Problems related to propagation of partially coherent fields can be greatly simplified if the correlation function of the field assumes certain specific forms, which allow their representations as incoherent superpositions of fully coherent fields of identical shape. The need for this type of representation is explained and suitable elementary-field decompositions are formulated in spatial, angular, temporal, and spectral domains. Their application to wave propagation in free space and to analysis of light interaction with micro- and nanostructures are discussed, and several illustrative examples are given.

: We propose a scheme based on extraordinary transmission of light through a single nanoaperture, surrounded by periodic corrugations, for direct characterization of focal-region optical fields with subwavelength-scale structure. We describe the design of the device on the basis of rigorous diffraction theory and fabricate a prototype using a process that involves electron beam lithography, dry etching, and template stripping. First experimental results performed with a transmission-type confocal optical microscope demonstrate the potential of the method.

A genuine representation of the cross-spectral density function as a superposition of mutually uncorrelated, spatially localized modes is applied to model the propagation of spatially partially coherent light beams in X-ray optical systems. Numerical illustrations based on mode propagation with VirtualLab software are presented for imaging systems with ideal and non-ideal grazing-incidence mirrors.

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 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.