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Comparison between monochromatic metasurface lenses and achromatic lenses. a Schematic of a monochromatic metalens composed of simple cylindrical meta-units, showing diffractive dispersion (focal length proportional to frequency). b Schematic of a broadband achromatic metalens composed of meta-units with complex cross sections, showing dispersionless focusing. c Spatial (left panel) and spectral (right panel) phase profiles required for a sample achromatic metalens (radius of 50 µm, focal length of 100 µm, operating in the wavelength range of λ = 1.3-1.8 µm) designed with the conventional choice of C ω ð Þ ¼ ω c f. Three different frequencies are represented by three colors, and three positions are represented by different symbols. d Similar diagrams as in c but for our choice of C ω ð Þ ¼ ω c ffiffiffiffiffiffiffiffiffiffiffiffiffiffi r 2 0 þ f 2 p . e, f Requirements of meta-units for the
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Small, high-performance imaging systems could be built using flat lenses made from specially arranged nanoscale pillars. Traditional lenses rely on the curvature and thickness of glass to focus light, but metalenses, which can be smaller, thinner, and more flexible, have surfaces comprised of thousands of nanoscale pillars whose geometries are care...
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... h Scanning electron microscope images of fabricated metalenses using Generation 1A and Generation 2 meta- units, respectively a convenient and intuitive option. Figure 1 summarizes the difference between the conventional design approach, which achieves focusing with chromatic aberration (Fig. 1a), and a novel design approach introduced herein, which produces dispersionless focusing (Fig. 1b). Fig- ure 1c depicts the required spatial phase profiles based on the conventional choice for three select frequencies, as well as the spectral phase profiles (phase dispersion) at three selected positions along the metalens. ...
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... space, while being feasible for nanofabrication. g, h Scanning electron microscope images of fabricated metalenses using Generation 1A and Generation 2 meta- units, respectively a convenient and intuitive option. Figure 1 summarizes the difference between the conventional design approach, which achieves focusing with chromatic aberration (Fig. 1a), and a novel design approach introduced herein, which produces dispersionless focusing (Fig. 1b). Fig- ure 1c depicts the required spatial phase profiles based on the conventional choice for three select frequencies, as well as the spectral phase profiles (phase dispersion) at three selected positions along the metalens. We propose a ...
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... of fabricated metalenses using Generation 1A and Generation 2 meta- units, respectively a convenient and intuitive option. Figure 1 summarizes the difference between the conventional design approach, which achieves focusing with chromatic aberration (Fig. 1a), and a novel design approach introduced herein, which produces dispersionless focusing (Fig. 1b). Fig- ure 1c depicts the required spatial phase profiles based on the conventional choice for three select frequencies, as well as the spectral phase profiles (phase dispersion) at three selected positions along the metalens. We propose a generalized choice ...
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... 1 summarizes the difference between the conventional design approach, which achieves focusing with chromatic aberration (Fig. 1a), and a novel design approach introduced herein, which produces dispersionless focusing (Fig. 1b). Fig- ure 1c depicts the required spatial phase profiles based on the conventional choice for three select frequencies, as well as the spectral phase profiles (phase dispersion) at three selected positions along the metalens. We propose a generalized choice of ...
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... makes the required phase ϕ r 0 ; ω ð Þ¼C 0 for all frequencies at the reference position r = r 0 . Figure 1d depicts the equivalent phase profiles of Fig. 1c for comparison. ...
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... makes the required phase ϕ r 0 ; ω ð Þ¼C 0 for all frequencies at the reference position r = r 0 . Figure 1d depicts the equivalent phase profiles of Fig. 1c for ...
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... dispersion" space. At each position on a metalens, Eq. 1 specifies the required values of phase and dispersion relative to a reference phase and a reference dispersion set by C(ω). These requirements can be plotted in the phase- dispersion space to visualize the extent of parameter space that a meta-unit library must fill to create the metalens ( (Fig. 1e). In contrast, the proposed form of C (ω) prescribes positive values of dispersion by setting the reference as a position r 0 ( Fig. 1f and Supplementary Information Sections I and II). The dielectric libraries can now match the required phase over a continuous band- width for positions r < r 0 but not outside of that domain. This ...
