natureCOMMUNICATIONSARTICLEOPENA broadband achromatic polarization-insensitivemetalens consisting of anisotropic nanostructuresMetasurfaces have attracted widespread attention due to an increasing demand of compactand wearable optical devices.For many applications,polarization-insensitive metasurfacesare highly desirable,and appear to limit the choice of their constituent elements to isotropicnanostructures.This greatly restricts the number of geometric parameters available in design.Here,we demonstrate a polarization-insensitive metalens using otherwise anisotropicnanofins which offer additional control over the dispersion and phase of the output light.As aresult,we can render a metalens achromatic and polarization-insensitive across nearly theentire visible spectrum from wavelength =460 nm to 700 nm,while maintainingdiffraction-limited performance.The metalens is comprised of just a single layer of TiOznanofins and has a numerical aperture of 0.2 with a diameter of 26.4um.The generality ofour polarization-insensitive design allows it to be implemented in a plethora of othermetasurface devices with applications ranging from imaging to virtual/augmented reality.Harvard John A.Paulson School of Engineering and Applied Sciences,Harvard University.Cambridge,MA 02138,USA.2University of Waterloo,Waterloo,ON N2L 3G1,Canada.Correspondence and requests for materials should be addressed to W.T.C.(email:weitingchen@seas.harvard.edu)or to F.C.(email:capasso@seas.harvard.edu)NATURE COMMUNICATIONS (2019)10:355 https://doi.org/10.1038/s41467-019-08305-y |www.nature.com/naturecommunicationsARTICLENATURE COMMUNICATIONS https://doi.org/10.1038/s41467-019-08305-yetasurfaces comprising sub-wavelength spaced nanos-dispersion (group delay and group delay dispersion)24.25.33.tructures at an interface provide the means to accu-However,this approach also comes with an unwanted polariza-rately control the properties of light,including phase,tion-sensitivity,i.e.these achromatic metalenses can only focusamplitude,and polarization!4.This allows for the possibility ofincident light with a particular circular polarization.highly compact and efficient devices5-13.Amongst these devicesOur design principle still involves Pancharatnam-Berry phase;metalenses have attracted intense interest due to their applic-however,we circumvent the aforementioned drawback byability to both consumer (phone cameras,virtual/augmentedlimiting the rotation angle of each anisotropic element to eitherreality headsets)and industry products(microscopy,lithography,0 or 90 degrees.Each element is comprised of multiple nanofinssensors and displays)14-23'Recent works have focused onto provide additional degrees of freedom to engineer thedeveloping the broadband achromatic focusing capabilities ofdispersion (Fig.1a,inset).The layout of a quarter of ourmetalenses in the visible spectrum24.25.However,these meta-achromatic and polarization-insensitive metalens is depicted inlenses suffer from polarization sensitivity,i.e.,they can only focusFig.la and a scanning electron microscope image from a regionlight of a given circular polarization.This challenge can beof our fabricated metalens is shown in Fig.1b.To tune the phaseovercome by using symmetric cylindrical or square-shaped nano-and dispersion,each nanofin's length and width is varied and thepillars in both the visible26 and the near-infrared regions27-29.gap(g)between nanofins is set to be either 60 nm or 90 nm.ByHowever,by doing so,we lose a degree of freedom in the designusing anisotropic elements instead of standard symmetric circularspace due to the symmetry of these constituent structures.Here,counterintuitively,we show that it is indeed possible tofor better dispersion control.More importantly,the anisotropicsimultaneously achieve an achromatic metalenscapableofelements offer the freedom to impart an additional n phase shiftfocusing any incident polarization in the visible using anisotropicwithout changing their dispersion characteristics.This is essentialTiO2 nanofins.This is a different solution compared to recentin order to fulfill both the required phase and dispersion givenpublications associated with spatial multiplexing and sym-by Eq.2,and can be understood from the Pancharatnam-Berrymetry30-32.These anisotropic nanofins allow us to accurately andsimultaneously implement the phase and its higher-order deri-electric field can be described by the Jones vector.36vatives(i.e.,group delay and group delay dispersion)with