Formation of hot image for attenuation-typed scatterer in laser beam through a defocusing nonlinear negative index medium slab

For high-power laser beams modulated by a small-scale attenuation-typed scatterer, the nonlinear imaging propagation where the imaging medium is a negative index medium slab with Kerr nonlinearity is investigated. The analytical solution of the propagation is presented under the plane wave approximation and thin-medium approximation. As a result, the formation of the hot image of the scatterer is demonstrated and the corresponding quantitative expressions for the intensity and on-axis position of image are obtained. It is found that the intensity of hot image is closely related to the value of the variable linear magnetic permeability of the negative index medium. Due to the negative nonlinearity of the medium, in the downstream area of the hot image plane, the beam intensity distribution is contrary to the conventional Kerr medium case, and the intense hot image fringe develops into a broad bright band. Besides, this paper also discusses in detail the differences between the intensity and on-axis position of hot image and their counterparts in the conventional Kerr medium case and shows some other beam propagation properties.