Study on Saturable Absorption Characteristics of Bi₂Se₃ Topological Insulators with Film Thickness Dependence and Its Laser Application

Abstract

In our work, a multi-layer topological insulator (TI) Bi₂Se₃ thin film was prepared by the chemical vapor deposition method (CVD), and its saturable absorption and damage characteristics were experimentally studied. The results show that when the wavelength is 1064 nm, the saturable absorption parameters of TI: Bi₂Se₃ film, including modulation depth α_s, non-saturable loss α_ns, and saturation power intensity I_sat, increase with the increase in film thickness, and the damage threshold is inversely proportional to the film thickness. The thicker the film layer, the lower the damage threshold. Among them, modulation depth α_s is up to 51.2%, minimum non-saturable loss α_ns is 1.8%, maximum saturation power intensity I_sat is 560.8 kW/cm², and the damage threshold is up to 909 MW/cm². The influence of the controllable thickness of TI: Bi₂Se₃ film on passive Q-switching and mode-locking performance of laser is discussed and analyzed when TI: Bi₂Se₃ film is prepared by the CVD method as a saturable absorber (SA). Finally, the performance of TI: Bi₂Se₃ thin film applied to nanosecond laser isolation at the 1064 nm band is simulated and analyzed. It has the natural advantage of polarization independence, and the maximum isolation can reach 16.4 dB.

1. Introduction

In recent decades, ultrafast lasers with peak power and short pulse duration have been widely used in nonlinear optics, free space optical communication, biomedicine, military, laser radar, laser spectroscopy, material micromachining, and other fields [1,2,3,4,5,6]. The saturable absorber (SA) is an important component of the laser. Currently, the most common is the use of semiconductor saturable absorption mirrors (SESAMs), and while SESAMs have become very mature and commercialized over the past two decades, they also have some limitations, including (1) a relatively narrow wavelength operating range and (2) complex manufacturing and expensive packaging. In recent years, emerging 2D materials such as graphene [7,8], carbon nanotubes (CNTs) [9], topological insulators (TIs) [10,11,12,13,14,15], transition metal dichalcogenides (TMDs) [16,17], and black phosphorus (BP) [18,19] have opened the door to exploring more simplified, low-cost, wideband responsive SA and have been successfully applied to different pulsed laser systems. For example, graphene-based SA has been successfully used to generate pulses in fiber lasers from 0.8 to 2.78 μm [7,8], and carbon nanotube-based SA can also facilitate Q-switched or mode-locked fiber lasers covering all major wavelengths between 0.78 and 2 μm [9]. However, each of these SAs has some inherent drawbacks. Graphene has a unique zero-band gap structure and a short exciton recovery time, but the nonlinear optical response of the single-layer structure is too weak, resulting in an excessively small modulation depth. Due to the limitation of diameter-dependent response spectrum range, single-walled carbon nanotubes have high unsaturated loss in wide-band operation. The transition metal dichalcogenides represented by MoS₂ and WS₂ have a long attenuation time, which cannot compress the pulse width effectively. Black phosphorus has high switching ratio and hole mobility, so it is a good material for optoelectronic devices, but its stability is very poor, and it is easy to oxidize and lose the original nonlinear optical properties. In the two-dimensional material family, the three-dimensional topological insulator (TI) has the advantages of wide spectral absorption, large modulation depth, high damage threshold, fast upper-level recovery time, etc., and has been widely used in laser passive Q-switching, mode-locking, and other fields. The first TI-based Er-doped ultrafast fiber laser was confirmed in 2012 [20]. In 2015, based on the interaction between Bi₂Se₃ and photonics crystal fiber, Gao et al. also demonstrated a conventional soliton mode-locked operation with a 908 fs pulse width and a dissipative soliton with a duration of 7.56 ps [21]. In addition, Guo et al. experimentally demonstrated several different Bi₂Se₃-based mode-locked generations including dual-wavelength harmonic, dark soliton, and multi-wavelength within Er-doped fiber lasers [22,23]. In 2019, Xu et al. achieved stable Q-switching operation at 1.55 μm by inserting this SA into a linear laser cavity, with a minimum pulse duration of 1.34 μs, a maximum pulse energy of 224.5 nJ, and a pulse repetition rate adjustable between 10 and 110.2 kHz [10]. After that, a series of Q-switched/mode-locked lasers based on TI were explored, with laser wavelengths ranging from 1 μm to 3 μm.

