Nonlinear Optical Properties of Tellurene Nanosheets for Harmonic Soliton Operations in an Er-Doped Fiber Laser

Abstract

Tellurene has a wide bandwidth and low propagation loss at near-infrared wavelengths due to its nonlinear absorption coefficient. Therefore, we prepared tellurene–polyvinyl alcohol (Te-PVA) film as a saturable absorber in an Er-doped fiber laser by liquid phase exfoliation and spin-coating. The modulation depth was 5.25% and the saturation intensity was 17.02 MW/cm. The nonlinear optical properties of the film and its application in high-stability mode-locked operation were studied. A mode-locked pulse with a fundamental frequency of 8.48 MHz and a central wavelength of 1560.10 nm was obtained, with a signal-to-noise ratio which was greater than 75 dB. A traditional soliton mode-locked operation with a pulse width of 1.41 ps was achieved. In addition, eighth- and 19^th-harmonic mode-locked operations were obtained by adjusting the pump power and polarization controller. Our results show that Te-PVA film functioned as a saturable absorber which enabled harmonic mode-locking with an SNR of 75 dB in an Er-doped fiber laser. It is thus an excellent ultra-fast photonics material.

1. Introduction

With advantages including high conversion efficiency, good beam quality and a simple and compact structure, the introduction of ultra-fast lasers has set off an upsurge in the fields of industrial micromachining, medical imaging, material manufacturing and processing, and national defense security [1,2,3,4]. An important development direction in laser technology is obtaining laser output with a narrower pulse width [5,6]. The mode-locking technique is the most important and most effective method for generating ultra-short laser pulses. To obtain ultra-short pulses in lasers, two methods have mainly been adopted, namely, the active mode-locking technique and the passive mode-locking technique. The active mode-locking technique mainly involves adoption of an active modulation device in the laser cavity, such as an acousto-optic modulator or an electro-optic modulator, with light being periodically modulated by external means to achieve increased energy and a more stable pulse output. Passive mode-locking refers to the use of the saturable absorption characteristics of passive devices to modulate the laser to obtain pulses. Compared with the active mode-locking technique, passive mode-locking technology does not require additional modulation devices, and is more compact, flexible and convenient in terms of pulse acquisition with saturable absorbers (SAs) [7,8,9,10]. With SAs, absorption or loss changes with the input light intensity, loss in the high light intensity part is small, and loss in the low light intensity part is large, so that compression pulse is achieved and noise pulse is eliminated. The saturated absorption device is the core of passive mode-locking technology. Real SAs include commonly used semiconductor saturable absorption mirrors (SESAMs), as well as new SAs based on carbon nanotubes, two-dimensional (2D) materials, etc. [11].

With the development of two-dimensional (2D) nanomaterials, a new road has been opened up for the production of new materials. In recent years, various 2D materials with the advantages of strong nonlinear saturation absorption, fast recovery time, and simple preparation have greatly boosted investigation of optical solitons within mode-locked fiber lasers [12,13]. In 2009, Bao et al. were the first to use atomic-layer graphene as an SA to obtain ultra-short pulses in fiber lasers [14]. Since then, 2D materials have been widely used in passively mode-locked fiber lasers. Due to their natural structural advantages and excellent optical properties, such as atomic layer thickness, high carrier mobility and high optical absorption, 2D materials have attracted extensive attention among researchers, offering a good choice for the new SAs with ultra-short pulse output in passive mode-locked lasers. At present, new 2D-layered materials (graphene [15,16,17,18], black phosphorus (BP) [19,20,21], topological insulators (Tls) [22,23,24], transition metal dihalides (TMDs) [25,26,27,28,29,30], ferromagnetic insulators [31,32,33], Xenes [34,35,36,37,38], etc.) are widely used in mode-locked fiber lasers. However, the various 2D materials have their own advantages and disadvantages in terms of pulse output characteristics and the thermal stability of SAs. Therefore, the search for 2D materials with excellent optical properties for use as SAs is an essential aspect of current research [39].

