Metasurfaces have the capability to boost the generation of distinct colors by improving the interaction between surface materials and photons. We present a straightforward and polarization-tunable aluminum nitride metasurface. This metasurface enables the display and concealment of the composition pattern and exhibits color switching by modifying the polarization state of the incident light. We further explore the impact of different substrates on metasurface performance. The results indicate that the full width at half maximum of the reflectance curves increases with the increase of the refractive index between the nanostructures and the substrate material, which leads to a broader dispersion of the structural colors in the spectrum. Moreover, the sizes of the nanostructures can be gradually reduced for the substrate with a high refractive index. These findings not only offer polarization-tunable structural color metasurfaces but also provide essential insights in selecting nanostructure and substrate materials, which will help in the design of nanostructures for such metasurfaces.

Color plays a crucial role in human perception of the world and the communication of information. In the age of rapid information progress, there is an increasing need for a wide range of vivid and dynamic colors. Conventional dyes and pigments commonly used for color production often exhibit limitations, including poor stability and uneven color distribution. In contrast, metasurfaces, which are nano-optical devices made of artificial nanostructures, can modify the subwavelength spectrum and produce vivid structural colors by enhancing the interaction between materials and photons. The devices not only overcome these drawbacks of the conventional dyes and also provide advantages such as environmental friendliness, non-toxicity, precise color rendering, and superior color quality.1–6 These benefits open up new opportunities for color fabrication and application. Therefore, metasurfaces have been extensively studied.

Initially, the high-resolution color rendering can be generated through the arrayed metal nanostructures metasurfaces within the wide subwavelength spectrum. However, due to the inherent ohmic losses in metals, the plasmon resonance effect7–9 that determines the colors is relatively inefficient, resulting in diminished color saturation and narrow color purity of the generated structural colors. To address this issue, researchers have proposed using dielectric materials with low loss and high refractive index, such as Si,10–12 TiO2,13–15 and Si3N4.16,17 These metasurfaces utilize the Mie lattice resonance effect18–20 to produce higher and purity saturation structure colors.

With nanomanufacturing technology advances, more high-performance metasurfaces with varied capabilities are being designed and fabricated.21–28 Among these investigations, the metasurfaces that have the capability of dynamic display with polarization switching have emerged as a new research focus due to the wide-ranging applications in anti-counterfeiting and encryption. For example, Chen et al.29 achieved dynamic display metasurfaces capable of polarization switching by meticulously designing Si nanoblocks on a quartz substrate, which can encode color information into the wavelength dependent polarization profile of a light beam. Similarly, Wang et al.30 developed dynamic display metasurfaces by crafting Si3N4 nanoblocks on a SiO2 substrate, which has the polarization-switching capabilities to turn on and off full-color images by changing the light polarization.

In these studies, researchers paired the higher indices materials with the low refractive indices substrates to achieve the desired functionalities. The selection of surface and substrate materials often relies more on the researchers’ experience and the current processing technology. However, the choice of substrate can significantly restrict the properties of the metasurface. To the best of our knowledge, detailed studies on substrates for the polarization-switching metasurfaces are still relatively scarce. Moreover, tunable permittivity control31 is critical in some metasurface applications, such as thermal metasurfaces.32 Recently, Nolen et al.33 have developed a thermal metasurface that adeptly modulates the phase and polarization of thermal radiation. Their findings indicate that variations in the substrate's refractive index significantly affect thermal emissivity intensity and operational range. It can be seen that the refractive index of substrate, has an important influence on the realization of the metasurface functionality. Therefore, our work focuses not only on the achievement of polarization-switching metasurfaces but also on the effects of substrate materials with different refractive indices.

For the surface, aluminum nitride (AlN), a new generation semiconductor material known for its excellent transparency in the ultraviolet and visible spectrum. High-aspect-ratio subwavelength nanostructures of AlN have been fabricated by either a dedicated reactive ion etch (RIE) process34 or a resist-based Damascene process incorporating low-temperature atomic layer deposition (ALD).35 Moreover, numerical studies36 and experimental37 demonstrations show the use of AlN metasurfaces for ultraviolet applications, as well as AlN nanofilms that display coloration within the visible light spectrum.38 

Specifically speaking, we first propose polarization-sensitive metasurfaces by laying AlN nanostructures on CeF3 substrates to generate full-color structural colors. The simulations show that the nano-rectangular AlN-structured metasurface will reflect a color when the polarization of the light coming in is parallel to the long axis. However, when the polarization of the light coming in is parallel to the short axis, the metasurface will not reflect any color because its reflection is almost zero. The nano-square AlN-structured metasurface shows color-switching effects with the change of polarization states and the sharp and highly efficient reflectance peaks that are completely spectrally separated under different polarized incident lights. We further investigate the impact of different substrate materials. The simulation results reveal that with increasing refractive index disparity between the substrate and nanostructural materials, the color gamut displayed broadens, and it is possible to fabricate nanostructures on the metasurface at progressively smaller scales. Our study introduced a metasurface that demonstrated remarkable sensitivity to linear polarization, making it highly valuable for applications such as color displays, data storage, and anti-counterfeiting technologies. It also provides valuable insights that can significantly aid researchers in selecting appropriate materials for substrates and nanostructures during the design of dielectric metasurfaces.

