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Manipulating light transmission and absorption via an achromatic reflectionless metasurface
PhotoniX volume 4, Article number: 3 (2023)
Abstract
Freely switching light transmission and absorption via an achromatic reflectionless screen is highly desired for many photonic applications (e.g., energyharvesting, cloaking, etc.), but available metadevices often exhibit reflections out of their narrow working bands. Here, we rigorously demonstrate that an optical metasurface formed by two resonator arrays coupled vertically can be perfectly reflectionless at all frequencies below the first diffraction mode, when the nearfield (NF) and farfield (FF) couplings between two constitutional resonators satisfy certain conditions. Tuning intrinsic loss of the system can further modulate the ratio between light transmission and absorption, yet keeping reflection diminished strictly. Designing/fabricating a series of metasurfaces with different interresonator configurations, we experimentally illustrate how varying interresonator NF and FF couplings can drive the system to transit between different phase regions in a generic phase diagram. In particular, we experimentally demonstrate that a realistic metasurface satisfying the discovered criteria exhibits the desired achromatic reflectionless property within 160–220 THz (0–225 THz in simulation), yet behaving as a perfect absorber at ~ 203 THz. Our findings pave the road to realize metadevices exhibiting designable transmission/absorption spectra immune from reflections, which may find many applications in practice.
Introduction
Freely controlling transmission, reflection, and absorption of light wave through a thin screen is highly desired in photonics [1,2,3,4,5,6]. For instance, while perfect absorption is favored in energy harvesting, perfect transmission is desired in applications related to sensing and cloaking. In many scenarios, reflection is undesired as it can cause efficiency reduction and failure of the expected functionality (say, cloaking). Unfortunately, switching between perfect light transmission and perfect absorption is extremely challenging in thinscreen systems where energy transports in different channels are usually coupled in a complex way.
Metasurfaces, ultrathin metamaterials composed by subwavelength microstructures exhibiting tailored electromagnetic (EM) responses, offer a new platform to control light waves [7,8,9,10,11]. Many fascinating effects were realized based on metasurfaces, including perfect absorption [12,13,14,15,16], perfect transparency [17,18,19,20,21], and many others [22,23,24,25,26,27,28]. However, strong reflections always appear in such metadevices at frequencies out of their narrow working bands in which perfect absorption/transparency is achieved. Recently, A few attempts appear to construct reflectionless metasurfaces based on different approaches such as antireflection coating [29, 30], anomalous Brewster effect [31, 32], specular reflection reduction [33], etc. One typical design approach is to put into a unit cell two resonators, exhibiting electric and magnetic responses, respectively, so that their back scatterings can exactly cancel each other under certain condition (e.g., the Kerker condition [34,35,36,37]). However, since two created resonance modes usually exhibit distinct frequency dispersions, in most cases the Kerker condition is satisfied only at a single frequency, making the constructed metasurfaces exhibiting narrow working bands [6, 38,39,40,41]. Despite of many efforts devoted to expanding the reflectionless bandwidths through structural optimizations [32, 33, 42,43,44,45], such an issue remains intrinsic, and new mechanism is highly desired for designing achromatic reflectionless metasurfaces.
In this work, we propose a new strategy to realize achromatic reflectionless metasurfaces (see Fig. 1). Distinct from metasurfaces consisting of resonators placed on the same plane [46,47,48,49], here we study a bilayer system containing two arrays of resonators placed on different planes. The interlayer distance is a new parameter to tune both NF and FF couplings between two resonators (see inset in Fig. 1), which is lacked in previously studied systems. Base on coupledmodetheory (CMT) calculations, we first establish a generic phase diagram showing how the reflection property of such system varies against the interresonator NF and FF couplings. We find that the Kerker condition can be rigorously satisfied at all frequencies below the first diffraction mode, as long as the NF and FF coupling strengths between two resonators meet a set of conditions. Moreover, adding Ohmic losses to the system does not violate the Kerker condition, but rather efficiently reallocate light power between transmission and absorption channels. We design/fabricate a series of bilayer metasurfaces and experimentally illustrate how varying their geometric configurations can drive them move inside the phase diagram via modulating two coupling strengths. We finally realize a metasurface satisfying the Kerker criterion, and experimentally demonstrate that it exhibits perfect absorption around 203 THz within an ultrawideband reflectionless frequency band (160–220 THz in experiment, 0–225 THz in simulation). Many applications can be expected based on our reflectionless platform, with a tunable absorber numerically demonstrated as a particular example.
