Silicon dielectric metasurfaces based on a square lattice of nanoparticles have been extensively utilized to create transmissive structural colors. Yet it is a huge challenge to obtain stable yellow color with high saturation due to the relatively large absorption of silicon in the short wavelength regime and the applied square lattice. In this study, we propose a new design strategy of independently altering the mutually perpendicular periods of a hydrogenated amorphous silicon nanodisk array-enabled metasurface to meticulously modulate the transmission spectra for the realization of high-saturation and stable cyan, magenta and yellow (CMY) color pixels. By introducing rectangular lattice, the yellow pixel can provide a narrowband transmission spectrum with a highly suppressed dip at 455 nm. The high suppression in transmission contributes to give rise to high-saturation yellow color. The attained narrowband spectrum that enables low spectral cross-talk is attributed to the overlap between magnetic dipole resonance excited by individual nanodisks and lattice resonance arising from the dipole coupling between the nanodisks. Compared with the square lattice, the proposed pixels exhibit fairly stable output color responses for a large period range. Meanwhile, the proposed CMY pixels are capable of both the relaxed angular tolerance and low dependence on the incident polarization states. It is anticipated that the proposed color pixels pave the way for extensive applications in compact color displays.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
Metasurfaces are an ultra-thin two-dimensional optical planar structure comprising a dense arrangement of nanoresonators, such as plasmonic nanostructures and high-refractive-index nanoparticles. As an alternative to the conventional three-dimensional metamaterials, metasurfaces are capable of conspicuous merits encompassing ease of fabrication, high compactness, and integration with other optical or electric devices, thus having gained a burgeoning amount of attention in high-resolution structural color generation application [1–10]. Compared to the typical approaches resorting to the thin-film interference structure that is composed of multiple layers with different thickness [11–13], metasurfaces also exhibit tremendous advantages in terms of high compactness and high resolution as they merely consist of a single layer of uniform ultra-thin nanoresonators. From the perspective of realizing highly efficient transmissive display/imaging devices, it is highly desired to concoct a metasurface enabling transmissive color with high efficiency and saturation. Here, the color saturation is known to be an attribute of visual perception, representing the degree to which color sensation differs from achromatic sensation at a constant brightness level . In the literature, the structural color generations often capitalize on the metallic nanostructures-based plasmonic metasurfaces, which can exhibit eminent output color responses in the reflective mode [1,4,8,15,16]. However, the plasmonic metasurfaces hardly create highly transmissive colors due to the inevitable conduction loss, severely restricting their potential applications in transmission-type devices. All-dielectric metasurfaces resorting to a high-refractive-index nanoparticle array are considered as an outstanding alternative approach to gain highly transmissive colors.
Recently, silicon, such as crystalline silicon (c-Si), non-hydrogenated amorphous silicon (a-Si), and hydrogenated amorphous silicon (a-Si:H), is intensively applied to construct the dielectric metasurfaces for creating structural colors by virtue of its low cost, high refractive index, and full compatibility with complementary metal-oxide-semiconductor process [17–28]. Among the reported works, the c-Si and non-hydrogenated a-Si metasurfaces principally operate in the reflective mode [17–25,28] for the reasons that c-Si faces the huge difficulties in growing on a transparent substrate, and non-hydrogenated a-Si has undesired high absorption loss in the short wavelength range. As an improved version of non-hydrogenated a-Si, a-Si:H can provide lower absorption loss in conjunction with a higher refractive index, and is therefore presumed to be the promising candidate for the transmissive color generation . Yet the transmissive subtractive colors of the reported a-Si:H metasurface, particularly yellow color, still feature unbearably low saturation.
Besides, the reported silicon metasurfaces are chiefly based on a square lattice of nanoparticles [17,18,24,26]. In those works, the primary focus is on the research of variations of optical resonance depending on the geometry of the individual nanoparticles in the metasurface, and it is well-established that the resonance wavelength can be tuned by altering the size of the nanoparticles. Period, as another common concerned parameter in the nanoparticle array, is either regarded to have little effect on the optical spectra and output colors [17,18] or not separately discussed in regard to its influence in the excited resonances [24,26]. However, it is recently proved that the above conclusion is true only when the period varies within an extremely small range [29,30], implying that the generated colors essentially feature period-sensitive properties. Unlike the electron beam lithography or nanoimprinting that enables precise control of pattern period, for those large-scale fabrications resorting to a self-assembled patterning technology, it is tough to precisely control the period during the self-assembly process. Hence, the designed color pixels are perceived to hardly provide stable output color responses with high saturation as intended after these large-scale fabrications.
