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, bio-sensing, 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 Eigen-mode 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.