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A method is presented for obtaining the scattered field due to a beam incident on a layered structure or on a dielectric grating whose properties vary slowly along a longitudinal direction. The scattered field is expressed in terms of a Green's function whose form is particularly simple for a large class of practical problems involving laser beams incident on structures capable of guiding leaky waves. The incident beam may then strongly couple to the leaky wave, thus producing a scattered field that contains a specularly reflected component and a diffracted component of the leaky-wave type. The presence of the latter component may cause the resulting scattered field to be considerably different from the field of the incident beam. A judicious choice of the leaky-wave structure can be used to produce a scattered field that exhibits any of a wide range of distributions. The method developed herein is illustrated by means of structures whose leakage-properties vary linearly. The results can be utilized either for efficiently coupling a beam into a surface wave, or for splitting the incident beam into two separate but closely similar outgoing beams, both applications being discussed in detail.