A schematic of the proposed nano-rectangular AlN metasurface, composed of numerous basic units, is shown in Fig. 1(a). Each basic unit contained two parts: a CeF3 substrate at the bottom and an AlN nanoparticle at the top, as shown in Fig. 1(b). The dimensions of the AlN nanoparticle are specified as follows: length (L), width (W), and height (H), and the separation distance between two nanostructures is denoted as P. The structure was illuminated from the top by x- and y-polarized light, as shown in Fig. 1(c). The schematic of the nanosquare metasurfaces and the single cell of the nanosquare metasurfaces are shown in Fig. 1(d). The dimensions of the AlN nanoparticle are specified as follows: length (L) and height (H), and Px and Py are the distances between two nanostructures in the x and y directions, respectively.

FIG. 1.

All-dielectric metasurfaces with polarization dependence. (a) Schematic of the nanorectangular metasurfaces. (b) A single cell of the nanorectangular metasurfaces. (c) Schematic of the nanosquare metasurfaces. (d) A single cell of the nano square metasurfaces.

FIG. 1.

All-dielectric metasurfaces with polarization dependence. (a) Schematic of the nanorectangular metasurfaces. (b) A single cell of the nanorectangular metasurfaces. (c) Schematic of the nanosquare metasurfaces. (d) A single cell of the nano square metasurfaces.

Close modal

The CeF3 is a scintillator with excellent magneto-optical properties and can be used as a new generation of ultraviolet laser working media. Its refractive index is much lower than that of AlN, which is between SiO239 and Al2O3.40 Therefore, based on the current experience, the combination of these two materials forms a metasurface that is expected to have polarization sensitivity and the ability to selectively reflect colors. We performed simulations of metasurfaces using the commercial software COMSOL Solutions. We obtained the refractive index of AlN from Pastrňák41 and the refractive index of CeF3 from Rodríguez-de Marcos.42 For normal incidence, periodic boundary conditions be used in the x- and y-directions to model infinite arrays and a perfect match layer in the z-direction to mimic free space. The environment is air. An incident plane wave port is provided at the top of the model. The remainder of the analysis was conducted using MATLAB.

The reflectance for the polarization of the light parallel to the long-axis is shown in Fig. 2(a). A super narrow peak was observed. By contrast, it is evident that the reflectance exhibits a stark contrast when the light’s polarization aligns with the short axis. The near-zero reflection can be observed. To illustrate the potential of metasurfaces for selective color rendering in different polarization states, we created a simple submarine image as shown in Fig. 2(b). The vivid blue color is calculated from spectral data of metasurface and color-matching functions, as defined by CIE.43,44

FIG. 2.

All-dielectric metasurfaces with polarization dependence. (A) Reflectance for x-polarization and y-polarization, respectively. The parameters used were P = 300 nm, L = 225 nm, W = 150 nm, and H. The thickness of the AlN layer was fixed at 325 nm. (B) (a) The images of the submarine, which is composed of nano-rectangular metasurfaces, under x-polarized light. (b) The submarine pattern disappears when it rotates 90° under x-polarized light, as the incident light is polarized parallel to the short axis of the pattern. (c) The submarine pattern reappears when the polarization state of the incident light changes from x-polarization to y-polarization. (d) The submarine pattern disappears again when it is rotated under y-polarized light. A single cell of the nanorectangular metasurfaces.

FIG. 2.

All-dielectric metasurfaces with polarization dependence. (A) Reflectance for x-polarization and y-polarization, respectively. The parameters used were P = 300 nm, L = 225 nm, W = 150 nm, and H. The thickness of the AlN layer was fixed at 325 nm. (B) (a) The images of the submarine, which is composed of nano-rectangular metasurfaces, under x-polarized light. (b) The submarine pattern disappears when it rotates 90° under x-polarized light, as the incident light is polarized parallel to the short axis of the pattern. (c) The submarine pattern reappears when the polarization state of the incident light changes from x-polarization to y-polarization. (d) The submarine pattern disappears again when it is rotated under y-polarized light. A single cell of the nanorectangular metasurfaces.

Close modal

In Fig. 2(B-a), the polarization of x-polarized incident light is paralleled to the metasurface’s long axis; the submarine pattern exhibits a vivid and highly saturated blue color. The pattern disappears when the metasurface is rotated 90° since the light polarization is parallel to the metasurface’s short axis, as shown in Fig. 2(B-b). It is noted that we can re-emerge the pattern when converting the incident x-polarized light to y-polarized light, as shown in Fig. 2(B-c). Furthermore, the submarine pattern can disappear when the metasurface is rotated 90° because its short axis is parallel to the polarization state once more, as shown in Fig. 2(B-d).

