Finding nanoparticles with visible light
Over the past two years researchers from the Centre de Recerca Matemática in Barcelona and Centre d’Elaboration de Materiaux et d’Etudes Structurales, Toulouse have been developing the mathematical theory and experimental techniques to view nanoparticles with visible light.
The reason we can see objects (that are not producing light themselves) is that light, either from the Sun or from, say, an electric lamp, reflects off them into our eyes. Now imagine a 1m high sea wave crashing into a large wall. The wave will bounce off the wall and travel back into the sea. An observer some distance from the wall will be able to see both incoming and outgoing waves. If the same wave passes over a grain of sand it will not bounce back, in fact its effect will be barely noticeable. Following this analogy it is easy to understand why visible light, with a wavelength of between 400-700 nm cannot be used to view nanoparticles. Viewing objects on the nanoscale typically requires some form of electron microscope. For example, a scanning electron microscope (SEM) scans a surface with a focused beam of electrons. The electrons interact with atoms in the sample, producing various signals that contain information about the surface topography and composition of the sample. SEM can achieve resolution better than 1 nanometer. However, they are very expensive: specimens are observed in high vacuum in conventional SEM, or in low vacuum or wet conditions in variable pressure or environmental SEM, and at a wide range of cryogenic or elevated temperatures with specialized instruments. For this reason it is desirable to invent a different form of microscope, which will be cheaper and simpler to operate.
Interference pattern caused by two silicon nanoparticles subjected to a 632nm wavelength laser.
Back to the wave-sand analogy. Although the wave may not reflect off the sand, the sand may cause some form of small ripple on the surface so it has an effect, even if it does not cause a reflection. If we knew how to interpret this ripple, then we could infer the presence of the grain of sand. When subjected to laser light nanoparticles can emit their own light which causes interference with the incident (and reflected) beam. If we can measure this interference pattern then we can detect the particle. In the Figure we show the interference pattern caused by two nanoparticles on a reflected laser beam. The image was recorded via an optical fibre placed approximately 50 µm from the surface.
The motivation for this study was in the development of nanoparticle infused materials. The distribution of particles affects the material properties hence when developing methods of material preparation it is important to determine the position of many particles. Using an electron microscope would be an extremely time-consuming task. However, as can be seen from the figure particles can be observed using visible light. The mathematical challenge in this project was to develop a model for the interaction and then use this to determine the whereabouts of the particle, when only the dimensions of the image and the wavelength of the laser light were known.
The project turned out to involve relatively simple mathematics, finding the interference peaks of two interacting electromagnetic waves. In fact it reduced to an algebraic problem, determining the shape of the (almost) ellipses observed. Initial calculations required the determination of the dimensions of the brightest ellipse axes by eye, which then provided the necessary input for the equations. The output was the height of the optical fibre above the plane, the relative position of the particle and, importantly, the phase shift (which gives information about the particle). The result was remarkably accurate and currently work is underway on automating the process.
Tim Myers (CRM) & Wolfgang Bacsa (CEMES)
 T.G. Myers, H. Ribera, W.S. Bacsa. Optical diffraction from isolated nanoparticles, 2019, arXiv:1902.08680.
 T.G. Myers, M. Calvo, C. Fanelli, M. Hennessy, W.S. Bacsa. Mathematics in nanotechnology. Valencia Intelligencer, 2019.
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