Generation and control of ultrashort-wavelength two-dimensional surface acoustic waves at nanoscale interfaces

In this work, we generate and probe the shortest wavelength surface acoustic waves to date, at 45 nm, by diffracting coherent extreme ultraviolet beams from a suboptical phononic crystal. The short acoustic wavelengths correspond to penetration depths of approximately 10 nm. We also measure the acoustic dispersion in two-dimensional nanostructured phononic crystals down to this wavelength for the first time, showing that it is strongly influenced by the ultrashort acoustic penetration depth, and that advanced finite-element analysis is required to model the dispersion. Finally, we use pulse sequences to control surface acoustic wave generation in one-dimensional nanostructured gratings, to preferentially enhance higher-order surface waves, while suppressing lower frequency waves. This allows us to reduce the generated surface acoustic wavelength by a factor of two for a defined nanostructure period.

Figure 1

(Left) Schematic diagram of the experimental setup: a femtosecond IR pump beam is focused onto the nanostructured sample to generate SAWs. The HHG beam probes the time-dependent surface displacement as a function of time delay between the pump and probe beams. (Right) Nanograting sample: the height $h$, nanopattern lateral size $L$, and periodicity $P$ are indicated for both 1D and 2D nanogratings.

Figure 2

SAW oscillation signal as a function of pump-probe delay for three samples. The SAW signal is extracted by removing the slowly decaying thermal signal (which transforms the blue curve to the green curve in the top left graph). A Fourier transform is applied to obtain the frequency spectrum. The top graph shows the SAW signal and spectrum for 1D Ni-on-sapphire nanogratings with period 220 nm, the middle graph plots the same for 2D Ni-on-sapphire nanopillars with 240-nm period, while the lower graph plots SAWs from 2D Co/Pd multilayer pillars of period 45 nm on Si.

Figure 3

Dispersion relations: frequency as a function of fundamental-order wavenumber $k$ $=$ 2π/$P$. (Top) Fundamental, diagonal and second order SAW frequencies for the 2D nickel-on-sapphire sample II. The inset shows the various SAWs. (Bottom) Fundamental SAW on the Co/Pd multilayer-on-silicon sample III. The solid lines show the Rayleigh acoustic velocity of the substrate multiplied by the SAW order. The dashed line is intended as a guide to the eye.

Figure 4

Velocity dispersion for the 2D nickel-on-sapphire sample II for the fundamental, diagonal and second-order SAW oscillations. The black solid line shows the Rayleigh velocity of the sapphire substrate. The velocities extracted from the fundamental, diagonal and second-order measurement are shown as circles, squares, and triangles, respectively. The purple dotted line is based on the Datta and Hunsinger approximation, while the blue dashed line is from a finite element simulation. In the inset we report the total displacement profile of the generated fundamental SAW, as calculated by finite element simulations.

Figure 5

Schematic of the modified experimental setup: a Michelson interferometer is introduced to produce a two-pulse pump sequence.

Figure 6

Time-resolved SAW signal from two-pulse pump sequence on a 1D Ni-on-sapphire sample with $P=800$ nm (amplitudes of the top three curves are normalized and shifted for presentation). From top to bottom shows the signal with the pump pulse 1 only, pump pulse 2 only, and the two-pulse sequence SAW signal before (blue line) and after (green line) removing thermal relaxation dynamics. Pump pulse 1 is synchronized with the probe beam and pump pulse 2 arrives 62 ps later, as indicated by the vertical dashed lines.

Figure 7

Fundamental and second-order SAWs in a 1D nanograting of 800-nm period, generated by two pump beams separated by varied time delays. Top to bottom: pumping scheme, extracted SAW signal and frequency spectrum for relative time delays of 0, 31, 62, and 93 ps, corresponding to phase shifts between the fundamental SAWs of 0, π/2, π, 3π/2. Selective control of SAW generation is demonstrated.

Figure 8

Controlling SAW generation in a $P=220$ nm nanograting for zero (top left) and $\pi$ (lower left) phase differences between the two pump pulses. The FFT on the lower right demonstrates selective enhancement of the second order with suppression of fundamental order SAWs.