1. General Step-Index Optical Fiber Modal Characteristic and Sensitivity Analysis
- Author
-
Yundong Zhang and Xun Xie
- Subjects
Optical fiber ,Modal ,Implicit function ,law ,Fiber (mathematics) ,Mathematical analysis ,Partial derivative ,Function (mathematics) ,Boundary value problem ,Sensitivity (control systems) ,Atomic and Molecular Physics, and Optics ,Mathematics ,law.invention - Abstract
An analytical approach about the general type of step-index optical fiber modes and their variations is presented in this paper. The theoretical model is solved through our analytical method. With the boundary conditions, a composite equation set is established and solved. The precise results of all modes are achieved with a high-precision numerical solution. The modal characteristic contains the distributions of electromagnetic fields, the effective refractive index, and its tendencies. The modal sensitivity is based on the former and the partial derivative of the effective refractive index (neff/ni and neff/ri). The derivative rule of implicit functions and determinant function allows our method to analyze the sensitivity of modes. Furthermore, four qualitative deductions are derived during the process, including the qualitative analysis of modes and their constraints, supporting previous experiments. Our work is beneficial for exploiting new fiber and researching relative fiber sensors.
- Published
- 2022