The coupled mode equations governing the interaction of the guided magnetic waves propagating in opposite directions along a ferrimagnetic film having a periodic array of shallow rectangular grooves on one of its surfaces are deduced using quasihyphen;optical techniques for the case in which the magnetization is normal to the surfaces of the film. Effects caused by the deviation of the wave frequency from the Bragg frequency and by the presence of small magnetic losses are also taken into account. For a surface corrugation extending only for a finite length along the film, the longitudinal boundary value problem is solved to obtain the reflection, the transmission, and the absorption coefficients. The coupled mode equations are found to yield correctly the power conservation relation.
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