Abstract
A generalized scattering matrices theory for open junctions between two dielectric waveguides is given, taking into account free modes and evanescent modes. This theory results in a formula giving the power launched from some incident wave into some guided mode as a cross product between the incident field and the field which is radiated by the junction when it is illuminated by the mode of interest. This formula includes the effect of evanescent modes in the coupling process; actually this effect may be neglected in optics except in the case of a very thin waveguide very close to a strongly divergent GaAs laser. A quantitative comparison between our theory and previous works is done in the case of coupling through the end of a slab waveguide; a coupling formula given by Marcuse proves to be accurate after a very simple correction describing the reflection at the end of the guide; good results are equally obtained from a formula proposed by Snyder. However, noticeable errors can be made when more general fields, such as those encountered in a GaAs-laser waveguide coupling experiment, are approximated by Gaussian fields.
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