The reflectance, multipole expansion, and field distribution were analyzed to illustrate the physical mechanism of the proposed metasurfaces.45,46 According to the multiple scattering theory, the scattering cross-section can be expanded into an electric dipole (ED), magnetic dipole (MD), toroidal dipole (TD), electric quadrupole (EQ), and magnetic quadrupole (MQ). In the case of the expression for the total far-field scattered intensity is as follows:
(1)
Here, c and ω are the speed of light in a vacuum and the angular frequency of light. P, M, Qαβ, Mαβ, and T are electric dipole (ED), magnetic dipole (MD), electric quadrupole (EQ), magnetic quadrupole (MQ), and toroidal dipole (TD) moments, respectively, α, β = x, y, z. j=iωε0(n21)E is the current density distribution in a unit cell.

Figure 3(a) illustrates the reflectance of light incident from the top onto the nano-rectangular AlN-structured metasurface, with its polarization parallel to the long axis. A super-narrow reflectance peak is observed at a wavelength of 578 nm. In Fig. 3(b), we present the resonance curve obtained through the multi-polarization unfolding of the scattering interface. Among these resonances, it is evident that the MD resonance is stronger than other resonances. Therefore, this narrow reflection peak is dependent on the coupling interaction between the strong MD resonance and other resonances. Moreover, the characteristics of this peak are heavily reliant on the size and shape of the subwavelength nanostructure. Since local modes are functions of certain locations, highlighting the independence of optical responses at a single meta-atom or metamolecule from neighboring unit cells, including LSPRs, Mie resonances, and defect modes with a subwavelength mode volume and negligible neighboring interactions.47 Therefore, this confirms that the peak from a Mie resonance is caused by local lattice resonances rather than a non-local high-Q Fano resonance effect.48–50 In addition, we also show the distribution of electric and magnetic fields at the peak position. In Figs. 3(c) and 3(d). The distinctive ring-shaped electric field distribution extending from the nanoparticle to the substrate is characteristic of the ED resonance. The magnetic field distribution of MD resonance is shown in Fig. 3(d). For comparison, Fig. 3(e) shows the near-zero reflection spectrum when the incident light’s polarization direction aligns with the short axis. It indicates that the reason for this situation is that these resonances are not effectively excited, as shown in Fig. 3(f).

FIG. 3.

Mechanism of the nanorectangular AlN structured metasurface. (a) and (b) Reflectance and multipole expansion for x-polarization, respectively. (c) and (d) Electric and magnetic field distributions of the metasurface at the central x−z plane for x-polarization at 578 nm. (e) and (f) Reflectance and multipole expansion for y-polarization, respectively. The parameters used were P = 350 nm, L = 252 nm, and W = 175 nm.

FIG. 3.

Mechanism of the nanorectangular AlN structured metasurface. (a) and (b) Reflectance and multipole expansion for x-polarization, respectively. (c) and (d) Electric and magnetic field distributions of the metasurface at the central x−z plane for x-polarization at 578 nm. (e) and (f) Reflectance and multipole expansion for y-polarization, respectively. The parameters used were P = 350 nm, L = 252 nm, and W = 175 nm.

Close modal

These findings suggest that the metasurfaces exhibit extremely high polarization sensitivity, which can selectively color by changing the light polarization state. They can be used for image hiding and display and offer superior performance in optical encryption. However, its storage capacity of encrypted information for the nano-rectangular AlN metasurface is limited due to the monochromatic tuning capability. To improve the information content and achieve multi-color tunability, we additionally propose a method to achieve the goal.

We present the reflectance of the nanosquare AlN-structured metasurface (Px = 330 nm, Py = 270 nm, and L = 200 nm) for the x and y-polarized incident light, as shown in Fig. 4(a). It is evident that the two independent reflection peaks with different colors are generated by the metasurface. This character can enhance the information storage capacity of the metasurface. As shown in Fig. 4(b), the simulation barque pattern appears blue and cyan under the two polarized incident lights, respectively. In solving crosstalk problems due to low color saturation and low brightness, this structure is less complicated than the traditional nanocross structure,51 which decreases the demands on fabrication precision. Therefore, there is significant potential in a variety of applications like optical filters, wavelength division multiplexing devices, and multi-channel devices.

FIG. 4.

(a) Reflectance for x-polarization and y-polarization. The parameters used were Px = 350 nm, Py = 270 nm, and L = 200 nm. The thickness of the AlN layer was fixed at 325 nm. (b) Simulation of the barque pattern using two colors.

FIG. 4.

(a) Reflectance for x-polarization and y-polarization. The parameters used were Px = 350 nm, Py = 270 nm, and L = 200 nm. The thickness of the AlN layer was fixed at 325 nm. (b) Simulation of the barque pattern using two colors.

Close modal

In addition, the multi-color tunable performance of the nanosquare AlN-structured metasurface was demonstrated by simulating the reflection spectra of the metasurface under x-polarization and y-polarization. Figure 5(a) shows that when the edge length Px in the x-direction increases from 270 to 350 nm, there is almost a small change in the reflection peak under y-polarization. In contrast, the reflection peak under x-polarization shifts by 100 nm with the Px length increase, as shown in Fig. 5(b). It can also achieve the same effect of reflection peak shifting under y-polarization and barely shifting under x-polarization by adjusting Py in the y-direction. The nanosquare AlN-structured metasurface exhibits different reflection colors under x and y polarization with high independence and displays high-quality and highly saturated colors.

FIG. 5.

