Concepts and use cases for picosecond ultrasonics with x-rays

Abstract

We discuss picosecond ultrasonics experiments that complement the established, versatile all-optical schemes by utilizing ultrashort hard x-ray probe pulses. We focus on the extraction of the transient strain response from Bragg peak shifts in the symmetric diffraction condition for layered, nanoscopic structures upon excitation of metallic transducers with femtosecond laser pulses. This type of experiment yields direct, layer-specific and quantitative information on the shape and amplitude of picosecond strain pulses and quasi-static strain even for structures thinner than the optical skin depth. We revisit the inhomogeneous elastic wave equation, which is established for modeling the picosecond strain response and express the driving stress using Grüneisen parameters. This elucidates that the laser-induced stress is proportional to the thermal energy densities in the microscopic subsystems of the solid, i.e., electrons, phonons and spins. The strain response may therefore serve as an ultrafast quantitative proxy for the local energy-density and temperature rise. We underline the importance of the Poisson effect for the quantitative interpretation of the ultrafast strain response. The homogeneous laser-excitation of continuous thin films constrains their ultrafast in-plane expansion, thus suppressing the associated out-of-plane Poisson stress. However, it is present in near equilibrium heating experiments calibrating thermal expansion coefficients which requires an individual treatment of the ultrafast expansion. The selected experimental use cases encompass opaque as well as ultrathin metal-heterostructures, nanostructures and negative thermal expansion materials, that each pose a challenge to all-optical approaches.