The expression for calculating mode effective indices of hollow-core anti-resonant fibers in non-resonant wavelength regions

摘要

We deduce the characteristic equations of different modes in the hollow silica tube fiber with an infinite wall thickness from Helmholtz equations and obtain the expression which is used to calculate the effective refractive indices of different modes by approximately solving the simplified characteristic equations, step by step. We further obtain the modified expression which can be used to calculate the effective refractive indices of different modes in a hollow-core anti-resonant fiber based on the original expression. Simulation results show that the original expression can accurately calculate the mode effective refractive indices of the hollow silica tube fiber with an infinite wall thickness and the effective refractive indices of different modes in a hollow-core anti-resonant fiber calculated by the modified expression are very close to those obtained by finite element method in the non-resonant wavelength regions. This work is essential to the theoretical study and structure design of hollow-core anti-resonant fiber.