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-established bounds on this product to a general focusing system. We then show that all metalenses designed thus far obey the appropriate bandwidth limit. The derived physical bounds provide a useful metric to compare and assess the performance of different devices, and offer fundamental insight into how to design better broadband metalenses.
Zoom metalens doublet exhibits unprecedented advantages over the traditional zoom lens in many aspects, like ultra-compactness, CMOS compatibility, and miniaturization. However, most of them can only work in a narrow band due to chromatic aberration. Here, we numerically demonstrate a broadband achromatic zoom metalens doublet inspired by the Moiré lens principle. This design is achieved by globally optimizing the multi-wavelength phase profiles of the metalens doublet in the visible. The doublet can achieve achromatic continuous 1-10 zoom range at wavelengths of 440 nm, 540 nm, and 640 nm, fe…
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…
Tunable metasurfaces provide a compact and efficient strategy for optical components that require active wavefront shaping. Varifocal metalens is one of the most important applications. However, the existing tunable metalens rarely serves broadband wavelengths restricting their applications in broadband imaging and color display due to chromatic aberration. Herein, we demonstrate an electrically tunable polarization-multiplexed varifocal achromatic dielectric metalens integrated with twisted nematic liquid crystals (TNLCs) in the visible region. The phase profiles at different wavelengths unde…
Metalenses are ultrathin optical devices designed to replicate behavior of conventional refractive lenses, or lens arrays, utilizing nanoscale resonant structures to redirect incident light. These are often comprised of discrete meta-atoms such as nanoscale dielectric pillars. Achromatic focusing - associated with traditional multi-element refractive counterparts - is frequently attempted with single-layer metalens designs, which has proven difficult to achieve with bounded refractive indices and total lens thickness. A recent study (F.Presutti and F.Monticone, 2020) formalized this, applying …
We use inverse design to discover metalens structures that exhibit broadband, achromatic focusing across low, moderate, and high numerical apertures. We show that standard unit-cell approaches cannot achieve high-efficiency high-NA focusing, even at a single frequency, due to the incompleteness of the unit-cell basis, and we provide computational upper bounds on their maximum efficiencies. At low NA, our devices exhibit the highest theoretical efficiencies to date. At high NA -- of 0.9 with translation-invariant films and of 0.99 with "freeform" structures -- our designs are the first to exhib…
Optical systems with wide field-of-views (FOV) are crucial for many applications such as high performance imaging, optical projection, augmented/virtual reality, and miniaturized medical imaging tools. Typically, aberration-free imaging with a wide FOV is achieved by stacking multiple refractive lenses (as in a "fisheye" lens), adding to the size and weight of the optical system. Single metalenses designed to have a wide FOV have the potential to replace these bulky imaging systems and, moreover, they may be dispersion engineered for spectrally broadband operation. In this paper, we derive a f…
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 …
Metasurfaces have the potential to miniaturize and improve the performance of any optical element, with applications spanning telecommunications, computing and wearable optics. However, the ability to retain functionality over a continuous, broad range of wavelengths is essential for their widespread adoption. So far, efforts to achieve this have been limited to either a reflection configuration or operation at wavelengths other than the visible. Here, we show that by judicious choice of nanostructures, one can independently control both the phase and group delay, leading to broadband transmis…
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…
Metasurfaces have attracted widespread attention due to an increasing demand of compact and wearable optical devices. For many applications, polarization-insensitive metasurfaces are highly desirable and appear to limit the choice of their constituent elements to isotropic nanostructures. This greatly restricts the degrees of geometric parameters available in designing each nanostructure. Here, we demonstrate a polarization-insensitive metalens using otherwise anisotropic nanofins which offer additional control over the dispersion and phase of the output light. As a result, we can render a met…
Metalenses offer the ground-breaking opportunity to realize highly performing low-weight, flat and ultrathin, optical elements which substantially reduce size and complexity of imaging systems. Today, a major challenge in metalenses design is still the realization of achromatic optical elements ideally focussing a broad wavelength spectrum at a single focal length. Here we present a fast and effective way to design and fabricate extremely thin all-dielectric metalenses, optimally solving achromaticity issues by means of machine learning codes. The enabling technology for fabrication is a recen…
Over the recent years, there have been many reports of achromatic metalenses and diffractive lenses. However, very few (if any) practical applications of such achromatic flat lenses have been demonstrated, which raises questions about the potential of these lenses to provide solutions for real world cases which involve broadband illumination. A recent paper placed limits on the performance of achromatic metalenses. However, is this limit also valid for a diffractive lens? Not necessarily so. In this paper we derive the limits on the performance of achromatic diffractive lenses. In particular, …
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…
A metric for evaluation of overall metalens performance is presented. It is applied to determination of optimal operating spectral range of a metalens, both theoretically and experimentally. This metric is quite general and can be applied to the design and evaluation of future metalenses, particularly achromatic metalenses.