respectto frequency.We designed and fabricated a metalens with anumerical aperture (NA)of 0.2.The metalens exhibits a mea-E2±i2(3)sured focal length shift of only 9%A=460-700 nm and hasdiffraction-limited focal spots across the entire range.Thefocusing efficiency of the metalens varies by only ~4%underwhere i and t,represent complex transmission coefficients whenvarious incident polarizations.To showcase the generality ofthe normalized electric field of the incident light is polarizedour principle,we also demonstrate a polarization-insensitivealong the long and short axis of the nanofin,respectively.The ametasurface with diffraction efficiency of about 92%atterm is defined as the counterdlockwise rotation angle of thewavelength入=530nm.nanofin with respect to the x-axis.The first term of Eq.3 causesunwanted scattering and can be minimized if the nanofin isResultsdesigned as a miniature half-waveplate.In this case,thePrinciple of polarization-insensitive and achromatic focusingTo achromatically focus a broadband incident beam in a dif-to maximal polarization conversion efficiency.The exp2 in thefraction limited spot,a metalens must impart a spatially andsecond term is accompanied by a polarization converted temm andfrequency-dependent phase profile given byillustrates the origin of Pancharatnam-Berry phase.Under left-handed circularly polarized incidence,a rotation of a imparts afrequency-independent phase of 2a to the right-handed circularlywhere r,w,and F are the lens radial coordinate,angular fre-polarized output light)without affecting the dispersion,quency,and a constant focal length,respectively.The Taylorexpansion of Eq.1:which is determined by This usually results in polarization-sensitivity because the values of expi2e and exp-i2,obtaineddoo(r.w)-g(r,wa)+a(w-@a)+under left and right circular polarized(LCP and RCP)incidentlight,respectively,are not identical.However,if one arranges thenanofin with a=0 or a=90,their values become equal.(2)Therefore,both RCP and LCP incident light will experience thesame phase profile upon interacting with a metalens consisting ofidentifies the required phase(,group delayandeither mutually parallel or perpendicular nanofins.Since anygroup delay dispersionthat needs to be fulfilled at everyincident polarization can be decomposed into a combination ofLCP and RCP,this property implies that the metalens islens coordinate r.An intuitive way to understand each termpolarization insensitive,capable of focusing any incidentin Eq.2 is to treat the incident light as wavepackets.The requiredpolarization.Figure 1c confirms the results predicted by Eq.3.phase profile sends incident wavepackets towards the focal point,A metalens element provides the same phase for both RCP (line)while the first and the higher order derivative terms ensure thatand LCP(circles)incidence,and,for a given circular polarization,the incident wavepackets arrive at the focal point simultaneouslya 90-degree rotation imparts a phase shift without affectingand identically in the time domain,respectively24.The challengegroup delay (slope)and group delay dispersion (curvature).here lies in the fact that the chosen nanostructures must satisfyeach derivative term in Eq.2 at every lens coordinate.PreviousDesign of an achromatic and polarization-insensitive metalens.designs made use of the geometric (or Pancharatnam-Berry)The design of our polarization-insensitive and achromaticphase principle to decouple the phase,(r,wa),from themetalens starts from a parameter sweep of the element shown inNATURE COMMUNICAT IONS (2019)10:355 |https://doi.org/10.1038/s41467-019-08305-y www.nature.com/naturecommunicationsNATURE COMMUNICATIONS https://doi.org/10.1038/s41467-019-08305-yARTICLEWavelength (nm)7496005004283655Tecp-CP10m400500600700800Frequency (THz)Fig.1 Principle behind polarization-insensitive and achromatic metalens.a Layout of a quadrant of the metalens.It has a NA of 0.2 and a diameter of 26.4um.The inset shows a schematic diagram of its constituent elements.Each element comprises TiO2 nanofins with the same height h=600 nm.These elements are spaced equally with a lattice constant of 400 nm.b A scanning electron microscope image of a part of the fabricated metalens.Scalebar:1 um.The inset shows a magnified and oblique view of the nanofins.Scale bar:500 nm.c Simulated phase shift of the component of the transmittedelectric field with polarization orthogonal to the incident circularly polarized light.The legend,for