Recent Progress in Chiral Absorptive Metamaterials

Eric Ashalley | Cui-Ping Ma | Yi-Song Zhu | Hong-Xing Xu | Peng Yu |Zhi-Ming Wang

Abstract—Chiral metamaterial absorbers (CMMAs),a particular class of chiral metamaterials that refuse the transmission of incident radiation and exhibit different optical responses upon interactions with left and right circularly polarized (RCP) light,have gained research traction in recent years.CMMAs demonstrate numerous exotic and specialized applications owing to their achievable compatibility with various physical,chemical,and biomolecular systems.Aside from their well-evolved fabrication modalities for a broad range of frequencies,CMMAs exhibit strong chiroptical effects,making them central to various detection,imaging,and energy harvesting applications.Consequently,within the past decade,studies encompassing the design,optimization,and fabrication,as well as demonstrating the diverse applications of CMMAs have emerged.In this review,the theory,design,and fabrication of CMMAs are discussed,highlighting their top-down fabrication techniques as well as recent algorithmic and machine-learning (ML)-based approaches to the design and optimization.Some of their broad-spectrum applications are also discussed,spanning their roles in enantioselective photodetection,chiral imaging,generation of hot electrons,selective temperature sensing,and active chiral plasmonics.

1.lntroduction

Metamaterial absorbers (MMAs),a branch of artificially engineered structures,have gained research traction owing to their ability to completely absorb electromagnetic waves with deeply subwavelength profiles(meta-atoms),prompting their applications in stealth[1],[2],energy harvesting[3],[4],various sensing applications[5]-[8],and photodetection[9]-[12].This group of metamaterials can achieve high absorption coefficients close to unity,especially for the so-called“perfect absorbers”when carefully designed.A typical MMA design uses a backreflector (mirror) which disallows light transmission such that with minimum reflection,near-perfect absorption can be realized[13],[14].These mirrors usually comprise either metals which are termed electric mirrors or metamaterial-based isotropic magnetic mirrors.Electric and magnetic mirrors reverse the direction of the electric and magnetic fields of the reflected electromagnetic wave,respectively.

Chiral nanostructures exhibit different optical properties upon interactions with circularly polarized light(CPL) of opposite handedness.The chiroptical effects emanate from structure-dependent high-order lightmatter interactions,such as dipolar and quadrupolar interactions which may lead to the phase retardation difference (termed optical activity) or differential absorption (termed circular dichroism (CD)).For each chiral structure design,there exists an inverted design that reverses the optical response perfectly.These are termed enantiomer pairs.They are designed such that they are mirror symmetry to each other.These nanostructures can achieve CD signals several orders of magnitude larger than that of naturally occurring molecules,especially when designed with plasmonic effects[15]-[18].The giant chiroptical effects are essential for the efficient control of the polarization states of light and also explain several intriguing physical effects,such as the negative refractive index[19]-[22],tunable atom trapping[23],the spin-Hall effect of light[24],and the repulsive Casimir effect[25],as well as enhancing the chiroptical response of naturally occurring structures,such as deoxyribonucleic acid (DNA) and protein molecules[26].However,the design has evolved into complex ones,such as twisting multiple layered isotropic or anisotropic structures to achieve symmetry breaking[27].Chiral nanostructures not only hold power to switch the handedness of metamaterials,but also can demonstrate strong optical activity as well as asymmetric transmission.Active materials,such as phasechange materials[28],[29],micro-electro-mechanical systems (MEMSs)[30],and semiconductors[31],[32],have been recently employed for the design of chiral metamaterials towards reconfigurable chirality and controllable electromagnetic properties.By incorporating plasmonic nanostructures,the chiroptical effects of chiral metamaterials can be extremely enhanced,leading to improvement in performance for a wide range of applications,including enantiomer discrimination among others[33].

MMAs can be designed to exhibit strong chiroptical effects across the electromagnetic spectrum.In such cases,chiral nanostructures and/or media are employed.Chiral nanostructures may possess twodimensional (2D) or three-dimensional (3D) chirality[34],[35].However,chirality is inherently a 3D geometrical feature.The importance of planar chirality was first theoretically highlighted by Hecht and Barron[36]using light scattered from planar chiral molecules.The 2D chirality in 3D space is not truly chiral as the planar shape can be rotated in thezdirection to be superimposable on its mirror image.That notwithstanding,ultrathin chiral metamaterials (considered as 2D chiral) benefit from lattice and Fano resonances that enhance their chiroptical responses when carefully arranged.The 2D chiral metamaterials also exhibit an inversion of CD transmission spectra when light is incident in the opposite normal direction,a characteristic that is absent in the case of 3D chirality.This is because 2D chiral metamaterials only possess 2D structural chirality.For planar metastructures,CD signals stem from the differential absorption of left circularly polarized (LCP) and right circularly polarized (RCP) light owing to the variation in near-field distributions of the CPL-induced localized surface plasmons.Chiral metamaterials that disallow transmission of incident light through its structure and exhibit high absorption signals are termed chiral metamaterial absorbers (CMMAs).The noticeably high absorption from MMAs (including CMMAs) can be explained by the interference theory owing to the formation of a Fabry-Perot cavity between the top and bottom metallic layers.CMMAs preferentially absorb one handedness of CPL,resulting in large differential absorption and,consequently,CD signals.This phenomenon with CMMAs has been extensively utilized in several applications including bolometry[37],enantiomer detection[38],photodetection[39],polarization-resolved imaging,and CD spectroscopy[40].

In this review,we discuss the recent trends in the design and fabrication of CMMAs.We shed light on the promising computational techniques assisting in the design and optimization process of CMMAs,such as machine-learning (ML)-based design routes.The fabrication of these structures has seen lots of improvement with the emergence of sophisticated lithographic techniques.This review is organized as follows.Section 1 briefly introduces the theories underpinning the CMMAs design as well as the computational methods for the simulation of their optical responses.Section 2 discusses the design and optimization of CMMAs,including the metamirror design (highlighting their roles in CPL handedness selectivity and preservation) and CMMAs bandwidth engineering,and concludes with ML and algorithmic approaches to their optimization.Section 3 summarizes CMMA fabrication techniques drawing from recent cost-effective top-down approaches for achieving strong chiroptical effects.Section 4 discusses some of the applications of CMMAs,such as chiral imaging,chiral selective photodetection,generation of hot electrons,photothermal enantioselectivity,and active chiral plasmonics.We conclude with the prospects of CMMAs in Section 5.

1.1.Theories of Absorption in CMMAs

Theories used to explain the ground for metamaterial absorbance include the impedance matching theory[41]-[44],interference theory[45],Fabry-Perot resonances[46],[47],cavity resonances[48],and conventional transmission line theory[49].There are also coupled modes and effective medium theories[50].These posited theories have created a variety of schools of thought on the basis of optical absorption in CMMAs.To provide a theoretical framework for the operation and design of CMMAs,one can treat CMMAs as chiral media,as shown inFig.1.Eigen waves in chiral materials can be characterized by the chiral parameterκ,which denotes the strength of the cross coupling between the magnetic and electric fields.The constitutive relationship equations can be described by (1) and (2):

Fig.1.Illustration of the transmission (T) and reflection (R)coefficients of chiral media.

whereεis the permittivity andμis the permeability;D and H are the electric displacement vector and magnetic induction intensity,respectively,and they are related to both the electric field (E) and magnetic field(B).The effective refractive index of the chiral media under LCP and RCP incidence is

where“+”and“–”stand for RCP and LCP,respectively;As the effective refractive indices are different,the absorption and phase have a discrepancy between CPL,leading to CD.The strength of CD can be expressed as

whereT+andT–are the complex transmission for RCP and LCP waves,respectively.

1.2.Computational Methods for CMMAs Design

There are two prominent approaches for the simulation of CMMAs including the finite element method(FEM) and the finite-difference time-domain (FDTD) approach.FEM is a numerical technique for solving problems that are described by partial differential equations or can be formulated as functional minimization.Here,a domain of interest is represented as the assembly of finite elements.Therefore,a continuous physical problem is transformed into a discretized finite element problem.Due to the partitioning of the physical problem across the physical structural geometry,good precision can be achieved with an increasing number of elements.For the problems with a large number of nodal unknowns,such as Maxwell’s equations,FEM is very efficient since the locality of the approximation leads to sparse equation systems for discretized problems.FEM solves physical problems in basically six steps:1) Discretizing the continuum into finite element meshes,2) selecting interpolation functions for the field variables,3) finding the element properties,4) assembling the element equations to find the global equation system for the entire solution region,5) solving the global equation system (which is typically sparse,positively definite,and symmetric) using direct and iterative methods,and then 6) computing for any additional parameters given the global solution.The formulation of finite element equations can be done by the Galerkin method or variational formulation.FEM has been adopted for the electromagnetic simulation of CMMAs revealing enormous details about the nature of the electromagnetic field distribution,optical chirality parameter,and surface charge density for varying handedness of incident CPL using FEM-based electromagnetic solvers implemented by simulation software,such as Comsol Multiphysics and High Frequency Structure Simulator (HFSS).However,for chiral media,the constitutive equations have to be modified to (1) and (2) in order to implement the chirality factor that regulates the handedness of the chiral medium.

