By means of an ultrafast optical technique, picosecond acoustic strain pulses in a transparent medium are tomographically visualized. The authors reconstruct strain pulses in Au-coated glass from time-domain reflectivity changes as a function of the optical angle of incidence, with ϳ1 ps temporal and ϳ100 nm spatial resolutions. © 2007 American Institute of Physics. ͓DOI: 10.1063/1.2432238͔ Laser picosecond acoustics is well adapted to the investigation of thin films and nanostructures. 1-5 Subpicosecond light pulses are typically used to generate and detect ϳ10-1000 GHz longitudinal acoustic strain pulses. The acoustic strain pulse shape depends on the optoacoustic generation and the acoustic propagation, related, respectively, to the electron and phonon scattering mechanisms. 1,4,6,7 Measuring the strain pulse shape is therefore useful for studying these mechanisms. In some materials it is possible to measure the strain pulse shape near a free surface by monitoring either surface displacements through beam deflection or changes in the phase of the optical reflectance. 2,8 However, no existing method can continuously monitor picosecond strain pulse shapes during propagation. Stimulated by progress in lower frequency acoustic tomography, 9 we present a method to achieve this.Our sample consists of a thin metal film ͑with complex dielectric constant 2 ͒ deposited on a transparent substrate ͑with real 1 ͒, both materials being isotropic. For s-polarized probe light incidence at angle from the substrate side, the optical amplitude reflection coefficient r 0 ͑also termed the optical reflectance͒ can be expressed as 10 r 0 = cos − ͱ 2 / 1 − sin 2 cos + ͱ 2 / 1 − sin 2 .
͑1͒If 1 is slightly perturbed by a ͑anisotropic͒ longitudinal strain distribution 33 ͑z , t͒ ͑ϳ10 −5 here͒ in the depth ͑z͒ direction, the reflectance is changed: 11-13where variations in 2 and the effect of the finite substrate thickness have been ignored. Here, is the ͑central͒ wavelength of the probe light, P 12 ץ=͑ 1 / ץ 33 ͒ is a photoelastic constant, and z = 0 at the 1-2 interface. Equation ͑2͒, which generalizes the formula derived in the past for reflectance changes at normal incidence, 1,11 is an example of an inhomogeneous Fredholm integral. 14 We calculate 33 ͑z , t͒ in the transparent substrate at a given time t from the observed reflectivity variation ␦R 0 / R 0 =2 Re͑␦r 0 / r 0 ͒ as a function of by solving the inverse problem ͑where R 0 = ͉r 0 ͉ 2 ͒. 14,15 ͑A similar approach involving optical phase variations should be feasible.͒ A polished 10 mm radius hemisphere of BK7 glass, whose flat surface is coated with a thin polycrystalline Au film of thickness of 600 nm, is mounted on a rotation stage to set ͑see Fig. 1͒. A photodetector is mounted on a separate coaxial rotation stage set to 2 . Visible s-polarized pump light pulses of duration of ϳ100 fs, repetition rate of 82 MHz, wavelength of 415 nm, and pulse energy of 1.1 nJ from the second harmonic of a Ti:sapphire mode-locked laser are used to illuminate an ϳ20 m diameter ͓full ...