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The characteristics of the output and input couplers for a dielectric-slab waveguide grounded by a corrugated-conducting surface are investigated for the transverse electric mode, taking into account the small gain or loss in the dielectric. A pair of canonical equations valid for a distributed coupler with a guided wave, an incident wave and a radiated wave are derived, and all the coupling coefficients are expressed in terms of the physical parameters of the coupler. The coupling coefficients are shown to satisfy four general properties which lead to the principle of power conservation and reciprocity. The analyses of the couplers, based on the solution of the canonical equations subject to the appropriate terminal conditions, lead to the determination of the various design parameters such as the output coupling efficiency, and the optimum incident angle and grating length for the maximum input coupling efficiency. The effects of the gain or loss in the dielectric on the abovementioned parameters and on the amplitude profile of the radiated wave are investigated. The coupler with the grating on the conducting surface is compared with the coupler having the grating on the film-cover interface.