Analytical model of a corrugated optical waveguide

An analytical model of the diffraction energy exchange between the radiative and the waveguide modes in a planar optical waveguide corrugated by a waveguide grating with an arbitrary form of teeth is developed on the basis of the coupled-wave method. It is shown that the mechanism of the energy exchange between the modes is determined by the partial interaction of all components of the spatial frequency spectrum of the waveguide modes with the corresponding components of the spatial frequency spectrum of the grating. It is established that gratings with an asymmetric tooth profile providing a shift of the peak of the spatial frequency spectrum toward matching are characterized by a higher diffraction efficiency α; however, at small thicknesses δ of the waveguide grating, the efficiency is almost independent of the tooth profile. It is shown that gratings with a symmetric profile give on average a decreasing dependence α(δ), while gratings with an optimized asymmetric profile yield a monotonically increasing saturating dependence α(δ).