example T represents the phase of RCPtransmitted light under LCP incidence.The blue and red colors show the same element,consisting of three nanofins,oriented along horizontal and verticaldirections,respectively.The nanofin parameters (w/w2,la w3ls g)=(50,50,170,370,50,90,60)in nanometer units.The element shows identicalphase under both RCP and LCP illuminations.Note that for a given incident circular polarization,a 90-degree rotation introduces ax phase shift withoutaffecting group delay (slope)and group delay dispersion (curvature)the inset of Fig.la to build a library.We used a finite-differenceFocal spot and focusing efficiency characterizations.We sub-time-domain (FDTD)solver to obtain each element's phase atsequently fabricated the achromatic and polarization insensitiveA=530 nm,as well as its group delay and group delay dispersion.metalens using electron beam lithography,followed by atomicMore simulation details can be found in our previous publica-layer deposition of TiO2 and resist removal37,and compared itstion24.Figure 2a plots the three quantities of interest:phase,performance to a chromatic metalens of the same diameter andgroup delay,and group delay dispersion,at the design wavelengthNA.The chromatic metalens was designed using rotated nano-of 530 nm for each element.There are thousands of geometricalfins with the same length and width to impart the Pancharatnam-combinations,resulting in a dense scatter plot from which weBerry phase.The chromatic metalens represents the case withoutidentify the optimal elements to fine tune the dispersion.Notedispersion engineering and has a focal length shift similar to athat due to the principle outlined in Fig.1c,an element rotated byFresnel lens.We also show in Supplementary Movie 1 simulation90 degrees (i.e.purple points)will experience a n phase shift forresults for a complete metalens with a smaller lens diameter and aall frequencies with no change in the values of its dispersion.As ahigher NA of 0.6,confirming its achromatic and polarization-result,the design library can be further extended,allowing forinsensitive focusing behavior(Supplementary Figure 1).The focalbetter implementation of the required phase and dispersionlength shifts of the fabricated achromatic and chromatic meta-(black symbols),which were calculated based on Eq.1 for anlenses were determined by measuring their point spread functionsachromatic metalens with a diameter of 26.4 um and an NA ofat each wavelength along the propagation direction(z-axis)with0.2.To realize the metalens,the elements selected must be those1 um resolution (Fig.3a).The left panel in Fig.3a demonstrates aclosest to the required (black)points in the 3-dimensional spacesmall focal length variation of about 6 um for the achromaticof phase,group delay,and group delay dispersion displayed inmetalens compared to that of 30 um in the chromatic metalensFig.2a.Because only the relative values of these parameters are(right panel).The normalized intensity profiles along the whiteimportant,the library can be shifted in this 3-dimensional spacedashed lines can be seen in Fig.3b and Supplementary Figure 2to better fit the required values.A partide swarm optimizationfor the achromatic and chromatic metalenses,respectively.Themethod was used to find the optimal shifts for phase,group delay,achromatic metalens is diffraction-limited and its focal spot sizesand group delay dispersion,which minimizes the distanceand Strehl ratios as a function of wavelength are given in Sup-between each required point and the values provided by theplementary Figure 3.Figure 3c shows achromatic imaging of aelements in our library.The final results can be better visualizedUSAF resolution target from blue to red wavelengths in thein Fig.2b-d.The phase,group delay,and group delay dispersionvisible.The results of imaging colored objects are given in Sup-of the selected metalens elements are shown in blue,together withplementary Figure 4.The achromatic metalens was also char-the corresponding required values (black curves).We only con-acterized by measuring the focusing efficiency of the focal spotsider terms up to the group delay dispersion because the values of under different polarizations of incident light.The focusing effi-any higher orders for our selected elements are very small.ciency is defined as the focal spot power divided by transmittedNATURE COMMUNICATIONS (2019)10:355 https://doi.org/10.1038/s41467-019-08305-y |www.nature.com/naturecommunications3