Analysis of an intermediate-mode-assisted directional coupler using Bloch theory

The exact numerical solution of the intermediate-mode-assisted directional coupler problem is obtained using the Bloch wave approach. The approach is based on a calculation of the Bloch waves and their matching with the ideal modes of an uniform waveguide. The approximate results obtained from the paraxial wave equation and from the three-mode model are compared with the exact ones. It is shown that the paraxial approximation, as well as the three-mode approximation, provide only a qualitatively correct physical picture. Using the Bloch wave approach, however, one obtains quantitatively correct results. It is demonstrated that one can control the exchange of power between two distant identical coupled waveguides using an embedded periodic structure along the z direction. The power exchange control is based on a symmetry of Bloch waves and results from the interaction of the lowest order waveguide modes with the high-order modes.