Multiple-scattering model for the effective refractive index of dense suspensions of forward-scattering particles.

We present a multiple-scattering model for the effective refractive index of an arbitrarily dense suspension of forward-scattering particles. The model provides a very simple formula for the effective refractive index of such a suspension and reproduces with high accuracy available experimental results. Furthermore, the derivation we present herein is mathematically transparent and enables us to obtain information on the underlying physical processes rather than obscuring them. We also provide insight into the extent of the model's validity and a simple way to determine whether or not it will be valid for an arbitrary suspension. Due to its simplicity, analytical closedness, and wide range of applicability, we believe the model can be used as a diagnostic tool for complex materials of vastly different natures.

Analysis of wavelength-scale 1D depth-dependent refractive-index gradients at an interface by their effects on the internal reflectance near the critical angle.

Light's internal reflectivity near a critical angle is very sensitive to the angle of incidence and the optical properties of the external medium near the interface. Novel applications in biology and medicine of subcritical internal reflection are being pursued. In many practical situations, the refractive index of the external medium may vary with respect to its bulk value due to different physical phenomena at surfaces. Thus, there is a pressing need to understand the effects of a refractive-index gradient at a surface for near-critical-angle reflection. In this work, we investigate theoretically the reflectivity near the critical angle at an interface with glass assuming the external medium has a continuous depth-dependent refractive index. We present graphs of the internal reflectivity as a function of the angle of incidence, which exhibit the effects of a refractive-index gradient at the interface. We analyze the behavior of the reflectivity curves before total internal reflection is achieved. Our results provide insight into how one can recognize the existence of a refractive-index gradient at the interface and shed light on the viability of characterizing it.

Unambiguous derivation of the effective refractive index of biological suspensions and an extension to dense tissue such as blood.

The van de Hulst formula provides an expression for the effective refractive index or effective propagation constant of a suspension of particles of arbitrary shape, size, and refractive index in an optically homogeneous medium. However, its validity for biological matter, which often consists of very dense suspensions of cells, is unclear because existing derivations of the formula or similar results rely on far-field scattering and/or on the suspension in question being dilute. We present a derivation of the van de Hulst formula valid for suspensions of large, tenuous scatterers-the type biological suspensions are typically made of-that does not rely on these conditions, showing that they are not strictly necessary for the formula to be valid. We apply these results specifically to blood and epithelial tissue. Furthermore, we determine the true condition for the formula to be valid for these types of tissues. We finally provide a simple way to estimate-and, more importantly, correct-the error incurred by the van de Hulst formula when this condition is not met.

Quantitative Label-Free Imaging of Lipid Domains in Single Bilayers by Hyperspectral Coherent Raman Scattering.

Lipid phase separation in cellular membranes is thought to play an important role in many biological functions. This has prompted the development of synthetic membranes to study lipid-lipid interactions in vitro, alongside optical microscopy techniques aimed at directly visualizing phase partitioning. In this context, there is a need to overcome the limitations of fluorescence microscopy, where added fluorophores can significantly perturb lipid packing. Raman-based optical imaging is a promising analytical tool for label-free chemically specific microscopy of lipid bilayers. In this work, we demonstrate the application of hyperspectral coherent Raman scattering microscopy combined with a quantitative unsupervised data analysis methodology developed in-house to visualize lipid partitioning in single planar membrane bilayers exhibiting liquid-ordered and liquid-disordered domains. Two home-built instruments were utilized, featuring coherent anti-Stokes Raman scattering and stimulated Raman scattering modalities. Ternary mixtures of dioleoylphosphatidylcholine, sphingomyelin, and cholesterol were used to form phase-separated domains. We show that domains are consistently resolved, both chemically and spatially, in a completely label-free manner. Quantitative Raman susceptibility spectra of the domains are provided alongside their spatially resolved concentration maps.