Fig. 3: Microdisk position and orientation control by elliptical and circular patterns.
a Trajectory of a microdisk of radius R = 1.2μm trapped in the perpendicular configuration above a circular pattern of radius a = 1.1μm. The bottom panels in (a) show a micrograph of the trapped microdisk (left) and its schematic representation (right). The white solid line highlights the circular pattern on the surface, and the white dashed line highlights the microdisk oriented almost perpendicularly to the surface. The microdisk tilting leads to an ellipse-like, rather than a rectangular contour, as seen in the micrograph. The angle θ within the surface is measured between an arbitrarily chosen axis of the circular pattern (denoted by the short black vertical segment) and the projection of the microdisk diameter chosen to lie parallel to the surface. The shaded area shows the orthogonal projection of the microdisk onto the surface. The micrograph shows the top view while the schematic drawing presents a side view in order to provide a clearer illustration of the angle θ. b, c Normalized one-dimensional histograms of the microdisk displacements along the x- and y-directions. d The orientation of the microdisk in (a) defined by the angle θ is nearly uniformly distributed from \(-90^{\circ }\) to \(90^{\circ }\). The dashed line shows the homogeneous probability density \({{{{{{{\mathcal{P}}}}}}}}=1/18{0}^{\circ }\). e Trajectory of a microdisk levitating above an elliptical pattern (long axis 2.2μm and short axis 0.6μm). The bottom panels show the experimental picture (left) and the schematic representation (right) of the trapped microdisk. Similarly to panel (a), the solid and dashed lines highlight the contours of the surface pattern and of a circular microdisk oriented perpendicularly to the surface, respectively. The angle θ is measured as indicated in panel (a), taking the long axis of the ellipse as a reference axis. The microdisk displacements along the x-direction (f) are much more confined than along the y-direction (g). h The orientation of the microdisk is sharply confined between ca. \(-7^{\circ }\) and \(7^{\circ }\). The dashed line shows a Gaussian fit to the experimentallzy measured histograms (orange) with a mean value of θ ≈ \(-0.58^{\circ }\) and a variance of 2.19(∘)2. All scale bars correspond to 2μm. The temperature is close to Tc, i.e., ΔT/Tc ≪ 1. The white bars in (a) and (e) represent 2μm. Source data are provided as a Source Data file.