Xenes are 2D materials of atomic thickness, with X referring to the possible groups elements from IIIA to VIA, and ene being a Latin word for nanosheets [40]. Xenes are of great interest to researchers due to their outstanding characteristics; these include wide absorption bandwidth, an ultra-high surface volume ratio, strong light absorption, and high carrier mobility. In 2017, Song et al. prepared antimonene by liquid phase exfoliation (LPE) for the first time, and obtained a passively mode-locked pulse with a pulse width of 550 fs [41]. In the same year, Xing et al. obtained a mode-locked pulse with a repetition rate of 13.68 MHz and a pulse width of 3.1 ps based on Selenene as a SA [36]. In 2018, Guo et al. used microfiber-based bismathene as an SA in an Er-doped fiber laser (EDFL) for the first time, and obtained a stable pulse near 1561 nm, the shortest pulse width being about 193 fs [35]. In 2019, Guo et al. obtained a mode-locked pulse based on tellurene as an SA; this had a repetition rate of 15.45 MHz and a pulse width of 829 fs [42]. In 2020, Liu et al. obtained a passively mode-locked EDFL with a central wavelength of 1531.48 nm and a repetition rate of 3.35 MHz through a tapered fiber using silicene as an SA [43]. Research into use of Xenes as SAs to generate mode-locked pulse is still in its infancy, so it is very important that optical research into new Xenes is expanded.

Tellurene (Te), a member of the chalcogen element family, has attracted significant attention due to its fascinating physical and chemical properties, such as hydration and oxidation catalytic activity, thermoelectricity, and photoconductivity [44]. It is one of the 2D mono-elemental materials (group-III, -IV and -V elements), elements near the border between metals and nonmetals which have garnered tremendous interest owing to their unique electronic, optical, and chemical properties. As a narrow-bandgap semiconductor, few-layer Te has a narrow band gap of 0.325 eV, and it has numerous potential applications in the fabrication of many modern devices [45,46]. Due to its chain-like structure, Te has a strong tendency to grow into a one-dimensional nanoarchitecture. In 2014, Wang et al. produced 2D hexagonal tellurium nanoplates on flexible mica sheets [47]. Huang et al. obtained Te films of monolayer and few-layer thickness by molecular beam epitaxy on a graphene/6H-SiC (0001) substrate. With thickness controlled at an atomic scale, they further demonstrated potential application in the fields of electronics and optoelectronics [48]. Lately, study of 2D Te has gained in popularity. Promising air-stable performance at ambient temperature, ultralow lattice thermal conductivity (2.16 W m⁻¹ K⁻¹), high hole mobility (almost 3000 cm²/vs at low temperature), and outstanding photo response have all been demonstrated by 2D Te [42].

In this work, Te-polyvinyl alcohol (Te-PVA) SA with a modulation depth of 5.25% and a saturation intensity of 17.02 MW/cm² is inserted into an EDFL, and stable mode-locked pulses are successfully obtained. Under the fundamental frequency of 8.48 MHz, the center wavelength of the mode-locked pulse is 1560.10 nm, and the signal-to-noise ratio (SNR) is greater than 75 dB. By adjusting the state of the laser cavity, high order mode-locked operation is also realized. These experimental outcomes show that Te has outstanding saturable absorption behavior and has broad potential in the development of ultra-fast photonics devices.

2. Preparation and Characterization of Te-PVA SA

Polyvinyl alcohol was adopted as the host matrix owing to its excellent film-forming capability, high optical transparency at 1.5 μm, good chemical stability, and low-cost fabrication process, which enables uniform dispersion of Te nanosheets and low-loss integration into the fiber laser cavity. In this section, we describe the whole process of preparing the Te-PVA SA using LPE and spin-coating. This method is usually used to prepare nanosheet SAs with small amounts of 2D materials dissolved in organic solvents. Compared with other film preparation methods, it is simpler and more economical, and the film produced is easier to peel. As shown in Figure 1, in the first step, 0.1 g of Te powder was added to 50 mL of 75% alcohol solution. The combination was centrifuged at 2000 rpm for 30 min and put into an ultrasonic cleaner for 6 h. In the second step, the initially obtained Te solution was mixed with PVA liquid in a 1:1 volume ratio. Sonication then continued for another 6 h to obtain a uniform Te-PVA dispersion solution. Then, 100 μL dispersion was uniformly spread onto the substrate, with rotation, and allowed to stand at 30°C for 48 h, forming Te-PVA films. Finally, the Te-PVA SA was prepared by cutting film into 1 × 1 mm² pieces which were then placed on the ends of fiber optic patch cords.

