Thick Dielectric Grating on Asymmetric Slab Waveguide

Diffraction gratings deposited on top of a thin-film waveguide are useful as input and output couplers. 1,2 A guided wave traveling in the thin-film waveguide is scattered out into the two regions (air and substrate) adjacent to the film as it encounters the region of the diffraction grating. Ordinarily, the power that is scattered out of the thin-film guide splits up into several grating lobes; the number and strength of these lobes depends on the grating period D, the depth of the grating 2a, and on the shape of its teeth, as shown in Fig. 1. The relationship between the propagation constant of the guided wave, the index of refraction m, of the medium into which the grating lobe escapes at angle dmii and the grating period length D is expressed by the following equation, 2 cos Bmi = fl - (2-irm/D) . (1)