Backward propagating acoustic waves in single gold nanobeams

Abstract

Femtosecond pump-probe spectroscopy has been carried out on suspended gold nanostructures with a rectangular cross section lithographed on a silicon substrate. With a thickness fixed to 110 nm and a width ranging from 200 nm to 800 nm, size dependent measurements are used to distinguish which confined acoustic modes are detected. Furthermore, in order to avoid any ambiguity due to the measurement uncertainties on both the frequency and size, pump and probe beams are also spatially shifted to detect guided acoustic phonons. This leads us to the observation of backward propagating acoustic phonons in the gigahertz range (∼ 3 GHz) in such nanostructures. While backward wave propagation in elastic waveguides has been predicted and already observed at the macroscale, very few studies have been done at the nanoscale. Here, we show that these backward waves can be used as the unique signature of the width dilatational acoustic mode.Probing the elasticity at the nanoscale is a challenge that led a wide community to study confined acoustic modes of nano-objects in the 10 GHz-1 THz range using time-resolved pump-probe experiments [1]. In such an approach, acoustic modes are excited by the absorption of a femtosecond laser pulse and detected in transmission [2,3] or reflectivity geometry in near [4,5] or far [6,7] field by the induced change in the material optical properties. As ensemble studies result in inhomogeneous broadening of the acoustic features[8, 9], single particle spectroscopy has been considered to circumvent this drawback and to clarify the acoustic response [3,10,11]. However, the strong damping at these extremely high frequencies has led several groups to isolate the nanoresonators from their substrate to avoid energy leaking through the nanoobject-substrate contact [12][13][14]. These breakthroughs have made possible the observation of an other source of acoustic energy leaks. Indeed, it has been proven that acoustic phonons are also guided along the nanoobjects [15,16]. Other major developments illustrate the possibility to use nano-objects as nanoscale acoustic transducers for hypersonic wave imaging [17]. Non destructive imaging with nanometric resolution in both depth and lateral direction is now one step ahead.Furthermore, there is a recent and growing interest in both the electromagnetic and acoustic wave communities for materials and waveguides that exhibit backward propagating waves [18]. In backward waves, the phase velocity describing the propagation of individual wave fronts in a wave packet and the energy flux of the wave, characterized by the Poynting vector are anti-parallel. This anti-parallel propagation constitutes the definition of a negative index material and opens the way to a large variety of intriguing physical phenomena [19]. There now exist multiple experimental evidences of this effect, and applications of negative index materials for electromagnetic waves have already been conceived [20]. The pos- * Laurent.Belliard@upmc.fr sibility of such backward wave motion in elastic waveg...

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