Results and discussion
Generic phase diagram of the bilayer systems
We establish a phase diagram for the proposed bilayer systems based on CMT analyses [49,50,51]. In our system, two layers of our system are both periodic arrays with subwavelength spacing, such that only the zeroorder mode of transmission/reflection can survive. As depicted in the inset to Fig. 2a, the bilayer system can be generically described by a 2mode 2port model, with time evolutions of the amplitudes a_{i = 1, 2} of two resonance modes satisfying the following equations:
Here, we assume that the two modes are identical, with f_{0}, Γ_{r} and Γ_{i} describing their resonant frequencies, radiation and absorption damping, respectively. Meanwhile, κ and X represent NF and FF couplings between two modes, d_{ji} describes the coupling between the jth external port and the ith excited mode, and \({s}_j^{+\left(\right)}\) denotes the amplitudes of incoming (outgoing) waves from (to) the jth port. \(\textbf{C}=\left(\begin{array}{cc}{r}_0& {t}_0\\ {}{t}_0& {r}_0\end{array}\right)\) denotes the scattering properties of the background which is set as vacuum at the moment (i.e. r_{0} = 0 and t_{0} = 1). According to energy conservation and time reversal symmetry, we prove that \({d}_{11}={d}_{21}=i\sqrt{\Gamma_r}\), \({d}_{12}=i\sqrt{\Gamma_r}\exp \left(i{\theta}_X\right)\) and \({d}_{22}=i\sqrt{\Gamma_r}\exp \left(i{\theta}_X\right)\), where θ_{X} measures the phase difference between radiated far fields from two excited resonators (see Fig. 2a). Finally, we find that the FF interresonator coupling X is not an independent parameter, but can be expressed as X = − Γ_{r} exp(iθ_{X}) [49]. All derivation details can be found in Section 1 of Supplementary Information (SI). In what follows, we consider the lossless case (i.e. Γ_{i} = 0) first, where only four independent parameters (f_{0}, Γ_{r}, κ and θ_{X}) are relevant. We note that all these parameters are assumed as frequencyindependent constants in CMT [49,50,51] derived under the highQ approximation.
Equation (1) can be analytically solved through standard CMT analyses. The identical symmetry possessed by two matrixes in the first line of Eq. (1) ensures that they can be simultaneously diagonalized with an orthogonal transformation \({\tilde{a}}_{\pm }=\left({a}_2\pm {a}_1\right)/\sqrt{2}\). After the transformation, we get two decoupled hybridized modes with
being their resonant frequencies and radiation damping, respectively. We note from Eq. (2) that the shift in frequency is determined by the NF coupling κ and the Hermitian part of FF coupling Im(X), while the shift in radiation damping is solely dictated by the nonHermitian part of FF coupling Re(X). Reflection coefficient of our metasurface can then be analytically derived as (see Sec. 1 in SI)
where r_{+} and r_{−} denote the scatterings due to two independent modes.
We employ Eq. (3) to study how the reflectance R = r^{2} varies against κ and θ_{X} with all singlemode properties (f_{0} and Γ_{r}) fixed. Fixing θ_{X} at 0, π/4 and π/2, respectively, we illustrate on three vertical planes in Fig. 2a how the obtained reflectance spectrum R(f) changes versus κ. While two branches of reflection peaks appear on the planes at π/4 and π/2, only one branch exists on the plane at θ_{X} = 0 since one mode becomes completely dark (\({\tilde{\Gamma}}_{}=0\)) dictated by the symmetry, which is also called a bound state in continuum [36, 52]. Set κ as 3 different values on the θ_{X} = π/2 plane, we depict in Fig. 2b the calculated reflection spectra R(f) (solid lines) and those contributed by two decoupled modes r_{±}(f)^{2} as defined in Eq. (3) (dotted lines). We find that varying κ modifies two peak positions keeping the bandwidths of two decoupled modes unchanged, in consistency with Eq. (2). The final reflection spectrum R(f) is thus significantly modulated by κ due to the interference between two modes (See Fig. S2 for more details in Sec. 2 of SI). Meanwhile, Eq. (2) predicts that the two hybridized modes exhibit identical resonance frequencies in the cases of κ = − Γ_{r} sin θ_{X}, corresponding to a curved surface in Fig. 2. Choosing three typical cases on the curved surface, we depict in Fig. 2c how changing θ_{X} further modulates the final reflection spectrum. As shown in Fig. 2c, now the R spectrum is an interference of two degenerate modes exhibiting different radiation damping, in consistency with Eq. (2). In particular, in the case of θ_{X} = π/2 (the #4 line in Fig. 2a), the two degenerate modes are out of phase and of identical bandwidths, and therefore, their interference leads to complete cancellation of reflections within the entire considered frequency range as shown in Fig. 2d (i.e., R(f) ≡ 0). Meanwhile, it is noticeable that the transmission phase covers a whole 2π range. Such a rigorous zeroreflection solution can be rephrased as the following condition
which states that the total effective coupling (including both Hermitian and nonHermitian parts) that we define as ξ = X − iκ between two original modes must be exactly zero.
