A variational coupled-mode theory including radiation loss for grating-assisted couplers

We calculate higher order effects such as frequency shifts and radiation loss in grating waveguides and grating couplers. The approach follows a vector variational principle which incorporates the Floquet components correct to first order. It is unnecessary to bring radiation modes into the formalism. This yields a simple coupled-mode formulation which includes attenuation due to radiation loss, and is correct to third order in the index contrast of the grating. Numerous examples are given which show excellent agreement with rigorous numerical simulations.