Electromagnetic Architectures: Structures, Properties, Functions and Their Intrinsic Relationships in Subwavelength Optics and Electromagnetics

through the copyediting, typesetting, pagination and proofreading process, which may lead to differences between this version and the Version of Record. Please cite this article as doi: 10.1002/adpr.202100023 This article is protected by copyright. All rights reserved Electromagnetic Architectures: Structures, Properties, Functions and Their Intrinsic Relationships in Subwavelength Optics and Electromagnetics Xiangang Luo*, Mingbo Pu, Yinghui Guo, Xiong Li, and Xiaoliang Ma Prof. X. G. Luo, Prof. M. B. Pu, Prof. Y. H. Guo, Prof. X. Li, Prof. X. L. Ma State Key Laboratory of Optical Technologies on Nano-Fabrication and Micro-Engineering, Institute of Optics and Electronics, Chinese Academy of Sciences, P.O. Box 350, Chengdu 610209, China. School of Optoelectronics, University of Chinese Academy of Sciences, Beijing 100049, China. E-mail: lxg@ioe.ac.cn


Historical remarks
For quite a long time, structures and functions of matters are the core of physics researches. From celestial bodies and buildings to the atomic and molecular structure of common materials, the structures of various scales determine their basic functions, wherein the underlying physical laws of the interaction between substances are called "structuralfunctional relationship". For example, the law of universal gravitation determines that most celestial bodies are approximately spherical in shape and move in nearly elliptical orbits.
Meanwhile, the molecules in crystals reach equilibrium states under the action of many molecular forces, thereby forming regular and orderly structures, which determine their mechanical, thermal, electromagnetic, and optical properties. Under the classical optical theoretical framework, the surfaces of both the refractive and reflective lenses are shaped to be curved to bend the light trajectory. The curved profile and large weight of refractive/reflective lenses and mirrors hinder the development of next-generation optical systems, especially in integrated space telescopes and wearable optical devices and systems.
In recent years, with the development of micro/nanofabrication technology, it has been discovered that artificial structures have many physical properties not occurring in traditional materials. It is expected to achieve many disruptive functions through artificial structures, such as photonic bandgap, [1] negative refractive index, [2] sub-diffraction imaging, [3] etc.
Therefore, research directions such as photonic crystals, metamaterials, and surface plasmons have become research hotspots in the field of optics and electromagnetics during the past two decades.
Humans have a long history of changing optical and electromagnetic properties through artificial structures. For example, structural color was created by light interactions with certain nanostructures that strongly influence the light scattering properties. As shown in Figure 1, due to the surface plasmon absorption effect of metal particles, the late Roman (4th century AD) Lycurgus cup exhibits different colors under transmission and reflection metamaterial. [22] Different from natural materials whose properties are primarily determined by the chemical constituents and bonds, metamaterials offer a significantly broader range of material properties by engineering the geometries and arrangements of the subwavelength building blocks (meta-atoms) and thus promise widespread potential applications. Thus far, metamaterials have been realized in the microwave, terahertz, infrared and visible ranges to exhibit many exotic properties, including but not limited to negative/zero/high refractive index, strong chiral, and anisotropic response as well as perfect absorption. For example, the use of plasmonic materials with negative dielectric permittivity is one of the most feasible ways to circumvent the diffraction limit and achieve localization of electromagnetic energy (at optical frequencies) into nanoscale regions as small as a few nanometers. As a result, like Feynman's statement on nanotechnology, there is plenty of room at the bottom that has not been utilized in traditional optics. [23] Although gradient index metamaterials offer a feasible way to construct planar lenses and other miniature optical devices, their sizes are usually bulky and the thickness is larger than the operation wavelength. As a result, there has been growing interest in planar, subwavelength-thick planar optical devices with multifunction. Fortunately, the recently emerging metasurfaces (two-dimensional metamaterials) are proved to be able to produce phase discontinuity within a vanishing thickness of structured materials, thus makes it possible to construct lightweight and flat optical elements. The difference between metamaterials and metasurfaces can be understood in the context of constitutive relations and boundary conditions of Maxwell equations. As a result, it was expected that the first generation of practical metamaterial devices will utilize metasurface implementations.
Materials with tunable properties upon external stimuli are crucial for the realization of versatile platforms with reconfigurable functionalities. For instance, by changing the lattice constant of a complex Au nanorod array fabricated on stretchable polydimethylsiloxane (PDMS) substrate, [24] a metasurface that can continuously tune the wavefront has been Accepted Article rials have been realized in the microwave, terahertz, infrared and visible ranges to Accepted Article rials have been realized in the microwave, terahertz, infrared and visible ranges to exhibit many exotic properties, including but not limited to negative/zero/high refractive Accepted Article exhibit many exotic properties, including but not limited to negative/zero/high refractive index, strong chiral Accepted Article index, strong chiral,

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, and anisotropic response as well as perfect absorption.

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and anisotropic response as well as perfect absorption.
use of plasmonic materials with negative dielectric permittivity is one of the most feasible Accepted Article use of plasmonic materials with negative dielectric permittivity is one of the most feasible ways to circumvent the diffraction limit and achieve localization of electromagnetic energy Accepted Article ways to circumvent the diffraction limit and achieve localization of electromagnetic energy (at optical frequencies) into nanoscale regions as small Accepted Article functional relationship in subwavelength structured materials and devices. More details can be found in the references therein.

Properties of typical artificial structures
This section briefly introduces the characteristics of various typical subwavelength structures and provides a basis for studying the structural-functional relationship between subwavelength structures and optical/electromagnetic functions.

