Shear polaritons from transformation optics

Natural in-plane hyperbolic crystals (such as α-MoO₃) and natural monoclinic crystals (such as β-Ga₂O₃) have recently drawn great research focus. Despite their obvious similarities, however, these two kinds of materials are usually studied as separate topics. In this Letter, we explore the intrinsic relationship between materials like α-MoO₃ and β-Ga₂O₃ under the framework of transformation optics, providing another perspective to understand the asymmetry of hyperbolic shear polaritons. It is worth mentioning that we demonstrate this novel, to the best of our knowledge, method from theoretical analysis and numerical simulations, which maintain a high degree of consistency. Our work not only combines natural hyperbolic materials with the theory of classical transformation optics, but also opens new avenues for future studies of various natural materials.