Bending loss analysis of TE and TM polarized fields in planar lightwave circuits

Planar lightwave circuits (PLCs) which include several kinds of the waveguide need bent waveguides to connect two straight waveguides. Optical power is lost at the entrance and exit of the bent waveguides and by the bending effect. The bending loss contains both these losses. 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 the paraxial wave equations. Then, TE and TM polarized fields in the single-mode planar waveguides are analyzed by 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 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