Exact step-coupling theory for mode-coupling behavior in geometrical variation photonic crystal waveguides

In this paper, an exact step-coupling theory is developed to describe the modes coupling behavior and lightwaves propagation for the power exchange between the waveguide modes in geometrical variation photonic crystal waveguide. The exact step-coupling theory provides a general description of the mode-coupling mechanism for light waveguide with geometrical variation with complete set of equations and solutions. The coupling equations of the exact step theory are derived and compared with the scattering matrix method, where simulation results show good agreement with an error of less than 2.2%. Subsequently, the coupling equations are applied to different case studies such as slab tapered waveguide and lossy "turn-on" waveguide. The transmission spectrum and field pattern distribution show that the lossy waveguide has a large radiation loss with an average transmission efficiency of less than 5%. The slab tapered waveguide can have more than 90% transmission efficiency with the convex curvature. The exact step-coupling theory can be applied to a vast range of geometrical variation photonic crystal based waveguides and it has quick and accurate convergence simulation results.