Calculation of cutoff frequency of arbitrary weak guidance optical waveguides by extended boundary condition method

The extended boundary condition method is applied to both circular and elliptical regions for calculating cutoff frequencies V_c of weakly guiding optical waveguides, which consist of a uniform cladding and a core with arbitrary shape and index profile. The frequency shift formula method is explained by means of the extended boundary condition method on circular regions. Comparing the method with analytic and other rigorous methods, we show that it is indeed a powerful tool. Numerical results confirm that the mode designation and arrangement order in elliptical and rectangular waveguides are, in general, dependent on the aspect ratio.