Darkfield colors from multi-periodic arrays of gap plasmon resonators

We present results on colors of metal disk arrays viewed under a darkfield microscope and show that the darkfield colors can be manipulated independently of the brightfield colors. We investigate the appearance of colors as disks are clustered to form a new array with double the pitch and a basis of four disks. These structures of aluminum disks on aluminum oxide on aluminum have resonances in the visible spectrum, so by arranging them in small tight clusters, a coupled plasmon resonant mode is produced at shorter wavelengths. This feature causes a reflectance minimum and leads to an increase in the gamut of darkfield colors produced. These colors are tuned by changing the size of the disk and the inter-disk gap within the clusters. Interestingly, the intensities of the reflectance peaks also demonstrate good agreement with the Fourier series coefficients for square waves. Polarization-tunable colors are also demonstrated by designing rectangular arrays that have dissimilar periods along the two orthogonal axes of the array, and a four-level security tag is fabricated that encodes images for viewing under brightfield, darkfield (both x and y polarization), and infrared illumination.

4th and 5th grade students’ structuring of 2D rectangular arrays

In this article we examine 4th and 5th grade Portuguese students’ performance on problems of structuring 2D rectangular arrays of squares, which was analyzed and categorized into the five levels of sophistication described by Battista, Clements, Arnoff, Battista, and Borrow (1998). In general, the results suggest that students in the higher grade exhibit higher levels of sophistication. Nevertheless, several students from both grades could not perceive the structure in rows and columns of such rectangular arrays; their spatial structuring of such arrays was still inadequate. The result for their learning may be even worse if we think that for students in these grades, many textbooks display rectangular arrays as the representation to teach area measurement.

Design and Tensorial Characterization of Rectangular Harmonic Shape-Morphing Mechanism Arrays

Shape-Morphing Mechanism Arrays (SMMAs) can be made by arraying harmonic four-bar mechanisms, i.e. four-bar mechanisms with a particular structure that insures high levels of symmetry. This paper discusses a particular genre of harmonic mechanism array that can forms rectangular grids without requiring the exclusive use of parallel mechanisms. Such arrays can be designed to preserve their harmonic (highly symmetric) structure through-out their range of motion, producing arrays capable of large deformations that nevertheless can be characterized by a 2D tensor, specifically, rectangular arrays deform as parallelograms.