Saturable absorption parameters and damage threshold are the core parameters that affect passive Q-switching, mode-locking, and noise light suppression functions. How to reveal the relationship between TI film properties and saturable absorption properties and between saturable absorption properties and laser application properties is a key scientific problem to be solved urgently. At present, most of the mainstream SA Bi₂Se₃ nanosheets are prepared in the laboratory by liquid-phase exfoliation (LPE), which has the advantages of low cost and convenient preparation. However, the stripping efficiency of this method is relatively low, and the prepared Bi₂Se₃ nanosheets have uneven morphology and uncontrollable saturation absorption parameters. Compared with the liquid-phase exfoliation method, the most important characteristics of two-dimensional materials prepared by chemical vapor deposition (CVD) are uniform shape and controllable layer number [24,25]. In this paper, Bi₂Se₃ nanosheets with controllable layer number were prepared by the CVD method, which provided convenience for precise regulation of saturable absorption parameters. Using the effect of SA layer number on saturation strength and modulation depth and further realizing pulse width, repetition rate and small signal rejection ratio control in laser applications, foundation can be laid for realizing narrower pulse width, higher repetition rate, and higher pulse energy.

In this paper, we first prepared TI: Bi₂Se₃ thin films with multiple film thickness by CVD method and experimentally studied their saturable absorption and damage characteristics. The results show that the saturable absorption parameters of TI: Bi₂Se₃ films are highly correlated with the thickness of the film at the wavelength of 1064 nm. When the thickness of the film increases, modulation depth α_s, non-saturable loss α_ns, and saturation power intensity I_sat of TI materials increase. In terms of damage, the material damage threshold is inversely proportional to the film thickness, and the thicker the film layer, the lower the damage threshold. Second, the performance parameters of TI: Bi₂Se₃ thin films used in passive Q-switching, mode-locking, and noise optical isolators were studied using the layer saturation parameters obtained from experiments as simulation inputs. Based on the advantages of controllable layer number and adjustable saturation parameters, the shortest pulse duration of the 1.55 μm Q-switched Er-doped fiber laser was expected to be reduced to 410.9 ns. TI was proposed to be applied to noise light isolation. For the 1064 nm nanosecond laser, the simulated maximum isolation was 16.4 dB, which has the natural advantage of polarization independence.

2. Experimental Section

2.1. Preparation and Characterization of TI Sample

It is the same as the insulator commonly known, the body of the topological insulator material is insulated, but there is always a conductive edge state on its boundary or surface, which is the most unique property that is different from ordinary insulators. TI is also a Dirac material, and in momentum space, the surface has a Dirac cone structure [26], as shown in Figure 1a, demonstrating Dirac-like linear dispersion. In particular, TI has a topologically non-trivial energy gap as narrow as 0.2–0.3 eV (e.g., TI: Bi₂Se₃, energy gap ΔE~0.3 eV), and when narrow-band TI is excited by a strong light with a single photon energy greater than TI’s bandgap ∆E, ultra-wideband saturation absorption occurs, like in graphene, due to the Pauli blocking principle [27,28]. Bi₂Se₃, for example, has a saturation absorption wavelength range from visible to mid-infrared 4.1 μm (0.3 eV). More importantly, different from the surface states caused by surface suspension bonds or previously found surface potential, the surface states of topological insulators are determined by the topological properties of physical energy bands, protected by the symmetry of time inversion, and they have very stable characteristics. Therefore, the thin films of topological insulators are not easily damaged by surface oxidation and pollution, and they have strong ability to resist interference from external environment. Saturable absorption characteristics are reliable.