Classification of subwavelength structures
Without the loss of generality, electromagnetic structures could be divided into three categories depending on their arrangement in space. The first kind of structure is single or few structures, which could act as miniaturized devices. [42][43][44] For instance, single V-shaped or catenary-shaped nanoantennas could convert normally incident electromagnetic waves into unidirectional waveguiding modes. [45,46] Few nano-antennas or nano-apertures could be utilized to collimate light waves to predefined directions. [43,47] The second kind of structure is a periodically arranged pattern array with identical geometric properties. Some typical examples include the century-old FSS, [22] photonic crystals, [11] negative-index metamaterials, and metasurface perfect absorbers. [48,49] Note that the lattice constant of photonic crystals is larger than the operational wavelength to produce photonic bandgap, while it should be in the deep subwavelength scale to enable effective index approximation of metamaterials. However, in many follow-up studies, the concept of metamaterials is broadened and the deep subwavelength condition is often discarded.
The third kind of structure is a gradient array with space-variant unit elements. The early gradient artificial structured materials in antenna engineering may date back to the 1940s-1960s, where metallic plates and waveguides are utilized as lens antennas. [50,51] Beginning from the late 1980s, as a result of the mature printable microstrip antennas, various reflectarrays with space-variant metallic structures have been proposed to realize flat antennas. [52][53][54] Meanwhile, in the optical bands, as a consequence of the development of  [11] Accepted Article [11] nega

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The third kind of structure is

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The third kind of structure is This article is protected by copyright. All rights reserved micro-and nano-fabrication techniques, subwavelength gradient structures were proposed and fabricated to introduce abrupt phase shift. [55][56][57][58][59] Along with the emergence of metamaterials, transformation optics, and metasurfaces, gradient subwavelength structures have been developed explosively during this century. Typical examples include the invisibility cloaks, [60,61] hyperlenses, [62,63] metalenses, [64] etc. optical functionalities. In FSSs, the transmission and reflection spectrum could be interpreted using equivalent circuit models and transmission line theory. These metasurfaces may be considered as impedance sheets composed of equivalent inductors and capacitors. The geometric shape and size of the elements will then determine the equivalent circuit parameters, e.g., inductance L, capacitance C, and resistance R.
Figure 4(c) shows two kinds of planar chiral elements, i.e., the spiral and gammadion, [65,66] which have different responses for opposite circular polarizations. Figure   4(d) shows two kinds of basic elements used for quasi-continuous phase modulation. [67,68] Since small pieces in these elements have space-variant sizes and orientations, smooth geometric and propagative phase shifts would occur naturally. Note that although the characteristic dimensions are smaller than the wavelength, the whole sizes are often larger than one wavelength, thus a single element may act as basic elements of metagratings, which could bend light to almost arbitrary direction with high efficiency.
In a structured array of basic elements, the electromagnetic coupling of adjacent structures has a great influence on electromagnetic properties. Figures 5(a) and (b) show two types of lattices that are usually adopted in current researches. If the optical functionality is sensitive to the variation of symmetry, the two kinds of lattices would have completely different performances. For instance, if the isotropic polygonal elements in Figure 5(a) are placed at the lattices, the anisotropic coupling between the adjacent elements would induce Accepted Article [60,61] Accepted Article [60,61] hyperlenses, Accepted Article hyperlenses,

Figure
Accepted Article     Accepted Article n, [65,66] Accepted Article [65,66] which have different responses for opposite circular polarizations.  This article is protected by copyright. All rights reserved nontrivial and lattice-dependent geometric phases, which are referred to as generalized geometric phase. [69] Note that the electromagnetic coupling in the subwavelength scale can be described using catenary-shaped intensity distribution for both metallic and dielectric elements. [70,71] 2.2. Structures for effective electromagnetic parameters Distinct from naturally occurring materials whose optical constants are determined by the inherent molecules and atoms, the electromagnetic properties of artificially structured materials are mainly determined by the geometries and arrangements of building blocks, which offer unprecedented freedom to tailor the effective materials parameters. For electromagnetic applications, these properties include the effective permittivity ε eff , permeability μ eff , refractive index n eff , and impedance Z eff . The refractive index and impedance can be calculated using the permittivity and permeability, which are stemming from the electric and magnetic resonances of the subwavelength structures and lie at the heart of effective medium approximation. It has been shown that Lorentzian resonances may be viewed as possible building blocks for engineering any desired metamaterial response, for example, simultaneous negative permittivity and permeability by use of metallic cut-wires and split-ring resonators of different parameters. [2,20] Many novel physical phenomena and application prototypes, such as negative refraction, [20] sub-diffraction imaging, [72] and cloak, [60] have been demonstrated based on metamaterials.
In the late 1990s, J. Pendry proposed to use metallic rods and rings to control the effective permittivity and permeability in the microwave frequencies, [73,74] which was subsequently combined to realize an effective negative index. [2,20] From then on, many efforts have been paid to increase the operational frequencies to terahertz, infrared, visible, and even ultraviolet bands. Meanwhile, many new kinds of structures have been put forward, including the nanorods pair, [75] fishnet structure, [76,77] the metal-dielectric multilayers, [78] and so on.

