Transformation Theory for Spatiotemporal Metamaterials
Fubao Yang, Liujun Xu, Jun Wang, Jiping Huang
Abstract
The transformation theory provides a distinct method for designing parameters in spatial dimensions, facilitating intriguing functions such as cloaking, concentrating, and rotating. However, with the introduction of temporal dimension, the transformation theory becomes particularly elusive because coordinate transformations apply only to static parameters. Here, we develop the transformation thermotics for designing spatiotemporal metamaterials. Specifically, we consider the transient heat-conduction equation with dynamic thermal parameters, whose transformation principles are theoretically derived and numerically confirmed. We further uncover spatiotemporal thermal cloaking, concentrating, and rotating with transformation thermotics as model applications. In contrast to conventional static parameters, dynamic parameters may provide unique opportunities for achieving thermal functions with the additional asymmetric feature. Our spatiotemporal scheme has remarkable advantages in dynamic heat regulation and provides insights into particle or plasma diffusion and wave propagation.