Electromagnetic control based on Lie symmetry transformation

Abstract

An design method of electromagnetic metamaterial based on Lie symmetry of Maxwell's equation is proposed, which is applied to the modulation of electromagnetic wave / light. Firstly, the electromagnetic control model based on metamaterials is introduced, then according to the theory of Transformation Optics (TO), Lie symmetry analysis is applied to the coordinate transformation of material physical space, and the key core is the determining equations of Lie symmetry is derived. Secondly, the analytical forms of constitutive parameters (permittivity and permeability) of metamaterials are introduced, which can be used to design all kinds of electromagnetic metamaterials. Finally, the Lie symmetry method is applied to the control of electromagnetic beam width. The results show that the metamaterial based on Lie symmetry of Maxwell's equation have good field distribution, and it overcomes the single subjectivity of traditional coordinate transformation in optical transformation. The wave simulation by COMSOL Multiphysics software verify the correctness of Lie symmetry method.