Coupling coefficients of synchronous modes on two arbitrarily-shaped weakly-guiding optical waveguides

Usually, coupling coefficients of parallel weakly-guiding waveguides of arbitrary crosssectional shape with uniform infinite cladding are calculated via two-dimensional overlap integrals of the refractive-index distribution of the concerned waveguide core and the field distributions of the two coupling isolated-core modes. In this paper it is shown that, in the case of synchronous coupled modes, the calculation can be reduced to the evaluation of a line integral involving only the field functions. Convenient formulations are obtained for typical forms of the field representation.