Coupled mode theory for resonant excitation of waveguiding structures

Resonant coupling of light beams via high-index media or gratings to planar waveguiding structures are of interest for both applications and from a th eoretical point uf view. Coupled Mode theory (CMT) can give an accurate des cription of the coupling process in terms of relatively simple expressions involving often a large number of coupling parameters. In this paper it is shown, using lime reversal and energy conservation how these parameters are interrelated. The evaluation of the remaining independent parameters is sh own to be possible using a few reflection and transmission coefficients for incoming plane waves. including in the calculations, if present, the effec t of the: grating. Further, it is proved that under certain condition a gra ting coupler may show exactly 100% reflection. Analytical expressions for t he reflected and transmitted beams and the amplitude distribution of the ex cited mode are given for the case of incoming Gaussian beams. A few applica tions of the theory and considerations on its applicability are presented.