Scientists have made progress in the geometry of non-reciprocal optical media

The propagation of light in complex media is a classic subject of optics and relativity. Shortly after Einstein proposed the general theory of relativity, W. Gordon, I. E. Tamm and G. V. Skrotskii et al. generalized the Fermat principle to curved spacetime. In 1960, J. Plebanski showed that the spatial component and the space-time mixed component of the curved space-time gauge are equivalent to the refractive index (dielectric constant and magnetic permeability) and the opposing non-reciprocal magnetoelectric coupling parameters of a non-symmetric anisotropic optical medium, respectively. The above results have been widely used in laboratory simulations of quantum effects of gravitational fields. In 2006, J. Pendry and U. Pendry The transformation optics proposed by Leonhart, in turn, use coordinate transformations to design non-uniform materials to achieve light control, and have important applications in devices such as electromagnetic cloaks, new waveguides, and antennas. However, relativistic electrodynamics and transformation optics cannot handle chiral and non-reciprocal optical materials, nor can they provide geometric schemes similar to coordinate transformations to control the polarization of light.

Recently, a collaborative team led by Chang Kai, academician of the Chinese Academy of Sciences and researcher of the Institute of Semiconductors of the Chinese Academy of Sciences, proposed the theory of generalized transformed optics in response to the above problems, and generalized the optical medium from the ordinary Cauchy continuum to the generalized continuum with internal degrees of freedom. In this theory, in addition to the coordinate degrees of freedom, each geometric point also has internal degrees of freedom represented by the local frame, which describes the rotation, stretching and twisting of point particles, and can be used to deal with linear optical media with complex constitutive relationships. The research team found that a continuum with local rotational degrees of freedom can describe non-reciprocal optical media at rest in the laboratory. Non-reciprocal optical media mainly include magneto-optical media (metal or rarefied plasma, magnetic insulator, dilute magnetic or ferromagnetic semiconductor), magnetoelectric coupling media (multiferrous materials, topological insulators and Weyl semimetals) and time-varying media. The antisymmetric imaginary part of the dielectric constant and magnetic permeability of the magneto-optical dielectric and the magnetoelectric coupling parameter of the magnetoelectric coupling medium bring cross-coupling between different components of the electromagnetic field, resulting in non-reciprocal polarization rotation, which is widely used in non-reciprocal electromagnetic devices such as isolators and circulators. Based on the generalized transformation optical theory, the research team introduces the time-varying Riemannian geometry theory describing non-reciprocal optical media and the equivalent Riemann-Cartan geometry theory based on frame rotation, uses the space-time torsion tensor to describe the magneto-optical and magnetoelectric coupling parameters, and uniformly explains the general linear non-reciprocal electromagnetic media including magneto-optical, magnetoelectrically coupled medium and time-varying medium with local rotation degrees of freedom.

On the one hand, this work introduces the microstructure of space-time torsion, and generalizes relativistic covariant electrodynamics to non-Riemannian spacetime. On the other hand, it shows that the control of the optical polarization state can be realized by frame transformation. By combining the frame transformation and the coordinate transformation, in principle, the light and polarization state of the electromagnetic field can be controlled at the same time, which provides a theoretical basis for the design of new optical and electromagnetic devices in the future.

The results of this research were recently published in Physical Review Letters (Phys. Rev. Lett. 130, 203801 (2023)). The corresponding authors of the paper are Chang Kai and Professor Feng Jianxiong of the Hong Kong University of Science and Technology.

This work is supported by the National Natural Science Foundation of China, the National Key R&D Program of the Ministry of Science and Technology, the University of Hong Kong Education Grants Committee, the Chinese Academy of Sciences and the Semiconductor Research Institute Talent Program. (Source: Institute of Semiconductors, Chinese Academy of Sciences)

Related paper information:

(a) Generalized continuum images with internal degrees of freedom; (b) Local rotation defines the torsion tensor.

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