Homogenization of nanostructure waveguides in the non-resonant and resonant regimes

A recent break-through in the domain of photonic integration is the use of sub-wavelength waveguide grating structures (SWG) to engineer the refractive index of integrated components. SWG has met with great success in reducing coupling loss, insertion loss and crosstalk; and increasing the operational bandwidth of on-chip components. In photonic crystals (PhC), a waveguide is typically created by introducing a line defect. SWG is a different sub-category of PhC, also known as metamaterials, that operate at frequencies below the band-gap and requires no surrounding lattice to guide. The fundamental principle is the propagation of the Floquet-Bloch modes of the SWG. Current tools for component simulation require sub-wavelength computational meshes that can only be applied to regions a few wavelengths in extent. Modeling at larger scales requires an abstraction of the properties of the nanostructure, which summarizes its properties pertinent to the larger scale and smoothes over the detail at the smaller scale.