The FDTD method is also a popular technique for the solution of electromagnetic problems.It has been extensively applied to a wide variety of problems,such as propagation,absorption,radiation,and scattering of electromagnetic waves from metallic and dielectric materials.The simplicity of the technique has inspired the implementation of its underlying code by several specific and general purpose simulators,such as Lumerical.The technique was first proposed by Yee in the 60s[51].The FDTD method discretizes Maxwell’s equations both in time and space with central difference approximations.Yee’s idea resides in the allocation in space of the electric and magnetic field components and the marching in time for the evolution of the procedure.In this case,the electric and magnetic field components shift by half a cell in space and by half a time step in time when considering the central difference approximations of the derivatives.In a onedimensional (1D) case,assuming propagation through free space,Maxwell’s equations can be written as

which is a plane wave traveling in thezdirection.Here,ε0andμ0are the permittivity and permeability of free space,respectively.Then according to Yee,considering a shift in space by half a cell and in time by half a time step for central difference approximations of the differentials,the leap-frog algorithm can be applied by first calculating allHfield values followed byEfield values,whiles always remembering thatEandHare also shifted in space by half of the discretization.Therefore,the FDTD method is characterized by the solution of Maxwell’s curl equations in the time domain after the replacement of their constituent derivatives by finite differences,providing a grid-based time-marched solution to Maxwell’s equations.The FDTD technique has evolved over time with several contributions since the 60s.Table 1summarizes the evolution of the FDTD technique over time[51]-[80].Other electromagnetic simulation software runs on a combination of theoretical techniques.For example,Computer Simulation Technology (CST) Microwave Studio implements the finite integration technique (which is a variation of the FDTD method) for its transient solver,FEM for its frequency-domain solver,and the method of moments (MoM) for its integral equation solver.

Table 1:Summary of the evolution of the FDTD technique

Apparently,these methods have been instrumental in the design of CMMAs recently,enabling the calculation of various chiroptical responses,such as optical chirality,CD,and optical rotation dispersion.However,the theoretical methods and their hybrids are unable to sufficiently generalize for the parameter space,especially for 3D electromagnetic problems,such as in chiral plasmonics.As a result,there is a fundamental limit to the exploration of the design space when analyzing the chiroptical responses from CMMAs solely using these theoretical methods.In addition,the computational process can be timeconsuming and resource-intensive owing to the iterative case-by-case simulation involved in solving Maxwell’s equations.Recently,ML approaches to the design of CMMAs have emerged,paving the way for the full non-intuitive exploration of their chiroptical responses in the entire design space.These ML techniques complement the theoretical techniques with hyperspace representation,enabling the sufficient generalization of the design space.Discussion on the ML-based design of CMMAs is relayed to a later section.

2.Design and Optimization of CMMAs

The common practice for the CMMA design is to adopt a metal mirror (ground plane) isolated from a top conducting layer by a dielectric inter-spacer.In such cases,the dielectric spacer acts as a Fabry-Perot cavity,allowing multiple reflection.The dielectric layer is responsible for regulating the input impedance and ensuring that the CMMA structure perfectly matches the impedance of free space.The ground plane has a thickness greater than the skin depth (optically thick) such that incident waves are blocked from penetrating the structure,thus reducing return losses and causing perfect absorption at resonant frequencies.Resonant absorption occurs upon the activation of surface charges by electric fields,which consequently yields magnetic field responses.The current generated thereof is due to the coupling of the harmonizing field of the incident wave with the magnetic and electric field responses.If the impedance matching condition[Z(ω)=Z0(ω)] is satisfied,this field enhancement can propel perfect absorption.As a result,the entire incident energy is confined in CMMAs.The presence of the mirror simplifies the absorption equation fromA=1–R–TtoA=1–RsinceT=0 (whereA,R,andTare the absorption,reflection,and transmission,respectively).Therefore,the CD response is computed by CD=ALCP–ARCP,whereALCPandARCPare the LCP and RCP absorption,respectively.In this section,we discuss some chiral mirrors with CPL handedness preservation and the ML-based design and optimization techniques for CMMAs.

2.1.Chiral Metamirrors with CPL Handedness Preservation

Mirrors are essential to achieving enhanced optical and chiroptical effects in CMMAs.A feature,based on the operation of conventional mirrors where the wave vector flips the direction of the reflected wave,introduces complexity to optical instruments and systems for circularly polarized waves,necessitating mirror designs that act as a reflective polarizer and filter such that they preserve the handedness of designated CPL upon reflection while entirely absorbing the other spin state[81].Plum and Zheludev[82]implemented chiral metamirrors at microwave frequencies,elucidating their potential in preserving reflected CPL handedness and drawing sharp contrast with conventional mirrors.Subwavelength chiral structures that break then-fold rotational and mirror symmetry are essential to the realization of such metamirrors[83].After their work[82],an avalanche of studies has concentrated on designing efficient handedness-preserving metamirrors.An effective metamirror should provide spin-selective absorption,suppress polarization conversion in reflection,and modulate the phase in the full 2πrange.Fig.2 (a)is an example of CMMA with a conventional Ag mirror for enantiomer A (Fig.2 (a) (i)) and enantiomer B (Fig.2 (a) (ii)) as well as the scanning electron microscopy(SEM) images of the fabricated structures.However,the recent design and fabrication of chiral mirrors have employed unconventional design approaches and achieved tremendous success.This subsection briefly discusses the unconventional chiral metamirrors using metasurfaces and chiral photonic crystals for reflected CPL handedness preservation.

Based on the guided-mode resonance as well as the simultaneous excitation of leaky transverse electric and transverse magnetic-like Bloch modes in photonic crystal slabs,chiral photonic crystal mirrors can realize selective reflection of CPL with handedness preservation alongside near-unity CD[38].For quasi-2D structures,achieving intrinsic chirality at normal incidence is a challenge.This is because intrinsic chirality originates from the simultaneous excitation of in-plane electric and magnetic dipole moments at normal incidence,which was only previously achieved with 3D chiral structures[84].Another option is to consider complex,multilayered structures with structural chirality[85].The crystal mirror designed by Semnaniet al.[38]is composed of a patterned layer of silicon nitride of thicknesst=309 nm at an 870-nm wavelength with a square-shaped Bravais lattice and subwavelength lattice constant.The pattern is a tripartite array of perforated holes such that they exhibit chiral symmetry in thexy-plane.The incident wave is generated by a quarter-wave plate placed before the focusing objective lens,forming a polarization ellipse.Fig.2 (b) (i)illustrates the photonic crystal mirror with the direction of the incident light.The major axis is tilted by the angleψwith respect to the polarization of the input,and the axial ratio is tanψsuch that atψ=±45°,the incident wave becomes circularly polarized,otherwise elliptically polarized.

That suffices to say that the reflection spectrum varies withψas illustrated byFig.2 (b) (ii).The spectra vary in various elliptical forms tillψ=±45° where the polarization is circular.Fig.2 (b) (iii)is the experimental and theoretical comparisons of the reflectivity of circularly polarized light-to-light with equal helicity.This chiral photonic crystal mirror achieves 80% reflectivity of the helicity to the same state of polarization with an extremely high extinction ratio (30:1) for the fabricated devices.Fig.2 (b) (iv)is the reflection spectra of elliptically polarized light withψ≈ ±30° to the same polarization for right-handed and left-handed elliptically polarized light,showing a high extinction ratio.By performing the polarization-resolved imaging in two experiments,the robustness of the photonic crystal mirror is established.Fig.2 (b) (v)is an optical microscope image for the first experiment where a“C”dual enantiomeric geometrical arrangement of the samples is considered under circular polarization.It can be seen that there is reflection of CPL to its co-circular polarization.Fig.2 (b) (vi)is the second experiment which is aimed at imaging an“IQC”letter pattern.This time,under a monochromatic spatially incoherent laser beam,the letters are bright with sharp contrast with respect to the background for the RCP illumination whiles the inverse is true for the LCP illumination as illustrated byFig.2 (b) (vi).The CPL selectivity and reflectivity are realized through the Bloch modes within the illumination continuum.

Fig.2.Handedness-preserving metamirrors:(a) CMMA mirrors with a conventional Ag mirror for (i) enantiomer A and(ii) enantiomer B with corresponding SEM images of the fabricated structures.Reproduced with permission[40].(b) Photonic crystal mirrors:(i) schematic of a thin photonic crystal mirror with an elliptically polarized incident wave with a polarization tilt ψ;(ii) color plot for the variation of ψ with a normalized reflection spectrum;(iii) reflectivity of CPL with the same helicity;(iv) reflectivity of elliptically polarized light at ψ=±30° to the same polarization for right-handed and lefthanded elliptically polarized light (reflectivity of the opposite enantiomers upon CPL illumination);(v) imaging with a focused and spatially coherent laser source;(vi) imaging with a laser beam with a scrambled wavefront.Reproduced with permission[38].(c) Metasurface mirrors:(i) normalized electric field pattern from a perfect electric conductor (PEC) mirror(left) and the metasurface (right);(ii) normalized magnetic field from PEC and the metasurface;(iii) chirality enhancement from the metasurface.Reproduced with permission[87].

