Transformation optics designed general optical Luneburg lens with flattened shapes
It is well known that the conventional lens design suffers from the aberration, which will lead to imperfect imaging. One way to solve this problem is to use gradient index (GRIN) lenses such as Luneburg lens. However, the spherical geometry of Luneburg lens imposes difficulty for manufacturing. Also, it is desired to design the Luneburg lens with arbitrary focal length. To address these issues, in this paper, we propose to apply the transformation optics techniques to the general Luneburg lens design. In this way, the spherical lens surface will be transformed to flattened shapes, which can be practically fabricated on a flat substrate. Specifically, three dimensional (3D) Luneburg lenses with different focal lengths will be studied. Moreover, discussion on the fabrications of proposed lens has been included. It is desired to ensure that the modified design lies within the available material properties of various polymer photoresists.
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