Imaging properties of a gradient lens with a divergent profile

This paper presents two equivalent single-lens models for analyzing divergent graded-index (GRIN) lenses in homogeneous and inhomogeneous media. Using paraxial matrix optics, the homogeneous case reduces the lens to a negative thin lens flanked by two equal optical spacings. For inhomogeneous media, the refractive-index difference between lens ends is incorporated as an effective longitudinal shift of the object plane within an identical structure. First-order imaging behavior is analyzed for both cases. Numerical ray-tracing simulations validate the models. By representing complex GRIN lenses with simple conventional elements, this work offers an intuitive design tool for optoelectronic systems that employ such components.