In this paper, we introduce a dielectric metasurface constructed by a-Si:H nanodisks arranged in a rectangular lattice substituting the typically adopted square lattice to realize transmissive color pixels with highly enhanced saturation and large structural tolerance. The independent modulation of the mutually perpendicular periods offers an additional degree to enhance the saturation of output cyan, magenta, and yellow (CMY) colors. Especially for the yellow pixel, a pronounced transmission dip with high suppression ratio, corresponding to high-saturation yellow color, is obtained by exciting dipole coupling-mediated lattice resonances. Compared with the square lattice, the color pixels based the rectangular lattice of a-Si:H nanodisks exhibit admirably stable colors in a large period range. Lastly, the mechanism underlying the obtained transmission dips is thoroughly interpreted by investigating the field distributions at resonance.
2. Proposed color pixels exploiting an a-Si:H nanodisk array with rectangular lattice
Figure 1(a) illustrates the schematic of the proposed color pixels exploiting an a-Si:H nanodisk array-based metasurface, which is overlaid with a polymethyl methacrylate (PMMA) layer and sits upon a SiO2 substrate. The height of the PMMA layer, denoted by H, is as same as the a-Si:H nanodisk. The proposed color pixels have the capability of inducing strong Mie resonances and lattice resonances, giving birth to a near-zero resonance dip in transmission. By varying the diameter of the nanodisks, marked by D, the transmission dip corresponding to an output color can be readily tuned so that primary subtractive colors of CMY are generated. Different from the previously reported configuration exploiting a square lattice of nanodisks, the proposed pixels allow for independently varying the periods along the x- and y-axes (Px, Py), aiming at tailoring the transmission spectra with a more meticulous way. As a result, the transmission spectra with highly suppressed resonance dip along the entire visible wavelength regime can be obtained.
The proposed a-Si:H metasurface-based color pixels have been rigorously designed and assessed by performing a Finite difference time domain (FDTD) method-based simulation tool. The polarization state of the incident light is fixed at the direction along the x-axis in the following simulations. The height of the a-Si:H nanodisk and the PMMA layer is fixed at H = 80 nm. Figure 1(b) presents the refractive index of a-Si:H applied in the simulation, which is obtained from the measured data in the previously reported work . The refractive index of non-hydrogenated a-Si is also given as a Ref. . Compared to non-hydrogenated a-Si, a-Si:H is observed to exhibit superior optical properties including higher refractive index and lower optical absorption loss, especially in the short wavelength regime. As the diameter of nanodisks serves as a vital parameter that dominantly determines the resonance wavelength of transmission spectrum and the corresponding output color response, the diameters are firstly chosen to be D = 180, 140 and 80 nm to create CMY colors. To enhance the color saturation, the transmission spectra are modified to feature better optical responses with high suppression ratio by adjusting the array period along one axis under the condition that the period along the other axis is fixed.
Figure 1(c) presents the attained transmission spectra of the proposed and the non-hydrogenated a-Si nanodisks-based CMY pixels, which adopt the periods of Px/Py=150/300, 260/350 and 370/400 nm to produce high-saturation yellow, magenta, and cyan colors, respectively. For both cases, the resonance wavelengths of the transmission spectra for the CMY pixels are located at similar wavelengths. Compared to the case exploiting the non-hydrogenated a-Si nanodisks, it is apparently observed that the transmission spectra of the proposed CMY pixels are characterized by the higher suppression ratios, which are resulted from near-zero resonance dips accompanied with high transmission efficiency up to 91% at the non-resonance wavelengths. Especially for the yellow pixel, narrow bandwidth is obtained for the transmission valley and the resonance dip is highly suppressed to 14%, which is three times lower than the previously reported work with 45% . Figure 1(d) depicts the corresponding chromaticity coordinates in a standard International Commission on Illumination (CIE) 1931 chromaticity diagram, indicating the generation of the high-saturation CMY colors by virtue of the proposed metasurfaces with the specially selected unequal periods of Px and Py. Likewise, the proposed CMY pixels, especially the yellow pixel, are confirmed to exhibit improvement on the color saturation as compared to the CMY pixels based on the non-hydrogenated a-Si nanodisks.