Optical performance of the nanosquare AlN structured metasurface. (a) and (b) Reflectance maps as a function of wavelength and Px under y- and x-polarized light, respectively. The height of nano square AlN is fixed at 325 nm, its side length is 100 nm, and the adjustment range of Px is 270–350 nm with a step size of 10 nm.

FIG. 5.

Optical performance of the nanosquare AlN structured metasurface. (a) and (b) Reflectance maps as a function of wavelength and Px under y- and x-polarized light, respectively. The height of nano square AlN is fixed at 325 nm, its side length is 100 nm, and the adjustment range of Px is 270–350 nm with a step size of 10 nm.

Close modal

To further investigate the substrate’s impact on metasurfaces, we replaced the CeF3 substrate with SiO2 and Al2O3 substrates and redesigned the polarization-sensitive structural color metasurfaces. The basic units of the three metasurfaces are shown in Figs. 6(a)6(c). Here, the average refractive indices of SiO2, CeF3, and Al2O3 in the wavelength range of 380–730 nm are 1.46, 1.62, and 1.78, respectively, with average refractive index differences compared to AlN in this range of 0.72, 0.56, and 0.4. P is the spacing between the nanostructures. It can be observed that the volume of the nanostructures in the three metasurfaces decreases with the increasing of the difference in refractive index between the substrate material and the nanostructure material. Figures 6(d)6(f) show the dynamic color display capabilities of the three metasurfaces, with the spacing between the nanostructures ranging from 265 to 400 nm. Figures 6(g)6(i) Chromatic diagrams showing simulated colors in ClE 1931 color space for panels (d), (e), and (f), respectively. It is evident that the color gamut of the metasurface with the Al2O3 substrate is smaller than that with the CeF3 substrate, and the color gamut of the metasurface with the CeF3 substrate is smaller than that with the SiO2 substrate.

FIG. 6.

Simulated results of polarization-dependent for the nanorectangular AlN structured metasurface. (a)–(c) The basic units of the three metasurfaces. The dimensions of the nanostructures in the metasurfaces with SiO2, Al2O3, and CeF3 substrates are as follows: for SiO2 substrate, L1 = 0.4P, W1 = 0.85P, and H1 = 325 nm; for CeF3 substrate, L1 = 0.5P, W1 = 0.85P, and H1 = 325 nm; for Al2O3 substrate, L1 = 0.5P, W1 = 0.9P, and H1 = 380 nm. (d)–(f) The reflectance of the metasurfaces with different structural parameters. P varied from 265 to 400 nm with a step length of 10 nm. (g)–(i) Chromatic diagrams showing simulated colors in CIE 1931 color space for panels.

FIG. 6.

Simulated results of polarization-dependent for the nanorectangular AlN structured metasurface. (a)–(c) The basic units of the three metasurfaces. The dimensions of the nanostructures in the metasurfaces with SiO2, Al2O3, and CeF3 substrates are as follows: for SiO2 substrate, L1 = 0.4P, W1 = 0.85P, and H1 = 325 nm; for CeF3 substrate, L1 = 0.5P, W1 = 0.85P, and H1 = 325 nm; for Al2O3 substrate, L1 = 0.5P, W1 = 0.9P, and H1 = 380 nm. (d)–(f) The reflectance of the metasurfaces with different structural parameters. P varied from 265 to 400 nm with a step length of 10 nm. (g)–(i) Chromatic diagrams showing simulated colors in CIE 1931 color space for panels.

Close modal

The reflectance and multipole expansion were analyzed to demonstrate the mechanism of the metasurfaces on three different substrates when subjected to incident light with polarization parallel to the long axis of the nanoblock. The reflectance is shown in Figs. 7(a), 7(d), and 7(g), respectively.

FIG. 7.

(a), (d), and (g), Reflectance for x-polarization, respectively. Here, the dimensions of the nanostructures in the metasurfaces with SiO2, CeF3, and Al2O3 substrates are as follows: for SiO2 substrate, L1 = 132 nm, W1 = 280.5 nm, H1 = 325 nm; for CeF3 substrate, L1 = 165 nm, W1 = 280.5, H1 = 325 nm; for Al2O3 substrate, L1 = 297 nm, W1 = 165 nm, H1 = 380 nm. (b), (e), and (h) Multipole expansion for x-polarization for these metasurfaces. (c), (f), and (i) The corresponding phases of magnetic dipole and electric dipole modes.

FIG. 7.

(a), (d), and (g), Reflectance for x-polarization, respectively. Here, the dimensions of the nanostructures in the metasurfaces with SiO2, CeF3, and Al2O3 substrates are as follows: for SiO2 substrate, L1 = 132 nm, W1 = 280.5 nm, H1 = 325 nm; for CeF3 substrate, L1 = 165 nm, W1 = 280.5, H1 = 325 nm; for Al2O3 substrate, L1 = 297 nm, W1 = 165 nm, H1 = 380 nm. (b), (e), and (h) Multipole expansion for x-polarization for these metasurfaces. (c), (f), and (i) The corresponding phases of magnetic dipole and electric dipole modes.

