1. C. Giannetti 1 *, B. Revaz 2, F. Banfi 2, M. Montagnese 5, G. Ferrini 1, P. Vavassori 3, V. Metlushko 4 and F. Parmigiani 5,6 1 Dipartimento di Matematica e Fisica, Università Cattolica del Sacro Cuore, I-25121 Brescia, Italy 2 Department of Condensed Matter Physics, University of Genève, Switzerland 3 Dipartimento di Fisica, Università di Ferrara, Italy 4 Department of Electrical and Computer Engineering, University of Illinois at Chicago, IL 5 Dipartimento di Fisica, Università degli Studi di Trieste, Italy 6 Elettra Sincrotrone Trieste, I-34012 Basovizza, Trieste, Italy *email: c.giannetti@dmf.unicatt.it, webpage: http://www.dmf.unicatt.it/elphos/c.giannetti@dmf.unicatt.ithttp://www.dmf.unicatt.it/elphos/ Elastic and thermodynamic properties of nano-structured arrays impulsively excited by femtosecond laser pulses INTRODUCTION The possibility to prepare macroscopic areas of ordered arrays of metallic nano-objects on different substrates led intensive efforts toward the use of these structures as potential transducers and sources of coherent acoustic excitations in the GHz and THz range. Time-resolved reflectivity experiments have been performed on gratings of metallic nanometric stripes (2-d confined) on transparent (SiO 2 ) or semitransparent (Si) substrates, evidencing oscillations in the GHz range [1–4]. However, the attribution of the measured modulations to one-dimensional SAWs, induced in the substrate, or to the oscillation modes of the single nano-objects has been a debated question. Less data are available on the mechanical properties of 3-d confined nanoparticles, as a consequence of the difficulties in measuring and modeling the elastic and thermodynamic properties of these systems. TIME-RESOLVED MEASUREMENTS OF THE DIFFRACTED PATTERN [1] H. Lin et al., J. Appl. Phys. 73, 37 (1993). [2] B. Bonello et al., J. Acoust. Soc. Am. 110, 1943 (2001). [3] G. Antonelli et al., J. Appl. Phys. 91, 3261 (2002). [4] D. Hurley et al., Phys. Rev.B 66, 153301 (2002). [5] R.G. Pratt et al., Appl. Phys. Lett. 15, 403 (1969). OUR APPROACH We developed a dedicated time-resolved optical technique, in order to investigate the mechanical and thermodynamic properties of square arrays of permalloy (Fe 20 Ni 80 ) nano-disks deposited on a Si(100) surface. Exploiting the periodicity of the system, we have measured the relaxation dynamics of the intensity of the first-order diffracted beam, after the excitation by sub-ps laser pulses. By changing the parameters of the samples, we demonstrate that: 1)Collective modes, i.e. two-dimensional surface acoustic waves (SAW), are excited in the silicon 2)The nano-objects interact with the silicon surface renormalizing the SAW velocity. This result suggests the possible opening of a phononic band-gap FUTURE: Brillouin scattering measurements to evidence the opening of the gap in the two-dimensional surface phononic crystal Decoupling of the thermodynamic and mechanical dynamics  CALORIMETRY ON NANOPARTICLES Applications to sub-wavelength optics TWO-DIMENSIONAL SURFACE ACOUSTIC WAVES We measured the frequencies and damping of the two-dimensional surface acoustic waves as a function of the array wavevector and disk diameter. This technique strongly increases the sensitivity to the periodicity of the system, allowing to follow the mechanical and thermodynamic relaxation dynamics of the system with high accuracy. The pump-induced variation of the geometrical radius of the disks (δ a (t)/ a ) induces a variation both of the reflected and diffracted intensities. By measuring the variation of the diffracted beam: THE S/N RATIO IS INCREASED BY A FACTOR ≈9 h CHANGING THE PERIODICITY D=2018±30 nm 2 a =990 ±10 nm h=31±1 nm D=1020±50 nm 2 a =470 ±10 nm h=21±2 nm D=810±10 nm 2 a =380 ±20 nm h=33±5 nm D=610±3 nm 2 a =320 ±10 nm h=60±20 nm Dispersion relation of the 2D SAW excited at the center of the Brillouin zone. SURFACE WAVE VELOCITIES V SAW =4900 m/s @ Si(100) [5] V SAW =5100 m/s @ Si(110) [5] The damping , due to energy radiation of SAWs to bulk modes, is proportional to G 4 [1]. SAW damping SAW dispersion CHANGING THE DISK RADIUS Initial transverse displacement u z0  h -1 frequency shift 2a=395 ±7 nm 2a=785 ±7 nm 2a=320 ±10 nm D=1000 nm h=50 nm Only a slight dependence of the SAWs frequency on the disk diameters is detected: 1.Oscillation frequencies are mainly determined by the wavevector 2.Strong coupling between the metallic disks and the substrate Constant periodicities and thicknesses 1st order perturbation theory predicts a frequency-shift due to the mechanical loading: r S : reflection coeff.  =  a 2 /D 2 filling factor Failure of the 1st order perturbative approach at large filling factors TIME-FREQUENCY ANALYSIS time-domain dynamicsfrequency analysis Si(110) Si(100) G1G1 G2G2  SAW 22 Detection of the diagonal collective mode:  2 /  SAW =1.386±0.004  influence of the substrate anisotropy WAVELET D=1005±6 nm 2a=785±7 nm h=51±2 nm data 3-frequency fit excitation  2 -  SAW beatinghighly damped  3 eigenmodes calculation Convolution with the wavelet C-Morlet wavelet  : heat-exchange time  : 1/  -   : (  0 2 -  2 ) 1/2 SAW modes 22  3 =8.56 GHz Periodic conditions on displacement, strain and stress Mode 1 Mode 3 Mode 2 Mode 4 1 µm 4.19 GHz 3.78 GHz 4.52 GHz5.80 GHz eigenmodes dependence on the disk radius Single disk modes Possible opening of a gap  TWO-DIMENSIONAL SURFACE PHONONIC CRYSTAL Symmetric mode  Form-factor modulation at  Asymmetric mode  Form-factor modulation at 2  Asymmetric mode  Form-factor modulation at 2  Asymmetric mode  Form-factor modulation at 2  The highly damped  3 frequency is close to the double of the asymmetric mode 2 frequency at the bottom of the band-gap Diffracted intensity variation Reflected intensity variation