natureCOMMUNICATIONSARTICLE角Check for updatesOPENOctave bandwidth photonic fishnet-achromatic-metalensBoubacar Kante(1,23,4Planar structured interfaces,also known as metasurfaces,are continuously attracting interestowing to their ability to manipulate fundamental attributes of light,including angularmomentum,phase,or polarization.However,chromatic aberration,limiting broadbandoperation,has remained a challenge for metasurfaces-based optical components and ima-gers.The limitation stems from the intrinsic dispersion of existing materials and designprinciples.Here we report and experimentally demonstrate polarization-independent fishnet-achromatic-metalenses with measured average efficiencies over 70%in the continuous bandfrom the visible (640 nm)to the infrared (1200 nm).Results of the scalable platform areenabling for applications requiring broad bandwidth and high efficiency including energyharvesting,virtual reality and information processing devices,or medical imaging.Department of Electrical Engineering and Computer Sciences,University of Califomia,Berkeley,CA94720 USA.2 Department of Electrical and ComputerEngineering University of California San Diego,La Jolla,CA92093-0407,USA.3Materials Sciences Division,Lawrence Berkeley National Laboratory.1CyclotronRoad,Berkeley,CA94720,USA 4Department of Mechanical Engineering,University of Califomia,Berkeley,CA94720,USA.SThese authors contributed equally:Abdoulaye Ndao,Livi Hsu.email:bkante@berkeley.eduNATURE COMMUNICAT IONS (2020)11:3205|https://doiorg/10.1038/s41467-020-17015-9 |www.nature.com/naturecommunicat ions1ARTICLENATURE COMMUNICATIONS https://doiorg/10.1038/s41467-020-17015-9n 1660,Newton published the discovery on the decompositionfabricated in TiO2 and experimental Strehl ratios larger thanof white light by prisms and color theory.Since then,optical80%are measured in the entire octave bandwidth demonstratingdispersion has continued to fascinate the scientific world.Dis-diffraction-limited operation.persion is used in cosmology to measure the expansion of theuniverse via the propagation of gamma rays!.It is also used in manyResultsoptical applications induding mode-locked lasers and prism spec-Conditions for broadband achromatic operation.In order totroscopy to cite a few,and,explains rainbows2.However,dispersionfocus light to a point for a nommal incident plane wave,a flat lensis a major challenge for imaging systems3.Chromatic aberration,needs to deflect light by a position(r)dependent angle (0)givenoriginating from the variation of the refractive index of materialswith frequency,limits the performance of broadband optical devices.The quintessential feature of chromatic aberration is thewavelength-dependent focal length leading to axial aberration thatdegrades the quality of images.To overcome this limitation,con-(1)ventional optical-imaging systems often use an appropriate combi-where (r,f)is the phase profile required,fis the frequency,F isnation of lenses,such as the achromatic doublet or a combinationof refractive and diffractive elements with opposite dispersion.the focal length,r is the radial position,c is the speed of light,andg is a reference phase function independent of r.The referenceRecently,interest has turned towards thinner,Ilighter devicesknown as metasurfaces4-8.They are subwavelength nanostructuredphase can be an arbitrary function of frequency because only thespatial phase difference matters for the interference of waves atinterfaces,capable of controlling optical waves.A large variety ofcomponents has been reported,including lenses-16,holograms,the same frequency after their interaction with the lens.We thusconsider the phase shift,i.e,the phase difference between thequarter-wave plates,half-wave plates,vortex plates carpet dloaks,concentrators,polarizers thin absorbers,or sensors7-31.Despitelocal phase and the phase at the reference position taken at r=0(center of the lens).Hence,the phase-shift equation for a normalexciting findings,achieving simultaneously high efficiencies andincident wave Ao(r,f)islarge bandwidths has remained a challenge.Recent state of the artresults in the visible reported a bandwidth from 470 to 670 nm withan efficiency of 20%14,while in ref.15 the efficiency of 40%was(2)obtained for the bandwidth from 400 to 660 nm.Here,we experimentally report polarization-independent,where m(r)is the frequency slope of the phase-shift.Equation (2)fishnet-achromatic-metalenses (FAM)with measured averagereveals the requirements of a broadband achromatic metalens.First,efficiencies over 70%in the continuous band from the visiblethe phase-shift for all positions is linear with respect to frequency.