Close modal

The multipole decomposition of the scattering cross-section for ED, MD, EQ, MQ, and TD is illustrated in Figs. 7(b), 7(e), and 7(h), respectively. Notably, the observed reflection peak corresponds to a significantly stronger MD resonance compared to other resonances, and the full width at half maximum (FWHM) of the MD resonance for the SiO2 substrate is larger than that for the other two substrates. The corresponding phases of MD and ED are depicted in Figs. 7(c), 7(f), and 7(i). At the MD resonance peak, the phase difference between the MD and ED resonances is 1.5π, and their phase magnitudes are not equal, which does not strictly conform to the second Kerker’s condition52 (where MD and ED have equal amplitude and a phase difference of π). Therefore, the reflection peak primarily results from the combined resonance effects dominated by the MD resonance. In addition, the FWHM of the MD resonance in the SiO2 substrate is higher than that in the CeF3 substrate, which in turn is higher than that in the Al2O3 substrate. This results in the reflectance FWHM following the same trend and is reflected in the color gamut: the SiO2 substrate’s metasurface exhibits a broader color gamut compared to the CeF3 substrate, which in turn has a broader gamut than the Al2O3 substrate.

Most notably, the trend in the FWHM of the reflectance peaks correlates with the refractive index difference between the substrate and its surface nanostructures. The FWHM of the reflectance peaks increases as the refractive index difference enlarges. When the refractive index difference between the substrate and its nanostructures is substantial, the metasurface can more readily produce a broader color gamut.

To demonstrate that this phenomenon is not due to variations in the dimensions of the nanostructures but rather differences in the substrates, Fig. 8 presents the reflectance curves, multipole decomposition curves of the scattering cross-section, and the corresponding phase curves of MD and ED resonances for three metasurfaces using nanoparticles of identical dimensions. For the same-size nanoparticles, it is evident that the FWHM of the MD resonances and the reflectance peaks of the three metasurfaces still exhibit a positive correlation with the refractive index difference between the substrate and its surface nanostructures. Furthermore, the primary cause of the reflection peak remains to be the combined resonance effects, mostly driven by the MD resonance.

FIG. 8.

(a), (d), and (g), Reflectance for x-polarization, respectively. Here the dimensions of the same nanostructures in the metasurfaces with SiO2, CeF3, and Al2O3 substrates are as follows: L1 = L2 = L3 = 297 nm, W1 = W2 = W3 = 198 nm, and H1 = H2 = H3 = 325 nm. (b), (e), and (h) Multipole expansion for x-polarization for these metasurfaces. (c), (f), and (i) The corresponding phases of MD and ED modes.

FIG. 8.

(a), (d), and (g), Reflectance for x-polarization, respectively. Here the dimensions of the same nanostructures in the metasurfaces with SiO2, CeF3, and Al2O3 substrates are as follows: L1 = L2 = L3 = 297 nm, W1 = W2 = W3 = 198 nm, and H1 = H2 = H3 = 325 nm. (b), (e), and (h) Multipole expansion for x-polarization for these metasurfaces. (c), (f), and (i) The corresponding phases of MD and ED modes.

Close modal

In conclusion, we first presented a metasurface with high-efficiency and polarization sensitivity comprising AlN nanoparticles on a CeF3 substrate. This metasurface yields high-efficiency structural color through the MD resonance from the Mie lattice resonance and achieves color with its inherent polarization-sensitive capabilities. Second, we also investigated the impact of various substrate refractive indices on metasurface performance. The simulation results show that as the difference in refractive index between the substrate and nanostructural materials grows, the strong MD resonance excited by the nanoparticles on different substrates gradually widens, ultimately broadening the color gamut. Additionally, it is possible to fabricate nanostructures on the metasurface with dynamic polarization responsiveness at progressively smaller scales. The optical properties of these metasurfaces suggest promising applications in fields such as full-color imaging, information encoding, high-density optical data storage, and optical encryption, and these findings also provide valuable insights that can significantly aid researchers in selecting appropriate materials for substrates and nanostructures during the design of dielectric metasurfaces.

This work was partly supported by the National Natural Science Foundation of China (Grant No. 11604205).

The authors have no conflicts to disclose.

Jiujiang Wang: Data curation (equal); Software (equal). Chenhui Lu: Funding acquisition (equal); Investigation (equal); Validation (equal); Writing – original draft (equal); Writing – review & editing (equal). Jiao Geng: Data curation (equal); Investigation (equal); Validation (equal); Visualization (equal). Liping Shi: Conceptualization (equal); Data curation (equal); Visualization (equal); Writing – original draft (equal); Writing – review & editing (equal).

The data that support the findings of this study are available from the corresponding author upon reasonable request.

