Operator-Level Description of Transient Thermal Grating Dynamics Across Transport Regimes

Abstract

Transient thermal grating (TTG) experiments provide a powerful means of probing material properties and heat-transport dynamics at small spatiotemporal scales through the temporal response to a spatially periodic excitation. However, quantitative interpretation of the measured transient requires a forward model that consistently connects energy deposition, subsequent heat transport, and the detected TTG observable over the experimental timescale. A unified formulation linking these stages remains insufficiently developed in the TTG context. Here, we formulate a continuum, operator-based TTG forward model that describes the sequence from energy deposition through thermal transport to the temporal evolution of the selected spatial temperature mode within a unified transfer-function framework, while leaving the instrument-specific detection process outside the scope of the present formulation. Heat-transport dynamics are represented by a temporal memory kernel, allowing unresolved relaxation processes to be incorporated into the macroscopic response. The framework provides a basis for assessing the identifiability of thermal diffusivity, heat-propagation speed, and heat-flux relaxation time when flux-memory effects are resolved on the experimental timescale. These macroscopic parameters can, in turn, inform the microscopic interpretation of the measured dynamics. Analysis of the resulting model further demonstrates that the observability of heat-flux memory is not equivalent to the presence of oscillations in the measured response. Oscillations can provide a clear signature of finite flux-relaxation dynamics, but their absence does not establish the validity of Fourier heat conduction: finite flux relaxation dynamics need not produce experimentally observable oscillations under all conditions.

28 pages, 6 figures, Accepted for publication in Open Transport