Bi₂Se₃, Bi₂Te₃, and Sb₂Te₃ are the three kinds of 3D topological insulators that have been studied most recently. Because the band structure of these topological insulators is simple, there is only one Dirac point in the band gap, which provides an ideal model for theoretical and experimental research. The TI material used in this paper is Bi₂Se₃. Figure 1b shows the crystal structure diagram of Bi₂Se₃. A–C are different placeholders. Bi₂Se₃ is a layered material, which consists of 2 Bi single atomic layers and 3 Se single atomic layers alternately to form a total of 5 atomic layers of periodic structure, called the Quintuple Layer (QL for short; the height is 0.95 nm, the unit of Bi₂Se₃ film thickness, and every 3 QL form a large periodic structure). Within each QL, the interaction between the atomic layers is the stronger covalent bond, but between QL and QL, there is the weaker van der Waals force interaction. Bi₂Te₃ and Sb₂Te₃ also have similar lattice structures. The saturable absorption and damage characteristics are closely related to the number of TI layers. Precisely controlling the number of TI layers is a prerequisite for regulating the saturable absorption parameters and damage threshold of TI.

Chemical vapor deposition (CVD) is the process of depositing the composite onto the substrate by gas reaction at high temperatures. This method is effective to synthesize two-dimensional layered materials with high crystal quality, and it can accurately control the film thickness of the material on the substrate. Compared with mechanical exfoliation (ME), liquid-phase exfoliation (LPE), the molecular beam epitaxy method (MBE), the solvothermal method (SM), the and pulsed laser deposition method (PLD) [10], Bi₂Se₃ prepared by the CVD method has the advantages of precise control of the number of growth layers, good crystal quality, smooth surface, uniform shape, and high damage threshold power.

In this paper, high-quality Bi₂Se₃ nanomembranes were first synthesized on a SiO₂ substrate by the CVD method and then transferred to a ZnSe substrate by substrate transfer so as to further study the saturation absorption characteristics of long-wave CO₂ laser band. First, the SiO₂ substrate was cleaned with ultrasound in acetone, ethanol, and deionized water to remove impurities on the surface of the substrate. Next, the Bi₂Se₃ powder was placed in the constant temperature zone of the horizontal tube furnace as the evaporation source, with the substrate about 15 cm away from the evaporation source. Then, during the deposition process, the mechanical pump was started and kept in the vacuum state (2–10 Pa), and the ultra-pure Ar was used as the carrier gas. The Ar flow rate was set at 50 sccm, and the Bi₂Se₃ film was synthesized under the condition of 550 °C constant temperature for 25 min. It should be pointed out that there is a certain distance between the evaporation source and the substrate, and along the direction of the air flow, the temperature of the film forming zone is divided into different temperature zones from high to low, and the quality of the TI: Bi₂Se₃ film formed in different temperature zones is also different. According to our previous preparation experience, the preparation of the film was carried out in the optimal film-forming region, where the growth temperature was 350 °C, which was lower than the 550 °C at the high-temperature center. In addition, the films with different film thickness values in this paper were produced by controlling the amount of evaporation sources, and our deposition time was basically about 25 min. After the entire preparation process was completed, the furnace was cooled to room temperature and high-quality Bi₂Se₃ nanomembranes were successfully prepared. Finally, we carried out substrate transfer (the PMMA anisole solution and the Bi₂Se₃ film were first used to separate the SiO₂ substrate together, then bonded together on the ZnSe substrate, and then soaked in acetone solution to etch PMMA; finally, only the Bi₂Se₃ film was left on the ZnSe substrate) to transfer the prepared high-quality Bi₂Se₃ nanomembranes onto the ZnSe substrate and successfully completed the preparation of Bi₂Se₃ nanomaterials.