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In the late 1990s, J. Pendry proposed to use metallic rods and rings to control the

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In the late 1990s, J. Pendry proposed to use metallic rods and rings to control the effective permittivity and permeability in the Accepted Article effective permittivity and permeability in the This article is protected by copyright. All rights reserved Structures exhibiting a near-zero index of refraction at the frequency of interest were defined as zero-index media, including epsilon-near-zero (ENZ), ε ≈ 0, [79][80][81][82] mu-near-zero (MNZ), μ ≈ 0, and epsilon -and-mu-near-zero (EMNZ), μ ≈ 0 and ε ≈ 0 , according to their predominant electromagnetic response. Among them, the metallic mesh of thin wires is the simplest type of metamaterials potentially used to form ENZ medium, since the Drude-like dispersion behavior can be tuned by adjusting the radius and period of the wires. [73] Besides negative index materials and near-zero index materials, artificial materials with unnaturally high index or chirality are also of particular importance for phase and polarization control. To obtain a high index, metallic patches or slits arrays with narrow gaps and large capacitance are usually adopted. [83,84] To realize chiral response, traditional planar structures are not suitable anymore. Instead, 3D spiral structures or multilayered metallic structures placed in a helical way are required. [85] The earliest such structures may be date back to the 1890s when Bose proposed to use helical jute as polarizers in the microwave and millimeterwave frequencies. [21] In the optical regime, Robbie et. al., have found the chiral optical response in sculptured dielectric thin films characterized by helical columns with pitches comparable to the visible light. [86] More recently, gold helices with stronger chiral responses are created using direct laser writing into a positive-tone photoresist followed by electrochemical deposition of gold. [85] Among the varieties of metamaterials proposed, hyperbolic metamaterials (HMMs) have rapidly gained a central role in nanophotonics. HMMs refer to mediums whose permittivity and permeability tensor elements (along principal axes) are of opposite signs, resulting in the hyperbolic equifrequency contour (EFC), including Type I hyperbolic metamaterials (ɛ x > 0 and ɛ z < 0) and Type II hyperbolic metamaterials (ɛ x < 0 and ɛ z > 0). [87] Many novel and unique properties result from this hyperbolic EFC. First, hyperbolic EFC gives rise to omnidirectional negative refraction for a certain polarization of the electromagnetic wave.
Second, hyperbolic metamaterials can support the transmission of evanescent wave Accepted Article simplest type of metamaterials potentially used to form ENZ medium, since the Drude Accepted Article simplest type of metamaterials potentially used to form ENZ medium, since the Drude dispersion behavior can be tuned by adjusting the radius and period of the wires.
Accepted Article dispersion behavior can be tuned by adjusting the radius and period of the wires.

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Besides negative index materials unnaturally high index or chirality are also of particular importance for phase and polarization Accepted Article wave frequencies. [21] Accepted Article [21] In the optical regime, Robbie et. al., have found the chiral optical components and transform them into propagating waves. This property forms the basis for the so-called hyperlens, enabling subwavelength imaging in the far-field. Finally, the hyperbolic EFC is shown to greatly enhance the photonic density of states in a broad range of frequencies, paving the way for boosting the efficiency of photonic devices. Several different structures have been shown to implement the HMMs, including layered metal-dielectric structures in planar profile, [88] curved and fishnet profile, as well as a lattice of metallic nanowires embedded in a dielectric matrix, termed nanowire array. [89] 2.3. Structures for surface impedance matching In general, metamaterials are 3D in nature, so they are described by an effective refractive index. However, the refractive index is not well suited for the description of 2D metamaterials, or the so-called metasurfaces. When the thicknesses of metasurfaces become much smaller than the wavelength or are virtually zero, they act as modified boundary conditions, which could be treated as effective impedances. [90] The structures and material compositions of the metasurface will determine the value of impedance.
According to electromagnetic theories, dielectric metasurfaces must have non-negligible thicknesses to perform functionalities, thus the surface impedance approach is widely utilized only in metallic metasurfaces. Since the impedance could be described using equivalent circuits and almost frequency independent parameters such as capacitance, inductance, and resistance, it has provided a versatile approach to control electromagnetic waves in a wide frequency range. [91][92][93][94] It was also shown that such an approach can also be extended to the optical regime. [95,96] For a metasurface described by its impedance, a proper change of the structural parameters could also result in a gradient phase. In this case, the reflection and transmission phase of a single layer metasurface could be obtained using electromagnetic boundary conditions described by the generalized Fresnel's equations: [90] Accepted Article where r and t are the transmission and reflection coefficients, Y 0 and Z 0 are the admittance and impedance of vacuum, Y e and Z m are the electric admittance and magnetic impedance of the metasurface. Obviously, if the impedance of the metasurface is purely imaginary, there is no ohmic loss and the phase can be arbitrarily tuned. [97] For dielectric resonators, similar expressions could also be obtained using some reasonable approximations. [98] Such metasurfaces are also termed Huygens' surfaces.