3. Period-tolerant properties of the proposed color pixels
To demonstrate the proposed rectangular lattice structure-enabled color pixels offering advantageous period-tolerant characteristics over the square lattice structure, we thoroughly scrutinize the transmission spectra for both structures with the array period changing within the range of 150 nm. To directly visualize the color variations, the virtual colors are presented by computing the obtained transmission spectra onto the RGB sets [32,33]. Figure 2 shows the period-dependent transmission spectra and corresponding output colors of the structure with a square lattice, which has identical periods along x- and y-axes (Px=Py). For the yellow pixel (D = 80 nm), as illustrated in Fig. 2(a), the transmission spectra are observed to locate at the same resonance wavelength with increasing the period, ensuring that the perceived color remains unchangeable. However, the depth of transmission dip tends to deviate dramatically from zero with increasing the period, leading to a strong fluctuation of yellow color saturation from high to low. Moreover, the transmission valley exhibits an undesired broad bandwidth with the increase of period from 150 to 270 nm, which easily causes the undesired spectral crosstalk. The transmission spectra of the magenta pixel are apparently seen to feature two resonance dips with different strength. With increasing the period, only the resonance dip at the longer wavelength almost maintains the same location, while the resonance dip at shorter wavelength tends to rapidly redshift, resulting in the output color changing from red to magenta. For the period ranges of 200-260 nm, it is worth noting that the period-sensitive resonance dip is located in the ultraviolet region and the resonance dip in the visible wavelength regime is observed to have low dependence on period so that the output color is not severely changed. With further increasing the period, the period-sensitive dip at the shorter wavelength starts to enter into the visible wavelength range and eventually merges with the resonance dip at the longer wavelength into a single resonance dip (P = 350 nm), thus giving rise to the variation in colors. As shown in Fig. 2(c), the color variation is more severe for cyan pixel as both of the two resonance dips appear in the visible wavelength regime since the beginning. Likewise, the resonance dip at the longer wavelength is slightly affected while the resonance dip at shorter wavelength is heavily changed in terms of its depth and the location with the period varying from 250 to 400 nm. Correspondingly, the output color is observed to be completely changed even for a small variation range of 30 nm. According to the above analysis, it can be concluded that it is a huge challenge for the a-Si:H metasurface based on the square lattice of nanodisks to generate a highly suppressed transmission spectrum and corresponding high-saturation color for the yellow pixel. Moreover, the observed period-sensitive transmission spectrum and varied output color imply that the pixel is hard to generate the stable high-saturation color as designed.
To mitigate the aforementioned issues existing in the square lattice of a-Si:H nanodisks, we attempt to modulate the transmission characteristics by independently altering the mutually orthogonal periods of the a-Si:H metasurface. Figure 3 presents the transmission spectra and the corresponding output colors as a function of the period along the y-axis (Py) while the periods along the x-axis (Px) are fixed at 400, 350 and 150 nm for the CMY pixels, respectively. For better comparison, the nanodisk diameters of CMY pixels are set at D = 180, 140 and 80 nm, which retain the same as the previous case based on the square lattice. As the period Py increases from 150 to 240 nm, the yellow pixel exhibits a broad transmission spectrum at a constant resonance wavelength like the square lattice. The depth of the transmission dip, however, maintains highly suppressed level accompanied with an extremely small fluctuation of 13%, which is superior to the case based on the square lattice that has the dip depth variation of 25%. The observed small depth variation in the transmission dip indicates the pixel can render a stable output yellow color with high saturation, which is clearly confirmed by the computed virtual colors next to the spectra. With further increasing Py from 270 to 300 nm, the bandwidth of the transmission valley tends to become narrower, and more importantly, the transmission is remarkably suppressed to 14% at resonance for Py=300 nm, which effectively avoids the undesired spectral crosstalk. The physical origin underlying the abrupt conversion from the broadband spectra to narrowband one via the adjustment of the period Py will be exhaustively expounded later. Figures 3(b) and 3(c) present the dependence of the transmission spectra of magenta and cyan pixels on the period Py at a fixed Px. For both cases, two resonance modes corresponding to two transmission dips are excited, which is in accordance with the square lattice. However, unlike the square lattice of nanodisks supporting period-sensitive transmission dips, the two resonance dips of the pixels based on the rectangular lattice are located spectrally close to each other and hardly affected by the period Py. The obtained period-tolerant properties signify that the proposed color pixels have a capability of stably offering high-saturation output colors even when the period varies within a fairly large variation range. It is verified by the vivid magenta and cyan colors presented by the side of the spectra, which are characterized by consistent high saturation. In addition, it is worth noting that high transmission efficiency exceeding 80% at the non-resonance wavelength are maintained all through.
