演绎了新式步长设置的极坐标系傍轴有限差分光束传播法(FD-BPM)理论,提出一种变换极坐标系FD-BPM思想,使精度更高,计算和分析更简便。基于这些工作,对严格圆弧形二维波导的传输特性进行了综合分析,指出光波在具有相同物理特性、不同曲率半径的波导中传输时,其导模能量与输入能量的比值存在一个极限值,不同波长的光在相同物理结构的波导中传输时,短波比长波更易于形成稳定的导模且损耗小。对S形和C形弯曲的波导计算分析发现:切变损耗的存在使S形波导比相同参数的C形波导导光性能更差,但随着曲率半径的增大,这一差距逐渐缩小,同时指出了不同曲率半径的波导相互连接呈S形或C形时的一些传输规律。对透明边界条件(TBC)对于极坐标FD-BPM的适用性做了分析讨论,认为TBC在应用傍轴极坐标系FD-BPM分析严格圆弧形二维波导时是普遍适用的,不存在反射干扰。

A polar coordinates N-axis finite-difference beam propagation method (FD-BPM) based on a novel step-length setting mode has been deducted,and an idea named variational polar coordinates FD-BPM is advanced in this paper,which will bring higher precision,more convenient computation and analysis. Comprehensive analysis to the rigorous two-dimensional (2D) circle waveguide is achieved. When the light wave is transmitted in the waveguide with different curvatures,a maximum ratio of conductible mode energy to initial energy existing is discovered,and short wave is easier to be formed conductible mode compared with in the same waveguide. Furthermore,investigation about S shape and C shape waveguide has been performed in depth. The propagation capability of C shape waveguide is more excellent than S shape waveguide,as the latter has a higher tangent loss,whereas this distinction reduces while the curvature increasing. Some available propagation rules of S and C shape waveguide with different curvatures are described. The transparence boundary condition (TBC) is thought as practicable while using the polar coordinates N-axis FD-BPM presented in this paper to research the rigorous 2D circle waveguide. So-called boundary echo disturbance caused by TBC,is proved inexistent.