NANOLetterETTERSpubs.acs.org/NanoLettAberration-Free Ultrathin Flat Lenses and Axicons at TelecomWavelengths Based on Plasmonic MetasurfacesFrancesco Aieta Patrice Genevet,t.s Mikhail A.Kats,Nanfang Yu,Romain Blanchard,Zeno Gaburro,and Federico CapassoSchool of Engineering and Applied Sciences,Harvard University,Cambridge,Massachusetts 02138,United StatesDipartimento di Scienze e Ingegneria della Materia,dell'Ambiente ed Urbanistica,Universita Politecnica delle Marche,via BrecceBianche,60131 Ancona,ItalySInstitute for Quantum Studies and Department of Physics,Texas A&M University,College Station,Texas 77843,United StatesDipartimento di Fisica,Universita degli StudidiTrento,via Sommarive 138100 Trento,ItalySupporting InformationABSTRACT:The concept of optical phase discontinuities is appliedto the design and demonstration of aberration-free planar lenses andaxicons,comprising a phased array of ultrathin subwavelength-spacedoptical antennas.The lenses and axicons consist of V-shaped nano.antennas that introduce a radial distribution of phase discontinuities,thereby generating respectively spherical wavefronts and nondiffractingBessel beams at telecom wavelengths.Simulations are also presented toshow that our aberration-free designs are applicable to high-numericalaperture lenses such as flat microscope objectives.212102LensAxicon。KEYWORDS:Metasurfaces,phase-discontinuities,lens,axicon,plasmonics,aberration-freeIn the microwave and millimeter-wave regimes,local controlof the phase ofelectromagnetic waves obtained with reflectarrayswavelength range where the choice of transparent materials isor frequency selective surfaces has enabled alternative designs forlimited.Usually it requires complex optimization techniquesflat lenses.For example,in reflectarrays,scattering units com-such as aspheric shapes or multilens designs,which are expen-prising metallic patch antennas coupled with a ground plane cansive and bulky.provide an arbitrary phase shift between the scattered andAxicons are conical shaped lenses that can convert Gaussianincident light.beams into nondiffracting Bessel beams and can create hollowAt optical frequencies,planar focusing devices have beenbeams.34 Since their invention in 1954,s axicons have founddemonstrated using arrays of nanoholes,optical masks-4ormany applications in telescopes,autocollimators,microscopes,nanoslits.sThese techniques require complex design rules or dolaser surgery,and optical trapping.not provide the ability to tailor the phase of the transmitted lightFocusing diffracting plates offer the possibility of designinglowfrom 0 to 2,which is necessary for a complete control of theweight and small volume lenses.For example the Fresnel Zoneoptical wavefront.In addition flat metamaterials based lensesPlate focuses light by diffracting from a binary mask that blockspart of the radiation.A more advanced solution is representedby the Fresnel lens,which introduces a gradual phase retardationThe concept of optical phase discontinuities,which has beenin the radial direction to focus light more efficiently.By limitingused in the demonstration of new metasurfaces capable ofthe absorption losses and gathering oblique light more efficiently,beaming light in directions characterized by generalized laws ofFresnel lenses are advantageous for optical systems with highnumerical aperture (NA).To guarantee a smooth sphericalflat lenses.In this approach,the control of the wavefront nophase profile responsible for light focusing,the Fresnel lenslonger relies on the phase accumulated during the propagation ofthickness has to be at least equal to the effective wavelength=A/n where n is the refractive index of the medium.Moreover,theReceived:July 7,2012thickness of the lens needs to be continuously tapered,whichRevised:August 2,2012becomes complicated in terms of fabrication.Published:August 15,20124932Nano LettersLetterlight but is achieved via the phase shifts experienced by radiationaas it scatters off the optically thin array of subwavelength-spacedresonators comprising the metasurface.This strategy resemblesreflectarrays and transmit-arrays used at much lower frequen-azimuthal phase gradients lead to the formation of complexwavefronts such as helicoidal ones,which characterize vortexbeams.In this paper,we experimentally demonstrated lightfocusing in free space at telecom wavelength A=1.55 umusing 60 nm thick gold metasurfaces.We fabricated two flatlenses of focal distances 3 and 6 cm and a flat axicon with anangle =0.5(which corresponds to a glass plano-convexaxicon with base angle 1);see Figure 1.Our experiments arelaserpinhole detectorflat lensflat axiconPhase Shift[degree]5000Figure 1.Schematic showing the design of flat lenses and axicons.Inorder to focus a plane wave to a single point at distance f from themetasurface,a hyperboloidal phase profile must be imparted onto theproportional to the distance PSL,where SL is the projection of PL ontothe spherical surface of radius equal to the focal length f.The resultinghyperboloidal radial phase distribution on the flat lens is shown in(b);Figure 2.