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We propose a set of more efficient basis functions prolate spheroidal wave functions of order zero, comparing with the conventionally used Chebyshev polynomials expanding the optical fields in interior subdomains, to improve significantly the convergence rate of pseudospectral mode solver for solving dielectric optical waveguides with step-index. The bandwidth parameter, which influences strongly the computational accuracy, in prolate spheroidal wave functions is also optimized in this work. First, the numerical examples of two-dimensional waveguides show that the new basis functions achieve faster convergence than Chebyshev polynomials. Furthermore, a 3-D rib waveguide based on the full-vectorial formulations demonstrates that the proposed approach reduces 23% of computational time and 25% of memory storage for obtaining the convergent values of the effective index for the tenth order quasi-TE and quasi-TM modes.