Structures for local phase modulation
Phase modulation is one of the most important tasks of functional optical materials and devices. In traditional optical technologies, the phase accumulation is accomplished by varying either the thickness or the refractive index of the lenses. Such a phase shift mechanism is called dynamic phase and results in large thickness and weight for the largeaperture optical system. Optical researchers have paid much effort to find out new ways to circumvent this barrier. Nowadays, it has been known that subwavelength structures could modulate the phase shift locally, which leads to the so-called generalized law of reflection and refraction: [12,90,99]     1 0 where Ф is the phase gradient in the metasurface plane, which is determined by the geometric structure and spatial distribution, and may be changed at different time T by external stimuli, leading to the adaptive tuning of the law of refraction and reflection. Accepted Article ohmic loss and the phase can be arbitrarily tuned.
expressions could also be obtained using some reasonable approximations.
Accepted Article expressions could also be obtained using some reasonable approximations.
Accepted Article metasurfaces are also termed Huygens' surfaces. Accepted Article refraction: [12,90,99] Accepted Article [12,90,99] Ф is the phase gradient in the metasurface plane, which is determined by the Accepted Article Ф is the phase gradient in the metasurface plane, which is determined by the geometric structure and spatial distribution, and may be changed at different time Accepted Article geometric structure and spatial distribution, and may be changed at different time shift mechanisms have been proposed, i.e., propagation phase, geometric phase, and circuit induced resonance phase, as indicated in Figure 6.
Different from the propagation phase accumulation in traditional optical materials and macrostructures, abrupt phase change can occur at a thin interface and a typical example is the plasmon phase retardation through narrow slits drilled in a thin metallic film. [58] The underlying reason is that coupled plasmonic mode is excited in the metallic slits, whose propagation constant is generally several times that in the free space. With the shrinking of the metallic slit width, the propagation constant of coupled plasmonic mode increases sharply.
Therefore, when the plasmonic phase retardation through two subwavelength metallic slits with unequal widths are opposite with each other, an extraordinary Young's interference (EYI) could be observed, i.e., a dark stripe appeared at the center of the interference pattern.
Since the propagation constant of plasmonic slits is related to their width, transversal phase gradient can be easily implemented by drilling a series of slits of different widths through a thin metallic film. Several plasmonic phased devices, such as plasmonic flat lenses [58] and beam deflectors [100] have been realized based on metallic slit arrays with variant widths, which were experimentally demonstrated in the visible band. [59,101] In parallel with the plasmonic approach, high-index dielectric nanopillars also provide a means to localize light into the subwavelength scale. Similar to the plasmonic metal-insulator-metal (MIM) waveguide, the propagation constant at a given frequency is dependent on the width and used materials, which promises the local phase modulation for dielectric metasurfaces. [102,103] Owing to the respective advantages (e.g., low cross-talk and low loss), both plasmonic and dielectric structures have been widely utilized in local phase modulation.
The second phase shift mechanism is the orientation-dependent geometric phase, which can be simply expressed as Φ = 2σξ, where σ = ±1 denotes the left and right-handed circularly polarized (LCP and RCP) incidence and ξ defines the orientation angle of nanoslits or stripes.
phase from the polarization path on the Poincaré sphere, [104] which is geometric and dispersionless for incident wavelength. By controlling the local orientation of the antennas between 0 and π, one can easily realize phase variation that covers the full 0 -to-2π range.
Although the geometric phase is dispersionless, its operation bandwidth is fundamentally limited by the bandwidth of the polarization conversion. To extend the operation bandwidth, dispersion engineering technology has been proposed and implemented through various kinds of resonators. [91,105] Recently, an approach to realize high-order geometric phases was proposed using meta-atoms with high-fold rotational symmetries. Broadband angular spin Hall effect of light and optical vortices were experimentally demonstrated by using plasmonic metasurfaces consisting of space-variant nanoapertures with C2, C3, and C5 rotational symmetries, which provides a fundamentally new understanding of the geometric phase as well as light-matter interaction in nanophotonics. [69] The third approach for local phase modulation is based on the local resonance in complex metallic [99,[106][107][108][109][110][111][112] or dielectric structures. [98] For example, for a V-shaped metallic antenna supporting symmetric and antisymmetric modes with different amplitude and phase due to their distinctive resonance conditions, the scattered light can have a polarization different from that of the incident light. [99] Accompanied with the polarization conversion, a local phase shift within π is generated, which can be adjusted by changing the arm length and the openangle of a V-shaped metallic antenna. [99,106] By exploiting the mirror structure of an existing antenna, one could create a new antenna whose cross-polarized radiation has an additional π phase shift. Similarly, C-shape split-ring resonators were also developed for realizing local phase modulation. [107,109] Different from the V-and C-shaped metallic antennas, H-and I-shaped metallic antennas do not rely on polarization conversion. [110][111][112] Nevertheless, to covering 2π phase shift and improving the manipulation efficiency, reflective configurations are generally adopted with strong magnetic resonance. Meanwhile, it has been shown that a high-index dielectric Accepted Article resonator can support both electric and magnetic dipolar Mie-type modes and exhibit very low intrinsic losses in the optical band. Thanks to the superimposing of the electric and magnetic resonances at the same frequency, a phase shift covering the whole 2π range can be realized. [113] An effective method to simultaneously tailor the phase-amplitude or phase-polarization is combining two kinds of phase shift mechanisms in a single metasurface, i.e., both the geometric parameters and spatial orientation of subwavelength structures are varied. In recent years, the concept of asymmetric photonic spin-orbit interactions (PSOIs) has been proposed to achieve spin-decoupled multifunctional meta-devices by merging propagation phase and geometric phase in plasmonic metasurfaces [93] and dielectric metasurfaces. [34,35,[114][115][116] Besides independent control of the wavefront of opposite-handedness, asymmetric PSOIs can also allow independent amplitude modulation by adopting super-atoms as building blocks, [117][118][119] which may be utilized for chiral imaging and elliptical polarizers. The symmetry breaking of PSOIs is attributed to the opposite spin dependence of the propagation phase and geometric phase. By employing their opposite frequency dependence, broadband achromatic metalenses have also been realized in multiple spectral bands, [120][121][122][123] where the geometric phase and propagation phase are utilized to independently control phase and dispersion, respectively.
More interesting, by suppressing the propagation phase in all-dielectric catenary-like streamline structures, a maximum diffraction efficiency approaching 100% is obtained in ultrawide spectral and angular ranges, and wide-angle (178°) diffraction-limited imaging has also been realized using a single planar metadevice. [124,125] Besides, multistate wavefront tunable meta-devices have also been realized based on phase-change meta-atoms, in which the combination of the two phases can increase the function complexity while decreasing the design complexity. [126] Besides phase, frequency and wavelength are key parameters to describe electromagnetic waves. Since the full electromagnetic spectrum covers the visible, infrared, ultraviolet, terahertz, and microwave, the tuning of frequency response is of critical importance for applications such as materials characterization, multispectral imaging, and biochemical sensing, etc. In the early days, spectral filtering is typically accomplished with the help of natural dyes, which often suffer from low transmittance, poor selectivity, and bad expansibility. Along with the development of micro-and nano-optics, it was demonstrated that structured materials could be designed as spectral filters at almost arbitrary frequencies in the entire electromagnetic spectrum. [127] Since the frequency response is mainly determined by the structures, the structural color filters may become more stable than natural dyes.
First of all, according to the interference theory, optical multilayered films can be designed as low-pass, band-pass, band-stop, and other kinds of filters. Since the design of multilayers is well understood in the textbook, [128] it will not be discussed in detail in this review. Nevertheless, it should be mentioned that these simple multilayered films are the basis of the 1D photonic crystal. Also, special film stacks such as the metal-dielectric multilayers with thickness much smaller than the wavelength could lead to many novel phenomena such as spatial frequency filtering, subwavelength interference, and sub-diffraction-limited imaging. [62,129] One of the most simple spectral filtering multilayer configurations is the Fabry-Perot resonators, which can be modified to construct space-variant color filters for multispectral imaging. [130] Another is the plasmonic holes or slits array, which could be used as compact color filters [131,132] as a result of the surface-plasmon-assisted extraordinary optical also been utilized as color filters. For instance, because dielectric guided-mode resonances bear lower losses and higher quality factors, a narrower spectral response is achievable. [134] Dynamic color tuning is a very important and fascinating direction in the field of structural colorations due to its possible applications in stealth, anti-counterfeiting, displaying techniques, etc. Tensile substrate (e.g., polydimethylsiloxane, PDMS) has been introduced into conventional plasmonic structures to demonstrate dynamic tunable structural colors via mechanical deformation. Recently, it is of great interest to develop dynamic structural colors by integrating phase-change materials in artificial structures, opening up more opportunities for further advancement. [27,[136][137][138][139] One development trend of structured color filters is the integration of color filtering and other functionalities in a single device. [140][141][142] For instance, by combining the plasmonic resonance and geometric phase in reflective metasurface, Zhang et al. proposed a novel approach to realize simultaneous structural color and holography. [143] Under incoherent white light, the metasurface appears as a polarization-and angle-encoded full-color image with flexibly controlled hue, saturation, and brightness, while switching to multiwavelength holograms under coherent laser illumination. Lim et al. developed a monolithically integrated pixel that overlays a structural color element onto a diffractive phase plate to achieve structural color and hologram simultaneously. [144] Besides the aforementioned applications, subwavelength structures are also of particular importance for local field enhancement associated with applications such as biochemical sensing [145] and nanolithography.

