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. In this paper, the key modal qualities contain electromagnetic fields' distributions, the effective refractive index, and its tendencies. And the modal sensitivity is based on the partial derivative of the effective refractive index ( $\partial$ n_eff/ $\partial$ n_i and $\partial$ n_eff/ $\partial$ r_i). The derivative rule of special function allows analyzing the sensitivity of modes. Furthermore, four qualitative deductions are derived during the process, including the qualitative analysis of modes and their variation, several of which are supported with previous experiments. Our work is beneficial for exploiting new fiber and researching relative fiber sensors.

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