1.
T.
Xu
,
Y. K.
Wu
,
X.
Luo
, and
L. J.
Guo
, “
Plasmonic nanoresonators for high-resolution colour filtering and spectral imaging
,”
Nat. Commun.
1
(
1
),
59
(
2010
).
2.
K.
Kumar
,
H.
Duan
,
R. S.
Hegde
,
S. C. W.
Koh
,
J. N.
Wei
, and
J. K.
Yang
, “
Printing colour at the optical diffraction limit
,”
Nat. Nanotechnol.
7
(
9
),
557
561
(
2012
).
3.
A. S.
Roberts
,
A.
Pors
,
O.
Albrektsen
, and
S. I.
Bozhevolnyi
, “
Subwavelength plasmonic color printing protected for ambient use
,”
Nano Lett.
14
(
2
),
783
787
(
2014
).
4.
H.
Wang
,
X.
Wang
,
C.
Yan
,
H.
Zhao
,
J.
Zhang
,
C.
Santschi
, and
O. J.
Martin
, “
Full color generation using silver tandem nanodisks
,”
ACS Nano
11
(
5
),
4419
4427
(
2017
).
5.
M.
Song
,
X.
Li
,
M.
Pu
,
Y.
Guo
,
K.
Liu
,
H.
Yu
,
X.
Ma
, and
X.
Luo
, “
Color display and encryption with a plasmonic polarizing metamirror
,”
Nanophotonics
7
(
1
),
323
331
(
2018
).
6.
J.
Geng
,
L.
Xu
,
W.
Yan
,
L.
Shi
, and
M.
Qiu
, “
High-speed laser writing of structural colors for full-color inkless printing
,”
Nat. Commun.
14
(
1
),
565
(
2023
).
7.
X.
Zhang
,
Y. S.
Lin
, and
B. R.
Yang
, “
Tunable color switch using split-ring metamaterial
,”
Opt Laser. Technol.
131
(
31
),
106461
(
2020
).
8.
J.
Dai
,
R.
Xu
,
Y. S.
Lin
, and
C. H.
Chen
, “
Tunable electromagnetic characteristics of suspended nanodisk metasurface
,”
Opt Laser. Technol.
128
(
28
),
106214
(
2020
).
9.
X.
Xu
,
Y. S.
Lin
,
R.
Fang
, and
B. R.
Yang
, “
Designs of metareflectors based on nanodisk and annular hole arrays with polarization independence, switching, and broad bandwidth characteristics
,”
Opt. Mater. Express
11
(
10
),
3577
3586
(
2021
).
10.
V.
Vashistha
,
G.
Vaidya
,
R. S.
Hegde
,
A. E.
Serebryannikov
,
N.
Bonod
,
M.
Krawczyk
,
N.
Bonod
, and
M.
Krawczyk
, “
All-dielectric metasurfaces based on cross-shaped resonators for color pixels with extended gamut
,”
ACS Photonics
4
(
5
),
1076
1082
(
2017
).
11.
Y.
Bao
,
Y.
Yu
,
H.
Xu
,
C.
Guo
,
J.
Li
,
S.
Sun
,
Z. K.
Zhou
et al, “
Full-colour nanoprint-hologram synchronous metasurface with arbitrary hue-saturation-brightness control
,”
Light: Sci. Appl.
8
(
1
),
95
(
2019
).
12.
W.
Yang
,
S.
Xiao
,
Q.
Song
,
Y.
Liu
,
Y.
Wu
,
S.
Wang
,
J.
Yu
et al, “
All-dielectric metasurface for high-performance structural color
,”
Nat. Commun.
11
(
1
),
1864
(
2020
).
13.
B.
Yang
,
W.
Liu
,
Z.
Li
,
H.
Cheng
,
S.
Chen
, and
J.
Tian
, “
Polarization‐sensitive structural colors with hue‐and‐saturation tuning based on all‐dielectric nanopixels
,”
Adv. Opt. Mater.
6
(
4
),
1701009
(
2018
).
14.
I.
Koirala
,
S. S.
Lee
, and
D. Y.
Choi
, “
Highly transmissive subtractive color filters based on an all-dielectric metasurface incorporating TiO2 nanopillars
,”
Opt. Express
26
(
14
),
18320
18330
(
2018
).
15.
D.
Wen
,
J. J.
Cadusch
,
J.
Meng
, and
K. B.
Crozier
, “
Multifunctional dielectric metasurfaces consisting of color holograms encoded into color printed images
,”
Adv. Funct. Mater.
30
(
3
),
1906415
(
2020
).
16.
B.
Yang
,
W.
Liu
,
Z.
Li
,
H.
Cheng
,
D. Y.
Choi
,
S.
Chen
, and
J.
Tian
, “
Ultrahighly saturated structural colors enhanced by multipolar-modulated metasurfaces
,”
Nano Lett.
19
(
7
),
4221
4228
(
2019
).
17.
Z.
Dong
,
J.
Ho
,
Y. F.
Yu
,
Y. H.
Fu
,
R.
Paniagua-Dominguez
,
S.
Wang
,
A. I.
Kuznetsov
, and
J. K. W.
Yang
, “
Printing beyond sRGB color gamut by mimicking silicon nanostructures in free-space
,”
Nano Lett.
17
(
12
),
7620
(
2017
).
18.
V. E.
Babicheva
,
M. I.
Petrov
,
K. V.
Baryshnikova
, and