(a)FDTD simulations are usedto obtain the phase shifts and(c)The axicon images a point source onto a line segment along thescattering amplitudes in cross-polarization for the eight elements used inoptical axis;the length of the segment is the depth of focus(DOF).Theour metasurfaces (see Supporting Information for details).Theparameters characterizing the elements from 1 to 4 are d 180,140,130,and 85 nm,and=79,68,104,and 1759.Elements from 5 to 8 arewhere Sa is the projection of Pa onto the surface ofa cone with the apexat the intersection ofthe metasurface with the optical axis and base angleobtained by rotating the first set of elements by an angle of90 counter-dockwise.The width of each antenna is fixed at w=50 nm.(b)B=tan(r/DOF)(r is the radius of the metasurface).The resultingconical radial phase distribution on the flat axicon is shown in (d).Thephase profiles for the flat lenses and axicons are implemented usingthe sample with y-polarization.The light scattered by the metasurface inV-shaped optical antennas.x-polarization is isolated with a polarizer.A detector mounted on athree-axis motorized translational stage collects the light passingthrough a pinhole,attached to the detector,with an aperture ofin excellent agreement with numerical simulations;our calcu-50 fm.Note that the lenses (and the axicon discussed later)work alsolations also point to the possibility of achieving high NAfor x-polarized illumination because of symmetry in our design (thelenses.antennas have their symmetry axis along the 45 direction).ThexThe design of our flat lenses is obtained by imposing apolarized illumination will lead toypolarized focused light.(c)SEMimage of the fabricated lens with 3 cm focal distance (left).Thehyperboloidal phase profile on the metasurface.In this way,corresponding phase shift profile calculated fromeq 1 and discretizedsecondary waves emerging from the latter constructivelyaccording to the phase shifts of the eight antennas is displayed on theinterfere at the focal plane similar to the waves that emergeright.Insets:close up of patterned antennas.The distance betweenfrom conventional lenses.'For a given focal length f,the phasetwo neighboring antennas is fixed at A 750 nm in both directionsshift L imposed in every point PL(x y)on the flat lens mustfor all the devices.satisfy the following equation (Figure 1a)For an axicon with angle B,the phase delay has to increase1linearly with the distance from the center,creating a conicalphase distribution.The phase shift at every point Py)haswhere is the wavelength in free space.to satisfy the following equation(Figure 1c)4933Nano LettersLetter2xLens f=3cmAxicon B=0.5(2)0.40.60.8500Optical antennas with equal scattering amplitudes and phasecoverage over the whole 0-to-2 range are necessary for designing250flat lenses with a large range offocal distances.Following the ap.proach previously discussed,we design eight differentplasmonic V-shaped antennas that scatter light in cross-polarization-250with relatively constant amplitudes and an incremental phase ofCalculationCalculation/4 between neighbors.Figure 2a shows the cross-polarized500scattering amplitudes and the corresponding phase shifts for theeight elements obtained with full-wave simulations using the250finite-difference time-domain technique (FDTD).Using egs 1and 2,we design two lenses with radius r =0.45 mm and focallengths f =3 cm (NA 0.015)and f=6 cm (NA =0.075),-250respectively,and an axicon with the same radius and an angle=Measured0.5.The devices are fabricated by patterning one face of axz cross sectiorxz cross section500double-side-polished undoped silicon wafer with gold nano-antennas using electron beam lithography (EBL).The antenna250arrays were surrounded by an opaque mask(15 nm titanium and200 nm silver),which completely reflects the fraction of the0incident beam that is not impinging on the arrays.To avoidmultireflections in the silicon wafer,a /4 antireflective coating250MeasuredMeasuredfilm of SiO was evaporated on the backside of the wafer that isyz cross sectionyz cross sectionnot decorated with antennas.The incident beam has a radius50033wo~0.6 mm (wo is the radius at which the field amplitude dropsz [cm]z [cm]to 1/e of the peak value)to ensure that the entire array isilluminated by a plane-wave-like wavefront.The measurementFigure 3.