In this paper, we consider the time-dependent Schrödinger equation: $i\frac{\partial \psi (x,t)}{\partial t}=\frac{1}{2}{(-\mathrm{\Delta })}^{\frac{\alpha }{2}}\psi (x,t)+V\left(x\right)\psi (x,t),$ $x\in \mathbb{R},t>0$ with the Riesz space-fractional derivative of order $0<\alpha \le 2$ in the presence of the linear potential $V\left(x\right)=\beta x$ . The wave function to the one-dimensional Schrödinger equation in momentum space is given in closed form allowing the determination of other measurable quantities such as the mean square displacement. Analytical solutions are derived for the relevant case of $\alpha =1$ , which are useable for studying the propagation of wave packets that undergo spreading and splitting. We furthermore address the two-dimensional space-fractional Schrödinger equation under consideration of the potential $V\left(\mathit{\rho }\right)=\mathbf{F}·\mathit{\rho }$ including the free particle case. The derived equations are illustrated in different ways and verified by comparisons with a recently proposed numerical approach.

A novel approach for precise determination of the optical scattering and absorption properties of porcine tissue using an optimized integrating sphere setup was applied. Measurements on several sample types (skin, muscle, adipose tissue, bone, cartilage, brain) in the spectral range between 400 nm and 1400 nm were performed. Due to the heterogeneity of biological samples, measurements on different individual animals as well as on different sections for each sample type were carried out. For all samples, we used an index matching method to reduce surface roughness effects and to prevent dehydration. The derived absorption spectra were used to estimate the concentration of important tissue chromophores such as water, oxy- and deoxyhemoglobin, collagen and fat.

The pollution of the environment with microplastics in general, and in particular, the contamination of our drinking water and other food items, has increasingly become the focus of public attention in recent years. In order to better understand the entry pathways into the human food chain and thus prevent them if possible, a precise characterization of the particles concerning their size and material is indispensable. Particularly small plastic particles pose a special challenge since their material can only be determined by means of large experimental effort. In this work, we present a proof of principle experiment that allows the precise determination of the plastic type and the particle size in a single step. The experiment combines elastic light scattering (Mie scattering) with inelastic light scattering (Raman scattering), the latter being used to determine the plastic type. We conducted Monte Carlo simluations for the elastically scattered light for different kinds of plastics in a microfluidic cuvette which we could reproduce in the experiment. We were able to measure the Raman signals for different microplastics in the same measurement as the elastically scattered light and thereby determine their material. This information was used to select the appropriate Monte Carlo simulation data and to assign the correct particle size to different materials with only one calibration measurement.

The most commonly used methods for the detection and identification of small microplastics generally require a complex sample preparation procedure and only allow for static measurements. Quality control of food and drinking water therefore requires a lot of effort. Especially in view of the increasing amount of plastic waste in the environment, the rising public awareness of the issue and the indications for adverse effects of microplastics on human health, more sophisticated measuring methods are required. In this paper, we present a measuring setup for the detection and identification of microplastics using flow Raman spectroscopy. We demonstrate the ability to acquire Raman spectra of individual particles as small as about 4 µm, enabling the identification of their plastic type. We show measurements of differently generated and shaped particles and particles made of different plastic types, highlighting the observed challenges and differences. Finally, we show possible applications of the measuring method. We demonstrate that the measuring principle is suitable for detecting and identifying microplastic particles among other particles and that aged plastics can still be distinguished by their Raman spectra. Overall, our results show that flow Raman spectroscopy is a promising method that could significantly reduce the effort required to detect microplastics.

We present a goniometer designed for capturing spectral and angular-resolved data from scattering and absorbing media. The experimental apparatus is complemented by a comprehensive Monte Carlo simulation, meticulously replicating the radiative transport processes within the instrument’s optical components and simulating scattering and absorption across arbitrary volumes. Consequently, we were able to construct a precise digital replica, or “twin”, of the experimental setup. This digital counterpart enabled us to tackle the inverse problem of deducing optical parameters such as absorption and scattering coefficients, along with the scattering anisotropy factor from measurements. We achieved this by fitting Monte Carlo simulations to our goniometric measurements using a Levenberg–Marquardt algorithm. Validation of our approach was performed using polystyrene particles, characterized by Mie scattering, supplemented by a theoretical analysis of algorithmic convergence. Ultimately, we demonstrate strong agreement between optical parameters derived using our novel methodology and those obtained via established measurement protocols.