# High-Mode Purity 1 μm Cylindrical Vector Beam All-Fiber Laser Based on a Symmetric Two-Mode Coupler

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## Abstract

**:**

_{01}mode and TE (transverse electric)

_{01}mode is 97.18% and 97.07%, respectively.

## 1. Introduction

_{01}mode generates a large gradient and light field scattering force; therefore, it has a stronger trapping ability than Gaussian light, and can be used for particle trapping [10,11] and particle acceleration [12,13]. In the environment constituting strong scattering in water, CVB has a higher transmittance than traditional Gaussian light and can be used for wireless optical communication [14,15,16].

_{01}(linear polarized) mode to an LP

_{11}mode when the transmission wavelength was 1550 nm, with a coupling efficiency of 91%, a mode purity of 92%, and an insertion loss of 0.5 dB. In 2017, Hongdan Wan et al. of Nanjing University of Posts and Telecommunications [31] made an asymmetric mode selection coupler and built a figure-8-shaped mode-locked resonator, obtaining an LP

_{11}mode output with a central wavelength of 1556.3 nm, and a pulse width of 17 ns, with a mode purity of 94.2% and an insertion loss of 0.65 dB. In 2018, Yiping Huang et al. of Shanghai University [32] fabricated an asymmetric mode selection coupler, and built a passive mode-locked fiber laser, obtaining an LP

_{11}mode output with an average power of 75 mW, a coupling efficiency of 89%, and a central wavelength of 1043 nm. In 2018, Mao Dong et al. of Northwestern Polytechnical University [33] made a 1550 nm band asymmetric mode selection coupler, and built a ring-cavity passive mode-locked laser, which realized an LP

_{11}mode output with pulse width adjustable from 39.2/31.9 ps to 5.6/5.2 ps. In 2019, Ya Shen et al. of Beijing Jiao Tong University [34] made an asymmetric mode selection coupler in the 1550 nm band and built a doped annular cavity fiber laser, and obtained an LP

_{01}mode output with a central wavelength of 1550 nm and a mode purity of 94%. In 2019, Zhang Jiaojiao et al. of Nanjing University of Posts and Telecommunications [35] made an asymmetric mode selection coupler to obtain an LP

_{11}mode output, and built a mode-locked laser to achieve an LP

_{11}mode output with a pulse width of 629 ps and a mode purity of 94.5%.

_{01}mode to an LP

_{11}mode. Then, we provide a feasible solution for CVB all-fiber lasers.

## 2. Materials and Methods

_{11}mode in the conical region and the output of the LP

_{11}mode in the coupling region to realize the conversion of the LP

_{01}mode to the LP

_{11}mode.

_{A}− β

_{B}≠ 0, Equation (3) is equal to an effective value within the coupling distance L, that is, only if there are two modes or the same mode with similar propagation constants (equal effective refractive index) can a valid value be obtained, in which case effective coupling occurs.

_{01}and LP

_{11}modes occurs, while in the STMC, taper pulling of the TMF can excite the LP

_{11}mode in the fiber [37]; therefore, there is a coupling of two modes in the coupling region of the STMC, that is, the coupling between the two LP

_{01}modes and the coupling between the two LP

_{11}modes. By controlling the cone size of the TMF, the LP

_{01}mode can be limited to the fiber core with minimal coupling to the other fiber, and the LP

_{11}mode can be leaked into the cladding in order to be more coupled; specific size control is shown in the simulation analysis below.

_{01}and LP

_{11}modes with the fiber diameter (cladding diameter) as in the SMF-28e fiber; the results are shown in Figure 2. According to the principle of total internal reflection, the condition under which the mode is tethered to the core in the SMF-28e fiber is 1.457 < neff < 1.4637. When the effective refractive index of the mode is less than 1.457, the mode leaks into the cladding.

