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The traditional Monte Carlo technique of photon transport in random media describes only single point properties of light, such as its intensity. Here we demonstrate an approach that extends these capabilities to simulations involving properties of spatial coherence, a two-point characteristic of light. Numerical experiments illustrate the use of this Monte Carlo technique for describing the propagation of partially spatially coherent light through random multiply scattering media.

Spatial coherence function (SCF) is a complex function of two spatial coordinates that, in general, carries more information than the bare intensity distribution. A fast and quantitatively accurate measurement of the SCF is extremely important for a range of applications in optical sensing and imaging. Here, we demonstrate an efficient two-step procedure for measuring the full-field complex coherence function. The measurement relies on an optimized design of a wavefront shearing interferometer capable of characterizing spatially inhomogeneous fields over an extended angular domain. The measurement precision is confirmed by the excellent agreement with a numerical estimation based on Fresnel calculations. We demonstrate that the sensitivity and the measurement range afforded by our instrument permits us to reliably describe the differences in the complex coherence functions that are due to subtle modifications in the shape, position, and orientation of radiation sources.

In classical diffraction theory, Babinet's principle relates the electromagnetic fields produced by complementary sources. This theorem was always formulated for single-point quantities, both intensities or field amplitudes, in conditions where the full spatial coherence is implicitly assumed. However, electromagnetic fields are, in general, partially coherent, and their spatial properties are described in terms of two-point field-field correlation functions. In this case, a generalized Babinet's principle can be derived that applies to the spatial coherence functions. We present both the derivation and the experimental demonstration of this generalized Babinet theorem.

The optical size and intrinsic material properties of scattering particles introduce inherent restrictions on their scattering patterns. We show that large size, core-shell dielectric structures with spherical symmetry provide the necessary flexibility for exciting higher-order spherical modes and, consequently, allow us to control the directivity of the scattered radiation. Significant scattering can be generated over angular domains that were formerly believed to be accessible only to dipolar scattering.

The symmetry in action and reaction between interacting particulate matter breaks down when the interaction is mediated by an out-of-equilibrium environment. Nevertheless, even in this case, the space translational invariance still imposes the conservation of canonical momentum. Here we show that optical binding of an asymmetric material system can result in non-reciprocal interactions between constituents. We demonstrate that a non-conservative force applies to the center of mass of an optically bound dimer of dissimilar particles, which leads to an unexpected action in the transversal direction. The sign and the magnitude of this positional force depend on the abrupt phase transitions in the properties of the asymmetric dimer.

We demonstrate that a nonvanishing interaction force exists between pairs of induced dipoles in a random, statistically stationary electromagnetic field. This new type of optical binding force leads to long-range interaction between dipolar particles even when placed in spatially incoherent fields. We also discuss several unique features of the dipole-dipole interaction in spatially incoherent Gaussian fields.

We show that optical anisotropy can exist in composite materials even when they consist of components that are isotropic in shape, spatial distribution, and optical properties. We demonstrate that the simple presence of a surface on a metal-dielectric composite induces an optical anisotropy that manifests itself in an unusual change of the state of polarization and spin Hall effect of reflected light.

The properties of light scattered from material systems depend on the characteristics of input optical fields. We study numerically the effect of the state of spatial coherence on the properties of scattered fields. Using a customized coupled dipole technique, we demonstrate that this influence manifests in changes of the statistics of intensities scattered at different angles.

In the practice of near-field scanning probe microscopy, it is typically assumed that the distance regulation is independent of the optical signal. However, we demonstrate that these two signals are entangled due to the inherent action of optically induced force. This coupling leads to artifacts in both estimating the magnitude of optical fields and recording topographic maps.

We show that the interferometric interaction between the tip and the sample is inherently measured by a near-field scanning optical microscope (NSOM) operating in reflection mode. This is demonstrated by measuring the phase of the sample reflectivity on a standard multilayer system with variable thickness. The demonstrated intrinsic sensitivity to the phase has implications in the interpretation of images collected by using reflection mode NSOM.

By solving a linear stochastic equation, we demonstrate how probability density functions of scattered intensities and order statistics can be used for reconstructing the statistical properties of fluctuating anisotropic polarizabilities. Depending on the statistical relationship between the elements of the polarizability tensor, we show how task optimized measurements can be conducted to reduce the number of necessary measurements. This approach is directly applicable to polarimetric measurements with limited control over the experimental conditions.