Structures for reconfigurable functionalities
Reconfiguration is another essential goal for Electromagnetic Architectures because dynamic manipulation of light waves with ultrahigh spatial and ultrafast temporal control can lead to entirely new applications and physics. [146] However, for most existing subwavelength structures, the function is usually fixed once the structure is fabricated. The emergence of Besides the aforementioned applications, subwavelength structures are also of particular

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Besides the aforementioned applications, subwavelength structures are also of particular importance for local field enhancement associated with applications such as biochemical Accepted Article importance for local field enhancement associated with applications such as biochemical [145] Accepted Article [145] and nanolithography.
Accepted Article and nanolithography. reconfigurable subwavelength structures enables lightweight, integrated, and flat hardware for optical/quantum communication and computation, light detection and ranging (LiDAR) for autonomous vehicles, [147,148] or other dynamic display applications such as augmented reality and holography. [149,150] Mechanical actuation offers an effective way to tune the optical properties of structures by reconfiguring their position, orientation, or spatial arrangement. Micro-electro-mechanical (MEMS) technology [151,152] offers high-precision control of position and orientation of metadevices at sub-nanometer and sub-degree angles. For example, varifocal metalenses have been demonstrated by combining one fixed and one movable metalens. [151,153] Compared with traditional bulky optical elements, the negligible mass of metadevices allows higher operating frequency, which shows great potential for reconfigurable metadevices and digital optics.
Subwavelength structures can also be fabricated on a stretchable substrate such as PDMS.
Under an external mechanical force, the arrangement of nanostructures and the spacing will change with the force, resulting in the change of its phase gradient and spectrum response.
With such flexible substrate, varifocal metalenses, [24] dynamic holograms, [154,155] and tunable structural colors [135,156] have been demonstrated. As shown in Figure 7a, with the increase of the stretching amount of the PDMS substrate (up to 30%), the peak wavelength of the resonance will experience redshift, realizing dynamic tunable structural colors.
Compared with the aforementioned mechanical methods, solid-state reconfiguration enables higher tuning frequency and stability. In the microwave region, solid-state tunable structures can be realized by using active elements such as diodes and adjustable capacitors. [157][158][159] In the optical region, the small wavelength makes it hardly applicable and one of the main ways of constructing solid-state tunable structures is to use reversible materials such as liquid crystals, [160,161] phase-change materials, [126,136,137,[162][163][164] and others, [165,166] whose refractive indices can dynamically respond to heat, electric, optical, or chemical stimulations. In general, solid-state tunable metadevices can be classified into two

