We present full-Maxwell topology-optimization design of a single-piece multlayer metalens, about 10 wavelengths~$λ$ in thickness, that simultaneously focuses over a $60^\circ$ angular range and a 23\% spectral bandwidth without suffering chromatic or angular aberration, a "plan-achromat." At all angles and frequencies it achieves diffraction-limited focusing (Strehl ratio $> 0.8$) and absolute focusing efficiency $> 50$\%. Both 2D and 3D axi-symmetric designs are presented, optimized over $\sim 10^5$ degrees of freedom. We also demonstrate shortening the lens-to-sensor distance while producing the same image as for a longer "virtual" focal length and maintaining plan-achromaticity. These proof-of-concept designs demonstrate the ultra-compact multi-functionality that can be achieved by exploiting the full wave physics of subwavelength designs, and motivate future work on design and fabrication of multi-layer meta-optics.
Metalenses are attracting a large interest for the implementation of complex optical functionalities in planar and compact devices. However, chromatic and off-axis aberrations remain standing challenges. Here, we experimentally investigate the broadband behavior of metalenses based on quadratic phase profiles. We show that these metalenses do not only guarantee an arbitrarily large field of view but are also inherently tolerant to longitudinal and transverse chromatic aberrations. As such, we demonstrate a single-layer, silicon metalens with a field of view of 86° and a bandwidth up to 140 nm …
This paper provides a mathematical approach to study chromatic aberration in metalenses. It is shown that radiation of a given wavelength is refracted according to a generalized Snell's law which together with the notion of envelope yields the existence of phase discontinuities. This is then used to establish a quantitative measure of dispersion in metalenses concluding that in the visible spectrum it has the same order of magnitude as for standard lenses.
Metasurface optics have demonstrated vast potential for implementing traditional optical components in an ultra-compact and lightweight form factor. Metasurface lenses, also called metalenses, however, suffer from severe chromatic aberrations, posing serious limitations on their practical use. Existing approaches for circumventing such aberrations via dispersion engineering are limited to small apertures and often entails multiple scatterers per unit cell with small feature sizes. Here, we present an alternative technique to mitigate chromatic aberration and demonstrate high-quality, full-colo…
The correction of multiple aberrations in an optical system requires different optical elements, which increases its cost and complexity. Metasurfaces hold great promise to providing new functionality for miniaturized and low-cost optical systems. A key advantage over their bulk counterparts is the metasurface's ability to respond to the polarization of light, which adds a new degree of freedom to the optical design. Here, we show that polarization control enables a form-birefringent metalens to correct for both spherical and off-axis aberrations using a single element only, which is not possi…
In planar metamaterial lenses, the focal point moves with the frequency. Here it is shown numerically that this movement can be controlled by properly engineering the dimensions of the metamaterial-based phase shifters that constitute the lens. In particular, such lenses can be designed to exhibit unusual chromatic aberration with the focal length increasing, rather than decreasing, with the frequency. It is proposed that such an artificial "reverse" chromatic aberration may optimize the transverse resolution of millimeter wave diagnostics of plasmas and be useful in compensating for the natur…
Chromatic aberration in optical systems arises from the wavelength dependence of a glass's refractive index. Polychromatic rays incident upon an optical surface are refracted at slightly different angles and in traversing an optical system follow distinct paths creating images displaced according to color. Although arising from dispersion, it manifests as a spatial distortion correctable only with compound lenses with multiple glasses and accumulates in complicated imaging systems. While chromatic aberration is measured with interferometry, simple methods are attractive for their ease of use a…
Metasurface lenses, namely metalenses, are ultrathin planar nanostructures that are capable of manipulating the properties of incoming light and imparting lens-like wavefront to the output. Although they have shown promising potentials for the future miniaturization of optics, the chromatic aberration inherited from their diffractive nature plagues them towards many practical applications. Current solutions for creating achromatic metalenses usually require searching through a large number of meta-atoms to find designs that fulfill not only phase but phase dispersion requirements, which leads …
Metalenses have shown great promise in their ability to function as ultracompact optical systems for focusing and imaging. Remarkably, several designs have been recently demonstrated that operate over a large range of frequencies with minimized chromatic aberrations, potentially paving the way for ultrathin achromatic optics. Here, we derive fundamental bandwidth limits that apply to broadband optical metalenses, regardless of their implementation. Specifically, we discuss how the product between achievable time delay and bandwidth is limited in any time-invariant system, and we apply well-est…
