Thin Flat Lens Research Articles

Scalar diffraction analysis of the dispersion effect on the focal length of low-index thin flat lenses

We analyze the dispersion effect of the focal length of low-index thin lenses by using scalar diffraction and finite difference time domain (FDTD) methods. We compare the dispersion results obtained by using these methods with reported experimental results, and the well-known analytical formula for focal length (f) of diffractive lenses as a function of wavelength ( λ ) , f ( λ ) = f 0 λ 0 λ where f0 is the designed focal length for wavelength λ0. We show that when the analytical formula is applied to thin flat lenses with low-refractive index, the results are accurate for small numerical aperture (NA) up to 0.2. For larger NA, the error between the analytical approximation and the FDTD analysis remains around 8% over a wide range of NA.

On-chip multiwavelength achromatic thin flat lens

Here we demonstrate a periodic array of thin flat lens defined on a silicon substrate on a standard silicon-on-insulator (SOI), which can focus light of broadband wavelength on the same focal plane. The on-chip thin flat lens has been implemented a periodic structure in the y-direction , but due to the high degree of dispersion of its structural units, the lens significantly suffers from large chromatic aberrations; And we also designed a fixed structure to keep the focal length of the thin flat lens unchanged at 1450 nm, 1550 nm, and 1650 nm, i.e. realizing the on-chip multiwavelength achromatic lens. In this way, functions previously unavailable for various on-chip imaging devices will be realized on this multi-band, which will help innovation in integration and imaging.

Spherical aberration in electrically thin flat lenses.

We analyze the spherical aberration of a new generation of lenses made of flat electrically thin inhomogeneous media. For such lenses, spherical aberration is analyzed quantitatively and qualitatively, and comparison is made to the classical gradient index rod. Both flat thin and thick lenses are made of gradient index materials, but the physical mechanisms and design equations are different. Using full-wave three-dimensional numerical simulation, we evaluate the spherical aberrations using the Maréchal criterion and show that the thin lens gives significantly better performance than the thick lens (rod). Additionally, based on ray tracing formulation, third-order analysis for longitudinal aberration and optical path difference are presented, showing strong overall performance of thin lenses in comparison to classical rod lenses.

Refraction in electrically thin inhomogeneous media.

This work presents a new formulation for refraction from flat electrically thin lenses and reflectors comprised of inhomogeneous material. Inhomogeneous electrically thin flat lenses and reflectors cannot make use of the Snell law since this classical formulation works solely at interfaces of planar homogeneous media. The refraction of a perpendicularly incident plane wave at a planar interface is physically explained through the phase advance of the rays within the medium. The Huygens principle is then used to construct the refracted wavefront. The formulation is validated using numerical full wave simulation for several examples where the refractive angle is predicted with good accuracy. Furthermore, the formulation gives a physical insight of the phenomenon of refraction from electrically thin inhomogeneous media.

Electrically thin flat lenses and reflectors.

We introduce electrically thin dielectric lenses and reflectors that focus a plane wave based on the principles of phase compensation and constructive wave interference. Phase compensation is achieved by arranging thin rectangular slabs having different dielectric permittivity according to a permittivity profile obtained through analytic design equations. All incident rays parallel to the optical axis converge to a focal point with equalized optical paths resulting in constructive interference. Plane wave simulations indicate strong focusing, even in the presence of impedance mismatch between free space and the dielectric layers composing the lens. We demonstrate focusing at 9.45GHz using a lens fabricated with commercially available dielectric materials. In addition to focusing, the flat lens proposed here demonstrates relatively high power gain at the focal point. We also present a flat reflector based on the same concept. We believe that the proposed dielectric lens and reflector are strong candidates to replace heavy metallic dishes and reflectors used in a variety of applications, especially satellites.

Analytical models for electrically thin flat lenses and reflectors.

This work presents analytical models for two-dimensional (2D) and three-dimensional (3D) electrically thin lenses and reflectors. The 2D formulation is based on infinite current line sources, whereas the 3D formulation is based on electrically small dipoles. These models emulate the energy convergence of an electrically thin flat lens and reflector when illuminated by a plane wave with specific polarization. The advantages of these models are twofold: first, prediction of the performance of electrically thin flat lenses and reflectors can be made significantly faster than full-wave simulators, and second, providing insight on the performance of these electrically thin devices. The analytic models were validated by comparison with full-wave simulation for several interesting examples. The validation results show that the focal point of the electrically thin flat lenses and reflectors can be accurately predicted through a design that assumes low coupling between different layers of an inhomogeneous media.

A new artificial material approach for flat THz frequency lenses

Stacked layers of metal meshes embedded in a dielectric substrate are routinely used for providing spectral selection at THz frequencies. Recent work has shown that particular geometries allow the refractive index to be tuned to produce practical artificial materials. Here we show that by spatially grading in the plane of the mesh we can manufacture a Graded Index (GrIn) thin flat lens optimized for use at THz frequencies. Measurements on a prototype lens show we are able to obtain the parabolic profile of a Woods type lens which is dependent only on the mesh parameters. This technique could realize other exotic optical devices.