We now discuss the role played by the absorption loss. Figure 3a and b depict, respectively, the calculated reflectance R on two θ_{X} − f planes (with κ = − Γ_{r} sin θ_{X} fixed) and two κ − f planes (with θ_{X} = π/2 fixed) with different absorption damping parameters (Γ_{i} = 0 and Γ_{i} = 0.5 Γ_{r}). Obviously, absorption loss does not affect the desired zeroreflection property of the system, as long as Eq. (4) is met (dashed lines in Fig. 3ab, more cases are presented in Figs. S3S4 of SI). In fact, turning on Γ_{i} in Eq. (1) does not violate the symmetry possessed by our system, and thus reflections from two decoupled modes still exactly cancel each other. Rigorously solving Eq. (1) with Γ_{i} present, we get the following analytical expressions (see Sec. 1 in SI for detailed derivations):
Remarkably, we find that the expression of t is exactly the same as that of the reflection coefficient of a 1port 1mode model, widely used to describe the metal/insulator/metal (MIM) system [13]. Therefore, all interesting physical behaviors revealed in the MIM systems are also expected here [13]. Indeed, increasing Γ_{i} can gradually enhance the absorbance A until the criticaldamping condition (Γ_{i} = Γ_{r}) is reached at which perfect absorption happens (A(f_{0}) = 1), while further increasing Γ_{i} in the region of Γ_{i} > Γ_{r} will decrease the absorbance (see blue lines in Fig. 3c). Along varying Γ_{i}, however, we find distinct behaviors exhibited by the transmission phase ϕ_{t}(f) = arg[t(f)] in two different cases with Γ_{i} < Γ_{r} and Γ_{i} > Γ_{r}, respectively (see insets to Fig. 3d). Color map in Fig. 3d depicts the variation range Δϕ_{t} of transmission phase ϕ_{t}(f) upon frequency changing, as the functions of Γ_{i} and Γ_{r}. The criticaldamping line (Γ_{i} = Γ_{r}) separates the whole Γ_{i} − Γ_{r} phase diagram into two parts, which are the underdamped region (Γ_{i} < Γ_{r}) with Δϕ_{t} covering a whole 2π range and the overdamped region (Γ_{i} > Γ_{r}) with Δϕ_{t} less than π. In all these cases studied, we have A(f) + T(f) = 1 strictly satisfied (see Fig. 3c), since the reflection channel of our system is completely blocked as long as Eq. (4) is satisfied. Therefore, tuning Γ_{i} in our system can efficiently reallocate the power of light between transmission and absorption channels, in an ideal achromatic reflectionless platform.
Experimental demonstration of the phase diagram
We now experimentally realize a series of bilayer metasurfaces exhibiting different NF and FF couplings, starting from designing two optical modes exhibiting identical resonance frequency f_{0} and radiation damping Γ_{r}. Since in reality it is still challenging to fabricate a freestanding sample with two resonators on two sides of a thin dielectric spacer, here we choose to design our bilayer metasurface in such a configuration that one plasmonic resonator (an Au bar) is on top of a SiO_{2} substrate while another Au bar is buried inside the substrate (see Fig. 4a). As the two resonators are now in different dielectric environments, they must possess different geometries in order to exhibit identical optical responses. Moreover, the presence of a dielectric substrate changes the background scattering matrix C and the coupling matrix d_{ji} in Eq. (1). Despite of these differences with the ideal case, we still analytically proved the following two conclusions for such metasurfaces (see Sec. 3 in SI): 1) as the Kerker condition (Eq. (4)) is met, such a metasurface in the lossless condition only exhibits the background reflectance within the entire frequency band below the first diffraction mode; 2) perfect absorption can still happen as the critical damping condition is met.
We fix the geometric structures of two basic resonators with the help of finiteelementmethod (FEM) simulations, and fabricate two singlelayer metasurfaces according to our designs using the standard electronbeam lithography (EBL) method. As shown in the right panels of Fig. 4bc, each metasurface contains resonators of one type arranged in a hexagonal lattice with periodicity 600 nm, while resonators in the second sample are buried inside the substrate at the depth h = 236 nm [53]. Illuminating two samples with ypolarized normally incident light, we experimentally measure their scattering spectra, with reference signals taken as those obtained with the sample replaced by a gold mirror (for reflection) and the quartz substrate (for transmission), respectively (Sec. 4 in SI). Figure 4bc clearly show that the two systems exhibit nearly identical measured transmission/reflection spectra (stars), which are in good agreement with their corresponding FEM simulations (circles). We further employ a recently developed leakyeigenmode (LEM) theory [49] to directly compute the optical characteristics (i.e., f_{0}, Γ_{r} and Γ_{i}) of the resonance modes supported by two systems, based on their LEM wavefunctions derived from Maxwell equations (see more details in Sec. 5 of SI). Put these LEMcomputed parameters into the CMT, we obtain the reflection spectra of two metasurfaces (solid lines in Fig. 4bc), which are in excellent agreement with simulation and experimental results.
With LEM wavefunctions of two designed resonance modes known, we can employ them to directly compute the FF and NF coupling parameters (e.g., κ and X) between two resonators, which are arranged in different relative configurations in forming our bilayer metasurfaces. Obviously, while the interlayer distance h dictates the FF coupling, the lateral relative configuration between two resonators and h are collectively responsible for the NF coupling. Figure 4e depicts how the LEMcomputed X and κ changes as a function of h with lateral positions of two bars fixed. We find both Re(X) and Im(X) vary periodically versus h, as expected, while κ decays as h increase since near field localize around the particles. In particular, we get Re(X) = 0 at h = 236 nm, which is very close to the prediction h = λ_{n}/4 (with λ_{n} = 985 nm being the resonance wavelength inside the dielectric substrate). The slight discrepancy is caused by the difference between the realistic structures and the ideal model. Fix the top bar at the unitcell enter (0, 0) and put the second bar at (d_{x}, d_{y}) on the h = 236 nm plane, we employ the LEMtheory to calculate how κ varies against d_{x} and d_{y}, and depict the results as a color map in Fig. 4d. In particular, we find that κ can continuously change from a negative value to a positive one as the relative horizontal angle α between two bars varies from 0^{∘} to 90^{∘} (see the circle with radius \(l=\sqrt{d_x^2+{d}_y^2}=345\ \textrm{nm}\) in Fig. 4d). These results suggest that we have enough tuning freedoms to design bilayer metasurfaces exhibiting different κ and X, and in turn, different optical responses.