In our work, four TI: Bi₂Se₃ films with film thickness values of 5 nm, 10 nm, 20 nm, and 40 nm were successfully prepared by chemical vapor deposition (CVD) with ZnSe as the substrate. Before the experiment on the saturable absorption characteristics of TI films, we characterized TI: Bi₂Se₃ films as follows. First, the surface morphology of the Bi₂Se₃ film was observed with a 50-fold optical microscope. As shown in Figure 2a, the Bi₂Se₃ film was uniformly attached to the ZnSe substrate, with clearly visible boundaries, regular shape profiles, and no preparation defects such as curled edges or upturned edges. Second, the microstructure of Bi₂Se₃ was characterized by Raman spectroscopy at a 532 nm wavelength. Figure 2b shows four typical Bi₂Se₃ Raman peaks centered on 40, 70.1, 131, and 170.8 cm⁻¹, corresponding to the Se-Bi-Se-Bi-Se in-plane vibration of lattice vibration mode ${\mathrm{E}}_{\mathrm{g}}^1$, outside surface vibration mode ${\mathrm{A}}_{1\mathrm{g}}^1$, in-plane vibration mode ${\mathrm{E}}_{\mathrm{g}}^2,$ and he outside surface vibration mode ${\mathrm{A}}_{1\mathrm{g}}^2$. Apparently, this Raman spectrum is consistent with what was previously reported [29]. Then, scanning electron microscopy (SEM, S-4800, produced by HITACHI, Tokyo city, Japan, maximum magnification 20,000×) was used to observe the surface fine morphology characteristics. Figure 2c shows the images of Bi₂Se₃ thin films under different SEM resolutions. It can be clearly seen that the TI: Bi₂Se₃ film has a two-dimensional lamellar structure and a complete and clear surface texture. After the TI film was inclined at a 30° angle, it was observed by scanning electron microscopy (SEM), which was basically consistent with Figure 2c, and no obvious three-dimensional structure was found, which once again confirmed that the TI: Bi₂Se₃ material prepared by us was a nanosheet structure rather than a block structure. Finally, the sample thickness was determined by atomic force microscopy (AFM, Bruker Dimension^® Icon™, produced by BRUKER, Karlsruhe City, Germany). The TI: Bi₂Se₃ sample with a 5 nm film thickness is shown in Figure 2d. By scanning the height difference between the ZnSe substrate and the sample surface, the sample thickness values were measured to be about 5, 10, 20, 40 nm, respectively.

2.2. Experimental Setup

In order to study the saturation absorption law and damage characteristics of TI: Bi₂Se₃ thin films of different thicknesses and measure their transmittance and damage conditions under different laser powers, we built an experimental platform based on open hole Z-scan measurement. The experimental testing schematic diagram of the saturable absorption characteristics of TI: Bi₂Se₃ material is shown in Figure 3 below.

The high-energy nanosecond laser at 1064 nm band is currently the most widely used and the most mature technology, and its performance is relatively stable. The TI: Bi₂Se₃ thin film is used as a saturation absorber to carry out Q-switching /mode-locking applications, which has more extensive application value. The saturable absorption and damage characteristics of TI material at 1064 nm band are studied. The nanosecond pulsed laser system (@1064 nm, 7 ns, 10 Hz, maximum single pulse energy 900 mJ) produced by Beamtech Optronics Co., Ltd. in Beijing, China is used. This system has an energy stability (RMS) of ≤1%. Through the knife-edge test, the waist radius of the nanosecond Gaussian beam measures 300 μm. To control the incident power on the test sample, an attenuating plate is placed at the exit of the laser head. The beam is then introduced through a beam expansion collimation device to reduce incident light power and prevent damage to the beam expansion system. Subsequently, a beam splitter is used to divide the light, with reflected light directed into Power meter 1 for monitoring incident light power, while transmitted light passes through the subsequent optical path. The TI: Bi₂Se₃ sample is positioned on the precise displacement platform behind the focusing lens, allowing for easy adjustment of the beam spot size and peak power density by altering the axial position of the sample. The maximum incident peak power density after focusing reaches approximately 4550 GW/cm², with a spot diameter of 0.06 mm. By continuously adjusting the output power of the laser, varying the axial position of the sample, and manipulating the 10× and 100× attenuator, the peak power density can be finely tuned from 0 to 100%. The input and output power are measured using a power meter, and the transmittance is calculated as T = I_out/I_in. Figure 4a shows the experimental device diagram of saturation absorption characteristics of TI: Bi₂Se₃ thin films with different thicknesses at 1064 nm. The typical laser output pulse waveform is shown in Figure 4b.

