For the purpose of accurately investigating the dispersion and transmission characteristics of thin-clad Chirped LongPeriod Fiber Gratings（CLPFGs）

this paper analyzes the differences of the effective Refractive Indices（RIs）and the center wavelengths in the core mode yielded from the two-and three-layered medium models of a uniaxial-crystal fiber.On the basis of these differences

it numerically analyses the effects of different cladding radii and cladding mode order on CLPFG dispersion properties.The results show that the core-mode effective RIs of the two fiber medium models differ significantly when the cladding radius and cladding mode order are small and for the fiber gratings of both models

either reducing the cladding radius or increasing the number of the cladding mode order is conducive to the increase of dispersion.The analytical method and conclusions presented in this paper provide a theoretical basis for the analysis and design of CLPFG.