Analytical qualitative modeling of passive and active metamaterials [Invited]

Metamaterials (MMs) are artificial media tailoring the propagation of light by a design of a unit cell (meta-atom, MA). There is the evident inclination in favor of numerical methods in the description of the optical properties of MMs at the expense of physical intuition. It is shown that complementary to the numerical ones, qualitative models can provide a deeper understanding of the basic physical processes. The phenomenological approach to the homogenization resulted in three possible representations of Maxwell equations: Casimir, Landau-Lifshitz, and new toroidal ones. The multipole approach has been formulated and extended to the case of coupling between MAs, including random MA positioning. It has been shown that the quadrupole moment inherently introduces nonlinear (second-order) material response. The multipole approach has been applied for the case of the quantum MM to the coupled carbon nanotubes, and for the case of MAs to regular and stochastic properties of the nanolaser (spaser), and monochromatic plane wave propagation in the MM consisting of nanolasers. (C) 2017 Optical Society of America