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Applications to equip semiconductor phased-array wavelength demultiplexers with nonbirefringent waveguides are increasing. In several applications, the waveguides are multimodal and elimination of first-order mode excitation is required for their design. The optimized offset for eliminating the first-order mode excitation at the junction of straight and curved waveguides with a two-dimensional (2-D) structure is analyzed theoretically. We assume that the waveguide has a laterally symmetric index profile. By the perturbation method, the offset is obtained to the first order in the inverse of the bending radius. The offset is simply expressed by the effective refractive indices of the straight waveguide.