Conditions for establishing the “generalized Snell’s law of refraction” in all-dielectric metasurfaces: theoretical bases for design of high-efficiency beam deflection metasurfaces

The generalized Snell’s law dictates that introducing a phase gradient at the interface of two media can shape incident light and achieve anomalous reflection or refraction. However, when the introduced phase gradient is realized via the scattering of nanoparticles in the metasurfaces, this law needs to be modified; certain conditions need to be met when the law is established. We present the conditions for establishing the “generalized Snell’s law of refraction” in all-dielectric metasurfaces under the incidence of different polarized light. These conditions can provide theoretical bases for the subsequent design of high-efficiency beam deflection metasurfaces. The relationship between the highest achievable anomalous refraction efficiency and the number of nanoparticles within one period of the metasurface is also summarized. In addition, the generalized refraction should not depend on the polarization states of incident light; however, the previous realization conditions of anomalous refraction were sensitive to the polarization states. Thus, conditions for establishing the polarization-independent generalized Snell’s law of refraction in all-dielectric metasurfaces are presented.

Development of an Automated Optical Inspection System for Rapidly and Precisely Measuring Dimensions of Embedded Microchannel Structures in Transparent Bonded Chips

This study aimed to develop an automated optical inspection (AOI) system that can rapidly and precisely measure the dimensions of microchannels embedded inside a transparent polymeric substrate, and can eventually be used on the production line of a factory. The AOI system is constructed based on Snell’s law. The concept holds that, when light travels through two transparent media (air and the microfluidic chip transparent material), by capturing the parallel refracted light from a light source that went through the microchannel using a camera with a telecentric lens, the image can be analyzed using formulas derived from Snell’s law to measure the dimensions of the microchannel cross-section. Through the NI LabVIEW 2018 SP1 programming interface, we programmed this system to automatically analyze the captured image and acquire all the needed data. The system then processes these data using custom-developed formulas to calculate the height and width measurements of the microchannel cross-sections and presents the results on the human–machine interface (HMI). In this study, a single and straight microchannel with a cross-sectional area of 300 μm × 300 μm and length of 44 mm was micromachined and sealed with another polymeric substrate by a solvent bonding method for experimentations. With this system, 45 cross-sectional areas along the straight microchannel were measured within 20 s, and experiment results showed that the average measured error was less than 2%.

An optic ray theory for durotactic axon guidance

During the development of the nervous system, neurons extend bundles of axons that grow and meet other neurons to form the neuronal network. Robust guidance mechanisms are needed for these bundles to migrate and reach their functional target. Directional information depends on external cues such as chemical or mechanical gradients. Unlike chemotaxis that has been extensively studied, the role and mechanism of durotaxis, the directed response to variations in substrate rigidity, remain unclear. We model bundle migration and guidance by rigidity gradients by using the theory of morphoelastic rods. We show that at a rigidity interface, the motion of axon bundles follows a simple behavior analogous to optic ray theory and obeys Snell’s law for refraction and reflection. We use this powerful analogy to demonstrate that axons can be guided by the equivalent of optical lenses and fibers created by regions of different stiffnesses.