Optimization of gradient index lenses using quasi-conformal contour transformations

Transformation electromagnetics (TE) has been used to predict many unconventional and potentially game-changing electromagnetic devices, but they are often left unimplemented due to the complexity of the required material properties. Restricting transformations to quasi-conformal mappings allows all-dielectric gradient-index (GRIN) lens implementations using approaches familiar to optical system designers. We demonstrate spherical-aberration-corrected lenses with spherical surface profiles by mimicking the optical behavior of aspherical lenses using quasi-conformal mappings. Several approaches for mapping aspherical to spherical contours are described and contrasted, including the use of bulk GRIN regions throughout the entire lens as well as layered designs where the GRIN profiles are restricted to thin laminar layers at the surface of the otherwise homogeneous lens. Hence, the proposed methodology provides engineers with a powerfully intuitive means to design, compare, and contrast various equivalently performing GRIN lenses, adding new modeling capabilities to the existing, well-known remedies for optical system optimization. Furthermore, such an approach facilitates straightforward monitoring and manipulation of material gradients and overall change in refractive index.