Photons with different spin states undergo different absorption when unpolarized light is incident on a metamirror.Therefore,with chiral metasurfaces,one can anomalously reflect particular CPL with highefficiency handedness preservation whiles totally absorbing the other spin state[86].In the near-ultraviolet regime,lossless dielectric metasurfaces can also enhance CD spectroscopy as well as achieve CPL handedness preservation.At this regime,it becomes very beneficial to molecular CD spectroscopy owing to the deep-ultraviolet resonances of chiral biomolecules.For instance,the dielectric metasurface composed by interacting TiO2nanocube-dimer arrays in a square lattice capitalizes on its high refractive index and lossless properties for a 50-fold molecular CD enhancement in the near-ultraviolet regime through adsorption of the chiral molecules[87].The dimer structures can as well be utilized as polarization-preserving mirrors such that over 90% of the incident power is carried by the co-polarized-reflected CPL at the magnetic dipole resonance.Figs.2 (c)(i)and(ii)compare the interference patterns from a conventional mirror (left) and from the TiO2nanocube metasurface array (right),showing strong electric and magnetic fields surrounding the nanocubes (white rectangular outline),resulting in surface-enhanced optical chirality as depicted byFig.2 (c)(iii).The total field,herein,is increased as the chirality of both the incident field and the reflected wave possesses the same sign which adds up to give the doubled chirality.Aside from these techniques,there have been other approaches to minimizing reflection,such as the matching technique used to transmit unwanted waves without reflection,achieving broadband transparent metamirrors[88].That notwithstanding,chiral metallic mirrors are dominant and central to the design and fabrication of CMMAs with CPL handedness preservation.

2.2.CMMAs Bandwidth

The bandwidth of CMMAs informs various application directions,including sensing,broadband optical communications,photovoltaics,and photocatalysis.While narrowband CMMAs are ideal for sensing and broadband CMMAs resonate well with optical communications applications.This section discusses the design of CMMAs along the band limit.

2.2.1.Narrowband

2.2.1.1.Single-Band CMMAs

In the visible regime,the LCP and RCP absorption peaks can occur at different resonances when adopting plasmonic metamaterials,and the chiral geometry can result in single,dual,and multiple absorption bands.In the study by Tanget al.[89],they adopted an ŋ-shaped metallic resonator on top of a dielectric spacer and a metallic mirror to achieve absorption of over 80% at different wavelengths of the visible regime.The chiral metasurface selectively absorbs CPL,yielding CD as high as 0.5.The chiral-selective absorption for different circular polarization is due to the constructive and destructive interference of the illumination.Their structure comprises periodically arranged ŋ-shaped silver resonators on top of the silicon dioxide (SiO2)spacer and an optically thick silver film,as depicted inFig.3 (a).For the numerical assessment of the optical response of chiral plasmonic metasurfaces,the most adopted techniques are the FDTD method and FEM.Fig.3 (b)toFig.3 (e)are the absorption and CD spectra of the structure,respectively.Theoretically,two inverted selective absorption bands are present for LCP and RCP illumination with a single structure.This is expected as the structure has longitudinal and transverse components.However,the fabricated structure exhibits a single-band CD peak,ascribed to the fabrication imperfections.The absorption and CD peaks achieved approach 0.9 and 0.5,respectively,with the CD peak overlapping with the absorption resonance in the visible regime.The structure can be adopted for hot electron generation as well as polarization-resolved imaging.The single bandwidth spans from 640 nm to 680 nm.

In the near-infrared regime,plasmonic CMMAs can achieve an even higher CD signal amplitude using the conventional metal-dielectric-metal structures.Ouyanget al.[90]studied the chiroptical response of chiral plasmonic metasurfaces in the near-infrared regime with specially engineered chiral structures.Their design reaches the maximum absorption and CD of up to 0.87 and 0.70,respectively,which is attributed to the top chiral geometry.The structure is comprised of 55-nm-thick double-rectangular Au chiral structures seated on 130-nm-thick SiO2on top of a 200-nm-thick Au ground plane (Fig.3 (f)).This design is similar to that of Tanget al.[89]except for the top chiral geometry,establishing the unique role of the chiral structures on the overall chiroptical response.The connecting double-rectangular Au chiral structure of widthW2and lengthLis such that they overlap by the width,W1,within the periods ofP1andP2for a unit cell.

Fig.3.Single-band and dual-band CMMAs:(a) schematic of the ŋ-shaped silver resonator-based metasurface composed by the top resonators,dielectric spacer,and Ag metal back-reflector;absorption spectra from (b) simulations and(c) experiments,respectively;(d) CD response from simulations showing two absolute resonances;(e) CD response from experiments showing a single resonance.Reproduced with permission[89].(f) Schematic of Z-shaped CMMA with (g) its electric field distribution,collected 10 nm down the top surface of the dielectric spacer under LCP and RCP illumination,as well as the electric field with current density (arrows) distributions across the top pattern;(h) simulated and measured absorption spectra of the Z-shaped CMMA and (i) measured absorption spectra for varying Z-shape sizes.Reproduced with permission[90].(j) Schematic and charge density of Γ-shaped CMMA;(k) reflectance,(l) absorptance,(m) CD,and(n) gCD spectra of Γ-shaped CMMA.Reproduced with permission[37].

Again,the Fabry-Perot cavity formed by the top resonator layer and the Au back-reflector enhances the selective resonant absorption of incident CPL by creating a chiral plasmonic resonant mode.Comparing the LCP and RCP electric field distributions with the surface charge distribution,one can verify the source of the strength of the chiroptical response.The electric field distribution shows a pronounced enhancement in the dielectric spacer layer at the chiral plasmonic resonance for one handedness of CPL,as illustrated inFig.3 (g).The absorption spectra inFig.3 (h)show a plasmon peak around the 1.6-μm wavelength for one structural configuration.Here,the bandwidth spans from 1.5 μm to 1.7 μm.However,for different sizes of the metastructure,the resonant wavelength shifts,spreading across several microns (Fig.3 (i)).

2.2.1.2.Dual-Band CMMAs

For MMAs,achieving dual-band absorption is well-researched with several reference examples,including the use of plasmonic nano-rings on the absorber substrate[91].To achieve dual-band CMMA with dual-band chiroptical effects,chiral structures with dual-band absorption spectra seem a logical choice.Dual-band CMMAs can be achieved by considering a chiral structure such that upon CPL incidence,both the longitudinal and transverse modes are resonantly excited.An example is the L-shaped and Γ-shaped chiral structures formed by two coinciding arms,which produces two resonant peaks.The two resonant peaks are a result of the two coupled modes of the two arms of the top structure.Konget al.[37]assessed the chiroptical response of the Γ-shaped CMMA illustrated byFig.3 (j)with its charge density upon CPL incidence.The reflection (Fig.3 (k)),absorption (Fig.3 (l)),CD (Fig.3 (m)),and chiral anisotropy factor (gCD) (Fig.3 (n))spectra exhibit a dual-band optical and chiroptical response.Another way is to adopt two asymmetric structures that are well-engineered on the same substrate such that their plasmon resonances occur at different spectral positions for one handedness of CPL.For multiband CMMAs,additional asymmetric structures are required.However,this approach works for structures whose CD resonances coincide with their plasmon resonant frequencies.

2.2.2.Broadband

The first reported metamaterial-based perfect absorber is of narrow bandwidth and also polarizationsensitive due to the resonant nature of plasmonic processes,which limits its full exploitation in practical applications[92].With the advances in fabrication techniques,efforts have been put into the design and fabrication of broadband MMAs which imply broadband CMMAs.Such attempts include using multiple resonant units for multiband MMAs[92]such that when the gap between the resonances in terms of frequencies is closed,broadband MMAs are produced.Broadband absorption can also be achieved via vertically standing nanowires[93]and multilayer structures[94].It must be noted that achieving broadband MMAs implies broadband CMMAs (with linearly polarized (LP) light at normal incidence) but does not translate into broadband CMMAs with broadband chiroptical effects (with CPL),although the structural variation between MMAs and CMMAs only resides in the chirality of the top geometry.This is because the differential absorption between LCP and RCP needs to span the broadband absorption range (overlap for LCP and RCP absorption spectra) in order to achieve broadband CMMAs with broadband chiroptical effects.At present,broadband perfect absorption for MMAs is theoretically and experimentally feasible.However,as it can be inferred,special engineering is necessary to maintain broadband LCP and RCP absorption to permit broadband chiroptical effects in CMMAs,which makes achieving broadband near-perfect chiroptical effects seem unrealistic at present.Even when theoretically achieved,fabrication imperfections may hinder the experimental realization of CMMAs with near-perfect broadband chiroptical effects.Broadband chiroptical effects have been achieved in transmission[95],and recently,broadband CD has been realized via coupled plasmon induced by the patternable film of Ag nanoparticles with chiral ligands[96].Ultrafast broadband CD in the deep ultraviolet(250 nm to 370 nm) has also been achieved with femtosecond time resolution employing an elastic modulator for shot-to-shot polarization switching[97],which is promising for chiral biomolecular detection.However,these broadband chiroptical effects are from nanostructures without metallic mirrors and thus allow the transmission of incident radiation.This subsection discusses broadband CMMAs with broadband CD in absorption.