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... and a reference dispersion set by C(ω). These requirements can be plotted in the phase- dispersion space to visualize the extent of parameter space that a meta-unit library must fill to create the metalens ( (Fig. 1e). In contrast, the proposed form of C (ω) prescribes positive values of dispersion by setting the reference as a position r 0 ( Fig. 1f and Supplementary Information Sections I and II). The dielectric libraries can now match the required phase over a continuous band- width for positions r < r 0 but not outside of that domain. This suggests making r 0 the radius of the metalens, which fixes the dispersion required at the edge of the metalens dϕ dω min as zero and causes ...
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... Previous efforts have been done to achieve dispersion manipulation, mainly chromatic aberration elimination, at discrete wavelengths or broadband through spatial multiplexing, such as sub-region [25][26][27] , interleaved meta-units [28][29][30] and stacking layers [31][32][33][34][35] . Meanwhile, with structural dispersion design freedom of different subwavelength structures, the chromatic aberration elimination at discrete wavelengths 36 , narrowband 37,38 , and broadband [39][40][41][42][43][44][45][46] in different wavelength bands with a single-layer non-interleaved metalens can be realized through linear phase compensation. However, this scheme is challenging for designing arbitrary dispersion-controlled metaoptics, especially in ultra-broadband cases. ...
... Single-layer achromatic metalenses designed using phase compensation methods are limited by the maximum phase dispersion (i.e. group delay) that the structure can provide 46,52,53 . Therefore, a single metric such as bandwidth cannot fully evaluate the design. ...
... Therefore, a single metric such as bandwidth cannot fully evaluate the design. To address this, we have introduced a more comprehensive evaluation factor, χ (limit proximity factor, LPF), which is based on the maximum phase dispersion limit 46 . The LPF is calculated using ...
Dispersion decomposes compound light into its monochromatic components, which is detrimental to broadband imaging but advantageous for spectroscopic applications. Metasurfaces provide a unique path to modulate the dispersion by adjusting structural parameters on a two-dimensional plane. However, conventional linear phase compensation does not adequately match the meta-unit’s dispersion characteristics with required complex dispersion, hindering at-will dispersion engineering over a very wide bandwidth particularly. Here, we propose an asymptotic phase compensation strategy for ultra-broadband dispersion-controlled metalenses. Metasurfaces with extraordinarily high aspect ratio nanostructures have been fabricated for arbitrary dispersion control in ultra-broad bandwidth, and we experimentally demonstrate the single-layer achromatic metalenses in the visible to infrared spectrum (400 nm~1000 nm, NA = 0.164). Our proposed scheme provides a comprehensive theoretical framework for single-layer meta-optics, allowing for arbitrary dispersion manipulation without bandwidth restrictions. This development is expected to have significant applications in ultra-broadband imaging and chromatography detection, among others.
... The specific design principle: using the point source method to calculate the int distribution of the axial diffraction light field, taking the depth of the focus (axia height full-width) length as the objective function and then selecting the appro structure from the unit structure database obtained from simulation via the optimiz algorithm. The formula for calculating the light field distribution via the point s method can be expressed using the following formula [37]: ...
... The specific design principle: using the point source method to calculate the intensity distribution of the axial diffraction light field, taking the depth of the focus (axial half-height full-width) length as the objective function and then selecting the appropriate structure from the unit structure database obtained from simulation via the optimization algorithm. The formula for calculating the light field distribution via the point source method can be expressed using the following formula [37]: ...
Longitudinal optical field modulation is very important for applications such as optical imaging, spectroscopy, and optical manipulation. It can achieve high-resolution imaging or manipulation of the target object, but it is also limited by its depth of focus. The depth of focus determines whether the target object can be clearly imaged or manipulated at different distances, so extending the depth of focus can improve the adaptability and flexibility of the system. However, how to extend the depth of focus is still a significant challenge. In this paper, we use a super-oscillation phase modulation optimization method to design a polarization-independent metalens with extended focal depth, taking the axial focal depth length as the optimization objective. The optimized metalens has a focal depth of 13.07 μm (about 22.3 λ), and in the whole focal depth range, the transverse full width at half maximum values are close to the Rayleigh diffraction limit, and the focusing efficiency is above 10%. The results of this paper provide a new idea for the design of a metalens with a long focal depth and may have application value in imaging, lithography, and detection.