3. Saturable Absorption Parameters

In order to extract the saturable absorption parameters of Bi₂Se₃ thin films at 1064 nm, Formula (1) was used to fit the experimental data [30,31], and the saturation absorption curve and saturation absorption parameters were obtained.

$$\mathrm{T}=1-{ \mathsf{\alpha }}_{\mathrm{s}}\ast \exp \left(-\frac{\mathrm{I}}{{\mathrm{I}}_{\mathrm{sat}}}\right)-{ \mathsf{\alpha }}_{\mathrm{ns}}$$

(1)

where T is the transmittance, α_s is the modulation depth, α_ns is the non-saturable loss, I is the input intensity, and I_sat is the saturation power intensity. The transmittance curves of Bi₂Se₃ films with different film thicknesses of 5 nm, 10 nm, 20 nm, and 40 nm were fitted after deducting the substrate loss. The fitting results in the range of 0~2000 kW/cm² are shown in Figure 5 and

Table 1. Saturable absorption parameters of TI: Bi₂Se₃ films fitted with different film thicknesses.

Film Thickness (nm)	αs (%)	αns (%)	Isat (kW/cm2)
5	30.8	1.8	230.2
10	35.1	4.9	302.5
20	42.9	10.2	400
40	51.2	21.9	560.8

.

The fitting results of the above saturation absorption parameters with film thickness show that the saturable absorption parameters of TI: Bi₂Se₃ film have great regularity with film thickness: the larger the thickness of TI: Bi₂Se₃ film, the larger the modulation depth α_s and saturation power intensity I_sat, but the non-saturable loss α_ns is also larger. Our saturation strength is close to what was previously reported as measured by the Z-scan technique (kW/cm² magnitude) [32]. Compared with the TI sheet synthesized by the simple solvothermal method [32], with the increase in solution concentration, the saturation power intensity and modulation depth are increased, and the instability loss is also increased from 11.02% to 12.73% and to 17.03%. The variation in film thickness is confirmed by our law, and the experimental results are universal. It is worth noting that the first two parameters increase slowly with the increase in film thickness, while the non-saturable loss and film thickness roughly linearly increase. Therefore, in the subsequent laser applications such as Q-switching, mode-locking and noise-light isolation, we cannot simply pursue the index requirements of high repetition frequency, narrow pulse width and high isolation, and excessively increase the modulation depth of TI film, but also consider the impact of insertion loss on the entire laser system. When TI is applied to the laser system, the optimum TI film thickness should be prepared by comprehensively considering the value design of these three parameters, referring to the above fitting law of saturation absorption parameters with film thickness, and using the CVD method to accurately regulate the advantages of film thickness.

4. Damage Threshold

The damage threshold of saturable absorbing material is the key factor affecting the ultrafast laser single pulse energy and the application threshold of the laser isolator. In order to investigate the damage characteristics of TI: Bi₂Se₃ thin film, we carried out an experimental study of the damage characteristics of the thin film based on a nanosecond pulsed laser at 1064 nm. The experimental device is shown in Figure 4a above (removed attenuator). Based on the one-to-one damage threshold test method, the damage forms of 10 points were tested under the same energy density, and the laser irradiation intensity gradually increased. The damage morphology was observed with a Nomarski microscope (EB-4, produced by Taiwan Yiye International Co., Ltd., Tainan City, Taiwan, with a total magnification of 200×). The ability of optical films to resist laser damage has long been stipulated in the International Standard Organization (ISO), that is, the Laser-Induced Damage Threshold (LIDT) is used for definition [33]. Here, due to the uncertainty of laser energy measurement and effective spot area measurement, the relative error of damage threshold measurement is close to 5%.

We measured the damage threshold of TI: Bi₂Se₃ films with film thickness values of 5 nm, 10 nm, 20 nm, and 40 nm, respectively, and the results are shown in

Table 2. Saturation power intensity and damage threshold of TI: Bi₂Se₃ films with different film thicknesses.

