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Grating-coupled radiation in GaAs:GaAlAs lasers and waveguides is analyzed. A general formulation is developed for arbitrary-shaped gratings which need not be small in size. Two methods are used to solve the resulting equations in the case of rectangular-shaped gratings. The first is a perturbation technique and the second is iterative in nature. The iterative procedure converges to a numerical exact solution in many cases of practical interest and indicates that the perturbation results are quite accurate. Curves are presented for radiated power from traveling waves as a function of grating tooth height, tooth width, refractive index, waveguide thickness, and period for rectangular gratings in heterostructure waveguiding geometries. It is shown that radiation is not a monotonically increasing function of tooth height, but rather maxima occur when the teeth are half the optical wavelength in the material. Also, in particular geometries with an air:GaAs grating interface, radiated power of a mode can exceed 100 cm-1.