Optical Nonlinearity of Violet Phosphorus and Applications in Fiber Lasers

Hui-ran Yang(杨慧苒)$^{1}$, Meng-ting Qi(齐梦婷)$^{1}$, Xu-peng Li(李旭鹏)$^{2}$, Ze Xue(薛泽)$^{1}$,\\ Chen-hao Lu(鲁晨浩)$^{1}$, Jia-wei Cheng(成嘉伟)$^{1}$, Dong-dong Han(韩冬冬)$^{3}$, and Lu Li(李璐)$^{1\hyperlink{s}{*}}$

doi:10.1088/0256-307X/41/1/014202

⇦Chinese Physics Letters, 2024, Vol. 41, No. 1, Article code 014202⇨ Optical Nonlinearity of Violet Phosphorus and Applications in Fiber Lasers Hui-ran Yang (杨慧苒)1, Meng-ting Qi (齐梦婷)1, Xu-peng Li (李旭鹏)2, Ze Xue (薛泽)1, Chen-hao Lu (鲁晨浩)1, Jia-wei Cheng (成嘉伟)1, Dong-dong Han (韩冬冬)3, and Lu Li (李璐)1* Affiliations 1School of Science, Xi'an University of Posts and Telecommunications, Xi'an 710121, China 2China Academy of Space Technology (Xi'an), Xi'an 710100, China 3School of Electronic Engineering, Xi'an University of Posts and Telecommunications, Xi'an 710121, China Received 10 November 2023; accepted manuscript online 13 December 2023; published online 16 January 2024 ^*Corresponding author. Email: liluyoudian@xupt.edu.cn Citation Text: Yang H R, Qi M T, Li X P et al. 2024 Chin. Phys. Lett. 41 014202 Abstract A D-shaped fiber is coated with a new two-dimensional nanomaterial, violet phosphorus (VP), to create a saturable absorber (SA) with a modulation depth of 3.68%. Subsequently, the SA is inserted into a fiber laser, enabling successful generation of dark solitons and bright–dark soliton pairs through adjustment of the polarization state within the cavity. Through further study, mode-locked pulses are achieved, proving the existence of polarization-locked vector solitons. The results indicate that VP can be used as a polarization-independent SA.

