Arbitrarily shaped thermal cloaks with non-uniform profiles in homogeneous media configurations.

We propose a novel class of "complete" arbitrary thermal cloaks through rotatory linear maps. Different from the conventionally circular and arbitrary shape cloaks, as well as the unconventionally non-continuous shape cloaks, the proposed cloaking performances are observed in non-uniformly structural devices. Four schemes are demonstrated with homogeneous media configurations, and expected cloaking behaviors are exhibited in the internal regions. Further investigations reveal that the proposed devices perform robustness on the thermal profiles. The findings may also open up a novel avenue to generally achieve novel behaviors in the fields of optics, electromagnetics, and so forth.