P. A.
Belov
, “
Reflection compensation mediated by electric and magnetic resonances of all-dielectric metasurfaces [invited]
,”
J. Opt. Soc. Am. B
34
(
7
),
D18
D28
(
2017
).
19.
S.
Sun
,
Z.
Zhou
,
C.
Zhang
,
Y.
Gao
,
Z.
Duan
,
S.
Xiao
, and
Q.
Song
, “
All-dielectric full-color printing with TiO2 metasurfaces
,”
ACS Nano
11
(
5
),
4445
4452
(
2017
).
20.
J. H.
Yang
,
V. E.
Babicheva
,
M. W.
Yu
,
T. C.
Lu
,
T. R.
Lin
, and
K. P.
Chen
, “
Structural colors enabled by lattice resonance on silicon nitride metasurfaces
,”
ACS Nano
14
(
5
),
5678
5685
(
2020
).
21.
L.
Shi
,
J. R.
Andrade
,
J.
Yi
,
M.
Marinskas
,
C.
Reinhardt
,
E.
Almeida
,
U.
Morgner
, and
M.
Kovacev
, “
Nanoscale broadband deep-ultraviolet light source from plasmonic nanoholes
,”
ACS Photonics
6
(
4
),
858
863
(
2019
).
22.
J.
Geng
,
W.
Yan
,
L.
Shi
, and
M.
Qiu
, “
Surface plasmons interference nanogratings: Wafer-scale laser direct structuring in seconds
,”
Light: Sci. Appl.
11
(
1
),
189
(
2022
).
23.
M.
Kim
,
D.
Lee
,
Y.
Yang
,
Y.
Kim
, and
J.
Rho
, “
Reaching the highest efficiency of spin Hall effect of light in the near-infrared using all-dielectric metasurfaces
,”
Nat. Commun.
13
(
1
),
2036
(
2022
).
24.
H.
Kwon
,
T.
Zheng
, and
A.
Faraon
, “
Nano-electromechanical spatial light modulator enabled by asymmetric resonant dielectric metasurfaces
,”
Nat. Commun.
13
(
1
),
5811
(
2022
).
25.
Y.
Jahani
,
E. R.
Arvelo
,
F.
Yesilkoy
,
K.
Koshelev
,
C.
Cianciaruso
,
M.
De Palma
,
Y.
Kivshar
, and
H.
Altug
, “
Imaging-based spectrometer-less optofluidic biosensors based on dielectric metasurfaces for detecting extracellular vesicles
,”
Nat. Commun.
12
(
1
),
3246
(
2021
).
26.
R.
Xu
,
C.
Chen
,
J.
Sun
,
Y.
He
,
X.
Li
,
M.
Lu
, and
Y.
Chen
, “
The design, manufacture and application of multistable mechanical metamaterials-a state-of-the-art review
,”
Int. J. Extreme Manuf.
5
,
042013
(
2023
).
27.
T.
Cao
,
M.
Lian
,
K.
Liu
,
X.
Lou
,
Y.
Guo
, and
D.
Guo
, “
Wideband mid-infrared thermal emitter based on stacked nanocavity metasurfaces
,”
Int. J. Extreme Manuf.
4
(
1
),
015402
(
2021
).
28.
N.
Wang
,
C.
Zhou
,
S.
Qiu
,
S.
Huang
,
B.
Jia
,
S.
Liu
,
J.
Cao
et al, “
Meta-silencer with designable timbre
,”
Int. J. Extreme Manuf.
5
(
2
),
025501
(
2023
).
29.
X.
Zang
,
F.
Dong
,
F.
Yue
,
C.
Zhang
,
L.
Xu
,
Z.
Song
,
M.
Chen
et al, “
Polarization encoded color image embedded in a dielectric metasurface
,”
Adv. Mater.
30
(
21
),
1707499
(
2018
).
30.
L.
Wang
,
T.
Wang
,
R.
Yan
,
X.
Yue
,
H.
Wang
,
Y.
Wang
,
J.
Zhang
et al, “
Color printing and encryption with polarization-switchable structural colors on all-dielectric metasurfaces
,”
Nano Lett.
23
(
12
),
5581
5587
(
2023
).
31.
A.
Forouzmand
,
M. M.
Salary
,
G.
Kafaie Shirmanesh
,
R.
Sokhoyan
,
H. A.
Atwater
, and
H.
Mosallaei
, “
Tunable all-dielectric metasurface for phase modulation of the reflected and transmitted light via permittivity tuning of indium tin oxide
,”
Nanophotonics
8
(
3
),
415
427
(
2019
).
32.
A. C.
Overvig
,
S. A.
Mann
, and
A.
Alù
, “
Thermal metasurfaces: Complete emission control by combining local and nonlocal light-matter interactions
,”
Phys. Rev. X
11
(
2
),
021050
(
2021
).
33.
J. R.
Nolen
,
A. C.
Overvig
,
M.
Cotrufo
, and
A.
Alù
, “
Local control of polarization and geometric phase in thermal metasurfaces
,”
Nat. Nanotechnol.
(published online)
(
2024
).
34.
B.
Sarkar
,
B. B.
Haidet
,
P.
Reddy
,
R.
Kirste
,
R.
Collazo
, and
Z.
Sitar
, “