Fresnel zone plates are diffractive elements that are essential to form images in many scientific and technological areas, especially where refractive optics is not available. One of the main shortcomings of Fresnel zone plates, which limit their utility with broadband sources, is their high chromatic aberration. Recently presented, Fractal Zone Plates (FZPs) are diffractive lenses characterized by an extended focal depth with a fractal structure. This behaviour predicts an improved performance of FZPs as image forming devices with an extended depth of field and a reduced chromatic aberration.…
Attosecond pulses created by high-order harmonic generation in gases often exhibit strong chromatic aberrations, arising from the broad bandwidth and wavelength-dependent nonlinear light-matter interaction. When the driving laser intensity varies spatially, as for Gaussian driving beams, the apparent source position of the harmonics differs significantly from one order to the next, thus affecting the achievable intensity and duration of the attosecond pulses when they are focused on a target. We show that these chromatic aberrations can be reduced by spatially shaping the fundamental beam to g…
The replacement of bulk refractive optical elements with diffractive planar components enables the miniaturization of optical systems. However, diffractive optics suffers from large chromatic aberrations due to the dispersion of the phase accumulated by light during propagation. We show that this limitation can be overcome with an engineered wavelength-dependent phase shift imparted by a metasurface and demonstrate a design that deflects three wavelengths without dispersion. A planar lens without chromatic aberrations at three wavelengths is also presented. Our design is based on low-loss diel…
Metamaterials and metasurfaces are widely used to manipulate electromagnetic waves over a broad range of wavelengths. Several recent efforts have focused on metalenses, ultra-thin optical elements that focus light using subwavelength structures. Compared to their refractive counterparts, metalenses offer reduced size and weight, improved manufacturability, and new functionality such as polarization control. However, metalenses that correct chromatic aberration also suffer from markedly reduced focusing efficiency. Here we introduce a Hybrid Achromatic Metalens (HAML), that overcomes this trade…
In this letter, we experimentally report an achromatic metalens (AML) operating over a continuous bandwidth in the visible. This is accomplished via dispersion engineering of dielectric phase shifters: titanium dioxide nanopillars tiled on a dielectric spacer layer above a metallic mirror. The AML works in reflection mode with a focal length independent of wavelength from wavelength of 490 nm to 550 nm. We also design a metalens with reverse chromatic dispersion, where the focal length increases as the wavelength increases, contrary to conventional diffractive lenses. The ability to engineer t…
We propose a lens for atoms with reduced chromatic aberrations and calculate its focal length and spot size. In our scheme a two-level atom interacts with a near-resonant standing light wave formed by two running waves of slightly different wave vectors, and a far-detuned running wave propagating perpendicular to the standing wave. We show that within the Raman-Nath approximation and for an adiabatically slow atom-light interaction, the phase acquired by the atom is independent of the incident atomic velocity.
Three-dimensional (3D) direct laser writing is a powerful technology to create nano- and microscopic optical devices. While the design freedom of this technology offers the possibility to reduce different monochromatic aberrations, reducing chromatic aberrations is often neglected. In this Letter, we successfully demonstrate the combination of refractive and diffractive surfaces to create a refractive/diffractive achromat and show, to the best of our knowledge, the first refractive/diffractive apochromat by using DOEs and simultaneously combining two different photoresists, namely IP-S and IP-…
It is generally thought that correcting chromatic aberrations in imaging requires multiple surfaces. Here, we show that by allowing the phase in the image plane of a flat lens to be a free parameter, it is possible to correct chromatic aberrations over an almost unlimited bandwidth with a single diffractive surface. Specifically, we designed, fabricated and characterized a flat multi-level diffractive lens (MDL) that images at the wavelengths from 450nm to 850nm. We experimentally characterized the focusing efficiency, modulation-transfer function, wavefront aberrations, vignetting, distortion…
In this work we study the impact of chromatic focusing of few-cycle laser pulses on high-order harmonic generation (HHG) through analysis of the emitted extreme ultraviolet (XUV) radiation. Chromatic focusing is usually avoided in the few-cycle regime, as the pulse spatio-temporal structure may be highly distorted by the spatiotemporal aberrations. Here, however, we demonstrate it as an additional control parameter to modify the generated XUV radiation. We present experiments where few-cycle pulses are focused by a singlet lens in a Kr gas jet. The chromatic distribution of focal lengths allow…
Label-Free Multiphoton Microscopy is a very powerful optical microscopy that can be applied to study samples with no need for exogenous fluorescent probes, keeping the main benefits of a Multiphoton approach, like longer penetration depths and intrinsic optical sectioning, while opening the possibility of serial examinations with different kinds of techniques. Among the many variations of Label-Free MPM, Higher Harmonic Generation (HHG) is one of the most intriguing due to its generally low photo-toxicity, which enables the examination of specimens particularly susceptible to photo-damages. HH…