(640 nm)to the infrared (1200 nm).The design approach isThis condition can be locally satisfied using waveguide modes.based on the simultaneous control of the slope and the phase-Second,the slope of the phase-shift(dispersion)varies with positionshift-intercept,two parameters that need to be continuouslyfollowing Eq (2)and the phase-shift A(r,f)is proportional tooptimized in the lens for achromatic operation.The lens isfrequency,i.e.,the phase-shift intercept with respect to frequency iszero.The metasurface is thus a waveguide array with,ideally,a localand simultaneous control of the slope and the intercept of thephase-shift.To satisfy the requirements of achromatic broadbandmetalenses,we propose to use the cross-cirde waveguide shown inFig.la as building block.The building block has four geometricalparameters that are the radius (R),the width (W),the length (L),and the period (P).Constraints impose for example Ws2R andL P.Using geometric parameters,the slope can be controlled witha quasi-control of the phase-shift intercept consisting of minimizingit (ideally zero).Because each position has a unique (slope,phase-shift intercept)coordinate,dimensions can be chosen accordingly.One of the unique aspects of the device is that the design accountsfor modified near-field interactions that usually hinder the perfor-mance of metalenses as explained in ref.23.This is done via the iso-slopes and iso-phase-shift intercepts used in the construction of ourmetasurfaces.It is important to note that the four geometricparameters are not independent,as a change in any of them canaffect the effective index of the waveguide they form.This signifiesthat it is challenging to have perfect achromaticity and efficiency asphase-shift intercepts and slopes cannot be fully independentlycontrolled in a planar design.The limitation confirms that this isintrinsically an optimization problem32-35.In metasurfaces,the spatial derivative of the slope controls thedirection of incident rays to make them reach the focal point.It isFig.1 Schematic and scanning electron micrograph of a fishnet-thus important to have the correct slope to prevent chromaticachromatic-metalens (FAM).a Schematic of the proposed broadbandeffects and a decrease in efficiency.The intercept,however,metalens and its unit-cell with multi-degrees of freedom.The period ofcontrols the superposition of waves at the focal point,i.e.,mostlythe unit-cell (P)is 370 nm,the height of the unit-cell (H)is 350 nm,and theaffects the efficiency of the lens,not the position of the focalmetasurface is made of titanium dioxide (TiO2).The design parameters arelength.We can thus compromise on the intercept in the design ofthe width of the cross (W),the length of the cross (L),and the radius (R).the lens.To quantify the impact of a non-zero phase-shiftb Top view of an optical microscope image of a fabricated FAM and zoom-inintercept on the efficiency of our metalens Monte Carloshowing the quality of the fabricated device.The scale bar represents 5um.simulations are performed with 100 simulations for each element2NATURE COMMUNICATIONS|(2020)11:3205 https://doi.org/10.1038/s41467-020-17015-9 www.nature.com/naturecommunicationsNATURE COMMUNICATIONS https://doiorg/10.1038/s41467-020-17015-9ARTICLEaSlope (.THz)Intercept (2502505200-0.020.04200-10-151500.06150-201000.0100290290280280270270260260250250240240406080100120140406080100120140R(nm)R(nm)Fig.2 Design strategy of the FAM.To control the slope a,c and the phase-shift intercept b,d,at least two parameters need to be controlled.Theconsidered two parameters are the width and the radius (W.R)(from step 1 to step 2 in a,b)and the length and the radius (L,R)(from step 3 to step 4 inc,d).From step 1 to step 2,W varies from 80 to 270 nm,and,R varies from 60 to 135 nm while L is fixed to 370 nm.From step 3 to step 4,L varies from240 to 290 nm while W is fixed to 80 nm to account for limitations in fabrication.Insets in a illustrate the evolution of the structure (top view)as onemoves from the center (step 1)to the edge of the FAM (step 4),and,red/back colors represent TiO2/SiO2.using a homemade finite difference time domain code.Eachparameters in Fig.2c and the