Local field analysis of bent optical waveguides

The scalar local field equations are derived from the Maxwell's equation in a bent local coordinate system, and the field transformation function for the TM (or the x‐polarized) modes in our recent papers is corrected as well. It is found that no pure geometry birefringence can be produced if the gradient‐index term of local field equations is neglected when the waveguide we considered is weakly guiding.