PROCEEDINGS OF SPIESPIEDigitalLibrary.org/conference-proceedings-of-spieHigh efficient metasurface forbroadband achromatic focusing invisible spectrumChang Wang,Rengmao Wu,Siqi Liu,Xiao Tao,WentaoZhang,et al.Chang Wang,Rengmao Wu,Siqi Liu,Xiao Tao,Wentao Zhang,ChenningTao,Shengqian Chang,Peng Sun,Xu Liu,Zhenrong Zheng,"High efficientmetasurface for broadband achromatic focusing in visible spectrum,"Proc.SPIE 10719,Metamaterials,Metadevices,and Metasystems 2018,107192F(19 September2018);doi:10.1117/12.2319566SPIE.Event:SPIE Nanoscience Engineering,2018,San Diego,California,UnitedStatesHigh Efficient Metasurface for Broadband Achromatic Focusing inVisible SpectrumChang Wang,Rengmao Wu,Siqi Liu,Xiao Tao,Wentao Zhang,Chenning Tao,Shengqian Chang,Peng Sun,Xu Liu and Zhenrong Zheng*State Key Laboratory of Modern Optical Instrumentation,Zhejiang University,Hangzhou 310027,China"Corresponding author:zzr@zju.edu.cnABSTRACTAbstract:Metasurfaces are expected to realize the miniaturization of conventional refractive optics into planar structures;however,they suffer from large chromatic aberration due to the high phase dispersion of their subwavelength buildingblocks,limiting their real applications in imaging and displaying systems.In this paper,a high-efficient broadbandachromatic metasurface (HBAM)is designed and numerically demonstrated to suppress the chromatic aberration in thecontinuous visible spectrum.The HBAM consists of TiOz nanofins as the metasurface building blocks(MBBs)on alayer of glass as the substrate,providing a broadband response and high polarization conversion efficiency for circularlypolarized incidences in the desired bandwidth.The phase profile of the metasurface can be separated into two parts:thewavelength-independent basic phase distribution represented by the Pancharatnam-Berry(PB)phase,depending only onthe orientations of the MBBs,and the wavelength-dependent phase dispersion part.The HBAM applies resonance tuningfor compensating the phase dispersion,and further eliminates the chromatic aberration by integrating the phasecompensation into the PB phase manipulation.The parameters of the HBAM structures are optimized in finite differencetime domain(FDTD)simulation for enhancing the efficiency and achromatic focusing performance.Using this approach,this HBAM is capable of focusing light of wavelengths covering the entire visible spectrum (from 400 nm to 700 nm)atthe same focal plane with the spot sizes close to the diffraction limit.The minimum polarization conversion efficiency ofmost designed MBBS in such spectrum is above 20%.This design could be viable for various practical applications suchas cameras and wearable optics.Keywords:Metasurface,achromatic focusing,PB phase,resonance tuning,phase compensation,diffraction limit1.INTRODUCTIONConventional optical lenses are bulky especially when designed for eliminating specific chromatic aberrations,and thislimitation makes it hard for the refractive lenses to be applied in future wearable optical systems such as augmentedreality (AR)glasses.In recent years,metasurfaces have merged and they are one of the most promising components forrealizing plat optical components due to their excellent capabilities of controlling the properties',such as phase andamplitude,of an incoming light wavefront at subwavelength scale.Metasurfaces can work as optical lenses whenhyperbolical phase profiles employed onto them (specified as metalens),however they suffer badly from chromaticaberration and low polarization conversion efficiency for broad bandwidth when initially designed2.To solve thisproblem,some studies proposed achromatic design for metasurfaces at discrete multi-wavelengths or in a very narrowbandwidth5.To date,several pioneering researches provided effective solutions for eliminating full-color chromaticaberrations by incorporating resonance tuning with the Pancharatnam-Berry (PB)phase65-8.Different fromsingle-wavelength optimized metalens,full-color achromatic metasurfaces require designing and arranging themetasurface building blocks (MBBs)specifically for different positions along the aperture in order to acquire thesynthetic phase profile composed of basic focusing profile tuned by PB phase and phase compensation tuned byresonance structures for achromatic engineering'.In this paper,a broadband achromatic metasurface working in the entire visible spectrum(400-700 nm)in transmissionmode was proposed and numerically demonstrated.The MBB of the achromatic metasurface in constructed by an almostMetamaterials,Metadevices,and Metasystems 2018,edited by Nader Engheta,Mikhail A.Noginov.Nikolay I.Zheludev.Proc.of SPIE Vol.10719.107192F©2018SPiE·CCC code:0277-786x/18/s18·doi:10.1117112.2319566Proc.of SPIE Vol.10719 107192F-1Downloaded From:https://www.spiedigitallibrary.org/conference-proceedings-of-spie on 20 Oct 2022Terms of Use:https:/www.spiedigitallibrary.org/terms-of-uselossless dielectric,titanium dioxide (TiO2),working as a phase shifter for offering the desired achromatic focusingphase profile with linear and smooth phase dispersion combing with PB phase2.METHODSCharacteristics of Achromatic Metasurface.Light focusing element is essential in numerous optical systems.Inprinciple,an achromatic focusing lens is able to converge incident light of arbitrary wavelength within the workingbandwidth in to the same focal plane,and the typical converging phase profile follows the equation below:where R=x2+yo2 is the distance from one arbitrary point (xo.yo)on the metasurface to the center point of it,Adis the desired wavelength and f is the designed focal length.The phase profile providing a fixed focal length isschematically shown in Fig.la.We can rewrite Eq.1 as5:(2)(3)Phase Profile for Converging WavefrontPhase Profile for Converging WavefrontA min1210Phase Shift8Phase Shift010position (m)Fig.1.a Phase profile of a normal converging wavefront.b Phase profile with a phase shift for each wavelength.Pancharatnam-Berry Phase.The achromatic lens can only be realized when the requirements in Eq.2 and Eq.3 aresimultaneously and precisely met for all the wavelengths within the desired bandwidth.The first part of the requiredphase,(R,Mx),is wavelength independent,since it is merely a function of position on the metasurface and alsodecided by the maximum wavelength rather than the working wavelength Aa.This kind of phase can be referred as thebasic phase and modulated by PB phase method,which is also named geometric phase,and is imparted by rotating theorientations of the MBBs with the incidence of a circularly polarized light.The MBB is high-aspect-ratio so it isreasonable to regard it as an anisotropic material,and if we take t and ts as the complex transmission coefficients ofthe MBB and a as its rotation angle,as shown in Fig.2,the Jones matrix of the MBB can be described as8.Proc.of SPIE Vol.10719 107192F-2Terms of Use:https:/www.spiedigitallibrary.org/terms-of-use