The radiative transfer equation (RTE) models the transport of light inside photonic scattering samples such as paint, foam, and tissue. Analytic approximations to solve the RTE fail for samples with strong absorption and dominant anisotropic scattering and predict unphysical negative energy densities and the diffuse flux in the wrong direction. Here we fully characterize the unphysical regions of three popular approximations to the RTE for a slab, namely the $P_1$ approximation (or diffusion approximation), the $P_3$ approximation, and a popular modification to $P_3$ that corrects the forward scattering in the approximation. We find that the $\delta$ function correction to $P_3$ eliminates the unphysical range in the forward scattering. In addition, we compare the predictions of these analytical methods to exact Monte Carlo simulations for the physical and unphysical regions. We present maps of relative errors for the albedo and the anisotropy of the scatterers for a realistic index contrast typical of a polymer slab in air and optical thickness. The relative error maps provide a guideline for the accuracy of the analytical methods to interpret experiments on light transport in photonic scattering slabs. Our results show that the $P_1$ approximation is significantly inaccurate to extract transport parameters unless the sample scatters purely isotropic and elastic. The $P_3$ approximation exceeds $P_1$ in terms of accuracy in its physical range for moderate absorption, and the $P_3$ with the $\delta$ function correction is the most accurate approximation considered here for the forward direction.

Interference of scattered waves is fundamental for modern light-scattering techniques, such as optical wavefront shaping. Recently, a new type of wavefront shaping was introduced where the extinction is manipulated instead of the scattered intensity. The underlying idea is that upon changing the phases or the amplitudes of incident beams, the total extinction will change due to interference described by the cross terms between different incident beams. Here, we experimentally demonstrate the mutual extinction and transparency effects in scattering media, in particular, a human hair and a silicon bar. To this end, we send two light beams with a variable mutual angle on the sample. Depending on the relative phase of the incident beams, we observe either nearly zero extinction, mutual transparency, or almost twice the single-beam extinction, mutual extinction, in agreement with theory. We use an analytical approximation for the scattering amplitude, starting from a completely opaque object, and we discuss the limitations of our approximation. We discuss the applications of the mutual extinction and transparency effects in various fields such as non-line-of-sight communications, microscopy, and biomedical imaging.

The accurate determination of the position-dependent energy fluence rate of scattered light (which is proportional to the energy density) is crucial to the understanding of transport in anisotropically scattering and absorbing samples, such as biological tissue, seawater, atmospheric turbulent layers, and light-emitting diodes. While Monte Carlo simulations are precise, their long computation time is not desirable. Common analytical approximations to the radiative transfer equation (RTE) fail to predict light transport and could even give unphysical results. Therefore, we experimentally probe the position-dependent energy fluence rate of light inside scattering samples where the widely used $P_1$ and $P_3$ approximations to the RTE fail. The samples are three-dimensional (3D) aqueous suspensions of anisotropically scattering and both absorbing and nonabsorbing spherical scatterers, namely, microspheres ($r=0.5\mu \mathrm{m}$) with and without absorbing dye. To probe the energy fluence rate, we detect the emission of quantum-dot reporter particles that are excited by the incident light and that are contained in a thin capillary. By scanning the capillary through the sample, we access the position dependence. We present a comprehensive discussion of experimental limitations and of both random and systematic errors. Our observations agree well with the Monte Carlo simulations and the $P_3$ approximation of the RTE with a correction for forward scattering. In contrast, the $P_1$ and the $P_3$ approximations deviate increasingly from our observations, ultimately even predicting unphysical negative energies.

The radiative transfer equation (RTE) models the transport of light inside photonic scattering samples such as paint, foam and tissue. Analytic approximations to solve the RTE fail for samples with strong absorption and dominant anisotropic scattering and predict unphysical negative energy densities and the diffuse flux in the wrong direction. Here we fully characterize the unphysical regions of three popular approximations to the RTE for a slab, namely the $P_1$ approximation (or diffusion approximation), the $P_3$ approximation, and a popular modification to $P_3$ that corrects the forward scattering in the approximation. We find that the delta function correction to $P_3$ eliminates the unphysical range in the forward scattering. In addition, we compare the predictions of these analytical methods to exact Monte Carlo simulations for the physical and unphysical regions. We present maps of relative errors for the albedo and the anisotropy of the scatterers for a realistic index contrast typical of a polymer slab in air and optical thickness. The relative error maps provide a guideline for the accuracy of the analytical methods to interpret experiments on light transport in photonic scattering slabs. Our results show that the $P_1$ approximation is significantly inaccurate to extract transport parameters unless the sample scatters purely isotropic and elastic. The $P_3$ approximation exceeds $P_1$ in terms of accuracy in its physical range for moderate absorption, and the $P_3$ with the delta function correction is the most accurate approximation considered here for the forward direction.

In this work, we report the feasibility of the silver nanowire (AgNW) foils as highly-sensitive, reproducible and facile detection tools for surface-enhanced Raman spectroscopy (SERS) applications. These flexible and free-standing AgNW foils, fabricated by vacuum filtration method following a modified polyol synthesis of AgNWs, are adequately structured for both biological specimen filtering and trace amount of molecule detection simultaneously. The compatibility of AgNW foil in SERS is investigated by using a Raman active molecule of different steric volumes across the filter cross-section. We have shown that AgNW foils exhibit extremely strong SERS activity with detection limit up to 10^-9 M of crystal violet (CV) molecule with 20% variation over ~cm², revealing reliable homogeneity of the acquired signal. While naturally occurring polyvinylpyrrolidone (PVP) layer during polyol synthesis contribute to controlled aggregation, oxidation prevention, and size - shape control purposes, it also creates a major challenge for obtaining enormous enhancement factors. However, controlled thickness of aluminum oxide (Al₂O₃) coating on PVP@AgNW foils affords to achieve higher enhancement factors than the uncoated ones. What is interesting is that the maximum intensity is achieved from two cycles of Al2O3 deposited on AgNW foils. This is attributed to the two different origins: first, a higher adsorption affinity of CV molecules to Al2O3 layer than PVP layer; second, tunneling barrier formation against quantum tunneling effects.