Zixin CAI ,Xin HE?? ,Xin LIU ,Shijie TU ,Xinjie SUN ,Paul BECKETT ,Aditya DUBEY,Arnan MITCHELL,Guanghui REN??,Xu LIU,Xiang HAO??,4,5

1State Key Laboratory of Modern Optical Instrumentation,College of Optical Science and Technology,Zhejiang University,Hangzhou 310027,China

2School of Engineering,RMIT University,Melbourne 3000,Australia

3Integrated Photonics and Applications Centre (InPAC),RMIT University,Melbourne 3001,Australia

4Intelligent Optics &Photonics Research Center,Jiaxing Research Institute Zhejiang University,Jiaxing 314000,China

5Jiaxing Key Laboratory of Photonic Sensing &Intelligent Imaging,Jiaxing 314000,China

Precise,wavelength-dependent phase retarding is essential in many fields,such as superresolution imaging,full-color holography,nanomanufacturing,and optical communications.This demand can be achieved by a combination of multiple optical devices but is challenging to implement using a single element.In this paper,we develop a method for metasurface design that allows wavelength-selective wavefront shaping.Specifically,we demonstrate a metasurface that can selectively modulate a beam with a spiral phase at 785 nm and leave another beam unaffected at 590 nm.The wavefronts are experimentally validated by an interferometer and the measurement of the cor‐responding point spread functions (PSFs).Compared to prior spatial multiplexing and dispersion engineer‐ing approaches,our strategy is straightforward and flexible during optimization for systems that need to selectively modulate one beam at a wavelength and leave another one unaffected.Such a planar device provides a compact method for wavelength-selective wavefront modulation.

1 Introduction

Phase modulation is demanding across a range of applications,such as optical communication (Huang et al.,2020),superresolution imaging (Hell and Wichmann,1994;Hao et al.,2021),beam shaping (Ouadghiri-Idrissi et al.,2016),quantum cryptography (Mirhosseini et al.,2015),and holographic displays (Sasaki et al.,2014).Conventional approaches to phase modulation involve devices such as phase plates (Ruffato et al.,2014;Guo et al.,2020),deformable mirrors (Ma et al.,2018;Yu et al.,2018),and spatial light modulators (Jesacher et al.,2014;Liu X et al.,2021,2022),which allow flexible wavefront shaping.How‐ever,they are always bulky and tend to dramatically increase the system’s complexity when multiple laser beams with diverse wavefronts are expected.

Metasurfaces,comprising surface-patterned nano‐structures with subwavelength geometries,have attracted much attention in recent years due to their excellent light modulation capability.These nanoscale patterned surfaces have been shown to interact with the modu‐lated incident wavefront in terms of polarization (Mueller et al.,2017;Liu MZ et al.,2021;Zheng et al.,2021),angle of incidence (Deng et al.,2018;Sp?gele et al.,2021),and wavelength (He et al.,2020;Zhang et al.,2021) multiplexing.In particular,compared to con‐ventional optical devices,metasurface structures show unprecedented flexibility to manipulate the properties of light,leading to various ultrathin optical elements,such as metalenses (Khorasaninejad et al.,2016b),holographic pulse shapers (Georgi et al.,2021),vortex beam generators (Hu et al.,2021),and filters (Yang et al.,2020).

Among them,wavelength-selective metasurfaces exhibit the additional ability to implement distinct modulation functions at different illumination wave‐lengths.Previous studies on wavelength-selective meta‐surfaces include sectoring regions (Khorasaninejad et al.,2016a;Maguid et al.,2016;Li et al.,2021),interleaved pixels (Arbabi et al.,2016;Bao et al.,2019;Feng et al.,2019),and dispersion engineering of subwavelength building blocks (Sell et al.,2017;Shi et al.,2018;Shrestha et al.,2018).In sectoring and interleaved ap‐proaches,the metasurface is divided into several regions or subpixels,each specifically aiming at a unique wave‐length.Owing to their partitioned geometry,these spatial multiplexing approaches inevitably suffer from crosstalk problems between adjacent regions or sub‐pixels.They also exhibit an inherent limit to their maximum efficiency since each subregion is designed for only one wavelength.In contrast,dispersion engi‐neering approaches can simultaneously fulfil the target wavefront modulation at all desired wavelengths,thereby addressing the crosstalk issue and overcoming the transmission efficiency limit.However,these methods require building a large meta-atom library to meet the multiwavelength response and thus mandate a bruteforce search of all these potential building blocks,which in turn requires huge computing resources.This pres‐ents an increasing design and optimization challenge as the number of operating wavelengths increases.