second trajectory (blue points alongsimulation was given a certain magnitude of the phase-shiftthe black arrow)also keeps the phase-shift intercept error belowintercept (error or deviation from the ideally zero phase-shift30(Fig.2d).The evolution of the geometry of the unit-cell fromintercept)that was randomly distributed between unit-cells.Thethe center of the lens to its edge is further discussed infocusing efficiency was then compared to the ideal metalenssupplementary information (Supplementary Fig.1).implementing not only the correct slope but also the correctphase-shift intercept.Results,presented in SupplementaryFabrication of the FAMs.The designed structure is fabricated byinfommation,indicate that an error on the phase-shift intercepttop-down methods and the SEM of a metalens,presented insmaller than 30 decreases the efficiency of the metalens by <10%Fig.1b,dearly shows the high quality of the implementation.Theand does not affect the position of the focal point.fabrication uses three major steps.The first step consists of pat-terning the polymethyl methacrylate(PMMA)resist using elec-Design of the FAMs.Figure la presents a sketch of the titaniumtron beam lithography (EBL)that is subsequently developed indioxide (TiO2)-based metasurface and the geometry of the unit-solution to remove the exposed PMMA.The pattern is the inversecell with multiple degrees of freedom.It is a fishnet-like structureof our final metasurfaces.In the second step,the exposed samplewith a period P=370 nm and a height H=350 nm.The struc-is transferred to an atomic layer deposition (ALD).The ALDture is fabricated by top-down nano-manufacturing methods andprocess deposits 350 nm of TiO2 so that all features are filled.Thea scanning electron micrograph(SEM)of a fabricated metalens asthird step consists of removing the residual TiO,film that coatsshown in Fig.1b.To design our metasurface,geometric para-the top surface of the resist using reactive-ion-etching.Aftermeters are controlled by pair,(W,R)in Fig.2a,b and (L,R)inremoving PMMA,the TiO2 metasurfaces were obtained.It isFig.2c,d.By considering fabrication limits,iso-slopes and iso-worth noting that FAMs have mostly connected structures andphase-shift intercept plots of realistic geometries are computedare thus more stable mechanically than metasurfaces based onusing full-wave numerical simulations(CST Microwave Studio)fully disconnected elements.Fabrication imperfections with aand the local phase method23,followed by least-square linearmagnitude of +5nm decrease the efficiency by at most 8%,fitting.The phase shift of elements is calculated using a referencemaking the FAMs robust(Supplementary Fig.10).at the center of the lens with geometric parameters W=270 nmR=135 nm,and L=P=370 nm.For all other geometries,theCharacterization of the FAMs.The fabricated metalenses wereparameters in Fig.2 are calculated.optically characterized using a custom setup consisting of twoFigure 2a,cshow that changes in R,W,and L enable slopes frommain systems dedicated to illumination and imaging (Supple-zero to -0.35THz-1 which in turn determines the maximummentary Fig.5).The illumination system comprises a super-achievable size of the metalens for a given focal length.The figurecontinuum laser and an acousto-optic tunable filter to select thealso confirms that it is not possible to fully independently controloperating wavelength.For the imaging system,a x50 extra-longthe slope and the phase shift-intercept.However,accepting anworking distance microscope objective lens with a numericalerror on the phase shift intercept enables designs sweeping all slopeaperture of 0.65 and a tube lens with a focal distance of 20 cmvalues.Figure 2a enables slopes from zero to -0.2 THz-1 whilewere used to image planes of interest on a camera.To image thekeeping a phase-shift intercept error below 30(Fig.2b).Forfocusing pattem,we moved the sample around the focal pointthe 20 umx 20 um metalens,we have chosen points indicated inusing a translation stage.blue(along the black arrow)to minimize discretization errors andFigure 3a presents the measured intensity profiles in thefocal plane z=F (transverse x-y plane)of the metalenses atFor absolute value of slopes larger than 0.2 THz-1,we useddifferent wavelengths.The dots in Fig.3b represent a normalizedNATURE COMMUNICATIONS (2020)11:3205|https://doiorg/10.1038/s41467-020-17015-9 |www.nature.com/naturecommunicat ions3