Performance improvement of ohmic contacts on Al-rich n-AlGaN grown on single crystal AlN substrate using reactive ion etching surface treatment
,”
Appl. Phys. Express
10
(
7
),
071001
(
2017
).
35.
H.
Van Bui
,
M. D.
Nguyen
,
F. B.
Wiggers
,
A. A.
Aarnink
,
M. P.
de Jong
, and
A. Y.
Kovalgin
, “
Self-limiting growth and thickness- and temperature-dependence of optical constants of ALD AlN thin films
,”
ECS J. Solid State Sci. Technology
3
(
4
),
P101
(
2014
).
36.
X.
Gao
,
R.
Wan
,
J.
Yan
,
L.
Wang
,
X.
Yi
,
J.
Wang
,
W.
Zhu
, and
J.
Li
, “
Design of AlN ultraviolet metasurface for single-/multi-plane holography
,”
Appl. Opt.
59
(
14
),
4398
4403
(
2020
).
37.
Z.
Hu
,
L.
Long
,
R.
Wan
,
C.
Zhang
,
L.
Zhang
,
J.
Yan
,
H.
Duan
, and
L.
Wang
, “
Ultrawide bandgap AlN metasurfaces for ultraviolet focusing and routing
,”
Opt. Lett.
45
(
13
),
3466
3469
(
2020
).
38.
X.
Shi
,
X.
Yu
,
C.
Nie
,
F.
Li
, and
S.
Zhang
, “
Controlled growth of nanocrystalline aluminum nitride films for full color range
,”
Ceram. Int.
47
(
15
),
21546
21553
(
2021
).
39.
L. V.
Rodríguez-de Marcos
,
J. I.
Larruquert
,
J. A.
Méndez
, and
J. A.
Aznárez
, “
Self-consistent optical constants of SiO2 and Ta2O5 films
,”
Opt. Mater. Express
6
(
11
),
3622
3637
(
2016
).
40.
R.
Boidin
,
T.
Halenkovič
,
V.
Nazabal
,
L.
Beneš
, and
P.
Němec
, “
Pulsed laser deposited alumina thin films
,”
Ceram. Int.
42
(
1
),
1177
1182
(
2016
).
41.
J.
Pastrňák
and
L.
Roskovcová
, “
Refraction index measurements on AlN single crystals
,”
Phys. Status Solidi B
14
(
1
),
K5
K8
(
1966
).
42.
L. V.
Rodríguez-de Marcos
,
J. I.
Larruquert
,
J. A.
Méndez
, and
J. A.
Aznárez
, “
Self-consistent optical constants of MgF2, LaF3, and CeF3 films
,”
Opt. Mater. Express
7
(
3
),
989
1006
(
2017
).
43.
H. S.
Fairman
,
M. H.
Brill
, and
H.
Hemmendinger
, “
How the CIE 1931 color‐matching functions were derived from Wright‐Guild data
,”
Color Res. Appl.
22
(
1
),
11
23
(
1997
).
44.
V. R.
Shrestha
,
C. S.
Park
, and
S. S.
Lee
, “
Enhancement of color saturation and color gamut enabled by a dual-band color filter exhibiting an adjustable spectral response
,”
Opt. Express
22
(
3
),
3691
3704
(
2014
).
45.
R.
Alaee
,
C.
Rockstuhl
, and
I.
Fernandez-Corbaton
, “
An electromagnetic multipole expansion beyond the long-wavelength approximation
,”
Opt. Commun.
407
,
17
21
(
2018
).
46.
A. E.
Miroshnichenko
,
A. B.
Evlyukhin
,
Y. F.
Yu
,
R. M.
Bakker
,
A.
Chipouline
,
A. I.
Kuznetsov
,
B.
Luk’yanchuk
et al, “
Nonradiating anapole modes in dielectric nanoparticles
,”
Nat. Commun.
6
(
1
),
8069
(
2015
).
47.
R.
Chai
,
Q.
Liu
,
W.
Liu
,
Z.
Li
,
H.
Cheng
,
J.
Tian
, and
S.
Chen
, “
Emerging planar nanostructures involving both local and nonlocal modes
,”
ACS Photonics
10
(
7
),
2031
2044
(
2023
).
48.
A. C.
Overvig
,
S. C.
Malek
, and
N.
Yu
, “
Multifunctional nonlocal metasurfaces
,”
Phys. Rev. Lett.
125
(
1
),
017402
(
2020
).
49.
Y.
Zhou
,
S.
Guo
,
A. C.
Overvig
, and
A.
Alù
, “
Multiresonant nonlocal metasurfaces
,”
Nano Lett.
23
(
14
),
6768
6775
(
2023
).
50.
Z.
Liu
,
Y.
Xu
,
Y.
Lin
,
J.
Xiang
,
T.
Feng
,
Q.
Cao
,
J.
Li
et al, “
High-Q quasibound states in the continuum for nonlinear metasurfaces
,”
Phys. Rev. Lett.
123
(
25
),
253901
(
2019
).
51.
T.
Ellenbogen
,
K.
Seo
, and
K. B.
Crozier
, “
Chromatic plasmonic polarizers for active visible color filtering and polarimetry
,”
Nano Lett.
12
(
2
),
1026
1031
(
2012
).
52.
M.
Kerker
,
D. S.
Wang
, and
C. L.
Giles
, “
Electromagnetic scattering by magnetic spheres
,”
J. Opt. Soc. Am.
73
(
6
),
765
767
(
1983
).