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Mechanical actuation offers an effective way to tune Accepted Article categories: pixel control and global control. For the former case, the amplitude or phase of each pixel can be independently controlled through the integrated circuit. Commercial spatial light modulators belong to the former but suffer from problems of low switching rate and small field of view. In recent years, many efforts have been paid on decreasing the size of an independent pixel and increasing switching frequency by combining subwavelength structures and reversible materials like liquid crystals [160] and indium tin oxide. [166] As shown in Figure   7b, a recent study shows that the switching rate can reach up to a high level (~5.4 MHz) but an independent pixel still consists of several nanostructures, resulting in large pixel size. [166] In contrast, global control requires the same stimulation on the whole device. As a result, it can effectively avoid the aforementioned problems but suffers from another problem of fewer functions. For amplitude or spectral control, one can realize multiple even unlimited levels by giving different degrees of external stimulation, [27,[136][137][138]162] such as different temperature and voltage. Although this action can also cause different phase shifts, practical applications usually require multiple independent wavefronts, which is of great challenge for pure propagation-phase design. [163] Switchable-PSOI-based metasurfaces have been proposed to code multichannel information into different function states, [164,165] but the interlaced arrangement would cause problems of high-order diffraction, low efficiency, and small field of view. Recently, Zhang et al. proposed a methodology to realize multistate switchable PSOIs (Figure 7c), namely, symmetric PSOIs, asymmetric PSOIs, and no PSOIs, by employing polyatomic phase-change resonators, [126] in which phase-change independent geometric phase and phase-change dependent propagation phase can be independently controlled. By merging the two phases, the design complexity can be effectively reduced and all elements can contribute to the wavefront control.

Methodologies for the research of structural-functional relationships
The governing equation of electromagnetic and optical problems is Maxwell's equations. To In the following, we first discuss some analytical, semi-analytical approaches, and then the numerical ones. Furthermore, some more advanced concepts such as deep learning and topological optimization are also introduced.

Analytical and semi-analytical approaches
The transfer matrix method (TMM) is a powerful tool to investigate light propagation through layered media. Within the framework of TMM, the electric or magnetic fields in one layer are related to those in the successive layer through a transmission matrix and a propagation matrix, which connects the fields across an interface and propagating over a distance within a homogeneous medium and can be mathematically expressed as: 1 1 , 1 1 1 where a j and b j represent the field coefficients along with different propagation directions, k j is the wavevector, and d j is the thickness of j th layer. Here, the harmonic oscillation phaseconvention of exp(kx-ωt) has been assumed, where ω and t denote the angular frequency and time. As a consequence of continuous boundary conditions, the parameter K is respectively In the following, we first discuss some analytical, semi

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In the following, we first discuss some analytical, semi the numerical ones. Furthermore, some more Accepted Article ogeneous medium and can be mathematically expressed as: TMM has been utilized to investigating photonic band structures, [167] constructing broadband angular selectivity, [168] plasmonic filters, reconfigurable color reflector, [136] absorptive and radiative cooling materials. For special curved multilayer film systems, the TMM is still applicable using different eigenmodes. For example, Richmond proposed a solution of the field in a cylindrical multilayer [169] by using the cylindrical Bessel function to obtain the transmission coefficient between adjacent layers.
Although the fabrication of multilayers is simple without structure patterning, the electromagnetic manipulation flexibility is restricted by the limited materials. On the contrary, when artificial effective conductive or impedance layers are locating at the interfaces, more design freedom can be obtained so that one can flexibly engineer the whole dispersion of the multilayers and develop broadband and wide-angle metamaterials such as absorbers, [49,95,170] polarization converters, [91,105] wide-angle focusing and imaging. [171] Assuming the effective conductivities of the alternative layers and subwavelength patterned layer are Y 1 , Y 2 , and Y s , then the transfer matrix between can be expressed as where Y i = (ε i ) 1/2 Y 0 and Y 0 are the impedance of the free space. For thin metallic patterns, equivalent circuit theory could be leveraged for qualitative analyses of the equivalent impedance/conductivity.

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With the TMM, one can easily calculate the optical spectra such as reflection (