Figure 2a shows the surface analysis of the Te obtained by scanning electron microscopy (SEM) (Sigma 500, ZEISS, Oberkochen, Germany). A distinct layered structure is evident in the image. The corresponding energy dispersive spectroscopy (EDS) (QUANTAX EDS, Bruker, Germany) is shown in Figure 2b, which clearly shows the peaks of Te, and better records the distribution of the elements, using an estimated Te. In addition, X-ray diffraction (XRD) (D8 Advance, Bruker, Billerica, MA, USA) spectra are provided in Figure 2c. As may be seen in the figure, obvious diffraction peaks at (100), (101), (012), (110), (003), (021) and (120) were recorded, consistent with previously reported works. The structural characteristics of Te excited by a 532 nm laser were also studied. As illustrated in Figure 2d, three Raman shift peaks of E₁, A₁ and E₂ modes were characterized at 90 cm⁻¹, 120.02 cm⁻¹ and 138 cm⁻¹, respectively, which corresponded well with the previous results [44]. Raman spectra and AFM images for different intensities of laser power irradiation were presented in our previous report [34]. The results indicate that tellurium nanosheets of uniform thickness, with negligible oxidation or structural degradation, were successfully prepared.

Figure 3a illustrates the linear transmittance of the Te-PVA film and the control substrate. The results show that transmission of the Te-PVA film at 1560 nm is about 77.47%. For the control experiment, we measured the linear transmittance of a pure PVA film at 1560 nm. The pure PVA film exhibits a linear transmittance of 93.9%, corresponding to a linear optical loss of only 6.1%. This confirms that the majority of the insertion loss in the Te-PVA film arises from the nanosheets rather than the polymer host. The nonlinear absorption properties of the Te-PVA film-type SA are obtained by adopting a balanced twin-detector measurement system. A homemade ultrafast fiber laser (1564.8 nm, 353 fs, 10 MHz) is employed as a laser source, a variable optical attenuator (VOA) is adopted to adjust the input laser power, these being separated in a ratio of 1:1 by an OC, with power at both ends tested by a power meter. The obtained experimental data are fitted by Equation (1) as follows:

$$T\left(I\right)=1-T_{ns}-∆T\times \mathrm{e}\mathrm{x}\mathrm{p}(-I/I_{sat})$$

(1)

where T(I) and ∆T represent the transmission velocity and modulation depth, respectively; I and I_sat stand for incident light intensity and saturation intensity; and T_ns is non-saturable absorbance. The experimental fitting results are given in Figure 3b, where non-saturable loss, saturation intensity, and modulation depth of 23.3%, 17.02 MW/cm² and 5.25%, respectively, may be seen. The smaller modulation depth is beneficial for long-term stability, but reduces the pulse narrowing effect during mode locking.

3. Experimental Setup

The experimental setup for an Er-doped mode-locked optical fiber laser based on Te-PVA SA is shown in Figure 4. A 30 cm Er-doped fiber (LIEKKI Er110, nlight, Vancouver, WA, USA) was used as the gain medium to control the overall cavity dispersion, lower the mode-locking threshold, reduce thermal effects, and achieve an appropriate fundamental repetition rate for stable soliton mode-locking. The pump light was supplied by a 980 nm single mode laser diode (LD) (Taizhou Tonghe Laser technology Co., Ltd., Wenling, China) and coupled to a ring cavity by a 980/1550 nm wavelength division multiplexer (WDM). The feedback loop of the ring laser was made by connecting the 90% interface of the optical coupler (OC) to another interface of the WDM. A total of 10% of output energy was used to record the output features of the experiment. Two polarization controllers (PCs) and a polarization insensitive isolator (PI-ISO) were also incorporated into the resonant cavity to optimize the laser state inside the cavity and enforce unidirectional laser operation. A 23.93 m single-mode fiber (SMF) with a dispersion parameter of −21.68 ps²/km lengthened the entire cavity length. Thus, the overall length of the resonant cavity was ~24.23 m and the calculated total net cavity dispersion was −0.63 ps². The pulse sequence parameters, the radio frequency (RF) spectrum, the output power, and the optical spectrum of the mode-locked fiber laser were measured by a digital oscilloscope (Wavesurfer 3054z, Teledyne LeCroy, New York, NY, USA), an RF spectrum analyzer (MXA Signal Analyzer N9020A, Agilent, Santa Clara, CA, USA), an intensity autocorrelator (FR-103XL, Femtochrome, CA, USA), power meter (D50, BAGGER, Bergkirchen, Germany) and optical spectrum analyzer (MS9710C, Anritsu, Tokyo, Japan), respectively.

