Metric-Torsion Duality of Optically Chiral Structures

Geometrical Theory of Electromagnetic Nonreciprocity

Recent advances in electromagnetic nonreciprocity raise the question of how to engineer the nonreciprocal electromagnetic response with geometrical approaches. In this Letter, we examine this problem by introducing generalized electromagnetic continua consisting structured points, which carry extra degrees of freedom over coordinate transformation. We show that general nonreciprocal media have a unique time-varying Riemannian metric structure with local spinning components. It is demonstrated that the nonreciprocity can be alternatively identified as the torsion tensor of a Riemann-Cartan space, which could provide analytic expressions for the magneto-optical effect and the axionic magnetoelectric coupling. Our theory not only gives a deeper insight into the fundamental understanding of electromagnetic nonreciprocity but also provides a practical principle to geometrically design nonreciprocal devices through frame transformation.

Transformation Metamaterials

Based on the form-invariance of Maxwell's equations under coordinate transformations, mathematically smooth deformation of space can be physically equivalent to inhomogeneous and anisotropic electromagnetic (EM) medium (called a transformation medium). It provides a geometric recipe to control EM waves at will. A series of examples of achieving transformation media by artificially structured units from conventional materials is summarized here. Such concepts are firstly implemented for EM waves, and then extended to other wave dynamics, such as elastic waves, acoustic waves, surface water waves, and even stationary fields. These shall be cataloged as transformation metamaterials. In addition, it might be conceptually attractive and practically useful to control diverse waves for multi-physics designs.