Abstract
A GRIN lens consists of a cylinder of inhomogeneous dielectric material with a refractive index distribution that has a maximum at the cylinder axis and decreases continuously from the axis to the periphery along the transverse direction. The focusing and transforming capabilities of GRIN lenses come from a quadratic variation in refractive index with radial distance from the axis. In a GRIN lens, rays follow sinusoidal trajectories as if they were curved (bent) by a force toward the higher refractive index. The imaging and transforming rules of GRIN lenses are, in principle, the same as those for homogeneous lenses, but there are differences in behavior between them. For instance, the focal length of a GRIN lens only depends on the lens thickness assuming planar input and output faces. This means that a GRIN lens can behave as a convergent, divergent, or telescopic lens depending on its thickness. Therefore, it is important that GRIN lenses be designed properly to perform typical functions as on-axis and off-axis imaging, collimation, and focusing in optical systems.
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