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The possibility of designing lossless discontinuities of optical waveguides is investigated by finding solutions that satisfy time reversibility of guided modes. It is found that these junctions are only possible for the TE modes. The use of the design condition for these junctions as a bound allows minimizing radiation loss. The results show that it is possible to minimize radiation loss under strong mode-coupling conditions. Two previously unreported designs are shown to significantly reduce radiation loss in grating couplers. The first design uses two coherently coupled gratings, instead of a single grating, for a 2 × 2 grating-assisted backward coupler. The second design uses an index-modulated buffer layer between the core and substrate of an index-modulation-grating coupler.