A generalized two-dimensional coupled-mode analysis of curved and chirped periodic structures in open dielectric waveguides

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 structures 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, minimum grating periodicity = 2 microns, maximum grating periodicity = 4.1 microns, and grating grooved length = 65 microns is presented.