Grating couplers provide an attractive method for the excitation of optical thin-film waveguides. We present here a perturbation analysis of etched or deposited grating couplers based upon both the transmission line and the Green's Function approaches, which predict the coupling efficiency, the output radiation beamwidth, the angular dependence of excitation, and the intensities of the other orders of the diffracted beams as functions of the grating periodicity, grating groove depth, and excitation direction. It is found that the maximum excitation efficiency is 81 percent, that high efficiency can be achieved by excitation from the substrate, and that higher efficiency is obtained when the radiation leakage to the side orders is minimized.
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