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A generalized two-dimensional coupled mode analysis of curved and chirped quasi-periodic structures in planar dielectric waveguides has been formulated. This analysis can be used to design curved and chirped quasi-periodic stuctures for obtaining phase matched interaction between two specific guided-wave beams. Alternatively, it can be used to calculate the amplitude and the phase of the diffracted guided-wave beam for a given quasi-periodic structure and for a specific incident beam, including the effect of the phase mismatch. The numerical example of linear chirped grating lenses with F= 10, f= 20 mm, Lambdamin = 2mu m, Lambdamax = 4.1mu m, and grating grooved length= 65mu m is presented.