Jinget al.[98]realized broadband chiroptical effects with CMMA composed by combining chiral resonant modes of two asymmetric split-ring resonators.The total thickness of the mirror is less than one-ninth of the wavelength and thus supports on-chip integration.The geometric parameters of the two split-ring resonators are different (G-shaped and C-shaped) to enable differences in resonant peaks.The dimensions of the two split-ring resonators ares=1.0 mm,l1=4.0 mm,l2=4.3 mm,g1=g2=1.0 mm,g3=1.5 mm,R1=2.3 mm,R2=2.2 mm,andw=1.0 mm.The geometry and parameters of the metastructure are described inFig.4 (a).The periods of the unit cell arePx=18 mm andPy=9 mm in thexandydirections,respectively.The dielectric spacer is FR4 with the relative permittivity of 4.2 and a loss tangent of 0.025 with a thickness of 3.1 mm.The homogeneous metallic layer to prevent transmission through the structure is copper with the conductivity ofσ=5.8 × 107S/m and a thickness of 0.105 mm,making a total thickness of 3.31 mm.The chiral structure with single top chiral geometry exhibits a single distinct narrowband absorption peak.Individually,the two chiral geometry designs exhibit distinct absorption peaks,some wavelengths apart.The closeness of the resonant peaks can trigger the coupling of the resonant modes of the split-ring resonators toward broadband spin-selective absorption at microwave frequencies.Fig.4 (b)shows the narrowband and broadband absorption produced by the single and double structures,respectively.The reflection spectra of the double top chiral structure inFig.4 (c)illustrate the high broadband magnitude ratio of the reflected RCP(rRR) and the reflected LCP (rLR) waves under RCP incidence.As expected,the structure produces two resonant absorption frequencies at 9.74 GHz and 10.04 GHz.The dependence of the absorption spectra on the distance between the meta-atoms and the dielectric thickness is illustrated inFigs.4 (d)and(e),respectively,showing weak near-field coupling for distant meta-atoms characterized by the periodpyand the spectra shifting with changing the dielectric thicknessh.This is because,at the 9.74-GHz resonant frequency,the resonance behaves like a combination of strong magnetic and weak electric dipoles as the surface currents on the two arms oscillate in the opposite direction.The inverse is true for the 10.04-GHz resonance.Broadband CD of 5.1% is achieved.Figs.4 (f)and(g)are the measured absorption and reflection spectra from their experiments,showing broadband CD in absorption.Achieving such broadband chiroptical effects with broadband chiral mirrors provides an avenue for device control over a wide range of frequencies[99].

As an extension of their work on near-infrared chiral plasmonic metasurface absorbers,Ouyanget al.realized broadband infrared CD spanning from the wavelength of 1.3 μm to 1.85 μm alongside the increase of the high broadband polarization-dependent local temperature[100].They used the same MMA structure as in[90] (which already exhibits a CD peak of 0.7 in absorption),with variations in the sizes of the top doublerectangular chiral structures within a unit cell to allow for multiple mergeable resonances.Fig.4 (h)shows the schematic,dimension definitions,and SEM image of their design.Instead of two top chiral meta-atoms[98],a unit cell of their structure comprises six of such spectra-position-shifted double-rectangular chiral structure with lengthLand widthWwith vertical and horizontal periods,PxandPy,respectively,as well as overlapping space,OP.Fig.4 (i)shows the SEM images of individual meta-atoms of specific sizes.Each of the six structures is engineered to exhibit a narrow-band chiroptical response around a specific wavelength such that their merger results in broadband chiroptical performance,as illustrated byFig.4 (j).The design dimensions ofL1,L2,L3,L4,andL5are 300 nm,410 nm,425 nm,540 nm,and 610 nm,respectively;W=135 nm,OP=10 nm,Px=1140 nm,andPy=2110 nm.The structure repeats one of the top resonators (specifically,L3) in order to maintain the CD resonance around the specific wavelength,which otherwise would shift due to the coupling between the resonators.Compared with CD of the individual resonators,broadband CD in absorption is relatively reduced when adopting this technique for the design of broadband CMMAs with broadband chiroptical effects.

Fig.4.Broadband CMMAs:(a) schematic of a handedness-preserving chiral metamirror comprising two top asymmetric G-and C-shaped split-ring resonators with different dimensions;(b) absorption and (c) reflection spectra of single and double structures upon LCP and RCP incidence;dependence of the absorption spectra on (d) period Py and (e) dielectric thickness h;measured (f) absorption and (g) reflection spectra of the double meta-atom structure.Reproduced with permission[98].(h) Geometry,dimensions,and the SEM image of a set of Z-shaped chiral metamaterials of different sizes;(i) SEM images of the individual Z-shaped metastructures of different sizes;(j) absorption spectra of both the single and set of meta-atoms showing broadband CD for the set and distinct narrowband CD for the single metastructures.Reproduced with permission[100].

Another way to achieve broadband CD is to approach the task from the materials perspective.Different metals possess different plasma frequencies and damping which occur in the visible regime for plasmonic metals.By blending multiple metals with a varying range of CD resonances,it is possible to achieve broadband CD in the visible regime.Mandal[101]achieved broadband CD via a multi-layered metallic structure with a bilayer top chiral structure.Such an arrangement enhances the CD response owing to the large differential near-field.The near-field interaction can kindle an additional chiroptical response that is absent in single-metal-based structures.The structure comprises a 2D asymmetric dagger-like multi-metal structure made of the Au-Al bilayer on a SiO2supportive layer.The thickness of the SiO2layer is 200 nm,and those of the Au layer and the Al layer are both 50 nm.For comparison,the single metal layered structure was also simulated with identical dimensions.When the arrangement is reversed to an Al-Au structure,a spectra blueshift is observed.In all,the multilayered metal bilayer structure achieves high differential absorption compared with the single-metal-layered structures.

Achieving narrow-band and ultra-broadband high CD is non-trivial in planar CMMAs,as highly narrow or broad resonant absorption peaks do not necessarily translate into correspondingly resonant chiroptical effects.As a result,the techniques for achieving narrow-band perfect absorption may not be applicable to achieving high narrow-band CD.Nevertheless,approaches that integrate multiple structures of different dimensions and/or compositions on a single substrate hold promise.This is highly dependent on the chiral geometry and the excited modes.

2.3.ML-Based CMMA Design

Complementing the computational methods for the metamaterials design outlined in subsection 1.2,ML-based metamaterials design and optimization techniques have chocked enormous success in recent years.Specifically,neural network models have been adopted as fast prototyping tools for establishing and generalizing the relationship between metastructures and their optical responses.These include neural network models that solve the intractable many-to-one inverse design problem such that given the optical response of the metastructures,the geometric parameter dimensions matching the optical response can be retrieved.ML is a data-driven technique that involves training a system to recognize patterns,identify attributes,and predict responses based on a generated dataset.A well-trained system may autonomously function without external aid or knowledge of the underlying physics and principles.This makes it ideal for tackling the inverse design problem.There are several approaches to achieving such well-trained models.However,the choice of method highly depends on the data type,structure,and size,i.e.,image and/or text.For instance,ML techniques,such as generative adversarial networks (GANs)[102],convolutional neural networks (CNNs) with image processing techniques[103],genetic algorithms[104],and those dedicated to layered structures[105],have been explored along the inverse design objective.Even hybrid approaches blending deep generative models with semi-supervised learning[106]as well as those consolidating compositional patternproducing networks and cooperative coevolution[107]have been explored.Genetic-algorithm-based approaches have also been used for the CMMAs design,though limited to the optimization of the top metallic layer.These approaches complement the theoretical techniques implemented by electromagnetic solvers and non-intuitively allow for the full exploration of the design space through ensemble learning of the physically relevant output,i.e.,optical and chiroptical responses.