In this paper,we employ a combination of wavelength-dependent polarization conversion and geometric phase (Mueller et al.,2017) to design a metasurface-based wavelength-selective phase modu‐lator that can exhibit unique wavefront responses at different illumination wavelengths.Specifically,we design a metasurface that focuses the beam to an an‐nular ring at 785 nm and a solid spot at 590 nm.For those systems that need to selectively modulate one wavelength wavefront and leave another unaffected,our design can break the inherent efficiency limit since every element simultaneously contributes at both target wavelengths in contrast to the spatial multiplexing ap‐proaches.Furthermore,brute-force searching of the unit cell in a large meta-atom library is not required so that the optimization process is less time-consuming.

2 Design and simulation

The basic building block of our design,shown in Fig.1a,consists of a rectangular nanofin arranged on a hexagonal substrate with the center-to-center distanceS.Each nanofin has the same height (H),length (L),and width (W),but has different azimuthal anglesφ’s at different positions.Such an element can be described as a conventional linearly birefringent waveplate with the Jones matrixJ(φ) (Devlin et al.,2016):

Fig.1 Metasurface design and simulation validation

whereR(φ) is the rotation matrix andandare the complex transmission coefficients along the long and short axes of the nanofin,respectively.With a circu‐larly polarized beam incidence,the transmitted beam can be expressed as

which shows that the transmitted beam includes two components: the copolarization part and the crosspolarization part.The modulated phase shift of the copolarization part includes only the dynamic phase (the phase part of,also called the propagation phase,which is a function of the nanofin material and its geometry.In addition to this propagation phase,the phase shift of the cross-polarization includes an‐other component: the Pancharatnam–Berry (PB) phase,also called the geometric phase,which is a function of the azimuthal angleφfor the nanofin (Berry,1987).An important difference here is that while the propa‐gation phase is wavelength-dependent and determined by the fin size,the PB phase is affected only by its azimuthal angle and is independent of its size.Once the lengthLand the widthWare fixed,so are the complex transmission coefficientsand,as well as the propagation phase of two beams with different circular polarization values.Thus,while the PB phase remains fixed unless the azimuthal angle is changed,the nanofin size affects the complex transmission co‐efficients and therefore affects the output polarization state of the transmitted beam.As a result,by suitably designing the size,a low polarization conversion rate (PCR) (mainly copolarization part with only propaga‐tion phase) at the desired wavelength and a high PCR (mainly cross-polarization part with propagation phase and PB phase) at another specified wavelength can be obtained.Here,PCR is defined as the ratio of the transmitted optical power with the opposite helicity to the total transmitted power.Based on this concept,a fixed phase shift of the copolarization part can be obtained according to Eq.(1) at a given wavelength.To generate an annular-shaped PSF at another wave‐length,the metasurface would have to impose a spiral phase on the incident beam,which can be achieved by rotating the nanofin to set the PB phase of the cross-polarization component.

As a demonstration,we explored the operation of the metasurface at two wavelengths: a constant phase modulation at 590 nm and a spiral phase modu‐lation at 785 nm.As the propagation phase in Eq.(2) depends on the nanofin material and its geometry,the selection of the metasurface material is an impor‐tant design choice.We used crystalline silicon (c-Si) in this demonstration due to the low extinction coeffi‐cient of its transparent window across the visible and near-infrared (NIR) regions (Ikezawa et al.,2022).First,we simulated the unit cell of our design using the COMSOL Multiphysics finite element analysis tool to find suitable fin dimensions.In the simula‐tion,periodic boundary conditions were applied atxandyboundaries,and perfectly matched layers were applied atzboundary.To satisfy the Nyquist sampling criterion and suppress high-order diffraction effects,the center-to-center distanceSwas set to 400 nm.A nanofin height (H) of 500 nm was found to optimize transmission properties at the two wavelengths.The width (W) and length (L) were determined to maxi‐mize PCR at a wavelength of 785 nm and minimize PCR at 590 nm.Fig.1b shows that a nanofin withW=93 nm andL=185 nm can provide the desired PCR at the two target wavelengths.At 785 nm,the trans‐mitted beam comprises just over 93% of the crosspolarization component,while at 590 nm,the copo‐larization component dominates at over 90%.The transmission efficiency is approximately 58% at 590 nm and 98% at 785 nm.Fig.1c shows the phase shift with different rotation angles at different wavelengths.At 785 nm,the phase shift of the cross-polarization part is twice the azimuthal angle,while the phase shift of the copolarization part is constant at 590 nm.The spiral phase distributionpat 785 nm can be expressed as follows:

where (r,θ) are the cylindrical coordinates of each nanofin on the metasurface andqis the topological charge.Thus,combined with Eq.(2),the azimuthal angle of each nanofin is

