Imaging Ripples on Phononic Crystals Reveals Acoustic Band Structure and Bloch Harmonics

Broadband surface phonon wave packets on a phononic crystal made up of a microstructured line pattern are tracked in two dimensions and in real time with an ultrafast optical technique. The eigenmode distribution and the 2D acoustic band structure are obtained from spatiotemporal Fourier transforms of the data up to 1 GHz. We find stop bands at the zone boundaries for both leaky-longitudinal and Rayleigh waves, and show how the structure of individual acoustic eigenmodes in $\mathbf{k}$ space depends on Bloch harmonics and on mode coupling.

Figure 1

(a) Cross section of the specimen. (b) Optical micrograph of the specimen before coating with Au. (c) Schematic experimental arrangement.

Figure 2

Experimental SAW images for the 1D phononic crystal: (a) in $x-y$ form for $t=4.6\mathrm{ns}$; (b) in angle-time form for $r=25\mu \mathrm{m}$ (with identified wave fronts). (c) Spatiotemporal Fourier transform $|F|$ of the theoretically calculated displacement field for shear waves in a superlattice with $2\mu \mathrm{m}$ copper and silicon oxide layers. Arrows: 1st BZ. (d) Cross section of $|F|$ in (c) at 500 MHz horizontal line in (c). (e), (f) Measured $|F|$ for our sample for $x$- and $y$-directed waves, respectively. (g) Frequency spectra for $x$- (solid curve) and $y$- (dotted curve) directed waves for $r=20\mu \mathrm{m}$. S. B.: stop band ($x$-directed case).

Figure 3

Experimental constant-$\omega$ surfaces ($k_y-k_x$) for (a) 458 MHz, (b) 534 MHz, (c) 611 MHz, and (d) 687 MHz. The upward arrows indicate the 1st BZ. The white dashed lines in (b) and (c) correspond to $\theta =30°$ and 40°, respectively. Mode identification is provided on the right. Dotted lines: branches arising from Bloch harmonics (BH). Blue lines: higher-order LW.