Negative refraction in nonlinear wave systems

¹  Department of Physics, Beijing Normal University - Beijing, 100875, China
²  Institute of Applied Mathematics, Academy of Mathematics and System Science, Chinese Academy of Sciences 55, Zhongguancun Donglu, Beijing, 100080, China
³  Zhejiang Institute of Modern Physics and Department of Physics, Zhejiang University - Hangzhou, 310027, China

Corresponding author: ganghu@bnu.edu.cn

Received: 11 April 2007
Accepted: 19 June 2007

Abstract

Scientists have been familiar with the phenomenon of wave refraction for several centuries. Recently, a novel type of refraction, i.e., negative refraction, where both incident and refractory lines locate on the same side of the normal line, has been predicted and realized in the context of linear optics in the presence of both right- and left-handed materials. In this work, we reveal, by theoretical prediction and numerical verification, negative refraction in nonlinear oscillatory systems. We demonstrate that unlike what happens in linear optics, negative refraction of nonlinear waves does not depend on the presence of the special left-handed material, but depends on suitable physical condition. Namely, this phenomenon can be observed in wide range of oscillatory media under the Hopf bifurcation condition. The complex Ginzburg-Landau equation and a chemical reaction-diffusion model are used to demonstrate the feasibility of this nonlinear negative refraction behavior in practice.