_{01}and mode LP

_{11}when the fiber diameter is 15–85 μm, the blue line is the cladding index of TMF.) by controlling the tensile diameter of the fiber, the LP

_{01}mode in the TMF can be bound in the core, and the LP

_{11}mode leaks into the cladding, so that the LP

_{01}mode is separated from the LP

_{11}mode. According to the simulation results, when the fiber diameter is 75 μm, the effective refractive index of the LP

_{11}mode in the TMF is 1.457; at this time, the LP

_{11}mode begins to leak into the cladding, and LP

_{11}mode coupling begins to occur in the coupling region of the STMC, while the effective refractive index of the LP

_{01}mode is 1.457 < neff < 1.4637. At this time, the LP

_{01}mode is bound to the core for transmission; therefore, the coupling of the LP

_{01}mode occurs only to a minor degree in the coupling region of the STMC. Similarly, when the diameter of the fiber is 29 μm, the effective refractive index of the LP

_{01}mode in the TMF is 1.457, at which time the LP

_{01}mode begins to leak into the cladding, and LP

_{01}mode coupling begins to occur in the coupling region of the STMC. When this happens, the purity of the LP

_{11}mode at port2 decreases. Therefore, in order to minimize LP

_{01}mode coupling in the coupling region and improve the output purity of the LP

_{11}mode, the diameter of the fiber cone should be between 29 μm and 75 μm.

_{11}mode gradually leaks from the core to the cladding for transmission. When the fiber diameter is stretched to 30 μm and 31 μm, the LP

_{11}mode has completely leaked out of the core and, at this time, the LP

_{01}mode is still bound in the core, only minimally leaking into the cladding. It can be seen that when the TMF fiber diameter is stretched to 30 μm and 31 μm, the separation of LP

_{01}and LP

_{11}modes can be effectively realized.

_{11}mode in the first fiber can be almost completely coupled to the other fiber. In this paper, it is said that the optimal coupling length is the shortest distance transmitted when the LP

_{11}mode energy is coupled from the first fiber to the second fiber maximally. According to the simulation results shown in the figure, when the diameter of SMF-28e’s coupling zone is 30 μm, the optimal coupling length is about 4.5 cm and 5.5 cm for the first and second fibers, respectively. Finally, based on the above simulation results of the STMC, we used the fused tapered method to complete the STMC. The physical picture of the STMC is shown in Figure 5.

## 3. Nonlinear Polarization Rotation Principle

## 4. Experimental Setup

_{01}mode output of the current laser cavity, because YDF and SMF have positive dispersion in the 1 μm band, the entire laser works in the full positive dispersion region. The LP

_{01}mode is converted to the LP

_{11}mode by the STMC with the output of the pulse laser, which is received by the CCD after attenuation, and the output of TM

_{01}and TE

_{01}modes can be realized by adjusting PC3.

## 5. Results and Discussion

_{11}mode is 5.56 mW. When PC3 is properly adjusted, we obtain CVBs with a maximum output average power of 5.2 mW. This is illustrated in the mode intensity distribution of the laser output.

_{11}mode is 5.5 mW and the maximum output average power of CVBs is 5.2 mW. This is illustrated in the mode intensity distribution of the laser output.

_{11}mode during the production process of the STMC, the LP

_{11}mode should leak into the cladding as much as possible, while the LP

_{01}mode should be restricted in the fiber core. Thus, the separation of LP

_{01}and LP

_{11}modes is maximized, which requires a specific fiber diameter range in the coupling region, thus limiting the CVB output power of the STMC. According to the simulation results above, when the diameter of the STMC-coupling region is larger than 75 μm, both LP

_{01}and LP

_{11}modes are bound in the fiber core and are not coupled to the second TMF. When the diameter of the STMC-coupling region was 29–75 μm, the evanescent field of the LP

_{11}mode was not strong, while the LP

_{01}mode was still bound in the fiber core, and the optical power coupling was very weak, which resulted in low optical power coupling efficiency and CVB output power. When the diameter of the fiber in the coupling region is further reduced to less than 29 μm, the LP

_{01}mode begins to be coupled to the second TMF. At this time, the output power is increased, but the increased power is the power of the LP

_{01}mode, and the purity of the LP

_{11}mode is reduced. Although the output power is low, the production process of the STMC is simple and the production cost is low, which eliminates the complicated pre-taper process used in the production of mode selection couplers. In addition, the commercial Corning SMF-28e is used to design and manufacture the STMC, so as to avoid the complicated design and production process of 1 μm band TMFs, which has great engineering application potential.