In our case,we set the topological chargeqto ±1,where the sign depends on the handedness of the incident circular polarization.The simulation of the overall device was performed using commercial finitedifference time-domain software (FDTD solutions,Lumerical Inc.).The diameter of the metasurface was set to 36 μm due to the computational cost concerns.In contrast to the simulation of the unit cell,perfectly matched layers were used atx,y,andzboundaries.Anx-polarized plane-wave source with its phase set to 0° and ay-polarized plane-wave source with its phase set to 90° were used to build a circularly polar‐ized incident beam.A perfect electrical conductor (PEC) aperture was set to match the diameter of our design and filter the unmodulated beam.

As shown in Figs.1d and 1h,the simulated am‐plitude distributions of the two wavelengths are al‐most uniform.The corresponding phase distribution results are given in Figs.1e and 1i.The results exhibit a spiral phase distribution at 785 nm and a relatively flat phase distribution at 590 nm.After being modu‐lated by the metasurface,the incident beam can then be focused to an annular PSF (Fig.1f) and a solid PSF (Fig.1j).These PSFs are calculated according to the vectorial diffraction theory described by Rich‐ards and Wolf (1959) and Liu X et al.(2021).Finally,the intensity profiles along the horizontal and vertical lines cutting through the center of the PSFs are shown in Figs.1g and 1k,respectively.

3 Fabrication and results

To physically verify our design,a circular meta‐surface with a diameter of 500 μm was fabricated on a crystalline silicon-on-sapphire (SOS) wafer (Section 1 in the supplementary materials for details of fabrica‐tion).Both optical and scanning electron microscopy (SEM) images of the fabricated metasurface are shown in Fig.2.In this section,we will discuss the perfor‐mance of the metasurface from the phase distribution to the PSF results.

To characterize the spiral phase distribution,we used a custom-built Mach?Zehnder interferometer as shown in Fig.3a (Section 2 in the supplementary ma‐terials for details of the configuration).The orienta‐tion of the Al2O3substrate we used is r-plane (1-102),and the thickness is 530 μm.As the substrate is aniso‐tropic,the linearly polarized beam should first be turned into an elliptically polarized beam (inset in Fig.3a).The Al2O3substrate then imposes circular polarization in a direction opposite to that of the ref‐erence beam.Thus,the rotation angle of the second quarter-wave plate (QWP2) in front of the metasur‐face must be carefully designed to alleviate the sys‐tematic error of the wavefront measurement.This can be determined by observing the interference fringe in the unmodulated area outside the metasur‐face.As shown in Figs.3b and 3c,the background outside the perimeter of the metasurface does not in‐terfere with the reference beam only when the QWP2 and the Al2O3substrate modulate the linearly polar‐ized incident beam into circular polarization.Mean‐while,the interference fringe in the area of the metasurface achieves the highest contrast,which can serve to increase the precision of the phase re‐trieval.If the wave plate is not at the correct rotation angle,the background will interfere with the refer‐ence beam because of its elliptical polarization,as shown in Figs.3d and 3e.In this way,the correct polar‐ization of the incident beam can be confirmed.Fig.3f shows the forked interference fringe captured by the camera at 785 nm.Then,the wavefront is extracted via the Fourier transform-based method (Zhao et al.,2021),as shown in Fig.3g.The observed phase is close to the simulated phase in Fig.1e and thus agrees well with our theoretical prediction.To quantify the quality of the phase,we calculated the error between the measured phase and the standard phase.The result (Fig.3h) shows an almost uniform distribution,indi‐cating that the measured phase distribution closely matches the target spiral phase.In addition,the root mean square (RMS) wavefront error is 0.2789.

Although the shape of the annular PSF is deter‐mined mainly by the phase distribution,other factors,such as amplitude and polarization,are still consid‐ered.To quantify the effect,we directly characterized the PSF at different wavelengths.The setup is avail‐able in Fig.S2 in the supplementary materials.Since the size of the metasurface is small,here we used a 4fsystem to match the pupil size of the aperture that filters out the unmodulated beam.As presented in Figs.3i and 3j,an annular PSF at 785 nm and a solid PSF at 590 nm are obtained,thereby verifying our initial design.Fig.3k shows the intensity profiles at different wavelengths across horizontal and vertical transects.At 785 nm,the transmitted beam consists almost entirely the cross-polarization component with spiral phase modulation.At 590 nm,a Gaussian beam profile is observed,which means that the beam con‐sists primarily of the copolarization component with‐out spiral phase modulation.A polarimeter was used to obtain the Jones vector of the transmitted beam,and the PCR was calculated from the vector.The result is approximately 91% at 785 nm and 8% at 590 nm.These results illustrate that our design can modulate the beam with different phase modulations at different wavelengths,one with spiral phase modulation and the other with a relatively flat phase shift.The beam can then be focused into either an annulus or a spot.

