Numerical implementation of three-dimensional vectorial complex ray model and application to rainbow scattering of spheroidal drops.

The rainbow patterns of oblate spheroidal drops have been observed in experiments nearly forty years ago [Nature312, 529 (1984)10.1038/312529a0]. However, the prediction for those complex patterns has been a challenge for conventional light scattering models. The vectorial complex ray model (VCRM) allows to account for the direction, the polarization, the phase, the amplitude and the wavefront curvature of waves and provides a powerful tool for the study of the light/electromagnetic wave interaction with a homogeneous object of any shape with smooth surface. In [Opt. Lett.46, 4585 (2021)10.1364/OL.434149], the authors have reported an important breakthrough of VCRM for the three-dimensional scattering (VCRM3D) and the simulated rainbow patterns of oblate drops. The present paper is devoted to the detailed description of the numerical implementation allowing the simulation of the 3D scattering field by a nonspherical particle. Its ability to predict both the fine and coarse intensity structures of the rainbows and the near-backward scattering patterns of spheroids is demonstrated. This work opens perspectives for exploring the 3D scattering characteristics of large objects with any smooth shape and developing relevant optical techniques for particle characterization.

Microfluidic lab-on-a-chip characterization of nano- to microparticles suspensions by light extinction spectrometry.

The analysis of nano- and microparticle suspensions with micro systems affords improved space-time yields, selectivity, reaction residence times and conversions capabilities. These capabilities are of primary importance in various fields of research and industry. The few microfluidic lab-on-a-chip approaches that have been developed are essentially designed to analyse fluid phases or involve the use of benchtop particle sizing instruments. We report a novel microscale approach to characterize the particle size distribution and absolute concentration of colloidal suspensions. The method is based on a photonic lab-on-a-chip with three scale-specific detection channels to record simultaneous light extinction spectra. Experiments carried out on particle standards with sizes ranging from 30 nm to 0.5 µm and volume concentrations of 1 to 1000ppm, clearly demonstrate the value and potential of the proposed method.

Generalized rainbow patterns of oblate drops simulated by a ray model in three dimensions.

The scattering patterns near the primary rainbow of oblate drops are simulated by extending the vectorial complex ray model (VCRM) [Opt. Lett.36, 370 (2011)OPLEDP0146-959210.1364/OL.36.000370] to three-dimensional (3D) calculations. With the curvature of a wavefront as an intrinsic property of a ray, this advanced ray model permits, in principle, to predict the amplitudes and phases of all emergent rays with a rigorous algebraic formalism. This Letter reports a breakthrough of VCRM for 3D scattering with a line-by-line triangulation interpolation algorithm allowing to calculate the total complex amplitude of a scattered field. This makes possible to simulate not only the skeleton (geometrical rainbow angles, hyperbolic-umbilic caustics), but also the coarse (Airy bows, lattice) and fine (ripple fringes) structures of the generalized rainbow patterns (GRPs) of oblate drops. The simulated results are found qualitatively and quantitatively in good agreement with experimental scattering patterns for drops of different aspect ratios. The physical interpretation of the GRPs is also given. This work opens up prominent perspectives for simulating and understanding the 3D scattering of large particles of any shape with a smooth surface by VCRM.

Bubbles, drops, and solid particles recognition from real or virtual photonic jets reconstructed by digital in-line holography.

The image of the photonic jet (also called caustic) formed by a large, transparent, and spherical particle, reconstructed by digital in-line holography, is shown to be similar to the Airy pattern observed at the focus of a diffraction-limited lens. The analysis of this image, real or virtual depending on whether the particle relative refractive index is above or below one, allows characterizing the particle composition via its refractive index. Experiments clearly demonstrate the value of this method for the simultaneous 3D characterization and differentiation of the dynamics, size, and composition of gas, liquid, and solid particles in multiphase flows.

Droplet sizing and mixture fraction measurement in liquid-liquid flows with rainbow-angle diffractometry.

