Grating Theory Approach to Optics of Nanocomposites

Nanocomposites, i.e., materials comprising nano-sized entities embedded in a host matrix,
can have tailored optical properties with applications in diverse fields such as photovoltaics, biosensing,
and nonlinear optics. Effective medium approaches such as Maxwell-Garnett and Bruggemann
theories, which are conventionally used for modeling the optical properties of nanocomposites,
have limitations in terms of the shapes, volume fill fractions, sizes, and types of the nanoentities
embedded in the host medium. We demonstrate that grating theory, in particular the Fourier Eigenmode
Method, offers a viable alternative. The proposed technique based on grating theory presents
nanocomposites as periodic structures composed of unit-cells containing a large and random collection
of nanoentities. This approach allows us to include the effects of the finite wavelength of
light and calculate the nanocomposite characteristics regardless of the morphology and volume fill
fraction of the nano-inclusions. We demonstrate the performance of our approach by calculating
the birefringence of porous silicon, linear absorption spectra of silver nanospheres arranged on a
glass substrate, and nonlinear absorption spectra for a layer of silver nanorods embedded in a host
polymer material having Kerr-type nonlinearity. The developed approach can also be applied to
quasi-periodic structures with deterministic randomness or metasurfaces containing a large collection
of elements with random arrangements inside their unit cells.