We choose 7 points on the phase diagrams (see Fig. 4de) to design the corresponding metasurfaces. Samples #1–4 exhibit identical interlayer distance h and different relative orientation angle α (Fig. 4d), while samples #5–8 have the same value of α but with h changing from 140 to 600 nm (Fig. 4e). We note that samples #4 and #6 are the same, although they are on different variation paths. To check whether these samples meet the Kerker condition Eq. (4), we depict the positions of 7 samples on the ξ~{κ, θ_{X}} phase diagram (Fig. 5a). We see clearly that sample #4 (the green star) just locates at the ξ = 0 point meeting the Kerker condition Eq. (4). We note that surface roughness caused by the presence of nanostructures in the bottom layer does not modify the EM responses of our metasurface obviously (See Fig. S9 in Sec.6 of SI).
We fabricate these bilayer samples with a twostep EBL process (see Sec. 7 in SI) and experimentally characterize their optical properties. The topview scanningelectronmicroscopy (SEM) pictures of samples #1–4 (see right panel in Fig. 5d) show that two resonators are in different relative lateral configurations, while the sideview FocusIonBeam (FIB)  SEM pictures of samples #5–8 (see right panel in Fig. 5e) reveal that two resonators exhibit different vertical distances h, in consistency with Fig. 4de. Shine these samples with ypolarized normally incident light, we measure their reflection and transmission spectra (stars in Fig. 5de), which are in excellent agreement with FEM simulations (see circles in Fig. 5de).
We first discuss the sample series #1–4. We find from experimental results (Fig. 5d) that decreasing α mainly changes the frequency interval between two reflection peaks, but has negligible influences on their bandwidths. To understand the physics, we employ the LEM theory to compute (κ, θ_{X}) of samples #1–4. We find from Fig. 5b that these samples exhibit continuously varying κ and identical θ_{X} as α changes, which well explains the salient features revealed in the reflection spectra. Put the LEMcomputed (κ, θ_{X}) into the CMT equations (see Sec. 3 in SI), we find that the CMTcalculated reflection spectra R(f) (solid lines in Fig. 5d) are in excellent agreement with both simulation and experimental results. Obviously, such a lineshape evolution is governed by essentially the same physics as that discussed in Fig. 2b for the model systems.
We next discuss the sample series #5–8. We find from the measured spectra (Fig. 5e) that changing h in this series modifies not only the frequency positions but also the bandwidths of two modes. These features can be well explained by the LEMcalculated (κ, θ_{X}) as varying h (Fig. 5c). Again, put the LEMcomputed values (κ, θ_{X}) in to the CMT equations, we find that the CMTcomputed reflection spectra R(f) (solid lines in Fig. 5e) are in good agreement with both numerical and measured results. Slight discrepancies between experimental and simulation results can be attributed to differences in material parameters in the doublelayer metasurface and their singlelayer counterparts, caused by fabrication imperfections. In particular, the calculated positions and bandwidths of two hybridized modes, labeled by the dashed lines and shaded areas in Fig. 5e, respectively, reenforce our notion that changing h affects both the frequencies and bandwidths of the hybridized modes through modifying both NF and FF couplings between two resonators.
Achromatic reflectionless metasurface
We now focus on the sample #4 (or #6), corresponding to the case of ξ = 0 in Fig. 5a. Experimental results clearly show that the reflectance of this sample nearly maintains at the background value within the whole experimentally accessible frequency range (160 to 220 THz) except at the resonance frequency. In fact, simulation results indicate that the sample maintains at the background value in a frequency range (0–225THz) far beyond that experimentally accessible (Fig. 6b). We note that diffractions inevitably appear at frequencies above 225 THz, since the realistic metasurface is a periodic structure. We note that our metasurface is designed under normal incidence, and its achromatic reflectionless property is maintained only as the incident angle lies in a narrow range centered at 0°, which can be enlarged by structural optimizations. Achromatic reflectionless metasurfaces under oblique incidence are also designable, as long as the system still works below the firstorder diffraction (see more details in Sec. 8 of SI).
We next study the absorption properties of the fabricated sample. Computing the absorption spectrum A(f) using A = 1 − R − T, we find that the experimentally measured absorbance A reaches 96% at the resonance frequency 203.1 THz (Fig. 6b) at which the transmittance T approaches zero. At frequencies away from the resonance one, A diminishes and T increases but A + T = 1 maintains approximately. To understand the intrinsic physics, we employ the LEM theory to calculate the intrinsic damping parameters of two resonance modes (see Sec. 5 of SI), which confirms that the critical damping condition (Γ_{i} = Γ_{r}) is indeed approximately satisfied for present system which already satisfies the Kerker condition Eq. (4).