Generally,for the ML-based design of metamaterials,the theoretical techniques,i.e.,FDTD and FEM,are used to generate a representative dataset made up of the physically relevant output.The generated dataset is partitioned into the training and validation sets which are mostly in a ratio of 80:20.The training set is used to train the model and thus should be representative of the design space.After training,the validation dataset(which is unseen by the model) is used for evaluation.Recently,neural network models implementing the deep-learning architecture have been proposed for the CMMAs design.The fundamental uniqueness of the models is the solution to the inverse design problem where given chiroptical responses,the geometric parameters can be retrieved.The forward prediction model which predicts the chiroptical response from a set of geometric parameters can be achieved in several ways,i.e.,simple regression.The sophistication of the intractable inverse design problem arises from the mismatch between the dimensions of the input and output parameters and necessitates the use of data-driven techniques,such as deep neural networks.In one of such neural network frameworks,Maet al.[108]implemented two bidirectional CNNs (termed as primary and auxiliary networks) with the primary purpose of performing an on-demand function.Fig.5 (a) (i)illustrates the structure of their deep-learning model as well as the design geometry of their metastructure (see the inset inFig.5 (a) (ii)).These tasks are connected through an ensemble learning strategy of partial stacking.The primary network handles the general prediction of the output spectra,whereas the auxiliary network captures the plasmonic resonances such that the overall predictive capacity of the model is enhanced.A unit cell of the chiral geometry is comprised of two stacked gold split-ring resonators twisted at an angle and separated by two dielectric layers.A gold back-reflector is employed at the base.The forward model predicts optical responses given the geometric parameters of CMMA whereas the inverse model solves the inverse problem of retrieving the CMMA geometric parameters required for a given optical response.Figs.5 (a) (ii)and(iii)illustrate the model performance for a forward prediction task with and without the auxiliary network,respectively.Comparatively,the model performs better with the auxiliary network,especially at the resonances.The auxiliary network is designed by setting a threshold for the response which lies above or below the resonance,isolating and re-assembling the entire model through forward and inverse combiners.The inverse design employs two consecutive convolutional layers,followed by a fully connected layer.The inverse retrieval model is trained in the full loop of the primary network with its error as a penalty term to enhance accuracy.Therefore,given an optical or chiroptical response,it is possible to retrieve the geometric parameter dimensions that match the response.Figs.5 (a) (iv)and(v)also compare the model’s outputs with and without the auxiliary network.The model with the auxiliary network clearly exhibits high accuracy with the retrieved geometric parameter dimension close to that of simulations.As a result,given some desired design specifications,such as the amplitude,frequency,and polarity of the CD signal,the model can provide the design parameter dimensions necessary to achieving the desired specifications,performing a design-ondemand function.A major downside to this approach is the bulkiness and complexity of the architecture which can weigh down heavily on model-training resources for high dimensionality problems.Also,setting up a cutoff point to allow for the isolated treatment of the resonant peaks can be tedious,and in extreme cases,somewhat impractical for optical responses with multiple inflection points.

With a difference in the learning approach and chiral metastructure design,Ashalleyet al.[109]proposed a multitask deep-learning model for the CMMA design that comprises a single bidirectional neural network that can implement joint learning of characteristic features for efficient generalization of the neural network.This approach reduces the network load and makes effective use of the generated training dataset by creating auxiliary tasks composed of the LCP and RCP spectra that assist the main task of the CD prediction in the forward prediction path.In the inverse design,the multitask model retrieves the geometric parameters associated with the known optical response by matching the input spectra to the output geometric parameters through dense and task specific layers.Fig.5 (b)shows their deep-learning architecture and results summary.The chiral structure comprises a double yin-yang-shaped meta-atom (at a distant,d,from each other),sitting on a polymer layer on an Au mirror.Multitask learning is a type of ensemble learning that adopts a divide-and-conquer approach to task execution.The main task is divided into tiny bits termed auxiliary tasks whose function is to assist the achievement of the set objective.This is similar to human learning processes where in order to learn new tasks,we draw from knowledge that we have acquired via learning-related tasks.This approach is as well applied in educational pedagogy where relevant previous knowledge is utilized as the basis for advanced learning.In ML,multitask learning can be seen as a form of inductive transfer where inductive bias provided by the auxiliary tasks assists the efficient and effective generalization of the solution of the model.In their design,conventionally,a part of simulated data generated through iterative computations (via FEM) are used as a training set to train the model with the remainder as the validation set.The architecture has a normalization layer,where the inputs are normalized to prevent the effect of parameter ratios,a shared hidden layer,and a task-specific layer comprised of a main task which is CD learning and two auxiliary tasks for LCP and RCP spectra learning.To test the robustness of the structure,the simulated spectra are passed through the architecture,and the retrieved parameters are re-fed into the system.The model exhibits high accuracy with a comparison of the simulated spectra and the retrieved spectra from the retrieved geometric parameters.Through a self-assessment,the multitask deeplearning model can autonomously function without external influence.Figs.5 (b) (ii)and(iii)show the CD spectra (green) simulated from their corresponding geometry inFigs.5 (b) (iv)and(v)(green bars),respectively.These retrieved curves are re-fed into the model to generate the geometric parameter dimensions inFigs.5 (b) (iv)and(v)(red bars),respectively.The CD spectra (red dots) retrieved from the retrieved geometric parameters are compared favorably with the initial CD spectra,as illustrated inFigs.5 (b) (ii)and(iii),respectively.

For high dimensionality problems,it is difficult for all the model parameters to converge within a specified degree of freedom.Evolutionary optimization techniques,such as the micro-genetic algorithm,particle swarm optimization techniques,ant colony optimization,gradient descent methods,topology optimization,and the steepest descent methods[110],coupled with deep-learning frameworks are promising design routes for such high dimensionality problems with rapid convergence.These techniques emanate from the biological sciences,mimicking the unique naturally-occurring behavior of organisms,and have demonstrated high efficiency and robustness in electromagnetic designs,such as broadband circular polarizers and broadband light absorption[111]-[113].A micro-genetic algorithm evolves very small populations that are very efficient in locating promising areas of the search space.Basically,genetic algorithms conduct a search for the fittest population based on the principles of natural selection,earning it the tag name“survival of the fittest”.Compared with simple genetic algorithms,micro-genetic algorithms reach the near-optimal region faster in the presence of multimodality and show great precision in solving both stationary and non-stationary problems[114].A unique problem associated with micro-genetic algorithms is premature convergence.Premature convergence arises when there is a particularly fit population that poses the risk of preventing the further exploration of the design space as the model converges to a local minimum.This can be avoided by restarting the population multiple times during the run of the genetic algorithm.Liet al.[115]assessed the influence of geometric parameter modifications in binary-pattern nanostructures on the CD performance of CMMA composed of a metal-dielectric-metal three-layer structure by implementing the micro-genetic optimization algorithm.The metasurface comprises a 55-nm-thick top Au layer either of two patterns A or B generated from the genetic optimization algorithm,a 145-nm-thick SiO2spacer layer,and an optically thick substrate—Au substrate (200-nm thick).The geometry is illustrated inFig.5 (c) (i).Both patterns A and B are composed of square Au pixels (with sides ofw=64 nm) with two kinds of components exhibiting two-fold symmetry.With the micro-genetic optimization algorithm,CD values as high as 0.71 (for simulations) and 0.62 (for experiments) are achieved for pattern A.Pattern B is designed with different objectives of CD in absorption over 0.5 in the wavelength range of 1.75 μm to 2.00 μm (seeFig.5 (c) (ii)).Again,the microgenetic algorithm achieves this objective with simulated and measured CD in the absorption values of 0.67 and 0.60,respectively,as illustrated byFig.5 (c) (iii).Further probing the influence of other geometric parameters on the CD response of the structures reveals the high efficiency of the micro-genetic algorithm-based CMMA design approach.Such a combination of genetic algorithms and binary-patterned structures is helpful in solving complex optical problems ranging from dual-beam aperiodic leaky wave antennas that arbitrarily diffract transverse electric and transverse magnetic waveguide modes,to visibletransparent infrared emitting/absorbing metasurfaces,especially when adaptive genetic algorithms are adopted[112].This technique is yet to be applied to the full design and optimization of CMMAs as Liet al.[115]applied the genetic algorithm to the optimization of the top metallic layer.However,restarting the population several times to avert the problem of premature convergence may cause significant delays to the training process comparatively to the deep-learning techniques discussed.

Fig.5.ML-based CMMA design approaches.(a) ML framework composed of two networks (the primary and auxiliary networks) for both forward and inverse retrieval design problems.The primary network ensures an accurate prediction at the off-resonant frequencies whereas the auxiliary network addresses the inaccuracy at and in the neighborhood of the resonant frequencies:(i) schematic framework;(ii) and (iii) CD predictions from the forward prediction model for two geometric structures;(iv) and (v) geometric parameters retrieved from the inverse prediction model for the two geometry designs.Reproduced with permission[108].(b) Multitask deep-learning model architecture ((i)) and accuracy:(ii) and(iii) simulated (green solid lines) and predicted (red dots) CD spectra;(iv) and (v) corresponding initial (green bars) and retrieved (red bars) geometric parameters.Reproduced with permission[109].And (c) geometry of both CMMA structures(pattern A and pattern B) ((i)):Experimental and simulated absorption spectra of the micro-genetic-algorithm-optimized(ii) pattern A and (iii) pattern B under LCP and RCP illumination.Reproduced with permission[115].

Although the strength of the ML-based models discussed depends strongly on the model’s architecture,the geometry and type of response features are factored into the effectiveness of the model.A model may perform excellently with a less-complex structure but fail with complex ones.For all the deep-learning and genetic-algorithm-based techniques for the chiroptical response prediction,the fundamental problem is the absence of a framework that harmonizes the approaches to make them comparable.This may be resolved by creating an accessible dataset for training metamaterial structures,such as in the computer sciences where standard datasets,like the Modified National Institute of Standards and Technology (MNIST) dataset,exist.Such a framework will be less dependent on the structural geometry and response features of the theoretical model,providing a baseline for a justifiable comparison of deep-learning models for the metamaterials design.By this means,all designed models can be measured according to their performance with the created standard dataset.However,this may be challenging to accomplish,owing to the diverse application directions of metamaterials and nanostructures.