To accurately evaluate the stability of the color saturation of proposed pixels, excitation purity representing a measure of the color saturation is calculated, as plotted in Figs. 3(d)–3(f). On the CIE chromaticity diagram, a line segment can be made by connecting the white point (with chromaticity coordinate E (0.3333, 0.3333)) to the calculated chromaticity coordinate. The excitation purity is defined as the ratio of the abovementioned line segment to its extension line segment which starts from the white point to the dominant wavelength [14,34]. The calculated excitation purity of the yellow pixels based on the square lattice of nanodisks is also presented in Fig. 3(d). It is apparently seen that the yellow pixel based on the rectangular lattice of nanodisks exhibits better stability in terms of high color saturation as the period varies. Noting that the excitation purity for the magenta and cyan pixels based on the square lattice of nanodisks are not calculated for the reason that they are not able to provide the consistent magenta and cyan colors, as verified by the calculated colors in Figs. 2(b) and 2(c). The calculated excitation purity of the CMY pixels remains fairly stable when the period Py varies. It is hence quantitively proven that the proposed color pixels resorting to the rectangular lattice of nanodisks are capable of exhibiting fairly stable output color with high saturation despite large variations of Py. Another notable discovery is that the highest excitation purity of the CMY pixels is attained by setting different values to the periods along the x- and y-axes, revealing that the proposed rectangular lattice-enabled structure can break the limit of the conventional square lattice-based silicon metasurface and generate the enhanced color saturation.
The dependence of the transmission spectra and corresponding output colors of the CMY pixels on the period Px at a fixed Py have been also inspected and displayed in Figs. 4(a)–4(c). From an overall perspective, the magenta pixel provides a further enhanced color saturation and stability by varying Px, as the transmission spectra of magenta pixel feature the near-zero resonance dip all the while, as depicted in Figs. 4(b) and 4(e). For the yellow and cyan pixels, the resonances occur at the same wavelengths within a wide range of Px and identical output colors can be correspondingly perceived, as illustrated in Figs. 4(a) and 4(c). The calculated excitation purity of the yellow and cyan pixels, as plotted in Figs. 4(d) and 4(f), slightly decrease with increasing Px, which is less stable than the case of altering Py at a fixed Px. Still, the stability of the color saturation for the cyan pixel is better in comparison to the metasurface utilizing a square lattice. Through the above analysis, it is concluded that the proposed metasurface can enhance the color saturation and supply fairly stable output color that shows low dependence on the period by resorting to a rectangular lattice array.
4. Angle- and polarization-dependent characteristics
The angle-dependent properties of the proposed CMY color pixels are inspected by calculating the transmission spectra with respect to the incident angle θ, as displayed in Fig. 5(a). For the yellow and magenta pixels, the achieved high transmission efficiencies, narrow bandwidths and the near-zero resonance dips at normal incidence are observed to be almost stably preserved for the angles ranging up to 30° and 40°, respectively, indicating a relaxed angular tolerance. For the cyan pixel, the resonance dip is monitored to be located at the approximately same wavelength while the transmission efficiency at non-resonance and the bandwidth of the transmission valley are changed for the incident angle exceeding around 15°. On the basis of the transmission spectra, the colors are calculated and shown in Fig. 5(b). The good angular tolerances of the yellow and magenta pixels are verified by the generated stable vivid yellow and magenta colors under the large angle of incidence. The cyan pixel is observed to retain the cyan color only within the incident angle of 15°, as the output color tends to change from cyan to purple for the incident angle exceeding 15°.
Given that the color pixels are preferably presumed to produce a stably maintained output color regardless of the polarization of incident light for the embodiment of the color displays and imaging devices, we examine the transmission spectra of the proposed CMY pixels at the normal incidence for the incident polarization angle (φ) rotated from 0 to 90° in steps of 10°, as plotted in Fig. 6(a). The locations of the transmission dips of CMY pixels are observed to retain nearly unchanged at 617, 557 and 456 nm, respectively, suggesting that the hue of CMY colors is very stable regardless of the incident polarization states. For the magenta and cyan pixels, the depth of transmission dip and the transmission efficiency at non-resonance are almost consistent due to the relatively small lattice asymmetry, resulting in the stable high-saturation colors, as confirmed by Fig. 6(b). The depth of the transmission dip for the yellow pixel, however, is undesirably deviated from nearly zero with changing the polarization angle from 0 to 90° owing to the relatively large lattice asymmetry. As a result, the corresponding color saturation of the yellow pixel is observed to degrade.
