Diffusive pseudo-conformal mapping: Anisotropy-free transformation thermal media with perfect interface matching

Transformation media provide a fundamental paradigm for field regulation, but their tricky anisotropy challenges fabrication. Though optical conformal mapping has been utilized to eliminate anisotropy, two key factors still hinder its development in thermotics, i.e., the distinct diffusion nature and inevitable interface mismatching. Here, we put forth the concept of diffusive pseudo-conformal mapping, overcoming the inherent difference between diffusion and waves and achieving perfect interface matching. The proposed mapping directly leads to heat guiding and expanding functions with anisotropy-free transformation thermal media, whose feasibility is confirmed by experiments or simulations. Besides diverse applications, we provide a unified perspective for two distinct types of prevailing bilayer cloaks by uncovering their profound ties with pseudo-conformal mapping. These results greatly simplify the preparation of transformation thermotics and have implications for regulating other diffusion and wave phenomena.