Advancements in transformation optics-enabled gradient-index lens design

Abstract

Transformation Optics (TO) provides the mathematical framework for representing the behavior of electromagnetic radiation in a given geometry by "transforming" it to an alternative, usually more desirable, geometry through an appropriate mapping of the constituent material parameters. Using a quasi-conformal mapping, the restrictions on the required material parameters can be relaxed allowing isotropic inhomogeneous all-dielectric materials to be employed. This approach has led to the development of a new and powerful design tool for gradient-index (GRIN) optical systems. Using TO, aspherical lenses can be transformed to simpler spherical and flat geometries or even rotationally-asymmetric shapes which result in true 3D GRIN profiles. TO can also potentially be extended to collapse an entire lens system into a representative GRIN profile thus reducing its physical dimensions while retaining the optical performance of the original system. However, dispersion effects of the constituent materials often limit the bandwidth of metamaterial and TO structures thus restricting their potential applicability. Nonetheless, with the proper pairing of GRIN profile and lens geometry to a given material system, chromatic aberrations can be minimized. To aid in the GRIN construction, we employ advanced multi-objective optimization algorithms which allow the designer to explicitly view the trade-offs between all design objectives such as RMS spot size, field-of-view (FOV), lens thickness, 𝛥𝑛, and focal drift due to chromatic aberrations. We present an overview of our TO-enabled GRIN lens design process and analysis techniques while demonstrating designs which minimize the presence of mono- and poly-chromatic aberrations and discuss their requisite material systems.