为了研究线性散焦宇称-时间对称双通道波导中分数阶衍射饱和非线性下孤子的模式以及孤子的传输与控制，通过改进的平方算子迭代法对含有线性势的分数阶饱和非线性薛定谔方程进行数值计算得到孤子模式，傅里叶配置法判断孤子线性稳定性，并利用分步傅里叶法模拟仿真孤子的传输。研究结果表明：在散焦饱和非线性中，该宇称-时间对称波导可支持稳定的双峰灰孤子模式。随着饱和非线性系数和传播常数绝对值的增大，双峰灰孤子的背景强度增大，灰度值减小，功率增大。Lévy指数、增益/损耗系数和饱和非线性系数的增加会导致孤子的横向能流密度变化增大，但在波导通道位置处接近于0。在聚焦饱和非线性下，线性散焦宇称-时间对称波导对亮孤子光束具有控制作用。当光束在波导中心输入，孤子以呼吸子的形式长距离传输；在非波导中心输入，光束以初始输入位置为边界振荡传输。随着饱和非线性系数的增大，光束的振荡频率增加，光束宽度变宽，峰值强度减小。宇称-时间对称波导势阱深度的增加会导致光束的振荡频率增加，峰值强度增加。该研究结果可为宇称-时间对称波导对光束的控制提供一定的理论参考。

In this paper, based on the normalized saturable nonlinear fractional Schr?dinger equation with linear potential, the transmission and control of solitons in linear defocusing two-channels PT-symmetric waveguide with fractional diffraction and saturable nonlinearity are studied. The equation can be numerically solved by the modified squared-operator iteration method to obtain soliton modes. The Fourier collocation method is used to judge the linear stability of soliton, and the split-step Fourier method is used to simulate the transmission of soliton in the PT (Parity-Time) -symmetric waveguide. According to the requirements of PT-symmetric, the refractive index distribution of two-channels PT-symmetric waveguide is even symmetric and the gain/loss distribution is odd symmetric. In addition, the refractive index of two channels is smaller than that of substrate, so it has the defocusing property. The results show that the PT-symmetric waveguide can support the stable double gray solitons modes in the defocusing saturable nonlinearity. The real part of double gray solitons is even symmetric and the imaginary part is odd symmetric due to the effect of PT-symmetric waveguide. The Lévy index and gain/loss coefficient of PT-symmetric waveguide have little effect on the shape of double gray solitons modes. But the saturable nonlinear coefficient has a great influence on the soliton modes. With the increase of saturable nonlinear coefficient, the background intensity of double gray solitons increases. The Lévy index, gain/loss coefficient, and saturable nonlinear coefficient can affect the transverse energy flow density of solitons. With the increase of Lévy index, gain/loss coefficient, and saturable nonlinear coefficient, the transverse energy flow density of solitons changes more sharply, but it is close to 0 infinitely at the position of waveguide channel. This means that the energies on the left and right of channels reach a balance, thus the double gray solitons are formed. At the same time, the propagation constant also has an effect on the double gray solitons. With the increase of the absolute value of propagation constant, the background intensity of the solitons increases, the gray value decreases and the power increases. Through linear stability analysis, the stable double gray solitons can be obtained at a low gain/loss level. The double gray solitons can transmit stably forward in the waveguide, keeping the width and intensity of original mode unchanged. The width of solitons increases with the increase of saturable nonlinear coefficient and propagation constant.In the focusing saturable nonlinearity, the two-channels PT-symmetric waveguide can control the transmission of bright soliton beams. When it inputs from the center of waveguide, the beam is transmitted as a respirator. With the increase of saturable nonlinear coefficient, the frequency of respirator decreases, the width of beam widens, and the peak intensity decreases. When it doesn't input from the center of waveguide, the beam occurs oscillation with the initial input position as the boundary. This is because the refractive index in the center is the largest, decreasing gradually away from the center between the two-channels PT-symmetric waveguide. This structure is similar to that of gradient index fiber, which has linear focusing effect on beam. When the input is not in the center, under the focusing effect of waveguide, the beams propagate toward the center, through the center to the other, and then reflect back. Thus, the propagation of beam occurs oscillation between two channels. With the increase of saturable nonlinear coefficient, the oscillation frequency of beam increases and the width widens. In addition, the increase of the absolute value of potential good depth in PT-symmetric waveguide will lead to the increase of oscillation frequency and peak intensity of beam. These results can provide some theoretical reference for the application of two-channels PT-symmetric waveguide in all optical control.