3.Fabrication of CMMAs

Chiral metamaterials can be fabricated by top-down and bottom-up approaches utilizing assorted techniques.The top-down approach utilizes the techniques,such as ion beam lithography;direct laser writing and electron-beam lithography for milling,cutting,and shaping materials into the desired shape,form,and order[33].The bottom-up approach builds with small components into more complex assembly and has been comprehensively reviewed[116].Indeed,the design and optimization process of CMMAs prepares a framework and background for their fabrication.However,the fabrication process comes with its challenges and limitations.Especially for complex designs,their fabrication can deviate widely from the theoretical predictions owing to fabrication imperfections mostly arising from the technique adopted as well as substrate conditions.A resonating example of chiral structures is the 3D helix.Structures with 3D chirality can be fabricated by direct laser writing,glancing-angle deposition,on-edge lithography,and focused ion beam (FIB) induced deposition.For chiral structures composed of both enantiomer pairs,only direct laser writing is insufficient due to the issues with the cut-off of electrolytes.Blending the direct laser writing approach with electroless silver plating averts this setback[117].The fabrication of planar CMMAs is synonymous with the fabrication of planar MMAs which are generally fabricated by top-down approaches.Planar structures cannot possess structural chirality in 3D space owing to the equality of the off-diagonal elements in the Jones matrices that come from the in-plane mirror symmetry.However,the planar metamaterial structure without any rotational symmetry exhibits strong chiroptical responses.This section discusses top-down fabrication techniques employed in realizing CMMAs and their associated challenges with an emphasis on planar CMMAs.

For an Au-polymer-Au structure,spin-coating can be used for their fabrication for the patterned and un-patterned structures[85].One concern is to fabricate this design with high quality since there exists relatively poor adhesion between the deposited Au layer and the polymer layer due to the fact that Au does not easily form strongly bonded oxides.It is a common practice to evaporate chromium to ensure adhesion of Au-glass interfaces.Mostly,an electron-beam writer is used to generate the master on a glass substrate coated with the polymer layer.Electron-beam lithography is followed by a conventional lift-off method with acetone.For the assembly of colloid nanoparticles through pit-arrays on polymethyl methacrylate (PMMA),the protonbeam writing can be used[118].The polymer substrate,such as PMMA,can then be coated with Au by thermal evaporation.By this means,no metal adhesion layer is needed[119].For patterned structures,injection molding using an injection-molder is completed prior to spin-coating with Au,as demonstrated by Karimullahet al.[120]for highly tunable plastic templated plasmonic chiral metamaterials.Figs.6 (a) (i)to(iv)show their design geometry and SEM images of the patterned“shuriken”enantiomer pair.Electron-beam lithography has been adopted for the fabrication of various other CMMAs,such as Z-shaped.Fig.6 (v)shows the SEM image of Zshaped CMMAs fabricated by electron-beam lithography.Fig.6 (vi)is also the SEM image of a U-shaped pseudochiral metasurface with an extensive application in chiral imaging[85].In addition,even though not yet applied to the fabrication of CMMAs,techniques,such as the glancing angle deposition,are promising[121].

Fig.6.Fabrication of CMMAs:(a) CMMAs with metal-polymer interfaces:(i) to (iv) templated plasmonic substrate with an Au-polymer interface fabricated by electron-beam lithography and electroplating,reproduced with permission[120];(v) Zshaped CMMA with an Ag-PMMA interface fabricated by spin-coating,reproduced with permission[39];(vi) U-shaped pseudo-chiral resonators fabricated by electron-beam lithography,reproduced with permission[85].(b) CMMAs with metaldielectric interfaces:(i) and (ii) SEM images of the plasmonic CMMA enantiomeric pair with a metal-SiO2 interface fabricated by electron-beam lithography and reactive sputtering,reproduced with permission[115];(iii) Z-shaped-based CMMA with a metal-SiO2 interface fabricated by FIB milling,reproduced with permission[90].

Generally,stacked-planar CMMAs can be fabricated by the electron-beam lithography technique with alignment in a layer-by-layer manner.For MMAs comprised of single top and bottom metallic layers spaced by a TiO2or SiO2dielectric,the top metallic layer can be deposited by electron-beam evaporation and the glass support can be deposited by reactive sputtering.An FIB system is normally used to mill-in the structures to form the top metallic arrays.The metal layer is normally deposited by sputtering,and the dielectric layer can be deposited by electron-beam evaporation.For characterizing the chiroptical response,the spectroscopy technique can be chosen depending on the frequency range.For example,for infrared incidence,the Fourier transform infrared spectroscopy (FTIR) is suitable.Similar techniques have been used to fabricate patterned chiral structures[115]as well as double-rectangular chiral structures[90].Fig.6 (b)shows patterned CMMAs (Figs.6 (b) (i)and(ii)) and Z-shaped CMMAs (Fig.6 (b) (iii)) with metal-dielectric interfaces fabricated by FIB milling,sputtering,and electron-beam evaporation[90],[115].First,the Au-SiO2-Au multilayer is deposited on a glass substrate.Specifically,the Au and SiO2layers are deposited by sputtering and electronbeam evaporation,respectively,followed by the milling of the double-rectangle pattern array into the top Au layer by FIB.To specify CPL,a set of linear polarizer and quarter-wave plate is used such that the polarization of the two linear polarizers is at a 90° phase shift to each other.

For broadband CMMAs,it is challenging to fabricate thin MMAs with broadband characteristics as these two are conflicting restrictions.There are several options to overcome the bandwidth-thickness challenge in MMAs,which can be extended to broadband CMMAs.Some of the popular approaches include nanocomposites,horizontal integration[122],magnetic medium substrates[123],circuit analog absorbers[124],chiral bi-anisotropy[125],optimization algorithms[126],[127],and multilayering and highly absorbent materials[128].Recent techniques have even included water-based MMAs[129],[130].

4.Applications of CMMAs

The applications of CMMAs are extensive as they as well include the applications of MMAs with LP light excitation.In this section,we consider the use of CMMAs in CPL detection,hot electron generation,chiral imaging,and photothermal and bolometric applications.

4.1.Hot Electrons

During the non-radiative decay of surface plasmons,plasmonic hot electrons are generated in large numbers with high kinetic energy.Their high kinetic energy enables them to overcome the potential at the Schottky barrier such that they are injected into any nearby semiconductor.This phenomenon is widely adopted for a wide range of applications,including solar energy harvesting,photodetection,photocatalysis,and ultrafast optical switches and modulators.Therefore,together with chiral plasmonic nanostructures,it is possible to selectively initiate hot electron transfer to regulate the injection process and offer a channel to conveniently detect CPL as well as enable effective enantioselective catalysis.In this subsection,we discuss the generation of hot electrons with CMMAs and their applications in CPL detection.

4.1.1.Generation of Hot Electrons for Photochemistry

In addition to their applications for CPL detection,hot electrons generated with perfect CMMAs can be adopted for polarization-sensitive photochemistry.Wanget al.[131]investigated a perfect CMMA structure composed by zig-zag-shaped Au nanoantenna arrays on the thin TiO2layer which acts as a spacer between the top Au nanoantenna arrays and a bottom optically thick Au back-reflector.Figs.7 (a)and(b)show the geometry and dimensions of their CMMA as well as the mechanism for the hot electron injection.The zig-zag Au nanoantenna shape is formed by continuous Au blocks with a wire-length-dependent rotation angle,θ,which affords CMMA the 2D chiral asymmetry.The 2D chiral asymmetry offers great advantages for photodetectors and optical absorbers as already theoretically realized[132].TiO2is a wide-bandgap semiconductor that exhibits high compatibility with photocatalytic processes owing to their low toxicity and excellent level alignment necessary for chemical reactions.It should be noted that hot electrons are generated as a result of the linear momentum change condition and thus present a nonthermal distribution profile.When molecules are attached to the top chiral metastructure,hot electrons are injected into TiO2,providing that these hot electrons gain energy that is higher than the Schottky barrier.By so doing,photocatalysis can be realized depending on the condition of constant illumination of CMMA.The differential hot electron generation for LCP and RCP incidence is recorded as illustrated byFig.7(c).Therefore,there is chiral selective hot electron transfer which even leads to CPL detection.

Fig.7.Hot electron generation:(a) and (b) geometry of the zig-zag wire formed by continuous blocks and mechanism for hot electron generation;(c) chiral selective hot electron generation under LCP and RCP illumination.Reproduced with permission[131].CPL detection:(d) structure of the Z-shaped chiral geometry;(e) SEM images of the chiral metamaterial enantiomers together with the experimental setup;(f) photoresponsivity of the enantiomeric pair and the spectra ratio of photocurrent polarization discrimination.Reproduced with permission[39].

