Ultra-thin, entirely flat, Umklapp lenses

TL;DR

This paper introduces ultra-thin, flat dielectric lenses based on Umklapp processes, enabling wave control and flat lensing without negative refractive index, demonstrated through simulations in silicon nitride at visible wavelengths.

Contribution

The work presents a novel flat lens design using crystal momentum transfer and Umklapp processes, eliminating the need for negative refractive index materials.

Findings

Successfully designed ultra-thin flat lenses using Umklapp processes.

Simulations show effective wave redirection at visible wavelengths.

Lenses operate as Pendry-Veselago lenses with a single unit cell width.

Abstract

We design ultra-thin, entirely flat, dielectric lenses using crystal momentum transfer, so-called Umklapp processes, achieving the required wave control for a new mechanism of flat lensing; physically, these lenses take advantage of abrupt changes in the periodicity of a structured line array so there is an overlap between the first Brillouin zone of one medium with the second Brillouin zone of the other. At the interface between regions of different periodicity, surface, array guided, waves hybridise into reversed propagating beams directed into the material exterior to the array. This control, and redirection, of waves then enables the device to operate as a Pendry-Veselago lens that is one unit cell in width, with no need for an explicit negative refractive index. Simulations using an array embedded in a slab of silicon nitride ($\text{Si}_3\text{N}_4$) in air, operating at visible wavelengths between $420 - 500\text{THz}$ demonstrate the effect.