The capabilities and resolution of the rainbow technique were extended to estimate the size distribution and composition of droplets in liquid-liquid systems. For these droplets, essentially characterized by a low relative refractive index (m≈1.001-1.20), the first-order rainbow is localized in the near-forward to sideways region. It exhibits an unusually higher contrast in the parallel polarization due to the vicinity of the rainbow and the Brewster angles. A numerical study revealed that a few thousand to ten thousand droplets were necessary to obtain reliable estimations of the first moments of typical droplet size distributions when the diffractometer is operated as an ensemble averaging technique. The importance of the accuracy of the light scattering model and the inverse methods used are also documented. Experimental results performed on free-rising submillimeter to millimeter droplets of various compositions showed that a global resolution of 1% to 5% of their mean diameter and about 1.6×10-4 of the dispersion on their refractive index (i.e., 3% in the mixture fraction of oily droplets in water) could be achieved, which enhances the perspectives on mixing and extraction studies in liquid-liquid systems.

Photonic jet reconstruction for particle refractive index measurement by digital in-line holography.

A new and computationally efficient approach is proposed for determining the refractive index of spherical and transparent particles, in addition to their size and 3D position, using digital in-line holography. The method is based on the localization of the maximum intensity position of the photonic jet with respect to the particle center retrieved from the back propagation of recorded holograms. Rigorous electromagnetic calculations and experimental results demonstrate that for liquid-liquid systems and droplets with a radius > 30µm, a refractive index measurement with a resolution inferior to 4 × 10-3 is achievable, revealing a significant potential for the use of this method to investigate multiphase flows. The resolution for solid or liquid particles in gas is expected to be lower but sufficient for the recognition of particle material.

Organic photo sensors for multi-angle light scattering characterization of particle systems.

Organic Photo Sensor (OPS) technology allows printing on conformable plastic-like substrates complex-shaped, arbitrarily-sized and pre-aligned photosensitive elements. This article reports, to the best of our knowledge, the first investigation to implement this emerging technology for Multi-Angle Light Scattering (MALS) characterization of nano- and microparticle suspensions. Monte Carlo and Lorenz-Mie theory calculations as well as preliminary experimental results on latex suspensions clearly demonstrate the potential of the proposed approach.

Experimental validation of the vectorial complex ray model on the inter-caustics scattering of oblate droplets.

We report the first experimental validation of the Vectorial Complex Ray Model (VCRM) using the scattering patterns of large oblate droplets trapped in an acoustic field. The two principal radii and refractive index of the droplets are retrieved with a minimization method that involves VCRM predictions and experimental light scattering patterns. The latter are recorded in the droplet equatorial plane between the primary rainbow region and the associated hyperbolic-umbilic diffraction catastrophe. The results demonstrate that the VCRM can predict the fine and coarse stuctures of scattering patterns with good precision, opening up perspectives for the characterization of large non-spherical particles.

Physical-optics approximation of near-critical-angle scattering by spheroidal bubbles.

A first-order approximation is derived for the near-critical-angle scattering of a large spheroidal bubble illuminated by a plane wave propagating along the bubble axis of symmetry. The intensity of the far-field scattering pattern is expressed as a function of the relative refractive index and the two radii of curvature of the spheroidal bubble at the critical impact point.

Near-critical-angle scattering for the characterization of clouds of bubbles: particular effects.

We report experimental investigations on the influence of various optical effects on the far-field scattering pattern produced by a cloud of optical bubbles near the critical scattering angle. Among the effects considered, there is the change of the relative refractive index of the bubbles (gas bubbles or some liquid-liquid droplets), the influence of intensity gradients induced by the laser beam intensity profile and by the spatial filtering of the collection optics, the coherent and multiple scattering effects occurring for densely packed bubbles, and the tilt angle of spheroidal optical bubbles. The results obtained herein are thought to be fundamental for the development of future works to model these effects and for the extension of the range of applicability of an inverse technique (referenced herein as the critical angle refractometry and sizing technique), which is used to determine the size distribution and composition of bubbly flows.