Film Thickness (nm)	Isat (kW/cm2)	LIDT (MW/cm2)
5	230.2	909
10	302.5	57.1
20	400	16
40	560.8	2.72

. The damage threshold is inversely proportional to the film thickness, and the thicker the film layer, the lower the damage threshold. When the film thickness is 5 nm, the damage threshold is 909 MW/cm², and when the film thickness is increased to 40 nm, the damage threshold is reduced to 2.72 MW/cm², and the difference is obvious. The reason may be that the closer the TI: Bi₂Se₃ film is to the substrate, the better its heat dissipation performance, and the damage threshold near the substrate is higher than the surface, so the thinner the film layer, the higher the damage threshold. In addition, the results of the damage threshold obtained by our experiment are similar to the law of the change in the damage threshold of graphene with the film layer in [34], which may be the commonality of the change law of the damage threshold of two-dimensional materials. It should be noted that as the thickness of the film increases, the gap between the saturation power intensity and the damage threshold becomes smaller and smaller. Therefore, when the TI film material prepared by the CVD method is used, when the film thickness is relatively large, it is necessary to pay attention to the fact that the laser power should not increase rapidly after reaching the saturation strength, and there is the risk of damaging the film material.

Figure 6 shows the damage morphology of 5 nm TI: Bi₂Se₃ thin films with film thickness collected by optical microscope under different laser energies. The core factor of nanosecond laser pulse damage to TI is thermal effect. With the increase in film temperature and energy under laser irradiation, the heat absorbed in the film continuously increases, resulting in corresponding thermal damage. As can be seen from Figure 6a, when the laser output energy is higher than the damage threshold of 5 nm TI: Bi₂Se₃ film (909 MW/cm²), damage spots begin to appear on the film layer, but the damage area is small. As the laser energy density continues to increase, as shown in Figure 6b, when the peak power density increases to about 1000 MW/cm², the damage area of the film layer expands. Due to the thermal effect, the heat deposition temperature of the film layer is increased and ablated. Moreover, when the film layer is irradiated by laser, the thermal effect causes the film material to undergo obvious oxidation reaction. Therefore, black ablative marks are produced in the damaged area of the film layer. With further enhancement of laser energy, as shown in Figure 6c,d, it is observed that the film layer warps and produces cracks, and molten material remains on the surface of the film layer due to thermal effect during laser irradiation. The higher the irradiation energy, the denser the black ablation marks. This is similar to the observed change in the surface morphology of the film layer with increasing laser energy in [35]. In addition, the high density of the film itself leads to the sputtering phenomenon, so a small amount of laser is sputtered near the damaged area on the film, resulting in new irregular damage points. It should be pointed out that impurity defects occur during the film deposition process and damage points are generated when the defects are sprayed around after excited irradiation.

5. Laser Application

5.1. Q-Switching or Mode-Locking

Laser passive Q-switching and mode-locking are the classic application scenarios of TI materials. For example, for ultrafast fiber lasers, in addition to the cavity structure, the saturable absorption parameter of SA affects whether the ultrafast laser operates in a mode-locked state or a Q-switched state. To obtain stable continuous wave mode-locking without Q-switching instability, the conditions of Formula (2) need to be met [36]:

$${\mathrm{E}}_{\mathrm{p}}^2{>\mathrm{E}}_{\mathrm{sat},\mathrm{G}}{\mathrm{E}}_{\mathrm{sat},\mathrm{SA}}\Delta \mathrm{T}$$

(2)

where ${\mathrm{E}}_{\mathrm{p}}^2$ is the cavity single-pulse energy, E_sat,G is the saturation energy of the gain, E_sat,SA is the saturation energy of SA (E_sat,SA = I_sat × t × S), and ΔT is the modulation depth of SA. When ${\mathrm{E}}_{\mathrm{p}}^2$ > E_sat,G E_sat,SA ΔT appears, it allows for the laser to operate in mode lock operation; instead, the laser operates in the Q-switched mode. In the right formula, when the laser gain medium and cavity type and other parameters are selected and fixed, the value of E_sat,G is determined. At this time, E_sat,SA ΔT becomes the decisive factor affecting the laser parameters. For the cavity saturable absorption material, the parameters that can be regulated are E_sat,SA and ΔT. The experimental results in Section 3 show that when the film thickness of TI-SA is small, the saturation intensity and modulation depth are both small, and the product of the two is also small. ${\mathrm{E}}_{\mathrm{p}}^2$ more easily exceeds E_sat,G E_sat,SA ΔT, and the continuous wave mode-locking operation can be easily obtained. When TI-SA film thickness increases, saturation strength and modulation depth increase, and the product of the two also increases correspondingly, resulting in relatively large E_sat,G E_sat,SA ΔT. In this case, the Q-switching operation is easier to achieve. This shows that the two-dimensional material prepared by the CVD method has the advantage of controllable layer number and can be effectively applied to the selection of specific laser working states. The discussion in this part can provide theoretical guidance for the operation of mode-locking and Q-switching.

