从有限高斯背景下空间暗光孤子诱导折射率分布出发，用等效衰减矢量法得到它所自诱导的波导的色散特性。并与理想情况的无限背景下空间暗光孤子诱导波导的色散方程进行了比较。结果表明，当高斯背景越来越宽时，它与无限背景下的结果越来越接近。为在全光器件中实际应用提出了理论依据。 Starting from the spatial dark soliton-induced refractive index distribution under the finite Gaussian background, the chromatic dispersion characteristics of the self-induced waveguides are obtained by the equivalent attenuation vector method. And compared with the dispersion equation of space-dull soliton-induced waveguide under the infinite background of the ideal situation. The result shows that when the Gaussian background gets wider and wider, it becomes closer to the result under the infinite background. It provides the theoretical basis for the practical application in all-optical devices.