The distributed coupling between one guided wave and a finite number M of freely propagating waves is considered as it applies to optical-grating couplers and prism couplers. Starting from a scattering-matrix representation, general amplitude and power relations among the various incident and outgoing waves are discussed. These relations are based on the reciprocity, symmetry, uniformity, or losslessness of the coupler. It is shown that the high efficiency (80%) of the prism coupler can also be obtained with a grating coupler, provided that the guided wave interacts with only one free wave (M = 1). Various methods of achieving this are proposed. Among them is a scheme that yields a wavelength-selective coupler. The optimization of couplers is discussed for a number of typical coupling situations. The effects of losses in couplers are also treated.
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