4.1.2.Hot Electron Based CPL Detection

Liet al.[39]adopted hot electrons generated from the resonant excitation of CMMA,composed of Z-shaped silver nanoantennas fabricated on top of the PMMA resist spacer on an optically thick silver back-reflector,to detect CPL.This is in a bid to relieve the cost of using traditional optical systems which comprise multiple optical elements and present a hurdle for the realization of integrated and miniaturized devices.Their approach combines engineered chirality from chiral plasmonic metamaterials with hot electron injection.As a result,the device can effectively and autonomously distinguish between left-and right-handed CPL without support from any additional elements.The design incorporates an Ag bar which connects to all the strands of top Ag nanoantennas such that the device is ready for electrical connectivity.Fig.7 (d)illustrates the chiral geometry andFig.7 (e)shows the experimental setup and SEM images of chiral enantiomers.For the device operation,an n-type silicon wafer is placed in contact with the antenna layer.Light incident on the frontside of the Si wafer is selectively absorbed by CMMA such that only the photons of particular handedness are absorbed.These generate hot electrons with energy greater than the Schottky barrier,which are emitted over the Schottky interface and translated into a detectable current.The photosensitivity spectra of the structures are very high and comparable to Schottky diode-based LP light photodetectors operating in the same wavelength regime.Fig.7 (f)is the measured (dots) and simulated (solid curve) photosensitivity of the structure under LCP (blue) and RCP (red) illumination,showing high responsivity as well as high distinction in the photocurrent for different CPL handedness.

4.2.Chiral lmaging

Another application of CMMAs is in chiral imaging.The measurable optical and chiroptical features that characterize the selectivity of CMMAs upon interactions with LCP and RCP light can be engaged for chiral imaging with sharp contrast.For instance,for a device that exhibits selective photocurrent generation,patterning of a variety of images can be explored as studied by Liet al.[39]with imaging of the Vanderbilt University logo.First,the chiral enantiomeric pair is arranged into the pattern of the logo,with each handedness occupying either the interior or the exterior of the logo,as illustrated byFig.8 (a).Under LP or unpolarized light,no image is visible (Fig.8 (b)).However,under CPL illumination,owing to the selectivity in photocurrent generation,the left-handed and right-handed meta-molecules selectively reflect the image of the logo as shown inFig.8 (c).The sharp contrast of the images under focused LCP and RCP excitation is confirmed through the scanning photocurrent measurement.Fig.8 (d)is the scanning photocurrent maps of the giant pattern under LCP and RCP illumination.

When designed right,CMMAs can drive nonlinear chiroptical effects,such as the second harmonics generation (SHG) and the third harmonics generation (THG),respectively.Nonlinearly-generated CD may be used for high-contrast imaging owing to the enhanced chiral-selective optical nonlinearity.

Using a gold patterned Au film,separated from an optically thick Ag back-reflector by an optically thin Al2O3dielectric spacer,Kanget al.[40]demonstrated a chiral metamirror that not only exhibits selectively large chiroptical responses with spin state preservation for particular CPL handedness but also enables nonlinear chiroptical responses in the near-infrared regime.The Au pattern is a hole formed by two intersecting rectangles such that there is symmetry-breaking as described inFig.2 (a)and determines the chirality of the nanostructure.This design can propel metamirror-based chiral-selective nonlinear optical imaging,such as SHG-CD imaging.In their experiment,the CMMA samples of both enantiomers are excited with the circularly polarized ultrafast laser,and the generated nonlinear optical signals are collected in the direction of reflection.The SHG-CD images produced via this metastructure with a high enantioselective SHG signal can exhibit sharper contrast compared with SHG images in the linear regime.Similar to Liet al.[39],the enantiomeric pairs are arranged to (this time) form a hand pattern.The patterned hand is pumped with the circularly polarized ultrafast light at two fundamental wavelengths (770 nm and 850 nm) of the highest SHG-CD resonance.Figs.8 (e),(f),and(g)are produced at the 770-nm wavelength.Fig.8 (e)shows a bright hand in a dark background with LCP excitation whose inverse is illustrated byFig.8 (f)for RCP excitation.The corresponding SHG-CD image of the hand pattern is obtained by implementing a point-by-point calculation of SHG-CD with photon counts retrieved from LCP and RCP illumination.The high-contrast SHG-CD image obtained is illustrated inFig.8 (g).Figs.8 (h),(i),and(j)are similar illustrations at the second resonant wavelength (850 nm) of the pump laser where the dominance of the excitation CPL handedness switches.Fig.8 (g)is obtained fromFigs.8 (e)and(f).Likewise,Fig.8 (j)is obtained fromFigs.8 (h)and(i).

Fig.8.Chiral imaging with selective photoresponsivity:(a) left-handed and right-handed Z-shaped wires adopted for patterning the Vanderbilt University logo (here,the left-handed and right-handed enantiomers fill the black and dark regions,respectively);(b) no visible image under LP light;(c) selective photocurrent induced image reflection for LCP and RCP excitation;(d) photocurrent scanning maps revealing sharp contrast for LCP and RCP incidence.Reproduced with permission[39].SHG-CD imaging with chiral absorption selectivity and CPL preservation:(e) and (f) nonlinear images of the hand pattern under LCP and RCP illumination,respectively,at a wavelength of 770 nm;(g) corresponding SHG-CD image from (e) and (f);(h) and (i) nonlinear images of the pattern under CPL excitation at the 850-nm wavelength;(j) corresponding SHG-CD image obtained from (h) and (i).Reproduced with permission[40].Chiral imaging with broadband CMMAs:(k) SEM image of the giant arrangement of the chiral enantiomers of varying sizes into six different sectors of a pie-like pattern (scale bar is 3 μm);(l) chiral reflective images of the six sectors at the wavelengths of 1.31 μm and 1.58 μm upon LCP and RCP illumination.Reproduced with permission[100].

The high-contrast switchable reflective image may be regulated by tuning external parameters like the polarization and wavelength of the incident light.For broadband CMMAs,this affords them a wider tunability range.By combining structures of varied sizes culminating into the broadband chiroptical response,interesting patterns emerge upon CPL illumination.It opens up applications in data encryption for optical communications and other exotic applications.Both enantiomer pairs of varied sizes can be used to build a spatially nonuniform pixelated frame such that acting as a giant photodetector,patterns of various complexity can be realized upon CPL excitation as described by Ouyanget al.[100].Fig.8 (k)is the SEM image of a pielike pattern with six sectors constituted by CMMAs of different sizes.When LCP,RCP,and LP light are incident on the metastructure,various reflective patterns emerge such that highly reflective sectors correspond to low absorption sectors and vice versa.Fig.8 (l)shows the reflective images of the six sectors under LCP,RCP,and LP illumination at two different wavelengths (1.31 μm and 1.58 μm),illustrating the distinct bright and dark sectors of the pie-like metamaterial as a result of the different working wavelengths at the various sectors.It can be noted the broadband metastructure is highly reflective to LP light for both excitation wavelengths but highly selective to CPL illumination.

4.3.Chiral Photothermal Effects

It is well established that plasmonic processes battle with intrinsic Ohmic losses owing to their nonradiative nature[133].This thermal effect is detrimental for light-emitting applications due to emission quenching.On the bright side,the photothermal effect can be harnessed for a wide range of applications,including CPL detection,chiral imaging,and designing bolometers.A bolometer is a thermal infrared detector,a sensitive electrical instrument for measuring radiant energy.Bolometers measure the power of incident electromagnetic radiation through heating a material with temperature-dependent electrical resistance and recording the change in resistance.Using plasmonic CMMA,Konget al.[37]derived relevance for the plasmoninduced photothermal effect by redirecting it towards chiral bolometry.Their structure utilizes Γ-shaped CMMA,which exhibits thermal-selectivity when illuminated by CPL of opposite handedness.The specificity of their structure is presented inFig.3 (j)toFig.3 (n).Figs.9 (a) (i)and(ii)show the increase in temperature at a specific pointP1,as well as the average temperature increase across the CMMA surface,showing thermalselectivity for LCP and RCP incidence.Their theoretically investigated device can be used to measure the extent of circular polarization of incident radiation,expanding its use to chiral bolometry,as illustrated inFig.9 (a) (iii).An enantiomer pair of plasmonic CMMA is illuminated with the same incident radiation such that the difference in bolometric responses of the two devices establishes the presence or otherwise of circular polarization.

Thanks to their theoretical investigation,several studies capturing photothermal CD in imaging and other applications have emerged,including a recent experimental confirmation of the effect though without CMMAs.Miandashtiet al.[134]experimentally demonstrated photothermal CD using Au helicoid clusters which theoretically exhibit high chiral fields (shown inFigs.9 (b) (i)and(ii)) as well as differential photothermal CD(seeFig.9 (b) (iii)).The thermal selectivity of the Au helicoid is biased towards RCP excitation,as illustrated byFig.9 (b) (iv).The experimental demonstration uses single-particle spectroscopy[135]of colloidally prepared Au helicoid on the AlGaN:Er3+thin film and observes an intensity-dependent photothermal chiral dissymmetry factor (g-factor) with slight reductions at higher temperatures for the Au helicoid clusters (seeFig.9 (b) (v)).The Au helicoids are designed such that each of their faces describes a gammadion structure as shown by the SEM image in the inset next toFig.9 (b) (v).The total temperature increase correlates to the number of Au helicoids in each hot spot from the illumination.The intensity dependence of the photothermal dichroism and photothermal g-factor is established by calculating the steady-state temperature using luminescent ratio thermometry.An experimental demonstration of the use of the photothermal CD effect proposed in [37] was in imaging,where CD of single metal nanoparticles can be measured via photothermal imaging.

