Although nonlinear optical frequency up-conversion offers a promising route to low-cost, high-performance infrared imaging, existing studies primarily focus on nonlinear detection mechanisms, with comparatively little attention devoted to infrared lens architectures. Here, we propose a nonlinear lens that simultaneously performs beam focusing and wavelength conversion through nonlinear optical frequency conversion. Based on the combined framework of paraxial diffraction theory and coupled-wave theory, a wavelength-conversion factor is introduced into the imaging process, leading to a generalized Gaussian imaging law and the corresponding transverse magnification formula for nonlinear lens imaging. The proposed theory is systematically validated by experiments, which demonstrate excellent agreement between the measured and predicted imaging characteristics over a wide range of focal lengths and wavelength-conversion factors. Furthermore, the nonlinear lens enables continuous focal-length tuning without mechanical motion and depth-resolved imaging. The nonlinear extension of the Gaussian imaging law establishes a fundamental theoretical framework for wavelength-converted imaging systems and provides guidelines for the design of nonlinear optical devices and next-generation infrared imaging systems.

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• Frequency conversion
• Nonlinear optics