DOI:10.1088/0256-307X/41/1/014202 © 2024 Chinese Physics Society Article Text In 1980, solitons were observed for the first time as stable localized nonlinear waves in experiments with single-mode fibers (SMFs).[1] As is well known, the phenomenon of optical solitons is caused by the balance between fiber dispersion and the Kerr effect, and can be mathematically expressed by the nonlinear Schrödinger equation.[2] Furthermore, it is theoretically shown that dark solitons can be formed in anomalous dispersion SMFs. When considering the birefringence of SMFs, the asymmetric structure and bending of SMFs result in different phase and group speeds in the two orthogonal polarization modes.[3-6] Also, when the soliton is periodic in a laser cavity, it is possible to achieve phase locking of two perpendicular polarizations, which leads to a vector soliton.[7] Research about the polarimetric properties of fiber lasers plays an important role in many applications such as optical sensors, optical communication, materials processing, and nano-photonics.[8-22] In recent years, no matter whether studying bright and dark soliton pairs or polarized solitons, the use of saturable absorbers (SAs) has become necessary.[23-26] Therefore, continuous optimization of SAs is crucial for studying soliton states in fiber lasers. Since 2004, graphene has found extensive applications in the domains of physics, chemistry, and industry owing to its remarkable optical properties.[27] The discovery of graphene has triggered further exploration of two-dimensional (2D) materials, such as topological isolators (TIs),[28-30] black phosphorus (BP),[31] carbon nanotubes,[32] and transition metal disulfides.[33-38] With the development of 2D materials and practical applications, the study of optical fiber lasers is becoming increasingly popular. Zhang et al. for the first time reported that atomic layer graphene could be used as an SA. Thus, the study of 2D materials as SAs in ultrafast photonics was initiated.[39] In 2014, Chen et al. presented an ultra-wideband and adjustable passive $Q$-switching erbium-doped fiber (EDF) laser with a TI (Bi$_{2}$Te$_{3}$).[40] In 2016, Song et al. found that an SA based on BP nanosheets could exhibit polarization-independent properties, giving rise to formation of vector solitons, vector soliton beams, and vector soliton bound states in fiber lasers.[31] It should be noted that Yang et al. developed a TaS$_{2}$ SA and successfully achieved polarization-locked vector solitons.[41] However, many of the above-mentioned 2D materials have several drawbacks. For example, the low absorption coefficient of graphene, the insulation characteristic of bulk TIs, poor stability of BP, and difficulty of synthesis of MXenes.[42,43] In recent years, researchers have found that violet phosphorus (VP) with a layered structure, as an allotrope of phosphorus, exhibits better environmental stability than BP and has a higher stable light response.[44,45] In 2023, Pan et al. implemented for the first time an EDF laser that used VP nanosheets as the SA to generate ultrashort pulses with a pulse width of 799 fs. Moreover, a stable soliton molecule mode-locking pulse with an 816 fs pulse width and 20.5 ps interval time was obtained by adjusting the polarization state in the laser cavity.[46] However, up to date no research has been carried out on polarization characteristics of solitons based on a VP SA. In this Letter, we construct a mode-locked optical fiber laser employing a VP SA and thoroughly investigate the properties of both bright and dark solitons as well as the polarization characteristics of solitons. VP nanosheets are deposited onto the surface of a D-shaped fiber to fabricate SA devices. By incorporating the SA into the cavity of the EDF laser we can effectively obtain dark solitons. Additionally, by adjusting the polarization controller (PC), we obtain bright and dark soliton pairs. Furthermore, the structure of the resonator and the polarization state are modified to obtain polarization-locked vector solitons, and their polarization properties are investigated. Preparation and Characterization of VP Nanosheets. In this work, a 0.1 mg/ml VP nanosheet dispersion solution was taken and ultrasonic treatment was carried out for several hours using a high-power ultrasonic cleaning machine. Subsequently, to eliminate the undesired large agglomerates, the solution was allowed to settle for 5 min and the supernatant was extracted. To obtain high-quality material characterization, the VP dispersion was dripped onto mica sheets and allowed to dry naturally. The scanning electron microscope (SEM) image of VP shown in Fig. 1(a) reveals its 2D layered structure. The measurement results for the surface morphology and thickness of the VP nanosheets are given in Figs. 1(b), 1(c), and 1(d). A three-dimensional atomic force microscope (AFM) image is presented in Fig. 1(b), illustrating the measured roughness of the VP nanosheets as $Ra = 0.467$. Figure 1(c) illustrates an AFM image of the VP nanosheets. The thickness of the marked regions is shown in Fig. 1(d), about 10.5 nm and 5.9 nm, respectively.

Fig. 1. Characterization of VP nanosheets: (a) SEM image, (b) three-dimensional AFM image, (c) AFM image, (d) height profile.

Fig. 2. (a) Crystal structure of VP. (b) Band structure of VP.

Figure 2(a) depicts the crystal structure of VP, with a gap of 2.9 Å between layers. The VP of the block is calculated by employing density functional theory and utilizing the Perdew–Burke–Ernzerhof correlation function within the generalized gradient approximation method. The band gap value of VP, as depicted in Fig. 2(b), is approximately 1.34 eV, confirming its semiconductor nature. The conduction band bottom and valence band top are located at different momentum space points ($K$ points). This indicates that VP is an indirect band gap material. Fabrication and Characterization of VP SA. To improve the interaction of VP with the laser, the evanescent field interaction scheme not only overcomes the thermal damage induced by the optical power but also ensures a strong nonlinear effect from VP due to the long interaction length. A D-shaped fiber is obtained by polishing one side of a standard SMF with a length of approximately 20 mm. The depth from the edge of the optical core to the surface of the D-shaped fiber is about 2 µm. To further investigate the nonlinear properties of SA based on VP nano-material, a balanced double-detector measurement system was used to measure the nonlinear absorption. The experimental setup is illustrated in Fig. 3(a). The optical fiber laser is used as the laser source and a PC is employed to control the input pulse. The input optical power is adjusted by an attenuator. Light is divided into two branches using a 90/10 optical coupler, with a VP SA positioned on one of the branches. Two optical power meters are utilized to measure the optical power of both branches. The measurement system is employed to measure the nonlinear absorption of the VP SA at 1565 nm, and the outcomes are presented in Fig. 3(b).

Fig. 3. (a) Schematic diagram of a balanced dual-detector measurement system. (b) Nonlinear absorption properties of the VP SA.