Moreover, we find that tuning the intrinsic loss in this sample can further modulate the ratio between light transmission and absorption, yet keeping reflection diminished. To demonstrate this point, we perform a series of FEM simulations assuming that the damping parameter \({\gamma}_i^{(m)}\left(m=1,2\right)\) in the Drude model (\(\varepsilon \left(\omega \right)={\varepsilon}_{\infty }{\omega}_p^2/\left({\omega}^2+i{\omega \gamma}_i^{(m)}\right)\)) describing our plasmonic metals forming the mth resonator (m = 1, 2) take different values. Since the two metallic resonators are in different dielectric environments, it is quite natural to expect that \({\gamma}_i^{(1)}\ne {\gamma}_i^{(2)}\). As shown in Fig. 6d, tuning \({\gamma}_i^{(m)}\) from \(0.1{\gamma}_0^{(m)}\) to \(3{\gamma}_0^{(m)}\) with \({\gamma}_0^{(m)}\) representing the experimental case, we find that the peak absorbance A first increase from 36% to 100% and then decreases, in consistency with the underdamping to overdamping transition discussed in Sec. 2 (see Fig. 3). Meanwhile, the reflectance keeps negligible in all these cases studied (black lines in Fig. 6c), which is again consistent with the notion that the reflection channel is blocked under the Kerker condition (Eq. (4)). Finally, transmission phase spectra of the system with different \({\gamma}_i^{(m)}\) (Fig. 6e) also exhibit the underdamping to overdamping transition, in consistency with Fig. 3d. These results suggest the possibilities to realize transmissionmode tunable metadevices for phase modulations and wavefront controls, through controlling the intrinsic damping of constitutional materials via electric or optical means.
Conclusion
To summarize, we employ CMT analyses to rigorously demonstrate that an optical metasurface formed by two arrays of resonators can be perfectly reflectionless at all frequencies below the first diffraction mode, when the NF and FF couplings between two constitutional resonators satisfy certain conditions. Tuning the intrinsic loss of the system can further modulate the ratio between light transmission and absorption, yet keeping reflection diminished strictly. We design/fabricate a series of metasurfaces and experimentally illustrate how the reflection lineshape of such metasurface is tailored by interresonator NF and FF couplings. In particular, we identify a specific metasurface from the sample series and experimentally demonstrate that it is immune from reflections within an ultrawide frequency range (experiment: 160–220 THz; simulations: 0–225 THz), yet behaving as a perfect absorber at ~ 203 THz.
Many future works can be stimulated from the present study. For example, realizing such reflectionless metadevices can find immediate applications in sensing, cloaking, and energy harvesting. Moreover, modulating transmission phase of light via tuning the intrinsic loss in our metadevice (Fig. 6) can inspire tunable transmissive metadevices for highefficiency wavefront controls. Finally, realizing freestanding samples exhibiting backgroundfree achromatic reflections in different frequency regimes are challenging and interesting future projects.
Methods
Simulations
All FEM simulations are performed with the commercial software COMSOL Multiphysics. Permittivity of Au is described by the Drude model \(\varepsilon \left(\omega \right)={\varepsilon}_{\infty }{\omega}_p^2/\left({\omega}^2+i{\omega \gamma}_i^{(m)}\right)\) with ε_{∞} = 9 and ω_{p} = 1.367 × 10^{16}s^{−1}. The damping parameter is set as \({\gamma}_0^{(1)}=3.182\times {10}^{16}{s}^{1}\) for top resonators and as \({\gamma}_0^{(2)}=3.672\times {10}^{16}{s}^{1}\) for the resonators buried inside the substrate, obtained by fitting with our experimentally measured optical spectra for corresponding metasurfaces (Fig. 4). The SiO_{2} substrate was considered as a lossless dielectric with permittivity \({\varepsilon}_{{\textrm{SiO}}_2}=2.25\). We note that additional losses caused by surface roughness, grain boundary effects, existence of adhesion layer as well as dielectric losses, have been effectively considered in choosing the values of two parameters \({\gamma}_0^{(m)}\left(m=1,2\right)\) describing the damping rates of Au forming two resonators.
Fabrications
All bilayer samples were fabricated using twostep EBL and liftoff processes. First, the positive resist MMA EL6 (200 nm) and PMMA A2 (80 nm) were successively spin coated on a SiO_{2} substrate. Next, bottom bars (270 nm × 320 nm), 4 global alignment marks (100 μm × 10 μm) and 4 chief alignment marks (25 μm × 2 μm) were lithographed with EBL (JEOL 8100) at an acceleration voltage of 100 kV. After exposure, the samples were developed in the solution with a 3:1 mixture of isopropanol (IPA) and methyl isobutyl ketone (MIBK). 3 nm  thick Cr and 30 nm – thick Au layers were subsequently deposited using electronbeam evaporation. After standard liftoff process, SiO_{2} with a desired thickness was deposited on the first metal array as a dielectric interlayer by magnetron sputtering. The top layer was fabricated using the same method but including a precise alignment process, where the gold alignment marks are applied to ensure the accurate stacking of the top layer. Finally, the reference area near the samples was prepared with a more alignment by direct writer, followed by depositing 5 nm – thick Cr and 150 nm – thick Au layers with magnetron sputtering and performing liftoff process. The topview pictures of fabricated samples were obtained using SEM (Zeiss Sigma). Note that the bumps in Figs. 4c and 5d are SiO_{2} bumps stemming from the deposition process corresponding to the location of the bottom Au bars. The sideview images of the samples were obtained using a dualbeam FIBSEM which can simultaneously obtain the local sectioning (with the FIB) and imaging (with SEM) of the samples. All samples have lateral dimensions of 100 μm × 100 μm.