... One of the major obstacles to widespread use of flat lenses is their inherent chromatic aberration (14), that is, the focal length of the flat lens is strongly dependent on the wavelength of illumination. Novel nanostructure design has introduced the ability to correct the chromatic aberration of metalenses (15)(16)(17)(18)(19)(20)(21)(22) and of diffractive lenses (5,(23)(24)(25)(26). Both have been shown to have fundamental performance limitations (27,28). ...
Motivated by their great potential to reduce the size, cost and weight, flat lenses, a category that includes diffractive lenses and metalenses, are rapidly emerging as key components with the potential to replace the traditional refractive optical elements in modern optical systems. Yet, the inherently strong chromatic aberration of these flat lenses is significantly impairing their performance in systems based on polychromatic illumination or passive ambient light illumination, stalling their widespread implementation. Hereby, we provide a promising solution and demonstrate high quality imaging based on flat lenses over the entire visible spectrum. Our approach is based on creating a novel dataset of color outdoor images taken with our flat lens and using this dataset to train a deep-learning model for chromatic aberrations correction. Based on this approach we show unprecedented imaging results not only in terms of qualitative measures but also in the quantitative terms of the PSNR and SSIM scores of the reconstructed images. The results pave the way for the implementation of flat lenses in advanced polychromatic imaging systems.
... 15,16 The Pancharatnam-Berry (PB) phase and the propagation phase in the visible and infrared (IR) bands have been combined to create an achromatic metalens for focusing and imaging. [17][18][19] Second near-IR (NIR-II) light in the 1000 to 1700 nm band can penetrate biological tissues, especially skin and blood, more deeply and efficiently than visible light and has emerged as an attractive optical region for bioimaging. 20 NIR achromatic metalenses are being introduced to bioimaging. ...
... First, by placing a dipole source at the focal point and propagating the emitted spherical wave onto the plane of the metasurface, the underlying phase distribution of the metalens can be deduced. 18 The specific light propagation process is shown in Fig. 10, where the yellow arc indicates the reference wave front of the dipole at the focal point. The phase function is related to the ray~l and the distance from the position r to the center of the circle E Q -T A R G E T ; t e m p : i n t r a l i n k -; e 0 0 6 ; 1 1 4 ; 4 7 9 ...
... Achromatic metalenses are first designed for optical imaging based on dielectric materials, working from infrared to the visible band [14][15][16][17][18][19][20]. The reported achromatic metalenses require close-packed meta-atoms [14][15][16] or meta-atoms with complex shapes [17,19,20] to provide the desired phase compensation and group delay. ...
... Achromatic metalenses are first designed for optical imaging based on dielectric materials, working from infrared to the visible band [14][15][16][17][18][19][20]. The reported achromatic metalenses require close-packed meta-atoms [14][15][16] or meta-atoms with complex shapes [17,19,20] to provide the desired phase compensation and group delay. Moreover, some achromatic metalenses only work for circularpolarization waves as the design employs geometrical phase [14][15][16]. ...
Achromatic lenses, which have the same focal length regardless of the illumination frequency, find strong applications in imaging, sensing, and communication systems. Making achromatic lenses with metasurfaces is highly desirable because they are flat, ultrathin, relatively light, and easily fabricable. However, existing metalenses experience combinations of limitations which include single polarization operation, narrow bandwidth, and small numerical aperture (NA). In this work, we propose a dual polarized, broadband and high NA achromatic metalens based on the Huygens’ metasurface. We use Huygens’ metasurface unit cells with three tunable resonances to realize a stable group delay over a large bandwidth, while also achieving high transparency and large phase tunability. With these cells, we construct a dual-polarized achromatic Huygens’ metalens with an NA of 0.64 that works from 22 to 26 GHz. Our achromatic metalens achieves diffraction-limited focusing with 2 % maximum focal length deviation and 70 % average focusing efficiency over a bandwidth of 16.7 %. Most key performance metrics for this lens surpass or are comparable with the best of previous metalenses. An achromatic metalens simultaneously achieving broad bandwidth, large NA, and polarization-independent operation will open wide-ranging opportunities for microwave and mm-wave imaging and communication applications.
... Therefore, a designer can alter the geometry of a material to create specific wave interference in the hope of achieving desired scattering effects. Examples include drilling air holes in the active layer of a solar cell to enhance its absorption efficiency [19,36,37] and judiciously laying out arrays of nano-pillars to create an ultrathin optical lens [38][39][40][41]. The state-of-theart method for geometrical designs is adjoint-gradient-based optimization [24][25][26][27][28]. ...
