Nonlinear imaging in optical path with linear negative and positive refractive-index media

The nonlinear imaging in laser beam propagation is investigated theoretically under the circumstance that the linear media in the optical path model have arbitrary negative or positive refractive index. Based on the linear diffraction theory and thin-medium approximation, the propagation is solved analytically. Numerical simulation results obtained by split-step Fourier method are also presented. It is found that hot image can also be formed when either or both of the two linear media have negative refractive index, and that the intensity of hot image is closely related to the combination of refractive indices. The intensity of hot image is discussed in detail for different cases. Furthermore, it is found that the refractive indices of the linear media play important roles in image distance, resulting in that the hot image is no longer constrained in the conjugate plane of the scatterer.