Solntsev, AlexanderKruk, SergeyNeshev, DragomirSukhorukov, AndreyKivshar, Yuri2015-12-10September9789526761152http://hdl.handle.net/1885/59569We develop a systematic procedure for deriving the coupled-mode equations describing the spatial evolution of the slowly-varying amplitudes of electromagnetic modes in nonlinear periodic structures with loss and gain. Our approach is rigorously based on the Lorentz reciprocity theorem, and therefore it can be applied to a broad range of structures with metal and dielectric non-magnetic components, including plasmonic waveguides and metamaterials. We verify our approach through a direct comparison with the earlier analysis based on a direct perturbation theory for planar metal-dielectric structures, and furthermore demonstrate the application of our method to the three-dimentional multilayer fishnet metamaterials.201310.1109/MetaMaterials.2013.68090132015-12-10