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