Objective Microstructure fiber (MF) has wide applications in fiber laser, fiber sensing, optical communication, and nonlinear optics owing to the controllable periodic arrangement of air holes in the cladding. It has new optical properties that distinguish it from traditional fibers, such as flexible and controllable dispersion, high birefringence, and high nonlinearity. However, the presence of dispersion will severely limit optical fiber transmission. The dispersion compensation fiber with large negative dispersion can effectively solve this problem. The birefringence of optical fiber has received a lot of attention as a result of the development of new transmission technology. There has been little research in the ~3 μm band on dispersion compensation and birefringence control. High birefringence and large negative dispersion at ~3 μm can be achieved simultaneously in another glass matrix, such as silicate glass and tellurite glass, by adjusting the waveguide structure parameters and the structure optimization design of optical fiber. However, Si-O-Si has strong vibration absorption in the infrared band, so the silica matrix material cannot meet the requirements of ~3 μm application. Moreover, tellurite glass has poor mechanical strength, so drawing fibers is difficult. Bismuthate glass has a broad infrared transmission region, good thermal stability, low phonon energy (approximately 750 cm ^-1), and a high refractive index. Bismuthate glass is considered an ideal gain medium material in the midinfrared band. Therefore, we proposed a new bismuthate glass microstructure fiber with high birefringence and large negative dispersion in the ~3 μm band. The proposed MF has some guiding significance for dispersion and birefringence control fiber lasers or fiber sensing in the ~3 μm band.

Methods Fig.1 shows the cross-section of the proposed MF. The MF consists of three regions, rectangular fiber core, inner cladding, and outer cladding. The main structure parameters of MF include air hole diameter (d_in, d_out), air hole lattice parameter (Λ_out, Λ_in, and Λ_out/Λ_in=3), and dimensionless parameter (d_out/Λ_out, d_in/Λ_in). To achieve the high birefringence, we designed a solid rectangular core with a 3∶2 aspect ratio. Through the unique rectangular arrangement structure (the ratio of length to width is 3∶2), the dispersion characteristics of MF can be controlled flexibly by the d_out/Λ_out, d_in/Λ_in. This method is used to establish the model of MF in this work, along with the perfectly matched layer boundary condition. Using the appropriate formula, we calculate the dispersion coefficient, birefringence, and effective mode field area. Note that the lattice constant of the inner cladding Λ_in=Λ_out/3 was found to be optimal in controlling both dispersion and birefringence.

Results and Discussions We investigated the effect of Λ_out on the dispersion and birefringence characteristics of MF when the structure parameters are d_out/Λ_out=0.68, d_in/Λ_in=0.86, Λ_out/Λ_in=3 (Fig. 4) and the peak positions of dispersion and birefringence change with different Λ_out. Meanwhile, the effect of Λ_out on the effective mode field area of MF under the same structure parameters was investigated (Fig. 5). When the structure parameters are Λ_out=1.5 μm, d_in/Λ_in=0.86, Λ_out/Λ_in=3, the influence of d_out/Λ_out on the dispersion, birefringence characteristics, and effective mode field area of MF were also studied (Fig. 6, Fig. 7). When the d_out/Λ_out is decreased from 0.70 to 0.68, the peak value of negative dispersion of y- and x-polarized fundamental modes increases by 74.3% and 50.16%, respectively. Further, when d_out/Λ_out decreases to 0.65, y- and x-polarized fundamental modes appear anomalous dispersion at 2300~2500 nm and 2700~2900 nm, respectively. Finally, we studied the influence of d_in/Λ_in on characteristics of MF (Fig. 8, Fig. 9) when the structure parameters are Λ_out=1.5 μm, d_out/Λ_out=0.68, Λ_out/Λ_in=3. In order to achieve large negative dispersion, d_in/Λ_in must larger than d_out/Λ_out. In addition, the effect of d_in/Λ_in on the dispersion and birefringence characteristics of MF is opposite to that of Λ_out and d_out. Similarly, Λ_out, d_out/Λ_out, and d_in/Λ_in has different effects on the effective mode field area of MF.

Conclusions In this paper, a new bismuthate glass microstructure fiber with high birefringence and large negative dispersion at ~3 μm band was designed. The full-vector finite element method and the perfectly matched layer boundary condition are used to investigate the effect of waveguide structure parameters on the birefringence and dispersion characteristics of the proposed fiber. The structure consists of an inner cladding with rectangular air holes and an outer layer with hexagonal air holes. The results indicated that the birefringence of the fundamental mode can reach 0.0296 and the dispersion coefficient of x-polarized fundamental mode can reach ~3204.75 ps·nm ^-1·km ^-1 at 2740 nm (corresponding to Er ³⁺∶ ⁴I_11/2 → ⁴I_13/2 emission band), when the structure parameters of MF are Λ_out=1.5 μm, d_out/Λ_out=0.68, d_in/Λ_in=0.86, and Λ_out/Λ_in=3. Furthermore, by changing key structural parameters of the MF, dispersion, and birefringence can be flexibly controlled over a relatively wide range. The results show that the proposed fiber has some guiding significance in the ~3 μm band for dispersion and birefringence control fiber lasers or fiber sensing.