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An accurate and numerically stable method based on the coupled-mode theory is presented.By applying the direct global matrix approach to obtain the modal expansion coefficients,this method is numerically stable.In addition,appropriately normalized range solutions are introduced,which resolves the overflow problem entirely.Furthermore,we put forward source conditions appropriate for the line-source problem in plane geometry.As a result,this method is capable of dealing with the scenario where a line source is located inside the region of a deformation.Closed-form expressions for coupling matrices are provided for ideal waveguides.Numerical results indicate that the present method is accurate and numerically stable.Consequently,this model can serve as a benchmark in range-dependent propagation modeling.