Traditional optical imaging systems can provide high-quality imaging with complicated and expensive optical design by eliminating aberrations. With the help of optical memory effect (ME), not independently improving single imaging parameter, but simultaneously improving several imaging parameters by adding scattering media to the imaging systems was demonstrated firstly. As an example, in a simple single-lens imaging system, except the depth-of-field (DOF) was improved greatly, spherical aberration, coma aberration and chromatic aberration were eliminated simultaneously by placing a scattering…
Conventional imaging systems comprise large and expensive optical components which successively mitigate aberrations. Metasurface optics offers a route to miniaturize imaging systems by replacing bulky components with flat and compact implementations. The diffractive nature of these devices, however, induces severe chromatic aberrations and current multi-wavelength and narrowband achromatic metasurfaces cannot support full visible spectum imaging (400-700 nm). We combine principles of both computational imaging and metasurface optics to build a system with a single metalens of NA ~ 0.45 which …
Nanostructured metasurfaces offer unique capabilities for local control of the phase and amplitude of transmitted and reflected optical waves. Based on this potential, a large number of metasurfaces have been proposed in recent years as alternatives to standard optical elements. In most cases, however, these elements suffer from large chromatic aberrations, thus limiting their usefulness for multi-wavelength or broadband applications. Here, in order to alleviate and correct the chromatic aberrations of individual diffractive elements, we introduce dense vertical stacking of independent metasur…
It is generally assumed that correcting chromatic aberrations in imaging requires optical elements. Here, we show that by allowing the phase in the image plane to be a free parameter, it is possible to correct chromatic variation of focal length over an extremely large bandwidth, from the visible (Vis) to the longwave infrared (LWIR) wavelengths using a single diffractive surface, i.e., a flat lens. Specifically, we designed, fabricated and characterized a flat, multi-level diffractive lens (MDL) with thickness £ 10μm, diameter ~1mm, and focal length = 18mm, which was constant over the operati…
It is generally thought that correcting chromatic aberrations in imaging requires multiple surfaces. Here, we show that by allowing the phase in the image plane of a flat lens to be a free parameter, it is possible to correct chromatic aberrations over a large continuous bandwidth with a single diffractive surface. We experimentally demonstrate imaging using a single flat lens of diameter > 3mm, focal length = 5mm (NA = 0.3, f/1.59) that is achromatic from 0.45um to 1um. This combination of size, NA and operating bandwidth has not been demonstrated in a flat lens before. We experimentally char…
Meta-optics has achieved major breakthroughs in the past decade; however, conventional forward design faces challenges as functionality complexity and device size scale up. Inverse design aims at optimizing meta-optics design but has been currently limited by expensive brute-force numerical solvers to small devices, which are also difficult to realize experimentally. Here, we present a general inverse design framework for aperiodic large-scale complex meta-optics in three dimensions, which alleviates computational cost for both simulation and optimization via a fast-approximate solver and an a…
A compact near-eye visor (NEV) system that can guide light from a display to the eye could transform augmented reality (AR) technology. Unfortunately, existing implementations of such an NEV either suffer from small field of view or chromatic aberrations. See-through quality and bulkiness further make the overall performance of the visors unsuitable for a seamless user experience. Metasurfaces are an emerging class of nanophotonic elements that can dramatically reduce the size of optical elements while enhancing functionality. In this paper, we present a design of composite metasurfaces for an…
Dispersion engineering is essential to the performance of most modern optical systems including fiber-optic devices. Even though the chromatic dispersion of a meter-scale single-mode fiber used for endoscopic applications is negligible, optical lenses located on the fiber end face for optical focusing and imaging suffer from strong chromatic aberration. Here we present the design and nanoprinting of a 3D achromatic diffractive metalens on the end face of a single-mode fiber, capable of performing achromatic and polarization-insensitive focusing across the entire near-infrared telecommunication…
Efficiently collecting light emitted or scattered from nanoscale systems, which can be embedded in a high-index medium, is a challenge for fundamental spectroscopic studies and commercial applications of quantum dots, color centers, single molecules, plasmonic antennas, etc. Solid immersion lenses offer a powerful solution to increase the numerical aperture of the optical system, while being robust and compatible with cryogenic temperatures. However, they suffer from strong chromatic aberrations, limiting their applications to narrow-band excitation and emission spectral windows. Here, we desi…
Despite recent advances, high performance single-shot 3D microscopy remains an elusive task. By introducing designed diffractive optical elements (DOEs), one is capable of converting a microscope into a 3D "kaleidoscope", in which case the snapshot image consists of an array of tiles and each tile focuses on different depths. However, the acquired multifocal microscopic (MFM) image suffers from multiple sources of degradation, which prevents MFM from further applications. We propose a unifying computational framework which simplifies the imaging system and achieves 3D reconstruction via comput…
