The polarization of light can exhibit unusual features when singular optical beams are involved. In 3-dimensional polarized random media the polarization orientation around singularities describe 1/2 or 3/2 Möbius strips. It has been predicted that if singular beams intersect non-collinearly in free space, the polarization ellipse rotates forming many-turn Möbius strips or twisted ribbons along closed loops around a central singularity. These polarization features are important because polarization is an aspect of light that mediate strong interactions with matter, with potential for new applications. We examined the non-collinear superposition of two unfocused paraxial light beams when one of them carried an optical vortex and the other one a uniform phase front, both in orthogonal states of circular polarization. It is known that these superpositions in 2-dimensions produce space-variant patterns of polarization. Relying on the symmetry of the problem, we extracted the 3-dimensional patterns from projective measurements, and confirmed the formation of many-turn Möbius strips or twisted ribbons when the topological charge of one of the component beams was odd or even, respectively. The measurements agree well with the modelings and confirmed that these types of patterns occur at macroscopic length scales and in ordinary superposition situations.

Nano‐sized particles in wastewater are generally considered colloids, but their production and size distribution are not well understood. Organic nano‐sized particles are more abundant than engineered nanomaterials in wastewater, where they may cause membrane fouling, harbor pathogens, and transport contaminants to the environment. To our knowledge, this study is the first to examine the seasonal behavior, removal, and the quantity and size of suspended particles (both unfiltered and filtered through a 450 nm filter) at multiple points within different processes along two water resource recovery facilities (WRRFs, formerly wastewater treatment plants). In Southern California where wastewater is often reused or reclaimed, a better understanding of nano‐sized particles generation and removal may help reduce cost. We found that both types of the biological secondary treatments investigated (conventional activated sludge process and trickling filter) were more efficient in removing suspended particles larger than 450 nm than they were smaller ones. However, the results show that current treatment processes are not designed to remove nano‐sized particles efficiently. We also investigated the factors that correlate with their occurrence and found that there was a significant and direct correlation between influent dissolved chemical oxygen demand (COD) and the abundance of suspended particles both larger and smaller than 450 nm, suggesting that the suspended particles increased with dissolved COD in the WRRFs and thus were biogenically generated during the wastewater treatment. Although no conclusive seasonal correlations were found, dissolved COD management may control nano‐sized particle production. Practitioner Points Conventional secondary treatments (activated sludge and trickling filter) could efficiently remove particles but not as efficiently for nano‐sized particles (40.1–52.7% removal). At one facility, particles of all sizes were found to correlate with dissolved carbon and EPS, meaning they were biogenic. Monitoring dissolved carbon or EPS precursors may help control membrane fouling post‐secondary treatment, and this warrants more studies.

Naturally occurring nanoparticles (NONPs) in wastewater are generally considered colloids, but their production and size distribution are not well understood. NONPs are more abundant than engineered nanoparticles (ENPs) in wastewater, where they may cause membrane fouling, harbour pathogens, and transport contaminants to the environment. In this study we aimed to understand the seasonal behaviour as well as the quantity and size of suspended particles (both unfiltered and filtered through a 450 nm filter) along two water resource recovery facilities (WRRFs, formerly wastewater treatment plants) located in Southern California. We also investigated the factors that correlate with their occurrence. We found that both of the biological secondary treatments investigated, conventional activated sludge process (ASP) and trickling filter (TF), were more efficient in removing suspended particles larger than 450 nm than they were smaller ones. The results show that current treatment processes are not designed to remove nano-sized particles efficiently. Additionally, there was a significant and direct correlation between influent dissolved chemical oxygen demand (COD) and the abundance of suspended particles both larger and smaller than 450 nm, suggesting that the suspended particles increased with dissolved COD in the WRRFs and thus were biogenically generated during the wastewater treatment.

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