Obliquely incident wave coupling on finite-aperture waveguide gratings

The problem of oblique incidence of plane waves and Gaussian beams on finit e-aperture gratings (the number of grooves and their length and depth are a ll finite) in slab waveguides is analyzed by means of a four-wave two-dimen sional coupled-made theory (2D-CIMT). This model considers the finite apert ure of the gratings and the correct simultaneous interaction among all four relevant waves (TE+, TE-, TM+, and TM-) by means of Bragg diffraction at o blique incidence. The grating's geometry and boundary conditions are proper ly accounted for, and the problem is solved numerically by a finite-differe nce method. Near-field and far-field distributions, as well as reflection a nd transmission (power) coefficients (as functions of the plane-wave incide nce angle), are calculated. The model is compared with the degenerate case of two-wave coupling that considers interaction only between pairs (e.g., T E+ <-> TE-), and significant differences may be observed. Compatibility and differences between the 2D-CMT and the one-dimensional CMT (grooves with i nfinite length) are also presented, in addition to the influence of the bea m width and the groove length on the emerging waves. The analysis is genera l and can be performed on many kinds of realistic beams, grating shapes, an d applications. (C) 1999 Optical Society of America [S0740-3232(99)01902-X] .