This concept combines the enantioselective signal from CD with the highly sensitive photothermal microscopy to realize a superior signal-to-noise ratio,which allows for the quantification of very small individual nanoparticles,and distinguish between relative absorption differences of CPL as small asgmin=4×10-3for 30-ms integration time.Here,gdenotes the measurable dissymmetry factor conventionally used for distinguishing between relative absorption differences of CPL.Therefore,gmincorresponds to the minimum dissymmetry factor.

Fig.9.Chiral photothermal effects.(a) Photothermal CD (theory):Temperature increase (i) at point P1 and (ii) averaged across the CMMA surface upon LCP and RCP illumination;(iii) photothermal CD theoretically adopted for a bolometric application.Reproduced with permission[37].(b) Experimental demonstration of photothermal CD effect:(i) to (iii)simulation of the thermal image and profiles of a 200-nm helicoid under LCP and RCP illumination (the cross-section of the thermal image is indicated by the dashed line in (i));(iii) thermal profile of the 200-nm helicoid upon LCP and RCP 532-nm excitation.The inset in (iii) is the photothermal CD spectra of a single helicoid structure.(iv) Temperature versus the LCP and RCP excitation intensity plot for one of the six hot spots;(v) photothermal g-factor versus laser intensity from(iv).The inset next to (v) is the SEM image of the fabricated Au helicoid structure with gammadion-shaped faces.Reproduced with permission[134].(c) Photothermal imaging:(i) photothermal CD microscopy setup comprising a 532-nm wide-field heating beam,a focused probe beam,an electro-optical modulator,a quarter-wave plate,and a removable polarizer;(ii) SEM image of the alternating gammadia array with a zoomed-in higher resolution image of the dashed rectangle;(iii) photothermal and (iv) photothermal CD images of the zoomed-in high-resolution image;(v) histogram of g-factor for the three types of structures.The dashed lines indicate the mean of the distribution.Reproduced with permission[136].

Fig.9 (c) (i)shows their experimental setup,implementing photothermal CD microscopy using a 532-nm wide-field heating beam and a tightly focused probe beam at 780 nm[136].The modulation of polarization is achieved via an electro-optical modulator,which acts as a zero and half-wave plate at 45° with respect to the incoming polarization.LCP and RCP light are obtained through the transformation of the vertical and horizontal linear polarization states by a quarter-wave plate (λ/4).The intensity modulation is also achieved by incorporating a removable polarizer.Three forms of the gammadion designed to exhibit left-handed and right-handed chirality,as well as non-chirality,are employed,as the inset inFig.9 (c) (i)shows.The structures are in an alternating order,i.e.,right-handed,achiral,and left-handed.The three alternating structures are fabricated on a glass substrate.Fig.9 (c) (ii)is the SEM image of the structures.The photothermal image of the zoomed-in sample inFig.9 (c) (ii)is shown inFig.9 (c) (iii).Fig.9 (c) (iv)is the photothermal dichroism image of the fabricated sample.Fig.9 (c) (v)shows different dissymmetry factor distributions for the three structures and consequently provides grounds for distinguishing between chiral and nonchiral structures.

4.4.Active Chiral Plasmonics with CMMAs

Active chiral plasmonics involves incorporating active materials into chiral plasmonic structures to migrate them from static to reconfigurable devices,affording them a range of applications in displays,all-optical photonic circuits,data storage,imaging,and sensing.Active chiral plasmonics provides handles for postfabrication control of the plasmonic optical mode behavior of the structure.Such post-fabrication control can be achieved in a number of ways,including graphene injection of free carriers in semiconductors[137],metal-VO2hybrid combination[138],and the use of the phase-change material GeSbTe (GST) as a middle layer sandwiched between two metallic layers in the top chiral structure[139].This chalcogenide phase change material,when brought into proximity with a plasmonic nanoantenna,results in significant plasmon resonance shifts[139].Therefore,the GST-chiral metamaterial combination can produce shifted CD signals when actuated and introduce a handle for switching/controlling the chiroptical response[28],[139],as well as introduce dynamism[140]under the influence of an external stimulus towards reconfigurability.

Instead of incorporating phase-change materials,Yanget al.[141]proposed active perfect CMMA based on planar anisotropic chiral metamaterials.The studied structures comprise Z-shaped planar anisotropic and gammadion-shaped isotropic CMMAs.The gammadion-shaped structure exhibits no circular conversion dichroism (CCD) with its square lattice.However,the Z-shaped one exhibits tunable CCD owing to its anisotropic nature.Figs.10 (a)and(b)are the schematics of the anisotropic and isotropic chiral geometry.This further proves that chiroptical effects are truly structure-dependent and that active tuning of CMMAs can be achieved using the intrinsic geometric properties of CMMAs.Therefore,CCD is central to achieving active chiroptical effects in CMMAs as it enables selective microcavity interference,i.e.,the Fabry-Perot cavity.The tunability of CD in reflection for the anisotropic structure spans from 0 to 0.882,whereas that of the isotropic structure moves to zero from the visible to the microwave,as shown byFigs.10 (c)and(d).Such active chiral structures and phase-change materials can be adopted for various sensing applications due to the highly tunable and sensitive chiroptical response.The refractive index of phase-change materials depends on several extrinsic factors,including temperature and illumination conditions.Yanget al.[141]incorporated VO2to better assess the modification sensitivity of the active CMMA.Fig.10 (e)illustrates a linear relationship between the refractive indexnand temperatureTof VO2at different regions (n=0.001Tin the slow-varying region andn=0.111Tin the quick-varying region).Atd=100 nm,the maximum modification sensitivity of the structure is 1.36825 °C–1and 151.8759 °C–1in the slow-varying and quick-varying regions,respectively,with modification periods of 6 °C and 0.06171 °C,respectively.Figs.10 (f)and(g)illustrate the modification sensitivity in the slow-varying and quick-varying regions with the 100-nm cavity length.The structure can also enable highly accurate temperature sensing comparatively to current commercial temperature sensors,reaching to about 3.067×10-8°C for temperatures from 65 °C to 70 °C.

Fig.10.Active chiral plasmonics with CMMAs:Schematic of (a) planar anisotropic and (b) planar isotropic chiral absorbers;reflectivity and CD in reflection as a function of spacer thickness d (cavity length) for (c) anisotropic and(d) isotropic planar chiral metamaterials;sensor performance of the active chiral absorber:(e) measured refractive index n of VO2 as a function of temperature,and the modification sensitivity in (f) slow-varying and (g) quick-varying regions(denoted by purple and blue dashes in (e)) at d=100 nm.Reproduced with permission[141].

5.Outlook and Conclusions

The theories,design and optimization,fabrication,and extensive applications of CMMAs have been summarized and discussed in this review.In particular,techniques for achieving narrowband and broadband CMMAs have been outlined.Single-band and dual-band CMMAs with the narrowband chiroptical response can be achieved via single-and/or dual-mode excitation of top chiral nanostructures,such as Z-shaped,L-shape,and Γ-shaped structures.Broadband CMMAs with broadband chiroptical effects can be achieved by carefully arranging multiple CMMAs of varying resonances provided by the differences in the structural geometry and/or chiral nanostructure sizes.The top-down fabrication techniques dominated by electron-beam lithography have also been discussed.

The chiroptical response of CMMAs can be optimized by ML-enabled techniques that offer a channel for an elaborate exploration of the design space.For the future design of CMMAs,however,it is important to underscore the relevance of the correlation of the circular differential optical absorption with geometric chirality of the chiral structures to enable efficient metastructure optimization for maximum chiroptical effects[142].Currently,electromagnetic solvers,such as Comsol Multiphysics,Lumerical,and CST Microwave Studio,are used to simulate the chiroptical responses of CMMAs before further optimization techniques are employed.However,they face the generalization challenge due to the iterative case-by-case parameter sweeping that is time-and resource-intensive.As ML techniques provide the support to the theoretical methods,geometric approaches to predicting the chirality of structures may provide significant additional support to the CMMA design and optimization process as well as complement emerging ML-based metastructure design techniques.Although,geometric approaches,such as the scale invariant“product of asymmetry”[143]and an overlapping method based on the chiral coefficient proposed by Gilat[144],have long been implemented for structural designs,Potts’ implementation[145]with 2D continuous media and planar metamaterials makes it relevant to the quest for highly optimized CMMAs with a maximum chiroptical response.Also,aside from the genetic and deep neural network algorithms,other nature-inspired optimization algorithms,such as the particle swarm optimization techniques,are expected to provide cushioning for the future design and optimization of CMMAs.For instance,the ant colony optimization technique (an example of particle swarm optimization algorithms) has already been applied to the design of broadband terahertz MMAs[146]and the synthesis of metamaterial coatings for cylindrical structures[147],but it is yet to be applied to the optimization of the chiroptical responses from CMMAs.

As their optimization techniques evolve steadily,we expect a corresponding surge in the design and application possibilities of CMMAs with novel materials integration.For instance,dielectric materials can be instrumental in the composition of future CMMAs with an added advantage of minimum to no loss compared with the current plasmon-enhanced structures.Though CMMAs primarily efficiently absorb light,studies on the extended use of the absorbed light are lacking.In future research,we envisage that the conversion of the absorbed light into other forms of energy,such as electricity,sound,light,and magnetism,will further broaden the application routes of CMMAs.

Disclosures

The authors declare no conflicts of interest.