... To demonstrate the power of this framework, we consider a fundamental question in the fields of analog optical computing [177][178][179][180][181] and metasurfaces [38,41,182]: what is the minimum size of a scatterer that achieves a desired scattering matrix S target ? A generic setup is depicted in Fig. 3.2(a). ...
... Bounds on multi-functional nanophotonics Nanophotonic devices that offer multiple functionalities, from liquid-crystal devices for beam steering [79][80][81] to polychromatic metasurface lenses [38][39][40][41], have tremendous design complexity because the multiple functions ought to be supported by a single photonic structure. ...
Nanoscale fabrication techniques, computational inverse design, and fields from silicon photonics to metasurface optics are enabling transformative use of an unprecedented number of structural degrees of freedom in nanophotonics. A critical need is to understand the extreme limits to what is possible by engineering nanophotonic structures. This thesis establishes the first general theoretical framework identifying fundamental limits to light--matter interactions. It derives bounds for applications across nanophotonics, including far-field scattering, optimal wavefront shaping, optical beam switching, and wave communication, as well as the miniaturization of optical components, including perfect absorbers, linear optical analog computing units, resonant optical sensors, multilayered thin films, and high-NA metalenses. The bounds emerge from an infinite set of physical constraints that have to be satisfied by polarization fields in response to an excitation. The constraints encode power conservation in single-scenario scattering and requisite field correlations in multi-scenario scattering. The framework developed in this thesis, encompassing general linear wave scattering dynamics, offers a new way to understand optimal designs and their fundamental limits, in nanophotonics and beyond.
... In contrast to diffractive optics, the wavelength-dependent aberrations are a direct result from non-linear imparted phase [Aieta et al. 2015;Lin et al. 2014;Wang et al. 2018b;Yu and Capasso 2014]. While methods using dispersion engineering [Arbabi et al. 2017;Khorasaninejad et al. 2017;Ndao et al. 2020;Shrestha et al. 2018;Wang et al. 2017] are successful in reducing chromatic aberrations, these methods are limited to aperture sizes of tens of microns [Presutti and Monticone 2020b]. Most recently, Tseng et al. [Tseng et al. 2021a] have proposed an end-to-end differentiable design approach for meta-optics that achieves full-color image quality with a large 0.5 mm aperture. ...
Today's commodity camera systems rely on compound optics to map light originating from the scene to positions on the sensor where it gets recorded as an image. To record images without optical aberrations, i.e., deviations from Gauss' linear model of optics, typical lens systems introduce increasingly complex stacks of optical elements which are responsible for the height of existing commodity cameras. In this work, we investigate \emph{flat nanophotonic computational cameras} as an alternative that employs an array of skewed lenslets and a learned reconstruction approach. The optical array is embedded on a metasurface that, at 700~nm height, is flat and sits on the sensor cover glass at 2.5~mm focal distance from the sensor. To tackle the highly chromatic response of a metasurface and design the array over the entire sensor, we propose a differentiable optimization method that continuously samples over the visible spectrum and factorizes the optical modulation for different incident fields into individual lenses. We reconstruct a megapixel image from our flat imager with a \emph{learned probabilistic reconstruction} method that employs a generative diffusion model to sample an implicit prior. To tackle \emph{scene-dependent aberrations in broadband}, we propose a method for acquiring paired captured training data in varying illumination conditions. We assess the proposed flat camera design in simulation and with an experimental prototype, validating that the method is capable of recovering images from diverse scenes in broadband with a single nanophotonic layer.
... Due to significant material dispersion and dispersive responses of metasurfaces, different spectral components passing through metalenses will focus on disparate spatial planes, negatively impacting image quality. Existing strategies to mitigate chromatic aberration include cascaded multi-layer metalenses (1)(2)(3)(4), interleaving meta-atoms for different wavelengths (5)(6)(7), metalens arrays (8), dispersion correction phase mask (9)(10)(11)(12), increased focusing depth (13) and computational optimization and correction of phase profiles (14,15). But these approaches increase system complexity while sacrificing other performance metrics such as scalable high-yield fabrication, imaging quality and freedom of material choices. ...