After fitting the experimental data, the blue curve exhibits a high degree of agreement with the empirical observations, and can be described by the following fitting formula: \begin{align} \alpha (I)=\frac{\alpha_{\rm s}}{1+(I/I_{\rm sat})}+\alpha_{\rm ns}. \tag {1} \end{align} In this case, $\alpha_{\rm ns}$ represents nonsaturable absorbance, $I_{\rm sat}$ represents saturable intensity, and $\alpha_{\rm s}$ represents saturable absorbance. The transmission intensity is modeled as a function of $1-\alpha (I)$. Based on the fitting curve depicted in Fig. 3(b), the values of $\alpha_{\rm s}$, $I_{\rm sat}$, and $\alpha_{\rm ns}$ for the VP-SA device are determined to be 3.68%, 93.03 MW/cm$^{2}$, and 30.56%, respectively. Results and Discussions. A schematic diagram of the EDF laser device based on VP is presented in Fig. 4. The laser cavity employs a 980 nm laser diode (LD) as the pump source, and a polarization-independent tap-isolator-wavelength-division multiplexer (PI-TIWDM), SA, SMF, and PC are employed to construct a ring cavity optical oscillator. The PI-TIWDM consists of wavelength-division multiplexers (WDMs), a polarization-independent isolator (PI-ISO) and an optical coupler. Its working principle is to combine two lights into a single fiber, limiting the propagation of the beam in one direction and dividing it into two parts. In this study, we adopt $70\!:\!30$ optical coupling and analyze the performance of the output pulse using 30% of the light. Cavity polarization is controlled by a PC, and VP is applied as the SA. Moreover, the formation of solitons is influenced by the balance between laser gain and loss as well as the nonlinearity and net dispersion of the laser cavity. Meanwhile, the length of the SMF is approximately 6.2 m to regulate the net dispersion with a dispersion parameter of 17 ps$\cdot$nm$^{-1}\cdot$km$^{-1}$, and an EDF (Liekki Er110-4/125) with a length of approximately 0.8 m and a dispersion parameter of $-46$ ps$\cdot$nm$^{-1}\cdot$km$^{-1}$ is utilized as the gain medium to achieve sufficient gain, resulting in a net cavity dispersion of approximately $-$0.087 ps$^{2}$.

Fig. 4. Schematic diagram of a VP-based fiber laser system. PBS: polarization beam splitter.

When the pump power reaches 63 mW, stable dark solitons are observed through precise adjustment of the state of the PC, as depicted in Fig. 5(a). Under the background of a uniform continuous wave, an intensity drop can be observed. The pulse train operates with a pulse interval of 34 ns, corresponding to a repetition rate of 29.4 MHz. Additionally, the relevant spectrum is shown in Fig. 5(b). The absence of Kelly sidebands in Fig. 5(b) may be attributed to the spectrum filtration effect caused by polarization of the PC and intracavity birefringence of the SMF. Notably, the spectrum exhibits an M-shape with two wavelength components centered at 1568.26 nm and 1569.20 nm, which is similar to earlier reports,[47-50] suggesting that it may also be influenced by cavity feedback and competition for gain.

Fig. 5. Experimental findings for the characteristics of dark solitons: (a) oscilloscope trace, (b) optical spectrum.

Fig. 6. Oscilloscope trace diagram of bright and dark soliton pairs.

