Loss coefficients for blazed waveguide corrugations

The coupling between bound modes of a corrugated dielectric-slab waveguide and modes of the radiation continuum is analysed by a perturbation method. Loss coefficients that account for the power coupled into radiation modes by any Bragg order of corrugations with an arbitrary profile are determined for the bound modes. Agreement is found with published results for sinusoidal profiles. The proportion of power coupled out through each dielectric interface of the slab waveguide is also determined. When the corrugation has an asymmetric (blazed) profile and coupling to radiation modes is by the first Bragg order, more power can be coupled out through one interface than the other, even if the refractive indices of the cladding regions are equal. If the coupling is by a higher Bragg order, then the division of power can be considerably more unequal than for first-order coupling, with the greater proportion leaving the side of the waveguide opposite to that for first-order coupling. The ratio of the power coupled out the two sides varies cyclically with radiation wavelength.