PLU for depth-profiling

The theory of the Brillouin scattering of probe laser light by the picosecond acoustic pulse propagating in spatially inhomogeneous medium was developed to support ultrafast opto-acousto-optic experiments intended to depth-profiling of transparent inhomogeneous materials with spatial resolution, which is not limited by the probe light wave length and can be deeply sub-optical (nanometers scale) (see ref.1, ref.2). The developed theory suggests that the latter is controlled by the lengths of the strain fronts in a coherent acoustic pulse (CAP) and their separation, because light is scattered not by the mechanical strain, but by the strain gradients. The theory suggests how the spatial in-depth inhomogeneity of acoustic, optic and acousto-optic parameters of the media could be extracted by conducting time-domain Brillouin scattering (TDBS) experiments, also known as picosecond ultrasonic interferometry, at different angles of probe incidence and measuring both the phase and the amplitude of the transient reflectivity signals. First successful experiments were conducted on revealing the profiles of the sound velocity, of optical refractive index and of photo-elastic constant in sub-micrometer films of nanoporous low-k material with spatial resolution of few tens of nanometers (see ref.). TDBS imaging was later applied to diagnostics of the polycrystalline water and argon ices in the diamond anvil cell (see ref.1, ref. 2, ref.3 , ref. 4). The TDBS provided opportunity to reveal for the first time the depth layering (texture) of the ices at about 20-40 micrometers distances between the anvils (cell thickness) caused by the preferential orientations of the crystallites (see. ref.) and photo-induced motion of the phase front between two different water ice phases (see ref.). The other applications of the TDBS to spatial imaging of the processes were observations of additional curing of low-k films by the two-photon absorption of green laser radiation, when it was used in the TDBS experiments (see ref.).

The TDBS was applied to evaluation of the polycrystalline and damaged (cracked) materials with a grain size exceeding the lateral dimensions of the pump/probe foci (see ref.1, ref.2, ref.3, ref.4). The experiments proved the opportunity to find crystallographic orientation of the individual grains and the inclinations of the inter-grain interfaces in the model polycrystalline ceramic from TDBS measurements with quasi-longitudinal acoustic (QLA) and quasi-transverse acoustic (QTA) photo-generated CAPs (see ref.). The TDBS imaging with quasi-shear acoustic waves provided better sensitivity to crystallographic orientations of the neighbor grains, than with quasi-longitudinal waves also in the high-pressure experiments with water ices (see ref.).

A theory of the TDBS scattering for the Gaussian CAP, heterodyning and scattered light beams, inclined one relative to another, i.e., for the case of non-collinear heterodyning of the acoustically scattered light, was developed (see ref.). The theory suggested that by fitting the TDBS signals, which, in the case of deviations from collinearity of the light beams, strongly depend on the “mismatch” angle and contain simultaneously both Brillouin oscillations and the CAP echoes arriving on the interfaces, it is possible to derive local inclination angle of the interface by a single measurement in a single point. The experiments in the lithium niobate plates destructed under non-hydrostatic pressure loading confirmed these theoretical expectations (see ref.).

The theoretical analysis contra-intuitively demonstrated that the depth of imaging and spectral resolution of the time-domain Brillouin scattering microscopy, with collinearly propagating paraxial sound and light beams, do not depend on the focusing/diffraction of sound (see ref.). The variations of the amplitude of the TDBS signal are only due to the variations of the probe light amplitude caused by light focusing/diffraction. Therefore, the theory explained, why in the experiments the focusing of the CAP-generating pump beam has much less influence on the TDBS microscopy depth of imaging, than the focusing of the probe light beam.

The theoretical developments explained possible existence of “invisible” acoustic frequencies in TDBS experiments (see ref.) and supported the applications of TDBS not to imaging of the materials inhomogeneity but to imaging of the CAPs evolution in homogeneous media, caused either by CAP focusing (see ref.) or by its transformation due to acoustic nonlinearity (see ref.1, ref.2).

First TDBS imaging experiments in the so-called plate geometry were initiated (see ref.). The advantage of this scheme is an independence of the measured Brillouin frequency on the refractive index of a material. Therefore, in a material with an inhomogeneity of optical properties, the imaging of the acoustic velocity can be accomplished independently of the refractive index imaging.

TDBS was applied to imaging of the evolution of a material inhomogeneity with time, opening the path to 4D (3D spacial+temporal).