A numerical solution, using the general formulation of the transcendental equation and eigenmode values, is proposed to demonstrate number of strongly guided modes propagating in sapphire crystal fibers (SCF). The SCF is considered to have hexagonal geometry of a single crystal and multimode step-index profile. Several distinguished characteristics are naturally embedded in SCF compared to other ordinary optical fibers. The eigenmodes of the SCF are numerically determined and are a combination of transverse electric, transverse magnetic, and hybrid modes. The numerical solution for wave-guiding in ultra-violet (UV), visible infrared (VIS/IR) spectrum, is investigated by the number of modal propagation under strongly guided approximation. The cross-sectional energy distribution of fundamental mode (FM) and higher order modes (HoM) describe the variation of the effective mode index with respect to the change in the core radius. The proposed waveguide is of ~35micron radius, exhibit −0.077 dB/m confinement loss at 200 nm. The simulations in this study are performed by the COMSOL multi-physics® software.

提出了一个使用超越方程和本征模值的一般公式的数值解，以证明在蓝宝石晶体纤维（SCF）中传播的强导模的数量。SCF被认为具有单晶和多模阶跃折射率分布的六边形几何形状。与其他普通光纤相比，SCF中自然嵌入了几个杰出的特性。SCF的本征模是通过数值确定的，并且是横向电，横向磁和混合模的组合。通过在强引导近似下的模态传播数，研究了在紫外线（UV），可见红外（VIS / IR）光谱中波导的数值解。基本模（FM）和高阶模（HoM）的横截面能量分布描述了有效模指数相对于芯半径变化的变化。拟议的波导半径约为35微米，在200 nm处表现出-0.077 dB / m的限制损耗。本研究中的仿真由COMSOLmulti-physics®软件执行。