The evanescent coupling between two-parallel circular dielectric waveguides with a weak rotatory effect is analyzed by using a singular perturbation technique which is based on the vectorial wave formulation.The coupled-mode equations are derived in closed form which satisfies the Maxwell equations and boundary conditions for the composite dielectric waveguide system within the first-order perturbation.The directional coupling and polarization conversion take place separately in the weakly guiding two-parallel weak waveguides with a weak rotatory effect.The directional coupling is governed by the coupling coeffcients κ

whereas the polarization conversion angle is controlled by the coupling coeffcient κ×.