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Based on the spherical vector wave functions, we research the internal and near-surface fields of a homogeneous chiral dielectric sphere to a plane wave. The expansion coefficients of scattered fields and internal fields are obtained through the boundary condition at the sphere interface. The logarithmic derivatives of Ricatti-Bessel functions are introduced in order to avoid the numerical overflow of high-order terms or larger argument spherical Bessel function and the problem of the accumulative error in the matrix calculation when calculate the internal and scattering coefficients. Thus, the internal and near-surface fields of a homogeneous chiral dielectric sphere can be studied numerically.