4. Results and Discussion

To verify that the Te-PVA SA has superior nonlinear saturable absorption characteristics, in this experiment we recorded the output characteristics of the EDFL without the Te-PVA film-type SA before the experiment began. By carefully adjusting the pump power and the PC machine, only continuous waves could be output, and no mode-locked pulses, harmonic mode-locking or pulse-like modulation were obtained, eliminating the possibility of mode-locking being caused by nonlinear polarization rotation or by the Fabry–Perot cavity effect. Then, the Te-PVA modulator was added to the laser cavity, and a stable mode-locked phenomenon was observed by finely adjusting the PC machine, indicating that the ultra-fast modulation effect was induced by the Te-PVA SA. The pulse train, optical spectrum, and RF spectrum all exhibited typical soliton mode-locking characteristics. The mode locking operation is not self-starting. When the pump power exceeds 80 mW, the mode locking operation can be achieved by adjusting the angle of the PC. This behavior is typical for fiber lasers with saturable absorbers based on 2D materials, where the intracavity polarization state directly influences the effective saturable absorption and the balance between gain, loss, dispersion, and nonlinearity.

When pump power increases from 80 to 180 mW, a stable pulse sequence can be obtained by carefully rotating the PC. Figure 5a shows the pulse sequence obtained at 144.7 mW, with a pulse interval of 123 ns which matches the round-trip time of the cavity. The typical optical spectral shape is shown in Figure 5b. A conventional soliton spectrum with distinct and symmetric Kelly sidebands was attained, and a spectral diagram with a central wavelength of 1560.10 nm is obtained at a resolution of 1 nm. Figure 5c depicts the relationships between output power, pulse energy, and pump power. It can be seen from the figure that the output power is linearly related to the pump power. At the maximum input power, the power conversion efficiency reaches 0.72%, indicating that the influence of SA on the whole laser cavity is relatively great. Therefore, improving power conversion efficiency is one of our future research objectives. In brief, then, we obtained a typical conventional soliton due to Kelly sidebands and single pulse energy. Furthermore, it was clear that pulse energy and output power were linearly related to pump power. An intensity autocorrelator was used to test the real pulse width of the mode-locked pulse, and the autocorrelation data were fitted by sech² function. As shown in Figure 5d, the real pulse width was calculated to be 1.41 ps. The time–bandwidth product (TBP) of the mode-locking pulse can be calculated as follows:

$$TBP=\tau \times {\displaystyle \frac{c\cdot \Delta \lambda }{{\mathsf{\lambda }}_c^2}}$$

(2)

where c is the speed of light, Δλ is the 3 dB bandwidth, and λ_c is the center wavelength. The ideal transform-limited TBP of a sech²-shaped soliton is ~0.315. Because the calculated TBP = 0.657, the pulse is not transform-limited. There is a positive chirp, and the pulse is broadened by frequency modulation.

The soliton area is invariant in the anomalously dispersive cavity. The combined effect of net cavity dispersion, gain clamping, and saturable absorption determines the equilibrium between pulse duration and spectral width. The non-transform-limited state reflects the joint influence of cavity loss, finite modulation depth, and multi-pulse harmonic operation. The single pulse energy is calculated to be is 0.14 nJ; this is greater than 0.1 nJ, the theoretical limit of soliton area, indicating the existence of positive chirp in the pulse.

Figure 6a shows the RF spectrum with a SNR of ~75 dB at a fundamental frequency of 8.48 MHz. Figure 6b depicts the RF spectrum over a bandwidth of 200 MHz, which was used to study the long-term stability of the mode-locked fiber laser. Figure 6c records the spectra of the mode-locked states at one-hour intervals over a six-hour period. There was little change in the shape or intensity of the spectrum. The experimental results show that stability of mode-locked pulse is successfully realized.