Optical characterizations
We used a homemade NIR microimaging system equipped with a broadband supercontinuum white light source (Fianium SC400), polarizers, a beam splitter, a CCD, a fibercoupled grating spectrometer (Ideaoptics NIR2500) and a Princeton Instruments HRS300 spectrograph with an InGaAs camera to characterize the optical properties of the fabricated samples.
Availability of data and materials
The datasets and figures used and analyzed during the current study are available from the corresponding author on reasonable request.
Abbreviations
 NF:

Nearfield
 FF:

Farfield
 EM:

Electromagnetic
 CMT:

Coupledmodetheory
 SI:

Supplementary Information
 MIM:

Metal/insulator/metal
 FEM:

Finiteelementmethod
 EBL:

Electronbeam lithography
 LEM:

Leakyeigenmode
 SEM:

Scanningelectronmicroscopy
 FIB:

FocusIonBeam
 IPA:

Isopropanol
 MIBK:

Methyl isobutyl ketone
References
Schurig D, Mock JJ, Justice BJ, Cummer SA, Pendry JB, Starr AF, et al. Metamaterial electromagnetic cloak at microwave frequencies. Science. 2006;314(5801):977–80. https://doi.org/10.1126/science.1133628.
Ni X, Wong ZJ, Mrejen M, Wang Y, Zhang X. An ultrathin invisibility skin cloak for visible light. Science. 2015;349(6254):1310–4. https://doi.org/10.1126/science.aac9411.
Jahani Y, Arvelo ER, Yesilkoy F, Koshelev K, Cianciaruso C, De Palma M, et al. Imagingbased spectrometerless optofluidic biosensors based on dielectric metasurfaces for detecting extracellular vesicles. Nat Commun. 2021;12(1):3246. https://doi.org/10.1038/s4146702123257y.
Park JH, Ndao A, Cai W, Hsu L, Kodigala A, Lepetit T, et al. Symmetrybreakinginduced plasmonic exceptional points and nanoscale sensing. Nat Phys. 2020;16(4):462–8. https://doi.org/10.1038/s415670200796x.
Landy NI, Sajuyigbe S, Mock JJ, Smith DR, Padilla WJ. Perfect metamaterial absorber. Phys Rev Lett. 2008;100(20):207402. https://doi.org/10.1103/PhysRevLett.100.207402.
Tian J, Luo H, Li Q, Pei X, Du K, Qiu M. Nearinfrared superabsorbing alldielectric metasurface based on singlelayer germanium nanostructures. Laser Photonics Rev. 2018;12(9):1800076. https://doi.org/10.1002/lpor.201800076.
Yu N, Genevet P, Kats MA, Aieta F, Tetienne JP, Capasso F, et al. Light propagation with phase discontinuities: generalized laws of reflection and refraction. Science. 2011;334(6054):333–7. https://doi.org/10.1126/science.1210713.
Sun S, He Q, Xiao S, Xu Q, Li X, Zhou L. Gradientindex metasurfaces as a bridge linking propagating waves and surface waves. Nat Mater. 2012;11(5):426–31. https://doi.org/10.1038/nmat3292.
Ni X, Emani NK, Kildishev AV, Boltasseva A, Shalaev VM. Broadband light bending with plasmonic nanoantennas. Science. 2012;335(6067):427. https://doi.org/10.1126/science.1214686.
Genevet P, Capasso F, Aieta F, Khorasaninejad M, Devlin R. Recent advances in planar optics: from plasmonic to dielectric metasurfaces. Optica. 2017;4(1):139–52. https://doi.org/10.1364/OPTICA.4.000139.
Sun S, He Q, Hao J, Xiao S, Zhou L. Electromagnetic metasurfaces: physics and applications. Adv Opt Photonics. 2019;11(2):380–479. https://doi.org/10.1364/AOP.11.000380.
Liu N, Mesch M, Weiss T, Hentschel M, Giessen H. Infrared perfect absorber and its application as plasmonic sensor. Nano Lett. 2010;10(7):2342–8. https://doi.org/10.1021/nl9041033.
Qu C, Ma S, Hao J, Qiu M, Li X, Xiao S, et al. Tailor the functionalities of metasurfaces based on a complete phase diagram. Phys Rev Lett. 2015;115(23):235503. https://doi.org/10.1103/PhysRevLett.115.235503.
Tian J, Li Q, Belov PA, Sinha RK, Qian W, Qiu M. Highq alldielectric metasurface: super and suppressed optical absorption. ACS Photonics. 2020;7(6):1436–43. https://doi.org/10.1021/acsphotonics.0c00003.
Li Y, Lin J, Guo H, Sun W, Xiao S, Zhou L. A tunable metasurface with switchable functionalities: from perfect transparency to perfect absorption. Adv Opt Mater. 2020;8(6):1901548. https://doi.org/10.1002/adom.201901548.
Liang Y, Lin H, Koshelev K, Zhang F, Yang Y, Wu J, et al. Fullstokes polarization perfect absorption with diatomic metasurfaces. Nano Lett. 2021;21(2):1090–5. https://doi.org/10.1021/acs.nanolett.0c04456.
Zhang S, Genov DA, Wang Y, Liu M, Zhang X. Plasmoninduced transparency in metamaterials. Phys Rev Lett. 2008;101(4):047401. https://doi.org/10.1103/PhysRevLett.101.047401.
