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 theoretical point of view. Coupled Mode theory (CMT) can give an accurate description 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 time reversal and energy conservation how these parameters are interrelated. The evaluation of the remaining independent parameters is shown to be possible using a few re ̄ection and transmission coecients for incoming plane waves, including in the calculations, if present, the e€ect of the grating. Further, it is proved that under certain condition a grating coupler may show exactly 100% re ̄ection. Analytical expressions for the re ̄ected and transmitted beams and the amplitude distribution of the excited mode are given for the case of incoming Gaussian beams. A few applications of the theory and considerations on its applicability are presented.