Inverse design of spatio-temporal-modulated thermal metamaterials*

Temporal-modulated materials provide enhanced tunability over traditional space-modulated metamaterials. For instance, in a recent experiment, frequency shifts were obtained by time interfaces [1]. Powerful inverse design approaches, based on the adjoint method, are routinely applied to space-varying systems; here, we implement the adjoint formulation to design time-varying composite materials to achieve a desired transient effective thermal conductivity.  We will use our in–house code OpenBTE [2] to attain inverse-design thermal transport both at the macro and nanoscales, the latter modeled by the mode-resolve Boltzmann Transport Equation.  We will apply our framework to design various systems from first principles, including nanoporous silicon. Our work extends the inverse design of thermal materials to the spatiotemporal domain, also serving as a template for other systems’ optimization. 

[1] Moussa, Hady, et al. "Observation of temporal reflection and broadband frequency translation at photonic time interfaces." Nature Physics (2023): 1-6.

[2] Romano, Giuseppe. "Openbte: a solver for ab-initio phonon transport in multidimensional structures." arXiv preprint arXiv:2106.02764 (2021).