Liu N, Langguth L, Weiss T, Kästel J, Fleischhauer M, Pfau T, et al. Plasmonic analogue of electromagnetically induced transparency at the drude damping limit. Nat Mater. 2009;8(9):758–62. https://doi.org/10.1038/nmat2495.
Gu J, Singh R, Liu X, Zhang X, Ma Y, Zhang S, et al. Active control of electromagnetically induced transparency analogue in terahertz metamaterials. Nat Commun. 2012;3(1):1151. https://doi.org/10.1038/ncomms2153.
Yang Y, Kravchenko II, Briggs DP, Valentine J. Alldielectric metasurface analogue of electromagnetically induced transparency. Nat Commun. 2014;5(1):5753. https://doi.org/10.1038/ncomms6753.
Wang C, Jiang X, Zhao G, Zhang M, Hsu CW, Peng B, et al. Electromagnetically induced transparency at a chiral exceptional point. Nat Phys. 2020;16(3):334–40. https://doi.org/10.1038/s4156701907467.
Khorasaninejad M, Chen WT, Devlin RC, Oh J, Zhu AY, Capasso F. Metalenses at visible wavelengths: diffractionlimited focusing and subwavelength resolution imaging. Science. 2016;352(6290):1190–4. https://doi.org/10.1126/science.aaf6644.
Zhang F, Pu M, Li X, Gao P, Ma X, Luo J, et al. Alldielectric metasurfaces for simultaneous giant circular asymmetric transmission and wavefront shaping based on asymmetric photonic spinorbit interactions. Adv Funct Mater. 2017;27(47):1704295. https://doi.org/10.1002/adfm.201704295.
Lou Y, Fang Y, Ruan Z. Optical computation of divergence operation for vector fields. Phys Rev Appl. 2020;14(3):034013. https://doi.org/10.1103/PhysRevApplied.14.034013.
Lee N, Kim R, Kim JY, Ko JB, Park SHK, Kim SO, et al. Selfassembled nano–lotus pod metasurface for light trapping. ACS Photonics. 2021;8(6):1616–22. https://doi.org/10.1021/acsphotonics.0c01882.
Kim M, Lee D, Yang Y, Kim Y, Rho J. Reaching the highest efficiency of spin hall effect of light in the nearinfrared using alldielectric metasurfaces. Nat Commun. 2022;13(1):2036. https://doi.org/10.1038/s4146702229771x.
Meng C, Thrane PCV, Ding F, Bozhevolnyi SI. Fullrange birefringence control with piezoelectric memsbased metasurfaces. Nat Commun. 2022;13(1):2071. https://doi.org/10.1038/s41467022297980.
Ma Q, Liu C, Xiao Q, Gu Z, Gao X, Li L, et al. Information metasurfaces and intelligent metasurfaces. Photonics Insights. 2022;1(1):R01. https://doi.org/10.3788/pi.2022.r01.
Chen HT, Zhou J, O’Hara JF, Chen F, Azad AK, Taylor AJ. Antireflection coating using metamaterials and identification of its mechanism. Phys Rev Lett. 2010;105(7):073901. https://doi.org/10.1103/PhysRevLett.105.073901.
Chu H, Zhang H, Zhang Y, Peng R, Wang M, Hao Y, et al. Invisible surfaces enabled by the coalescence of antireflection and wavefront controllability in ultrathin metasurfaces. Nat Commun. 2021;12(1):4523. https://doi.org/10.1038/s41467021247639.
Lavigne G, Caloz C. Generalized Brewster effect using bianisotropic metasurfaces. Opt Express. 2021;29(7):11361–70. https://doi.org/10.1364/oe.423078.
Luo J, Chu H, Peng R, Wang M, Li J, Lai Y. Ultrabroadband reflectionless Brewster absorber protected by reciprocity. LightSci Appl. 2021;10(1):89. https://doi.org/10.1038/s41377021005292.
Chu H, Xiong X, Gao YJ, Luo J, Jing H, Li CY, et al. Diffuse reflection and reciprocityprotected transmission via a randomflip metasurface. Sci Adv. 2021;7(37):eabj0935. https://doi.org/10.1126/sciadv.abj0935.
Epstein A, Wong JPS, Eleftheriades GV. Cavityexcited huygens’ metasurface antennas for nearunity aperture illumination efficiency from arbitrarily large apertures. Nat Commun. 2016;7(1):10360. https://doi.org/10.1038/ncomms10360.
Chen K, Feng Y, Monticone F, Zhao J, Zhu B, Jiang T, et al. A reconfigurable active huygens’ metalens. Adv Mater. 2017;29(17):1606422. https://doi.org/10.1002/adma.201606422.
Liu M, Choi DY. Extreme huygens’ metasurfaces based on quasibound states in the continuum. Nano Lett. 2018;18(12):8062–9. https://doi.org/10.1021/acs.nanolett.8b04774.
Liu M, Powell DA, Zarate Y, Shadrivov IV. Huygens’ metadevices for parametric waves. Phys Rev X. 2018;8(3):031077. https://doi.org/10.1103/PhysRevX.8.031077.
Pfeiffer C, Grbic A. Metamaterial huygens’ surfaces: tailoring wave fronts with reflectionless sheets. Phys Rev Lett. 2013;110(19):197401. https://doi.org/10.1103/PhysRevLett.110.197401.
