We have applied the effective index method to reduce the two-dimensional (2-D) refractive index profile into the 1-D refractive index structure and modified the wave equations to obtain the paraxial wave equations. Then, transverse electric (TE) and transverse magnetic (TM) polarized fields in the curved single-mode planar waveguides are analyzed by using the scalar beam-propagation method (BPM) employing the finite-difference method with a slab structure. The bending loss in bent waveguides is analyzed for optical fields obtained from the BPM and comparisons are made between the loss for the waveguides; with various radius of curvature and the refractive index difference. The outward shift of the optical field, which is generated at the connection between a straight and a bent waveguide, is obtained from the results of calculation of location of the maximum optical intensity. The transition loss can be reduced by introducing an optimized inward offset at a straight-to-bend junction. The birefringence for TE and TM polarized fields in bent waveguides is calculated from the phase difference of the optical fields. The wavelength shift due to the birefringence of TE and TM polarized fields in bent waveguides is also calculated.