The saturable absorption parameters such as modulation depth and saturation power intensity are the key factors affecting the output pulse width and peak power of passive Q-switched/mode-locked lasers. For a typical TI-SA passive Q-switched/mode-locked laser, when the pumping power reaches the Q-switched/mode-locked starting threshold, the pulse repetition rate increases and the pulse width decreases with the increase in pumping power. This is because under stronger pumping, the cavity light of the rapidly bleached TI-SA builds up in a shorter period. Empirical pulse width Formula (3) for passive Q-switched lasers [37]:

$$\mathsf{\tau }=\frac{3{.52\mathrm{T}}_{\mathrm{R}}}{\Delta \mathrm{T}}$$

(3)

where T_R is the cavity round trip time and ΔT is the modulation depth of SA. It can be concluded that the pulse duration can be further reduced by increasing the modulation depth of TI-SA in addition to conventional methods such as compression cavity length. In addition, the saturable absorber with great modulation depth can also suppress the wave-breaking effect, which is an inherently nonlinear phenomenon that limits the maximum energy per pulse and has good application advantages in the formation of high-power pulses. However, for TI-SA, the law of saturable absorption parameters and film thickness change obtained above shows that the modulation depth and non-saturable loss are proportional to film thickness, and the large non-saturable loss of multilayer TI also leads to the increase in laser threshold and the decrease in slope efficiency. It is noteworthy that TI-SA with low saturation strength and non-saturable loss can effectively reduce the threshold of Q-switched/mode-locked laser, facilitating the generation of Q-switched/mode-locked pulse. However, excessively low saturation intensity and modulation depth may lead to unstable operation of Q-switched/mode-locking, making it challenging to maintain short pulse output over time. Therefore, when actually carrying out the laser Q-switching/mode-locking operation, it is necessary to comprehensively consider the selection and design of three parameters, namely saturation strength, modulation depth, and non-saturable loss, and then use the advantages of the controllable layer number of the two-dimensional material prepared by the CVD method to design the optimal film thickness of the TI-SA device.

Taking the large-energy passively Q-switched Er-doped fiber laser reported by Xu et al. in 2019 as an example [10], stable Q-switching operation at 1.55 μm is achieved by inserting TI-SA into the linear laser cavity. The shortest pulse duration is 1.34 μs. If the 40 nm TI: Bi₂Se₃ film prepared by our CVD method (modulation depth is 51.2%) is selected, the calculation shows that the modulation depth of TI-SA is increased from 15.7% to 51.2%, and the pulse width is expected to be compressed to 410.9 ns under the same configuration.

5.2. The 1064 nm TI:Bi₂Se₃ Isolator

The 1064 nm classical Faraday isolator is polarization-dependent and is powerless against amplified spontaneous emission (ASE) noise light with no significant polarization characteristics. According to the saturable absorption parameters and damage thresholds of TI: Bi₂Se₃ films with different film thickness obtained in Part 3 and Part 4, TI: Bi₂Se₃ films with 5 nm film thickness have small nonlinear loss, not low modulation depth (the difference between the transmittance of high light intensity and low-power light signals), and large damage threshold, and have great potential to suppress light with small signal noise.

