Microscale architected materials for elastic wave guiding: Fabrication and dynamic characterization across length and time scales

Abstract

We present an experimental protocol for the fabrication and characterization of scalable microarchitected elastic waveguides. Using silicon microfabrication techniques, we develop free-standing 2D truss-based architected waveguides with a maximum diameter of 80 mm, unit cells size of 100 micrometer, and minimum beam width of 5 micrometer, thus achieving scale separation. To characterize elastic wave propagation, we introduce a custom-built scanning optical pump-probe experiment that enables contactless excitation of elastic wave modes and full spatio-temporal reconstruction of wave propagation across hundreds of unit cells with sub-unit cell resolution. Results on periodic architectures show excellent agreement with finite element simulations and equivalent experimental data at larger length scales. Motivated by scalable computational inverse design, we fabricate a specific example of a spatially graded waveguide and demonstrate its ability to guide elastic waves along an arbitrary pre-designed path.

Figures (8)

• Figure 1: Schematic description of the microfabrication protocol. Fabrication was performed on as-received SOI wafers. Color references are indicated at the bottom of the figure. The inset in Step 10 shows the aluminum film deposited on the free-standing waveguide for optimal reflectivity during pump-probe characterization (Sec. \ref{['subsec:photacoustic']}).
• Figure 2: Schematic (left) and optical micrographs of a free-standing periodic microarchitected waveguide with $\sim$600,000 unit cells of dimensions 100 µ m and beam width 10 µ m within a SOI wafer of 100 mm diameter. The star-shaped patterns in the micrographs are windows etched in the back (handle layer) for optical access for dynamic pump-probe characterization.
• Figure 3: Overview of the pump-probe experiment. (a) Top view schematic. The section to the left of the sample holder is the probe section -- a home-built heterodyne interferometer with the associated electronic components. To the right of the sample holder is the pump section of the experiment, involving a pulsed laser source with optical elements for filtering and alignment. (b) Side view. The photograph on the left shows the sample assembly (in yellow) with the Mitutoyo objective on the top to focus the probe laser beam to the point of measurement, and a second objective at the bottom to focus the pump beam (scale bar: 100 mm). Sample and pump objective are mounted on a series of linear stages for alignment and scanning control. The schematic on the right shows details of the optical path, scanning and alignment stages. Acronyms: M - mirror; ND - neutral density filter; HWP - half-wave plate; QWP - quarter-wave plate; PBS - polarizing beam splitter; RP - reflecting prism; RR - retro-reflector; L - plano-convex lens; AOM - acousto-optic modulator; A - aperture; WP - Wollaston prism; BPD - balanced photodetector; P - periscope assembly; AFG - arbitrary function generator; LIA - lock in amplifier.
• Figure 4: Wave propagation in a periodic film. (a) Schematic of the experimental scanning protocol superimposed over an optical micrograph of a periodically architected sample with square unit cells (same dimensions as in Fig. \ref{['fig:fabmicro']}) with an inset showing scanning locations. A line scan was performed with pump excitation at the red circle (see inset), and probes along the line corresponding to the blue circles. A scanning resolution of $\sim 25$ µ m was used for this experiment. (b) Reconstruction of the position-time data from a single scanning experiment. Raw data was plotted after windowing and interpolated using a nearest-neighbor bilinear fit.
• Figure 5: Windowed displacement-time data for all measurement points of the experiment on a periodic square unit-cell architecture. On the left, the data at each spatial location is offset along the $y$-axis for visualization. The scale bar on the left indicates the amplitude of each time resolved signal. Images on the right (with matching colors) show selected raw and windowed time-resolved data and the corresponding Fourier spectra. Gray spectra correspond to raw data, while the blue ones are windowed data. Dashed lines indicate the maximum frequency where changes in the Fourier spectra relative to excitation are observed. Data cannot be resolved beyond 10 MHz due to the physical limitation of electronic demodulation (marked by the gray region).