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With the TMM, one can easily calculate the optical spectra such as reflection ( To quantitatively determine the equivalent surface impedance/conductivity, a generalized Fresnel equation has been established, which bridges a link between the equivalent surface impedance/conductivity and the transmission and reflection coefficients. [90] Generally, fullwave simulations are required to obtain these transmission and reflection coefficients of subwavelength patterns. For some regular metallic structures, e.g., 1D metallic meshes, it has been shown that the equivalent impedance/conductivity can be described by a catenary dispersion function with satisfactory accuracy. Specifically, the normalized admittance Y eff is characterized by [70]   where Z eff is the surface impedance, p is the period of the grating, w is the width of the slit, λ is the wavelength, n 1 and n 2 are the refractive indexes for the background materials. Note that the right side of Equation (5) is similar to the mechanical "catenary of equal strength", [41] which follows the function y = Λln(|csc(πx/Λ)|)/π and different from the normal catenary function, i.e., y = αcosh(x/α). Apart from simple metallic 1D gratings, many complex structures could also be described using the catenary dispersion function, [164,[170][171][172] providing an efficient way to understand the broadband electromagnetic response of these functional metasurfaces. With the catenary dispersion theory, the design efficiency of structured functional materials can be greatly improved since time-consuming full-wave simulations and parameter sweeps are avoided.
For subwavelength slits drilled in a thick metallic film, one can approximately take them as truncated MIM waveguides. In the visible band, the near-field coupling between decaying evanescent waves along the two metal-insulator interfaces of the MIM waveguide causes the formation of the symmetric and asymmetric catenary field. [71] By matching the field distributions at the interfaces, the dispersion relations of coupled SPPs can be also obtained Accepted Article subwavelength patterns. For some regular metallic structures, e.g., 1D metallic meshes, it has Accepted Article subwavelength patterns. For some regular metallic structures, e.g., 1D metallic meshes, it has been shown that the equivalent impedance/conductivity can be described by a catenary Accepted Article been shown that the equivalent impedance/conductivity can be described by a catenary dispersion function with satisfactory accuracy. Specifically, Accepted Article dispersion function with satisfactory accuracy. Specifically, characterized by Accepted Article characterized by [70] Accepted Article [70] eff Accepted Article eff is the surface impedance, Accepted Article parameter sweeps are avoided.
For subwavelength slits drilled in a thick metallic film, one can approximately take them

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For subwavelength slits drilled in a thick metallic film, one can approximately take them with ease. [37] Details about catenary dispersion and field can be found in a recent review and a book. [38,173] Different from metallic slits arrays that each slit can be taken as an isolated plasmonic waveguide, the coupling between adjacent dielectric nanostructures make it difficult to accurately describe their electromagnetic responses through the full-analytical method.
Alternatively, RCWA, a semi-analytical method in computational electromagnetics, is most typically applied to solve scattering from periodic dielectric structures. In 1981, Moharam [174] first proposed the RCWA method for vector analysis of electromagnetic wave diffraction problems of sub-wavelength or resonant gratings. RCWA is often utilized to investigate the electromagnetic response of periodic gratings or unit cells of metamaterials/metasurfaces [102,[175][176][177][178] . Since RCWA can be easily implemented numerically, the simulation times will be greatly reduced compared to the full-wave simulation, which is preferred in the parameters sweeping of periodic subwavelength structures.

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For complex structures that possess a couple of design freedom

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For complex structures that possess a couple of design freedom population of randomly generated individuals and is an iterative process in which the population in each iteration is called a generation. [179,180] In each generation, the fitness of each individual in the population is evaluated, which is usually the value of the objective function.
More suitable individuals are randomly selected from the current population, and the genome of each individual is modified (recombined and possibly stochastically mutated) to form a new generation. This new generation of candidate solutions is then used in the next iteration of the algorithm. Typically, the algorithm terminates when the maximum number of generations has been created or a satisfactory fitness level has been achieved.
Alternatively, a basic variant of the PSO algorithm works by a group (called a swarm) of candidate solutions (called particles). These particles move through the search space according to a few simple formulas. The motion of the particles is guided by their own bestknown positions in the search space and the best-known position of the entire swarm. These will guide the movement of the group when an improved position is found. This process is repeated, and by doing so, it is hoped but not guaranteed that a satisfactory solution will eventually be found. PSO has been utilized in designing broadband achromatic metalens, [121,122] where the phase shift, group delay and group delay dispersion of light at each coordinate of the metalens should be elaborately optimized. It should be noted that although these methods have made great successes, however, are typically restricted to optimizing a relatively small number of geometric parameters, and scale poorly with additional degrees of freedom.

Deep learning
The past decade has witnessed the rise of deep learning with unprecedented impact on a plethora of research topics. As a data-driven method, deep learning can produce fast and accurate designs without the need for case-by-case, time-consuming numerical calculations. Accepted Article movement of the group when an improved position is found. This process is repeated, and by doing so, it is hoped but not guaranteed that a satisfactory solution will Accepted Article repeated, and by doing so, it is hoped but not guaranteed that a satisfactory solution will eventually be found. PSO has been utilized in designing broadband achromatic Accepted Article eventually be found. PSO has been utilized in designing broadband achromatic [121,122] Accepted Article [121,122] where the phase shift, group delay and group delay dispersion of light at each occurs and the generalized model can predict unseen data. As shown in Figure 8, a series of subwavelength devices has been designed via deep learning method, including chiral metamaterials, [181,182] self-adaptive microwave cloak, [183] all-dielectric metalens, [184] plasmonic nanostructures, [185] as well as silicon photonic device. [186] Among them, the networks in Figures 8(a), (b), and (c) respectively focus on the structural-functional relationship at the unit cells, meta-molecules, and functional devices level. Various network models include multilayer perceptron, convolutional neural networks, recurrent neural networks, and deep generative models have been leveraged and more information can be found in recent reviews. [187,188] Another important issue that should be noted is that today's computing hardware is inefficient at implementing neural networks, in large part because much of it was designed for von Neumann computing schemes. Recently, fully optical neural networks, both interferences and diffractive types have been proposed, [189,190] which, in principle, could offer an enhancement in computational speed and power efficiency over state-of-the-art electronics for conventional inference tasks. Inspired by the diffractive deep neural network, [190] where each layer's neurons were physically encoded using the relative thickness of each 3D-printed neuron, metasurfaces with powerful local phase modulation ability may find potential applications in diffractive all-optical neural networks.
One intriguing feature that distinguishes artificially structured materials from conventional optical components is their multifunctional capability owing to the more degrees of freedom in structural parameters. Especially, for multifunctional metasurfaces operated under different illuminations, [191][192][193] the large number of design parameters and intricate electromagnetic intercoupling make the design of multifunctional artificial structured materials a complex task, as shown in Figure 9. Over the past two decades, there have been increasing interest in topology optimization (TO) combined with adjoint and gradient-descent methods for freeform electromagnetic structures design in various scenarios, including photonic crystals, [194][195][196] microcavity, [197,198] multilayer thin films, [199][200][201] waveguides, [194,194,[202][203][204][205] metalens design, [125,192,[206][207][208][209][210][211][212] and other applications. [213][214][215][216][217] This approach allows the topology of the electromagnetic structures to change in a free-form way, opening up large design space, while converging comparatively quickly to an optimal solution. The audiences may refer to recent reviews for more details. [187,[218][219][220][221] As a gradient-based optimization algorithm, the TO process begins by defining a design region with a random and continuous distribution of permittivity ε between different materials, i.e., ε = ε a +ρ(ε b -ε a ), where ε a and ε b are the permittivities of materials and ρ∈[0,1] denotes the relaxation parameter. [194] The optimization goal is to find an optimal permittivity distribution that satisfies the user-defined figure-of-merit (FOM), such as the intensity of the electric field at the focus for metalens. Therefore, how the change of ε affects the FOM during each iteration should be investigated. Different from the conventional approaches that achieve it by changing the permittivity of each cell in sequence and performing a time-costing simulation depending on the number of unit cells, gradient-based adjoint simulation can calculate the gradient of FOM (∂F OM/∂ε) at each pixel through only two full-field simulations with the help of Born approximation, [219,222]