When the pump power is maintained at a fixed value of 63 mW, a stable bright–dark soliton pair is generated by adjusting the PC. Figure 6 displays the pulse train of a bright–dark soliton pair, with a distance of 34 ns between the solitons, which corresponds to the cavity's return time. It is evident from Fig. 6 that both solitons have equal amplitude, indicating stable lock operation. Additionally, the profiles of bright–dark solitons exhibit symmetry in the background of a uniform continuous wave, with the intensity of the bright pulse being approximately equal to the depth of the dark pulse. The results indicate that pairs of bright and dark solitons exhibit relatively stable behavior, which is consistent with earlier research.[48] This steady pattern suggests that the damage threshold of a VP SA is high because the heat generated by optical transmission can be effectively dissipated from the surface of the D-shaped fiber. In addition, no $Q$-switching operation can be observed in the experiment, regardless of the state of adjustment of the PC. To further investigate VP-based fiber lasers, a 28 m SMF was added to the laser cavity. When the pump power is 68 mW, mode locking is achieved through careful adjustment of the PC status within the cavity. As shown in Fig. 7(a), a typical single-pulse mode-locking state is achieved by the fiber laser, and the center of the spectrum of the mode-locked pulse is at approximately 1568 nm. It has been found that the Kelly sideband is a typical feature of solitons in laser cavities with net anomalous dispersion, indicating that the mode-locking pulse is a conventional soliton.[51,52] The self-correlation trace of a pulse is measured to determine its pulse duration, as illustrated in Fig. 7(b). The width at half height is determined to be 2.21 ps, and the fitting sech$^{2}$ function indicates a pulse duration of 1.44 ps. Figure 7(c) shows the pulse train on a larger time scale with a duration of 2.0 µs and a time interval of about 170 ns between the two adjacent pulses, which agrees well with the time needed for light to cycle around the laser cavity, indicating that the optical fiber laser operates in single-pulse operation. In addition, the amplitude fluctuation of the pulse train is mainly caused by reverse reflection and environmental interference, and is extremely low, indicating that the mode-locking operation is relatively stable. In order to ascertain the exclusive contribution of the VP SA to the mode-locking operation, it was deliberately removed from the laser cavity. Despite adjusting both pump power and PC state within a relatively wide range, no mode locking could be observed. Hence, it can be concluded that the appearance of mode-locking operation is induced by the VP SA rather than other optical components. It is worth mentioning that the light phenomenon was stable throughout the experiment, and no damage to the VP SA was observed, which further proves that the thermal damage threshold of a VP SA is large.

Fig. 7. Characteristic features of laser operation in the mode-locked state: (a) optical spectrum analysis, (b) autocorrelation trace, (c) oscilloscope trace.

Fig. 8. Output characteristics of polarization-locked vector soliton operation: (a) optical spectra, (b) oscilloscope traces.

A number of sharp spectral peaks can be observed in the mode-locked spectrum. The two prominent peaks observed in the vicinity of the central wavelength correspond to first-order Kelly sidebands, as previously elucidated.[53,54] Another group of weak spectra near the central wavelength is not composed of Kelly sidebands, and their emergence is considered to be the result of the existence of a vector soliton, which is consistent with the previous studies.[41,55] To study the polarization vector characteristics of VP mode-locked solitons accurately, a polarization beam splitter is connected to the laser output, enabling simultaneous measurement of two orthogonal polarizations. The polarization resolution spectra of solitons centered at $\sim $ 1568 nm is illustrated in Fig. 8(a). On the spectral lines of the two orthogonal polarizations, besides the Kelly sidebands, there is a sideband on the spectral lines of polarizations and its location changes with the intensity of the linear birefringence. This is very similar to the results in our previous work.[56] Although there is a spectral peak in the horizontal component, a steep drop in the spectrum is observed in the other components, as illustrated in Fig. 8(a). These peak–slope bands are caused by the coherent exchange of energy between vector solitons.[57] This phenomenon can only be observed in vector solitons. Figure 8(b) illustrates two polarization-resolved pulse sequences, covering a time range of 2.0 µs. They all have uniform pulse heights with no modulation. The results indicate that the polarization in the direction of the cavity is fixed, suggesting the generation of vector solitons with locked polarization.[40] In summary, we have utilized the optical deposition method to deposit VP on a D-shaped fiber, achieving a VP SA with modulation depth of 3.68%. The VP SA is inserted into an EDF laser to obtain dark solitons, bright–dark soliton pairs, and vector solitons by adjusting the pump power and PC status. The polarization characteristics of a VP-SA based erbium-doped fiber laser are investigated. Although the nonlinear polarization rotation effect caused by the D-shaped fiber affects the pulse characteristics of the laser, mode-locking operation cannot be initiated in the laser cavity without the VP SA. The experimental findings demonstrate that VP serves as an effective SA for ultrafast mode-locked lasers and has extensive potential applications in fiber lasers and nonlinear optical systems. Acknowledgments. This work was supported by the National Natural Science Foundation of China (Grant Nos. 62005212 and 12075190), the Young Talent Fund of University Association for Science and Technology in Shaanxi, China (Grant No. 20210112), the New Star Project of Science and Technology of Shaanxi Province (Grant No. 2022KJXX-69), the Fund for Outstanding Young Talents of China Academy of Space Technology (Xi'an) (Grant No. Y21-RCFYJQ1-03), the Young Elite Scientists Sponsorship Program by CAST (Grant No. 2022QNRC001), and the Open Foundation of State Key Laboratory of Transient Optics and Photonics (Grant No. SKLST202207). 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