This paper presents the concept of using TI as small signal noise optical isolator. When the saturable absorber is used as a small signal noise optical isolation device, the isolation degree, insertion loss, and upper-level lifetime are the core parameters to evaluate its isolation capability. In terms of upper-level lifetime, the upper-level relaxation time of the topological insulator Bi₂Se₃ is in the sub-picosecond order, and the absorption effect persists in the nanosecond pulse duration. Therefore, the time pulse waveform of the nanosecond laser system does not change significantly, which meets the isolation requirements of nanosecond laser at the 1064 nm band. Furthermore, the optical isolator must possess high isolation degree and low insertion loss. As the number of layers increases, the isolation degree also increases, but this is accompanied by a corresponding increase in insertion loss and a reduction in damage threshold, which represents an inherent contradiction of two-dimensional saturable absorbent materials. Utilizing isolators that transmit single-layer TI multiple times offers advantages in both aspects and provides a comprehensive approach to enhancing isolation performance.

In order to explore the small signal noise optical isolation performance of the TI isolator, the isolation degree and insertion loss of the multi-pass isolator based on TI are simulated with the saturable absorption parameters and damage threshold obtained by the experiment as the simulation input. Taking TI: Bi₂Se₃ with 5 nm film thickness as an example, the isolation characteristics of the nanosecond laser at 1064 nm are simulated. We cut any input pulse I_in(t) into M small segments of duration Δt in the time domain. Total sampling time τ = M × Δt, where Δt is the sampling interval and M is the sampling time (integer). Each segment is treated as a square pulse, and the output pulse waveform is calculated by I_out(t) = T · I_in(t). As shown in the figure below, the peak power of the main pulse is 1000 kW/cm² (<damage threshold) and the pulse width is 15 ns. The small signal pulse is 80 ns before the main pulse, and the pulse width is half of the main pulse width. Figure 7 shows the evolution of pulse waveform of a light beam with a 1% contrast ratio after passing through a 5 nm Bi₂Se₃ thin film 5 and 10 times. After five passings through 5 nm Bi₂Se₃ film, the small signal contrast is reduced to less than 15%, and the main pulse transmission efficiency is about 90%, effectively suppressing the small signal noise light. After 10 passings of 5 nm Bi₂Se₃ film, the small signal contrast is reduced to 2.3% (16.4 dB), and the main pulse transmission efficiency is about 80%, although part of the main pulse light power is sacrificed, but the small signal noise light is more effectively suppressed. This study can provide a new polarization-independent optical isolation method for small signal noise in the 1 μm band.

Finally, it should be noted that compared with traditional ultrafast optical technologies, TI materials have stronger and more wide-band nonlinearity, which can be used in application scenarios where the material size is limited to achieve better performance. A saturated absorber can be used as a Q-switched or a mode-locked laser. By virtue of its anisotropy and nonlinearity, the modulation of optical signal characteristics such as light intensity and polarization can be realized in optical signal processing and optical communication. Using its strong nonlinearity and saturation absorption effect, combined with the micro-nano structure on chip, it can realize the functions of optical switching and optical routing and promote the development of on-chip photonic devices. However, the authors of this paper believe that the TI film material cannot completely replace the traditional ultrafast optical devices because in the current preparation process, its thermal stability and mechanical stability is still poor, the prepared sample properties are not stable, and repeatability is poor. This is the biggest challenge facing TI film materials at present. It is hoped that with the continuous development and improvement of thin film preparation technology, its application potential can be further increased.

6. Conclusions

In this paper, TI: Bi₂Se₃ thin films with multiple film layers were prepared by chemical vapor deposition, and their saturable absorption properties were experimentally investigated. The results show that the saturable absorption parameters of TI: Bi₂Se₃ films change significantly with the thickness of the film at 1064 nm. When the thickness of the film changes from small to significant, modulation depth α_s, non-saturable loss α_ns, and saturation power intensity I_sat of TI materials increase. It is worth noting that the damage threshold is inversely proportional to film thickness, and the thicker the film layer, the lower the damage threshold. The influence of controllable film thickness on passive Q-switching and mode-locking performance of laser when TI: Bi₂Se₃ film is prepared by the CVD method as saturation absorber is discussed and analyzed, which provides theoretical basis for the subsequent optimization of Q-switching and mode-locking performance. The performance of TI: Bi₂Se₃ thin film applied to nanosecond laser isolation in the 1064 nm band is also simulated and analyzed. The maximum isolation degree can reach 16.4 dB, which can provide a new polarization-independent small signal noise optical isolation method for a 1 μm band.