Fig.3 Characterization of the designed metasurface

From the measured PSF profile shown in Fig.3k,thex-andy-transect plots are slightly different from each other,which may have been caused by aberration and irregular illumination.Furthermore,the minimum at the center of the PSF is nonzero (i.e.,slightly over 20% of the peak in Fig.3k),which is different from the simulation result.This can be explained by the fact that the geometric size of the nanofin (shown in Fig.2) does not perfectly match the designed geometry due to fabrication error,leading to a lower PCR and introducing some copolarized noise to the annular PSF.It is possible to circumvent this limitation by advanced manufacturing technology.In addition,it is possible to improve the transmission performance by using a SiO2substrate instead of Al2O3but at the expense of a more complex manufacturing process (Bao et al.,2019).Since the SiO2substrate does not change the polarization state of the incident beam,as does the Al2O3substrate,it can reduce the difficulty of using the metasurface without an elliptically polarized inci‐dent beam.

Although the spiral phase modulation of the meta‐surface is designed for a single wavelength,the meta‐surface still performs adequately over a reasonably wide range of wavelengths.As shown in Fig.4,a Gaussian PSF can be obtained at 545 nm,555 nm,565 nm,and 575 nm,while a clear annulus is still visible at 645 nm,705 nm,755 nm,and 795 nm.This can be explained by noting that the device has a low PCR between 545 nm and 575 nm,as shown in Fig.1b;thus,the transmitted beam consists mainly of the copolarization component with constant phase modu‐lation.For other wavelengths,the device has a high PCR,and the transmitted beam consists mainly of the cross-polarization component with spiral phase modulation.Although the contrast between the bright and dark regions varies nonmonotonically and may not be sufficient for some applications,these results indicate that it would be straightforward to expand the design to other combinations of wavelengths or even to multiwavelength configurations.

Fig.4 Measured point spread functions (PSFs) and the intensity profile across horizontal and vertical transects at different wavelengths

4 Conclusions

In summary,we have proposed a wavelengthselective shaping metasurface based on a combination of wavelength-dependent polarization conversion and geometric phase modulation.To verify the theory,we designed and fabricated a metasurface that can modu‐late an incident beam with a spiral phase at 785 nm and another with a relatively flat phase at 590 nm.The beams can then be focused into either an annular or a solid PSF depending on the wavelength,which may be useful for photolithographic systems,stimulated emission depletion (STED) microscopy systems,and other applications where auto-alignment of the beam is demanded.This scheme can also be expanded to any other combination of wavelengths or multiwavelength configurations.This ultracompact wavelength-selective device is a promising building block in the develop‐ment and integration of complex optical systems.

Contributors

Zixin CAI,Xin HE,Xu LIU,and Xiang HAO designed the research.Zixin CAI and Xin HE processed the data,performed the theoretical analysis and the measurement of the sample,and drafted the paper.Aditya DUBEY,Arnan MITCHELL,and Guanghui REN fabricated the samples.Xin LIU,Shijie TU,Xin‐jie SUN,and Paul BECKETT helped organize the paper.Zixin CAI,Xin HE,and Xiang HAO revised and finalized the paper.

Acknowledgements

We thank the Westlake Center for Micro/Nano Fabrica‐tion for facility support and technical assistance.

Compliance with ethics guidelines

Zixin CAI,Xin HE,Xin LIU,Shijie TU,Xinjie SUN,Paul BECKETT,Aditya DUBEY,Arnan MITCHELL,Guanghui REN,Xu LIU,and Xiang HAO declare that they have no conflict of interest.Data availability

The data that support the findings of this study are avail‐able from the corresponding authors upon reasonable request.

List of supplementary materials

1 Fabrication of the metasurface

2 Phase characterization with Mach?Zehnder interferometer

3 Point spread function characterization system

Fig.S1 Scheme of the interferometric setup used to characterize

the phase distribution of the modulated beam

Fig.S2 Scheme of the point spread function characteriza‐

tion system