In addition, it is valuable to explore the potential of tellurium mode-locked fiber lasers to operate in higher repetition frequency patterns in many applications. When the pump power in a fiber laser is high, a single pulse cycling in the cavity splits into multiple pulses due to the principle of energy limitation. Consequently, when other factors in the fiber laser are changed, it is possible to achieve a pulse sequence which is stable and well-ordered. In this case, the repetition frequency of this pulse sequence is far higher than the pulse spacing of the fundamental mode-locking [49,50]. Therefore, we used an integrated adjustment method to adjust the pump power and polarization controller to make the tellurium mode-locked laser work in a harmonic mode-locked system. When we increased the pump power to 141 mW, an eighth-harmonic mode-locked system was obtained. The results are shown in Figure 7a–c. Figure 7a shows the pulse sequence of the eighth-harmonic mode-locked system with a pulse separation time is 15.76 ns. The pulse train exhibits a constant repetition rate of 67.87 MHz, with no amplitude modulation or pulse dropouts over the measured time window. The power monitoring results over 30 min remain stable at ~0.89 mW, with fluctuations < 2%. Figure 7b demonstrates a typical spectrum of a harmonic mode-locked state: the central wavelength is located at 1560.3 nm, and the 3 dB bandwidth is 3.42 nm. Figure 7c shows the RF spectrum of an eighth-harmonic mode-locked state where the central frequency is 67.87 MHz, approximately eight times that of the fundamental frequency mode-locked state. The SNR is about 59 dB, indicating that the mode-locked state is operating stably at this time. Meanwhile, when we further increase the pumping power to 151 mW, the pulse sequence is no longer stably arranged. However, we obtained a stable 19th-harmonic mode-locked state by carefully adjusting the PC. Figure 7d shows a pulse sequence where the pulse separation is 6.23 ns. The illustration shows that the pulses remain equally spaced with consistent intensity, confirming stable multi-pulse distribution in the cavity. Output power is maintained at ~0.99 mW, with negligible variation (<1%). These data demonstrate the excellent long-term stability of the harmonic mode-locking operation. Figure 7e depicts the spectrum of the 19th-harmonic mode-locked state, in which the central wavelength and 3 dB bandwidth are 1559.25 nm and 1.91 nm, respectively. Figure 7f illustrates the RF spectra recorded for the harmonic mode-locked operation with a central frequency of 161.19 MHz and an SNR of 76 dB. The higher SNR shows that we obtained a stable 19th-harmonic mode-locked state. As harmonic mode-locking arises from intracavity pulse spacing rather than changes in pulse shaping, the pulse width remains unchanged at ~1.41 ps (sech²fit) for both harmonics, consistent with the fundamental mode-locking state.

As mentioned, various Xenes have been used as SAs to demonstrate pulsed fiber laser operations. In order to more intuitively express the material properties of Te SA, we compare Te with existing material research results.

Table 1. Comparison of Xene-based mode-locked fiber lasers.

Materials	∆T (%)	Isat	Tns (%)	τ (fs)	f (MHz)	SNR (dB)	λc (nm)	Ref.
Tellurene	27	78.14 GW/cm2	25.9	829	15.45	53	1556.57	[42]
Bismuthene	5.1	209.1 MW/cm2	70.9	835	9.23	52	1530.6	[51]
Antimonene	15	0.11 MW/cm2	34	1300	12.6	64	1897.4	[52]
Silicene	20	5.07 MW/cm2	10.05	937	3.35	43	1531.48	[43]
Germanium	6.17	11.69 MW/cm2	25	1.07 ns	6.66	75	1568.85	[53]
Germanium	13.9	2.266 GW/cm2	11.90	901	4.8	60	1569.7	[54]
NbAs	3.92	0.96 MW/cm2	32.9	640	21.28	53.16	1569.07	[55]
Nb2SiTe4	9.56	2.36 KW/cm2	39.79	747	21.50	50.8	1574.43	[56]
GaGeTe	10.61	13.9 KW/cm2	9.32	830	20.31	46.12	1573.72	[57]
Tellurene	5.25	17.02 MW/cm2	23.3	1410	8.48	75	1560.10	This work

summarizes typical output characteristics of mode-locked fiber laser operations based on Xenes and on other 2D materials. Key parameters are compared, including modulation depth, saturation intensity, non-saturable loss, pulse width, frequency rate, center wavelength, and signal-to-noise ratio. The Te-PVA composite film is prepared by a simple liquid-phase exfoliation and spin-coating method, which has the advantages of simple process, low cost, and high scalability. Compared with the complex synthesis and transfer processes of other 2D material-based SAs, this preparation method is more suitable for large-scale production and practical device integration. As shown in the table, Te-based SA in fiber laser exhibits a high SNR of 75 dB, indicating its good stability.

5. Conclusions

To sum up, a Te-PVA SA was successfully made; this had a saturation intensity of 17.02 MW/cm² and a modulation depth of 5.25%, and it was successfully applied in the study of a passive mode-locked EDFL. Stable mode-locked operation was realized in a fiber laser based on the Te-PVA SA. In this fiber laser, a mode-locked pulse was obtained with a fundamental frequency of 8.48 MHz, an SNR greater than 75 dB, a pulse energy of 0.15 nJ, and a pulse width of 1.41 ps. Eighth- and 19th-harmonic mode-locked operations were also obtained in this fiber laser. The experimental results show that Te nanosheets have good nonlinear absorption characteristics, providing an important reference for future research into Xenes.