Simultaneous Recovery of Dielectric Constants, Photoelastic Constants, and Strain Profiles from Picosecond Ultrasonic Echoes

Abstract

Light reflected from a deforming solid depends on boundary motion and strain-induced modulation of the dielectric response. For a propagating acoustic field, scattering from different depths interferes coherently, so the measured optical amplitude and phase depend jointly on the strain profile, dielectric constant, and photoelastic constant. Optical tomography often makes such reconstructions tractable through independent projections. To probe mechanical strain, however, the optical measurement also depends on the material properties that mediate its observation, requiring those properties to be known or assumptions about the field. Here we show that broadband picosecond ultrasonic echoes in an opaque solid can supply the missing information. Fourier transformation of the measured complex relative reflectance change obtained with monochromatic light at normal incidence gives access to many acoustic frequency components. We recover the complex dielectric and photoelastic constants together with the nanoscale depth-dependent strain profile by formulating the reconstruction as a multiparameter nonlinear eigenvalue problem. We demonstrate the method using experimental echoes from a chromium film. The recovered refractive index agrees with ellipsometry, whereas the recovered strain profile closely follows a two-temperature-model prediction including electron and thermal diffusion and frequency-dependent ultrasonic attenuation. Synthetic echoes test robustness to added noise. Broadband response thus replaces additional optical projections, making the measurement self-calibrating and enabling simultaneous recovery of an unknown physical field and the material properties that mediate its optical observation.