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.

中文翻译：

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具有线性负和正折射率介质的光路中的非线性成像

在光路模型中的线性介质具有任意负或正折射率的情况下，从理论上研究了激光束传播中的非线性成像。基于线性衍射理论和薄介质近似，对传播进行了解析求解。还介绍了通过分步傅立叶方法获得的数值模拟结果。发现当两种线性介质中的任一个或两者都具有负折射率时也可以形成热像，并且热像的强度与折射率的组合密切相关。针对不同情况详细讨论了热图像的强度。此外，发现线性介质的折射率在图像距离中起着重要作用，