Pfeiffer C, Emani NK, Shaltout AM, Boltasseva A, Shalaev VM, Grbic A. Efficient light bending with isotropic metamaterial huygens’ surfaces. Nano Lett. 2014;14(5):2491–7. https://doi.org/10.1021/nl5001746.
Yu YF, Zhu AY, PaniaguaDomínguez R, Fu YH, Luk’yanchuk B, Kuznetsov AI. Hightransmission dielectric metasurface with 2π phase control at visible wavelengths. Laser Photonics Rev. 2015;9(4):412–8. https://doi.org/10.1002/lpor.201500041.
Fan K, Suen JY, Liu X, Padilla WJ. Alldielectric metasurface absorbers for uncooled terahertz imaging. Optica. 2017;4(6):601. https://doi.org/10.1364/OPTICA.4.000601.
Asadchy VS, Faniayeu IA, Ra’di Y, Khakhomov SA, Semchenko IV, Tretyakov SA. Broadband reflectionless metasheets: frequencyselective transmission and perfect absorption. Phys Rev X. 2015;5(3):031005. https://doi.org/10.1103/PhysRevX.5.031005.
Zhou H, Zhen B, Hsu CW, Miller OD, Johnson SG, Joannopoulos JD, et al. Perfect singlesided radiation and absorption without mirrors. Optica. 2016;3(10):1079. https://doi.org/10.1364/OPTICA.3.001079.
Londoño M, Sayanskiy A, AraqueQuijano JL, Glybovski SB, Baena JD. Broadband huygens’ metasurface based on hybrid resonances. Phys Rev Appl. 2018;10(3):034026. https://doi.org/10.1103/PhysRevApplied.10.034026.
Feng T, Potapov AA, Liang Z, Xu Y. Huygens metasurfaces based on congener dipole excitations. Phys Rev Appl. 2020;13(2):021002. https://doi.org/10.1103/PhysRevApplied.13.021002.
Prodan E, Radloff C, Halas NJ, Nordlander P. A hybridization model for the plasmon response of complex nanostructures. Science. 2003;302(5644):419–22. https://doi.org/10.1126/science.1089171.
Fan JA, Wu C, Bao K, Bao J, Bardhan R, Halas NJ, et al. Selfassembled plasmonic nanoparticle clusters. Science. 2010;328(5982):1135–8. https://doi.org/10.1126/science.1187949.
Zhang S, Ye Z, Wang Y, Park Y, Bartal G, Mrejen M, et al. Antihermitian plasmon coupling of an array of gold thinfilm antennas for controlling light at the nanoscale. Phys Rev Lett. 2012;109(19):193902. https://doi.org/10.1103/PhysRevLett.109.193902.
Lin J, Qiu M, Zhang X, Guo H, Cai Q, Xiao S, et al. Tailoring the lineshapes of coupled plasmonic systems based on a theory derived from first principles. LightSci Appl. 2020;9(1):158. https://doi.org/10.1038/s41377020003865.
Fan S, Suh W, Joannopoulos JD. Temporal coupledmode theory for the Fano resonance in optical resonators. J Opt Soc Am A. 2003;20(3):569–72. https://doi.org/10.1364/JOSAA.20.000569.
Suh W, Wang Z, Fan S. Temporal coupledmode theory and the presence of nonorthogonal modes in lossless multimode cavities. IEEE J Quantum Electron. 2004;40(10):1511–8. https://doi.org/10.1109/JQE.2004.834773.
Hsu CW, Zhen B, Lee J, Chua SL, Johnson SG, Joannopoulos JD, et al. Observation of trapped light within the radiation continuum. Nature. 2013;499(7457):188–91. https://doi.org/10.1038/nature12289.
We choose to design/characterize our resonator #2 with h set as the optimized value yielding the achromatic reflectionless bilayer metasurface. While optical response of such a resonator slightly changes as h varies, we neglect such deviations in the discussions followed.
Acknowledgements
We acknowledge technical supports from Fudan Nanofabrication Laboratory for sample fabrications. We thank Kun Ding, Shulin Sun and Zhenyu Qian for useful discussions and technical support.
Funding
This work was funded by National Key Research and Development Program of China (No. 2017YFA0700201), National Natural Science Foundation of China (No. 11734007, No. 12221004, No. 62192771), Natural Science Foundation of Shanghai (No. 20JC1414601) and China Postdoctoral Science Foundation (No. 2021 M690710).
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X.Z and J.L. contributed equally to this work. X.Z. carried out simulations and data analyses, fabricated all samples and conducted all experimental measurements. J.L. carried out the analytical modeling and simulations. H.Z. and Z.W. provided technical support for simulations and data analyses. L.Z., Q.H. and J.L. conceived the idea and supervised the project. All authors contributed to the discussion and preparation of the manuscript. The authors read and approved the final manuscript.
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Zheng, X., Lin, J., Wang, Z. et al. Manipulating light transmission and absorption via an achromatic reflectionless metasurface. PhotoniX 4, 3 (2023). https://doi.org/10.1186/s4307402200078w
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DOI: https://doi.org/10.1186/s4307402200078w
Keywords
 Metasurfaces
 Couplings
 Coupledmode theory
 Kerker condition
 Perfect absorber