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, [194 Accepted Article [194-Accepted Article -196]  Accepted Article up large design space, while converging comparatively quickly to an optimal solution.
audiences may refer to recent reviews for more details.

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audiences may refer to recent reviews for more details.

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. [194] Accepted Article [194] fies the user Accepted Article at the focus for metalens. Therefore, how iteration should be investigated. Different from the conventional approaches that achieve it by Accepted Article iteration should be investigated. Different from the conventional approaches that achieve it by changing the permittivity of each cell in sequence and performing a time Accepted Article changing the permittivity of each cell in sequence and performing a time used in training neural networks), with the changes proportional to the gradient. Appling the process above iteratively can then lead to a local optimum. [125,222] Although the nonintuitive and nontrivial functionalities of freeform metasurfaces enabled by adjoint-based TO have recently attracted considerable interest and reached the stage of an explosion, there is still a non-negligible challenge for practical application. Specifically, the small features spontaneously appearing in the optimization process make the freeform metasurfaces impossible for high-throughput manufacturing with photolithography technology. Instead, most of the devices are experimentally fabricated by using electron-beam lithography, which greatly limits the applications of TO-based metasurfaces. Therefore, we should re-examine the optimization procedure as the TO is performed and additional considerations should be employed to solve the above challenge. Typical solutions include pixelation of topology structure with a size larger than the smallest feature size or using erosion and dilation operations to increase the robustness to fabrication imperfections. [223][224][225]

Conclusions and Outlooks
In summary, we have reviewed the history and recent advances of structured electromagnetic and optical functional materials and devices. Based on the similarity of functional structures and architectonics, the term Electromagnetic Architectures was proposed.
It is shown that the construction of structured materials and devices has drawn many inspirations from the construction of buildings. In both cases, the structures determine the functionalities. So it is of critical importance for us to find out the most suitable structures for particular applications.
In our opinion, future research directions of Electromagnetic Architectures may include but not limited to the following aspects: Accepted Article functional structures and architectonics, the term Electromagnetic Architectures was proposed.
It is shown that the construction of structured materials and dev

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It is shown that the construction of structured materials and dev Accepted Article inspirations from the construction of buildings. In both cases, the structures determine the Accepted Article inspirations from the construction of buildings. In both cases, the structures determine the functionalities. So it is of critical importance for us to find out the most suitable structures for Accepted Article functionalities. So it is of critical importance for us to find out the most suitable structures for particular applications Accepted Article particular applications.

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. classical models and deep learning are promising candidates, but the prediction accuracy and extendibility need to be further increased.
2. Fast and accurate fabrication of large-area functional devices with minimal critical dimensions smaller than several hundreds of nanometers. Owing to the replicative nature, imaging nanolithography and nanoimprint are very promising in these applications.
3. Dynamic and fast modulation of optical functionalities via electrical and optical approaches. Although there have been many efforts to realize tunable structured devices, the tuning speed, and pixel numbers are still limited.
Finally, it should be noted that although our discussion is focused on electromagnetic structures, similar concepts may be extended to other researching areas, such as mechanics, acoustics, thermal physics, and quantum physics, etc.  Classification of spatial-temporal shaping of electromagnetic waves with subwavelength structures. According to the manipulation object of the electromagentic field, spatial-temporal modulations are classified into six categories. High frequency wavevector excited in the subwavelength structures and high-index waveguide can be utilized for superresolution imaging and subwavelength integrated optics; With local phase modulation ability, various flat optical devices and microwave antennas can be constructed for imaging, beam shaping, as well as holographic display. Through on-demand dispersion engineering of the phase and group velocity, achromatic metalens can be realized; Thanks to the strong anisotropy of subwavelength structures, ultra-thin polarizers and polarization converters can be developed. The electromagnetic amplitude can be adjusted by artificial absorbers, subwavelength patterns enhanced emitters. The local field enhancement help boost the nonlinear optical effect, such as harmonic generation and four-wave mixing frequency.