Coupling efficiency of butt-joined planar waveguides with simultaneous tilt and transverse offset

An efficient method has been proposed for evaluating the junction loss between two nonidentical arbitrarily graded-index planar optical waveguides caused by simultaneous transverse and angular misalignments. The salient feature of the method is an exact representation of the modal. Fields which is particularly adapted to loss evaluation at imperfect junctions. The power transmission coefficient at the junction is expressed via the overlap integral method as a weighted sum of simple Laguerre-Gaussian functions, the weight factors being determined by solving a linear matrix eigenvalue problem. The present formulation has a very broad scope of validity and can be used for the modal analysis of integrated optical planar components such as waveguide lenses and to estimate the coupling efficiency of more practical fiber-to-channel butt-joints. The method can also he used to test the accuracies of other approximate methods such as those based on the Gaussian approximation of the lowest order planar waveguide mode.