Metasurface optics provide an ultra-thin alternative to conventional refractive lenses. A present challenge is in realizing metasurfaces that exhibit tunable optical properties and achromatic behavior across the visible spectrum. Here, we report the design, fabrication, and characterization of metasurface lenses ("metalenses") that use asymmetric TiO2 nanostructures to induce a polarization-dependent optical response. By rotating the polarization of linearly-polarized input light, the focal length of a 40 micrometer-diameter metalens is tuned from 220-550 micrometers with nearly diffraction-li…
Two key metrics for imaging systems are their magnification and optical bandwidth. While high-quality imaging systems today achieve bandwidths spanning the whole visible spectrum and large changes in magnification via optical zoom, these often entail lens assemblies with bulky elements unfit for size-constrained applications. Metalenses present a methodology for miniaturization but their strong chromatic aberrations and the lack of a varifocal achromatic element limit their utility. While exemplary broadband achromatic metalenses are realizable via dispersion engineering, in practice, these de…
We demonstrate an inverse designed achromatic, flat, polarization-insensitive diffractive optic element, i.e., multilevel diffractive lens (MDL), operating across a broadband range of UV light (250 nm - 400 nm) via numerical simulations. The simulated average on-axis focusing efficiency of the MDL is optimized to be as high as ~86%. We also investigate the off-axis focusing characteristics at different incident angles of the incoming UV radiation such that the MDL has a full field of view of 30 degrees. The simulated average off-axis focusing efficiency is ~67%, which is the highest reported t…
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…
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…
A plethora of metalenses and diffractive lenses (flat lenses) have been demonstrated over the years. Recently, attempts have been made to stretch their performance envelope, particularly in the direction of wide-band achromatic performance. While achromatic behavior has been demonstrated, an actual improvement in imaging performance relative to conventional (non-chromatically corrected) flat lenses has not. The reasons for this are use of inappropriate performance metrics, lack of comparison to a baseline conventional design, and lack of a performance metric that combines signal-to-noise ratio…
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…
We demonstrate a metalens with NA = 0.98 in air, a bandwidth (FWHM) of 274 nm and a focusing efficiency of 67% at 532 nm wavelength, which is close to the transmission performance of a TiO2 metalens. Moreover, and uniquely so, our metalens can be front-immersed into immersion oil and achieve an ultra-high NA of 1.48 experimentally and 1.73 theoretically, thereby demonstrating the highest NA of any metalens in the visible regime reported to the best of our knowledge.
Optical fiber is a well-established efficient way to guide and manipulate light and allowing high bandwidth optical transmission for long distance communication with low attenuation. Although a dielectric optical waveguide is efficient for transmitting light, its functionality is limited by the dielectric properties of the materials of core and cladding.The light coming out from optical fiber is typically diverging, and the numerical aperture is determined by the refractive index of the fiber materials. Thus, the light intensity decreases significantly upon exiting the fiber. The use of metasu…
We demonstrate that a photonic gauge potential, which arises from the phase degree of freedom in dynamic refractive-index modulation and hence is achormatic, can be used to achieve a broadband optical switch using the configuration of a photonic Aharonov-Bohm interferometer (ABI). The resulting ABI switch has a far larger bandwidth and lower cross talk than the conventional Mach-Zehnder interferometer. Using coupled-mode theory and full-wave numerical modeling, we compare the response of the two interferometers in the presence of nonidealities. Our results indicate the importance of the photon…
Recent theoretical work suggested upper bounds on the operating bandwidths of flat lenses. Here, we show how these bounds can be circumvented via a multi-level diffractive lens (MDL) of diameter = 100 mm, focal length = 200 mm, device thickness = 2.4μ m and operating bandwidth from ? = 400 nm to 800 nm. We further combine the MDL with a refractive lens to demonstrate a hybrid telescope. By appealing to coherence theory, we show that the upper bound on relative bandwidth is surprisingly independent of lens diameter or numerical aperture, but is only limited by the bandwidth of the image sensor.…
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…
Optical cavities are a cornerstone of photonics. They are indispensable in lasers, optical filters, optical combs and clocks, in quantum physics, and have enabled the detection of gravitational waves. Cavities transmit light only at discrete resonant frequencies, which are well-separated in micro-structures. Despite attempts at the construction of `white-light cavities', the benefits accrued upon optically interacting with a cavity -- such as resonant field buildup -- have remained confined to narrow linewidths. Here, we demonstrate achromatic optical transmission through a planar Fabry-Perot …
Spaceplates are novel flat-optic devices that implement the optical response of a free-space volume over a smaller length, effectively "compressing space" for light propagation. Together with flat lenses such as metalenses or diffractive lenses, spaceplates have the potential to enable a drastic miniaturization of any free-space optical system. While the fundamental and practical bounds on the performance metrics of flat lenses have been well studied in recent years, a similar understanding of the ultimate limits of spaceplates is lacking, especially regarding the issue of bandwidth, which rem…
Wavefront aberrations can reflect the imaging quality of high-performance optical systems better than geometric aberrations. Although laser interferometers have emerged as the main tool for measurement of transmitted wavefronts, their application is greatly limited, as they are typically designed for operation at specific wavelengths. In a previous study, we proposed a method for determining the wavefront transmitted by an optical system at any wavelength in a certain band. Although this method works well for most monochromatic systems, where the image plane is at the focal point for the trans…
Increasing the refractive index available for optical and nanophotonic systems opens new vistas for design: for applications ranging from broadband metalenses to ultrathin photovoltaics to high-quality-factor resonators, higher index directly leads to better devices with greater functionality. Although standard transparent materials have been limited to refractive indices smaller than 3 in the visible, recent metamaterials designs have achieved refractive indices above 5, accompanied by high losses, and near the phase transition of a ferroelectric perovskite a broadband index above 26 has been…