Meta-optics are attracting intensive interest as alternatives to traditional optical systems comprising multiple lenses and diffractive elements. Among applications, single metalens imaging is highly attractive due to the potential for achieving significant size reduction and simplified design. However, single metalenses exhibit severe chromatic aberration arising from material dispersion and the nature of singlet optics, making them unsuitable for full-color imaging requiring achromatic performance. In this work, we propose and validate a deep learning-based single metalens imaging system to overcome chromatic aberration in varied scenarios. The developed deep learning networks computationally reconstruct raw imaging captures through reliably refocusing red, green and blue channels to eliminate chromatic aberration and enhance resolution without altering the metalens hardware. The networks demonstrate consistent enhancement across different aperture sizes and focusing distances. Images outside the training set and real-world photos were also successfully reconstructed. Our approach provides a new means to achieve achromatic metalenses without complex engineering, enabling practical and simplified implementation to overcome inherent limitations of meta-optics.
... [1,2] Metasurfaces are usually constructed by a www.advancedsciencenews.com www.afm-journal.de control of phase and its wavelength dispersion, achromatic [6,22] and dispersion-engineered [23] diffractive devices can be achieved. Angle-dependent phase gradients over a monolayer dielectric metagrating have also been developed to realize a class of angleselective metasurfaces. ...
Metasurfaces with engineered phase discontinuity offer extra degrees of freedom to control the angular spectrum characteristics of light and can be used to construct planar metalenses with a variety of anomalous functionalities. Here, off‐resonance spin‐locked metasurfaces empowered by quasi‐bound states in the continuum are reported, in order to achieve a concept of hybridized analog computing over both frequency and angular spectrum domains. By introducing two types of asymmetric degrees, high‐quality resonance empowered by the symmetry‐protected bound states in the continuum emerges in an image‐coupled resonance system. Such high‐quality resonance can be excited in a broadband spin‐locked scattering spectrum, promising required functions for scalar multiplication and convolution operations. Off‐resonance meta‐splitter and meta‐deflector are experimentally implemented to verify the concept of hybridized analog computing in two domains, as well as providing an advantage of high robustness against scattering interference from environment. Optical spatial‐frequency processing by engineering the off‐resonance metasurfaces is also discussed. The findings provide an alternative approach toward optical analog computing over multi‐domains.
... [24][25][26][27][28][29] A metalens element consisting of two TiO 2 nanofins was utilized to demonstrate diffraction-limited achromatic focusing and imaging from 470 to 670 nm, while the peak efficiency was 20% at 500 nm with numerical aperture (NA) of 0.2. 25 The focusing efficiency has been further improved. 26,30,31 For example, an achromatic metalens based on the GaN metasurface achieved an average focusing efficiency of 40% with NA of 0.106 for 400-660 nm, where the working bandwidth was about 49% of the central wavelength. 26 A polarization-independent fishnetachromatic-metalenses with average efficiencies over 70% and NA of 0.12 was demonstrated in the continuous band from 640 to 1200 nm. ...
... A polarizationindependent BAM with NA = 0.88 was demonstrated in the nearinfrared wavelength range (λ = 1200-1400 nm). 30 For visible wavelengths, high-NA BAMs were achieved by inverse design. 33 However, full width at half maximum (FWHM) of the optimized metalenses is larger than the diffraction limit. ...
... Besides, there are fundamental design limitations and manufacturing constraints for achromatic metalenses with high NA, large structural size, and broad bandwidth simultaneously. According to Ref. 30, the maximum NA of an achromatic metalens is determined by ...
The correction of chromatic aberration and achievement of high numerical aperture (NA) are two main issues for the realistic application of metalenses in imaging and display systems. In this work, we design a broadband achromatic metalens (BAM) with high NA, which is composed of hybrid all-dielectric meta-atoms in the visible region. By simultaneously and independently manipulating the geometric phase and propagation phase, meta-atoms can focus the incident lights on the same spot. Besides, a large phase compensation can be obtained through the variation in structural parameters of the hybrid meta-atom, which is essential to achieve high-NA BAM. For demonstration, the achromatic metalens with NA of 0.68 over the spectrum from 420 to 700 nm is numerically simulated. The metalens possessing high NA, broad bandwidth, and diffraction-limited achromatic focusing performance can be potentially applied in the field of imaging, spectroscopy, display, etc.
