Electromagnetic control based on Lie symmetry transformation

Abstract

An design method of electromagnetic metamaterial based on Lie symmetry transformation is proposed, which is applied to the regulation of electromagnetic wave / light. Firstly, the electromagnetic control model based on metamaterials is introduced, and the determination equations of Lie symmetry transformation is derived, then the analytical forms of constitutive parameters of metamaterials are introduced. Finally, the Lie symmetry method is applied to the control of electromagnetic beam width. The results show that the metamaterial based on Lie symmetry transformation has good field distribution and overcomes the single subjectivity of traditional coordinate transformation. The wave simulation with COMSOL multiphysicsresults verifies the correctness.