Structures resistant to Manipulation by all Wavefronts

Abstract

Using light to manipulate small particles is a tool with many practical applications throughout biophysics and nanotechnology. These tools have seen a significant increase in performance by utilizing shaped wavefronts, most commonly created with spatial light modulators. Wavefront shaping has also enabled the manipulation of seemingly arbitrary objects, which was impossible with conventional beams. In contrast, we show here the existence of a wide variety of objects that cannot be manipulated as desired, even with the optimal wavefront shaping protocol. The counterintuitive shapes of these objects are found using inverse design. Specifically, we show that the maximal pulling force is reduced by up to three orders of magnitude, and the maximal trapping stiffness is reduced by up to nearly two orders of magnitude. Our findings could prove useful in the development of micromachines that require a predictable mechanical reaction to an arbitrary wave.

Figures (3)

• Figure 1: Reduction of optimal tractor beam strength with inverse design. Intensity distribution resulting from the optimal tractor beam for a conventional structure (a) with a uniform refractive index distribution ($n=3$) and for an inverse-designed structure (b) to minimize the optimal pulling force. Here, the maximal pulling force ($F$) on the inverse-designed structure is reduced by nearly two orders of magnitude compared to the conventional structure. We restrict the aperture of the incoming wave to one-quarter of the circular boundary. Insets display the refractive index distributions of both structures and the modal distributions of the optimal tractor beam wavefronts. The gray square indicates the extent of the design region.
• Figure 2: Broad parameter range for tractor beam and trapping resistant particles. Plots show by how much the optimal micromanipulation has been reduced for an inverse-designed target compared to a conventional structure with a uniform refractive index. The top row and bottom give the reduction factor for the optimal tractor beam (i.e., the largest eigenvalue of $Q_x$) and optimal trapping stiffness (i.e., the largest eigenvalue of $W_x$), respectively. The reduction factor is shown for different distances (a, e), widths of the design region (b, f), maximal refractive index of the structure (c, g), and wavelength (d, h). Insets show examples of inverse-designed structures that minimize this ratio. The black dashed line indicates the parameter value used in the other scans.
• Figure 3: Maximum trapping stiffness and stable trapping. Force exerted as a function of displacement from the initial position for two different initial positions [(a) 2.8$\lambda$ and (b) 1.7$\lambda$, respectively]. In both cases, we compare the response of both the inverse-designed structure (for small optimal trapping stiffness) and the conventional structure with a uniform refractive index distribution. Furthermore, we apply two different wavefronts (left and right sides in a and b, respectively). One produces the optimal trapping stiffness as it corresponds to the largest eigenvalue of $W_x$, while the other maximizes the trapping stiffness under the constraint of stable trapping. Insets show the structures used and the ratio of the trapping stiffness between the inverse-designed and conventional structures by computing the ratio of the slopes at 0 displacement.