_{01}and TE

_{01}modes can be distinguished by rotating the polarizer. The mode intensity distribution of TM

_{01}and TE

_{01}modes was obtained using a CCD camera (DataRay, WinCamD-LCM). The results are shown in Figure 10. The purity of TM

_{01}and TE

_{01}modes was measured to be 97.18% and 97.07%, respectively. We can conclude that the STMC achieves a high-quality TM

_{01}or TE

_{01}mode output, and the output mode is tunable.

## 6. Conclusions

_{01}mode to the LP

_{11}mode with high purity is designed and produced, and a feasible solution for CVB all-fiber lasers is provided. Finally, we obtain a CVB output with working central wavelengths of 1038.97 nm/1067.72 nm, a repetition of 8.78 MHz, pulse widths of 660 ps/656 ps, and maximum output average powers of 5.25 mW/5.2 mW. By adjusting PC3, we can obtain TM

_{01}and TE

_{01}modes with mode purity values of 97.18%/97.07%, respectively. To our knowledge, this is the first time that a symmetrical two-mode coupler has been obtained using two identical commercial Corning SMF-28e fibers, and the highest mode purity 1 μm all-fiber CVB output was obtained, which minimizes the manufacturing process of mode selection couplers and reduces manufacturing costs. In future work, the process of taper excitation of the LP

_{11}mode should be simulated and analyzed to investigate the factors affecting the mode conversion efficiency of the STMC, and special optical fibers should be designed to improve the mode conversion efficiency of the STMC.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 3.**LP

_{11}mode longitudinal energy flow simulation during TMF cone pulling, diameter (μm) after TMF cone pulling: (

**a**) 30 μm; (

**b**) 31 μm.

**Figure 8.**The output characteristics of mode-locked fiber laser at a pump power of 300 mW (central wavelength: 1038.97 nm): (

**a**) spectrum; (

**b**) output pulse train; (

**c**) single pulse; (

**d**) the change curve of output power with pump power.

**Figure 9.**The output characteristics of mode-locked fiber laser at a pump power of 300 mW (central wavelength: 1067.72 nm): (

**a**) spectrum; (

**b**) output pulse train; (

**c**) single pulse; (

**d**) the change curve of output power with pump power.

**Figure 10.**(

**a**) TM

_{01}mode; (

**b**–

**e**) mode distribution after TM

_{01}mode passes through polarizers in different directions; (

**f**) TE

_{01}mode; (

**g**–

**j**) mode distribution of the TE

_{01}mode passes through polarizers in different directions.

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## Share and Cite

**MDPI and ACS Style**

Yang, B.; Pei, S.; Zhang, T.; Zhang, Y.; Hao, H.; Zhang, K.; Liu, X.; Lan, T.; Yan, A.; Liu, Y.; Wang, Z. High-Mode Purity 1 μm Cylindrical Vector Beam All-Fiber Laser Based on a Symmetric Two-Mode Coupler. *Appl. Sci.* **2023**, *13*, 6490.
https://doi.org/10.3390/app13116490

**AMA Style**

Yang B, Pei S, Zhang T, Zhang Y, Hao H, Zhang K, Liu X, Lan T, Yan A, Liu Y, Wang Z. High-Mode Purity 1 μm Cylindrical Vector Beam All-Fiber Laser Based on a Symmetric Two-Mode Coupler. *Applied Sciences*. 2023; 13(11):6490.
https://doi.org/10.3390/app13116490

**Chicago/Turabian Style**

Yang, Boyi, Siqi Pei, Tianyu Zhang, Yizhuo Zhang, He Hao, Kun Zhang, Xuesheng Liu, Tian Lan, Anru Yan, Youqiang Liu, and Zhiyong Wang. 2023. "High-Mode Purity 1 μm Cylindrical Vector Beam All-Fiber Laser Based on a Symmetric Two-Mode Coupler" *Applied Sciences* 13, no. 11: 6490.
https://doi.org/10.3390/app13116490