(a-c)Theoretical calclations and experimental results of thesetup is shown in Figure 2b.intensity distribution in the focal region for the flat lens with f=3 cm.(a)To facilitate the design of the metasurfaces,we used a simpleCalculation using the dipolar model (b,c)The experimental resultsanalytical model based on dipolar emitters.28 The emissionfar-field distributions.(d-f)Theoretical calculations and experimentalof our antennas can be well approximately by that of electricresults of the intensity distribution for the planar axicon with =0.5.dipoles We can calculate the intensity of the field()scattered from a metasurface for a particular distribution of am-plitudes and phases of the antennas by superposing the con-the cross sections of the intensity at the focal plane of the lensestributions from many dipolar emitters.This approach offers awith NA =0.015 (as in the fabricated device)and NA =0.77.The design of this new dlass of focusing devices is free fromThe metasurface is modeled as a continuum of dipoles withmonochromatic-aberrations typically present in conventionalidentical scattering amplitude and a phase distribution given byrefractive optics.The phase distribution created from a sphericaleqs 1 and 2.By comparing calculations based on this model andlens focuses light to a single point only in the limit of paraxialthe experimental data,we can determine whether the phase dis.approximation;a deviation from this condition introducescretization and the slight variations in the scattering amplitudesmonochromatic aberrations such as spherical aberrations,of the eight elements create substantial deviations from thecoma,and astigmatism.To circumvent these problems,complexoperation of ideal devices.The measured far-field for the lens withoptimization techniques such as aspheric shapes or multilensdesigns are implemented.In our case,the hyperboloidal phase3 cm focal distance and the corresponding analytical calculations aredistribution imposed at the interface produces a wavefront thatpresented in Figures 3a-c.Theresults foranideal axicon and for theaxicon metasurface are presented in Figures 3d-f.Note that theremains spherical even for nonparaxial conditions.This will leadto high NA focusing without aberrations.actual nondiffracting distance of the axicon metasurface is shorterthan the ideal DOF because the device is illuminated with aA present limit of our design is the focusing efficiency,collimated Gaussian beam instead of a plane wave.3approximately 1%.Increasing the antenna spacing from thecurrent value of 750 to 220 nm will lead to ~10%efficiency,In Figure 4,we present the calculated and the measuredbased on our simulations.Additional efficiency increases areintensity profiles in the transverse direction for the three devices.For the lenses,we choose the focal planes to be at z 6 cmother plasmonic materials.Finally we wish to note that by(Figure 4a,d,g)and z=3 cm (Figure 4b,e,h).For the axicon,theexploiting antenna designs with higher scattering amplitude (e.g.tranverse cross section was taken at a distance of 3.5 cm from theantennas with a metallic back plane operating in reflectioninterface which is within the DOF (Figure 4c,f,i).mode),focusing efficiencies up to 80%should be possible.To prove the possibility of creating lenses with high NA weIn conclusion,flat lens and axicon designs based on plasmonicperformed FDTD simulations of the metasurfaces.Instead of themetasurfaces are presented.They are characterized by lack ofwhole lens comprising a two-dimensional array of antennas,we simu-monochromatic aberration even at high NA.We have fabricatedlated only the unit cell(Figure 5a).This simplified design is equi.and demonstrated two lenses with centimeter scale focal lengthsvalent to a cylindrical lens;it is useful for understanding theand an axicon with angle=0.5.The experimental results are infocusing proprieties of high NA objective.Figure 5b,c showsgood agreement with analytical calculations using a dipolar4934