Practical approaches to designing and fabricating flat lenses

Abstract

This work presents two approaches to design and implement three-dimensional (3D) graded index (GRIN) flat lenses consisting of concentric annular segments. Generally, the design of GRIN flat lenses calls for segments with very specific tailored permittivity which makes the realization of the lens challenging. To meet this challenge, each segment of the lens is replaced with a three-layer structure consisting of two materials with a high and a low dielectric constant in such a way that the high permittivity layer is sandwiched between two low permittivity layers. By treating the lens segments as transmission lines and taking the effect of multiple reflections into account, the layer thicknesses are adjusted in such a way that the rays passing through different segments interfere constructively at a focal point. To further improve the focusing performance, a practical design approach is introduced in which each segment of the lens is made of a symmetric seven-layer structure using only two materials (alternating in arrangement) with a high and a low dielectric constant. This design provides the following features: (1) almost all of the incident power passes the lens without considerable reflection, (2) the lens provides a constructive interference of the incident wave at a focal point, and (3) the lens has the potential to be manufactured using available material and technology. Numerical examples are provided in which silica and silicon are utilized as low and high permittivity materials, respectively.