the most stable (standard deviation: 0.493 mW), this is due to SA with high modulation depth can promote the stability of the system according to the previous research³³. In addition, SA with large modulation depth seems to have a slight advantage in achieving short pulse. Because a large modulation depth means that the low-intensity signals at the leading and trailing edges of the pulse will be absorbed more, and the pulse narrowing effect will be stronger. Because SA with low saturation intensity is easy to saturate, the 4 nm-SnS₂ with saturation strength of 0.52 MW/cm² shows the the minimum threshold.

Currently, passive QSFLs based on various SAs have been extensively studied. Table 2 compares the performance of lasers based on several widely used SAs. By comparison, we find that SnS₂ SA seems to have some advantages in the realization of short pulse. Both the laser realized in ref³⁰, and the lasers obtained in this experiment show a pulse duration of about 500 ns, which is almost an order of magnitude better than other lasers. It is worth noting that the great disparity in modulation depth between SnS₂ in this experiment and PVA-SnS₂ in ref.³⁰ may be due to the difference in preparation methods. Crystal SnS₂ in our experiment is prepared using a combination of CVT and ME, therefore, it may perform better than PVA-SnS₂ in ref.³⁰ in terms of material quality, light reaction efficiency and scattering loss, which is beneficial to the enhancement of modulation depth. In addition, the output power of the laser obtained in this experiment is as high as 12.7 mW, and at the same time, the conversion rate of pump power to output power in the system is also more than 2%. This indicates that the laser based on SnS₂ can ensure high pump conversion efficiency under the condition of high power output. Therefore, in-depth investigation of SnS₂ has a bright prospect and practical value in the field of nonlinear optics.

Structure optimization and band structure calculations were performed based on density functional theory (DFT) as implemented in the Vienna ab-initio simulation package (VASP)^38-39. The projector-augmented-wave (PAW) method was utilized to describe the interactions between the ionic cores and the valence electrons^40-41. The Perdew-Burke-Ernzerhof parameterized generalized gradient approximation (PBE-GGA) functional was employed to treat the electronic exchange-correlation effects⁴². Electronic wave functions were expanded using a plane wave basis set with an energy cutoff of 340 eV. The thickness of vacuum layers was set to be at least 15 Å (1 Å=10⁻¹⁰ m) to avoid periodic interactions. The DFT-D3 method was adopted to include the van der Waals interactions during the structure relaxations⁴³. The surface Brillouin zone was sampled using a Monkhorst-Pack grid⁴⁴. The ionic relaxations were performed until the force on each atom was less than 0.005 eV·Å⁻¹ and convergence criterion for the self-consistent electronic minimization loop was set to 10⁻⁵ eV. For accurate band gap prediction, the nonlocal Heyd-Scuseria-Ernzerhof hybrid functional (HSE06), which contains 25% Hartree-Fock and 75% PBE-GGA, is adopted for electronic structure calculations^45-46.

The relaxation time related to the carrier mobility μ, and μ in 2D semiconductor film of finite thickness is calculated based on the deformation potential^47-49. The deformation limited mobility is calculated by⁵⁰:

$ {\kern 1pt} {\mu _{{\rm{film}}}} = \frac{{{{\rm{\pi}}}e{\hbar ^4}{C_{{\rm{film}}}}}}{{\sqrt 2 {{({k_{\rm{B}}}T)}^{3/2}}{{(m^*)}^{5/2}}{{({D_A})}^2}}} \cdot F\;, $ (2)

where F is a crossover function that bridges 2D and 3D

$ {\kern 1pt} F = \dfrac{{\displaystyle \sum\nolimits_n {\left\{ \dfrac{{\sqrt {\rm{\pi}} }}{2}{{[1 - {{\rm{erf}}}(}}{{\Omega}} {{({{n}})) + }}{{\Omega}} {{({{n}})}}{{{{\rm{e}}}}^{ - {{{\Omega}} ^2}(n)}}{{] }}\right\}} }}{{\displaystyle \sum\nolimits_n {[1 + {{{\Omega}} ^2}(n)]{{\rm{e}}^{ - {{{\Omega}} ^2}(n)}}} }}\; , $ (3)

here, erf() represents the error function, and the summation over integer n is due to quantum confinement along the z-direction (finite thickness direction). Ω(n) is defined as

$ {\kern 1pt} \Omega (n) = \sqrt {\frac{{{n^2}{{\rm{\pi}} ^2}{\hbar ^2}}}{{2{m^*}W_{{\rm{eff}}}^2{k_{\rm{B}}}T}}}\; , $ (4)

W_eff is the effective thickness of the film, which can be calculated analytically by assuming a square-well confinement potential.

In Eq. (2), D_A is the deformation potential, which is calculated from its definition $\delta {E_i} = {D_{{\rm{A}}i}}\dfrac{{\delta_α}}{α}$. δE_i is the energy change of the i_th electronic band under proper cell compression and dilatation, α is the lattice constant, and δ_α is the deformation of α. C_film is related to the elastic constant which is calculated from $\dfrac{{\delta {E_{{\rm{tot}}}}}}{{{V_0}}} = \dfrac{{{C_{{\rm{film}}}}}}{2}{\left(\dfrac{{\delta_α}}{α}\right)^2}$, where δE_tot refers to the total energy change and V₀ is the lattice volume at equilibrium. m* is the effective mass along the transport direction. More computational details can be found in Kang’s work⁵⁰. The intrinsic carrier concentration in 2D semiconductor materials can be calculated by⁵¹:

$ {\kern 1pt} {n_i} = \frac{{\sqrt {m_h^*m_{\rm{e}}^*} {k_{\rm{B}}}T}}{{{\rm{\pi}} {\hbar ^2}}}{\rm{exp}} \left( - \frac{{{E_{\rm{g}}}}}{{2{k_{\rm{B}}}T}}\right) \;, $ (5)

where E_g is the band gap. Our DFT calculations indicate that the electron mobility is thickness-dependent, it increases with increased thickness, and converges to bulk state when the thickness reaches either-layer as shown in Fig. 6.

The intrinsic carrier concentration is rather sensitive to the band gap and less sensitive to the variation of the effective mass. Due to the decreased band gap of SnS₂ with increased thickness, our DFT calculations in Table 3 clearly reveal that the intrinsic carrier concentration is significantly increased as the thickness increases, thus corresponding to the enhanced modulation depth.

In short, three kinds of SnS₂ with different thickness are characterized in terms of nonlinearity and used to realize the Q-switched pulses. The SnS₂ SA is prepared through the combination of CVT and ME to double guarantee the high quality of materials. By comparing the nonlinear performance of SnS₂ SA with different thickness, it is found that the thicker material shows higher modulation depth due to the influence of large relaxation time. Because of the combined effect of scattering loss and relaxation time, the initial transmission and thickness do not show a simple linear trend, but there is an optimal value. In addition, the saturation intensity is related to the initial transmittance of the material. Furthermore, the performances of the QSFLs with these three kinds of SA are compared. It is found that large modulation depth is beneficial to the stability of the laser, and at the same time, it seems to have a weak advantage in the realization of ultrashort pulse. A small saturation intensity of SA tends to make the laser have a small start threshold. In addition, combined with previous research, SnS₂ seems to have inherent advantages and potential in achieving ultrashort pulse. These results clarify the thickness-dependent nonlinear optical properties of SnS₂, and the impact of various optical nonlinear parameters of SA on the performance of the corresponding laser, which provides a meaningful reference for further research on the application of SnS₂ or similar TMDs materials in nonlinear optics.