Analysis of Bragg grating coupling between two channel waveguides intersecting at a right angle

The coupling between two channel waveguides intersecting at a right angle and having a thin film grating set on their intersection is analyzed. A general expression of the power coupling rate between a mode of the input waveguide and a mode of the other waveguide is derived by integrating, on a region surrounding the intersection, an equation equivalent to the classical coupled mode equations. It is shown that the condition required for maximum coupling between the higher modes differs from the condition for maximum coupling between the fundamental modes because of the transverse propagation constants. Approximate expressions of the maximum values of the intermodal coupling rates are given. If the grating is such that the fundamental mode coupling is maximum, the other intermodal coupling rates decrease rapidly with the order numbers. The effects on the intermodal coupling rates caused by a shift of the grating orientation are discussed.