5. Mechanism underlying the resonance dip in transmission
In an attempt to expound the mechanism underlying the wavelength-selective transmission dips, the transmission spectra of the magenta pixel (D = 140 nm) under the x-polarized incident light are thoroughly investigated as a function of period. Figure 7 depicts the transmission spectra of the pixel with different period Py. The period along the x-axis is fixed at Px=350 nm. For Py smaller than ∼350 nm, the transmission spectra are observed to exhibit a broadband characteristic featuring two partially overlapped resonance dips at similar resonance wavelengths. The two resonance dips are deemed to be attributed to electric dipole (ED) and magnetic dipole (MD) resonances excited by the individual nanodisks in the periodical array, in which the electromagnetic coupling between nanodisks can be neglected. When Py exceeds around 350 nm, ED resonance-enabled transmission dip tends to drastically redshift, accompanied by substantially narrowed bandwidth, while the MD resonance dip is located at the nearly unchanged wavelength. According to the literature, the observed narrowband resonance dip originates from an ED lattice resonance (EDLR), which is owing to the dipole coupling between nanodisks at the wavelength in the vicinity of Rayleigh anomaly (RA) [29,35]. The wavelength of RA, marked by a black dotted line in Fig. 7(a), is given by λRA=nPy , where n refers to the refractive indices of PMMA and SiO2 and sets at n = 1.47. It can be seen that the transmission spectra are predominantly determined by the ED and MD resonances supported by the individual nanodisks when the wavelength of RA is smaller than the wavelength of ED resonance. Once the wavelength of RA exceeds the ED wavelength, EDLR will introduce an additional narrow transmission spectrum, which is easily tuned via the adjustment of Py. By choosing a proper Py (Py=385 nm), the MD resonance can overlap with the EDLR, and thus a single highly suppressed transmission dip, which is desired for high-saturation color pixel, can be readily obtained, as confirmed by Fig. 7(b).
To further verify the intrinsic nature of the resonances supported in the proposed pixel, electric (E) field distributions in the x-z plane for four representative resonance cases, labeled as i, ii, iii and iv in Figs. 7(a) and 7(b), are meticulously inspected. For the resonance i at 521 nm, as illustrated in Fig. 7(c-i), highly reinforced E-field is concentrated at the center of nanodisk and oriented parallel to the incident E-field, indicating the presence of ED resonance. While for the resonances ii and iii in Figs. 7(c-ii) and 7(c-iii), a strengthened E-field circulation loop occurs inside the nanodisk, which verifies the excitation of MD resonance. With respect to the resonance iv at 609 nm, the enhanced E-field is aligned with the incident E-field inside the nanodisk and exhibit a dipolar field pattern as resembling the ED resonance in Fig. 7(c-i), but the field confined around the nanodisk is strongly enhanced as compared to the ED resonance. The enhanced E-field indicates the excitation of EDLR arising from the coupling of electric dipoles in the nanoparticle . Similarly, we can conclude that the obtained narrowband transmission spectrum of the proposed yellow pixel, as presented in Fig. 1(c), results from the overlap of the MD resonance and EDLR by analyzing the variation tendency of transmission spectra with the period and the corresponding E-field distributions at resonance.
Figure 8(a) illustrates the transmission spectra of the pixel with different Px. Similarly, the transmission dips is attributed to the ED and MD resonances for the Px smaller than ∼350 nm. However, different from the above case that ED and MD resonances are spectrally separated, ED and MD resonances are overlapped, thus resulting in a relatively narrowband transmission dip. As the Px is larger than ∼350 nm, MD lattice resonance (MDLR) in correspondence to a period-sensitive narrowband dip is excited, while the ED resonance maintains at the same wavelength. The MDLR can be effectively tuned by varying Px in a similar manner as EDLR tuned by Py [29,30,35,36]. The period-tuned narrowband characteristic of the metasurface with a large lattice period can make it accessible to potential application in high-performance sensors. Figure 8(b) shows the transmission spectra for three typical cases that satisfy the following conditions: (1) ED and MD are overlapped (Px=250 nm); (2) ED and MDLR are overlapped (Px=365 nm); (3) ED and MDLR are separated (Px=410 nm). Through the E-field distributions at resonance for the pixel with Px=410 nm, as shown in Fig. 8(c), it confirms that the narrow transmission dip vi at 604 nm and the broad transmission dip v at 555 nm are ascribed to the MDLR and ED resonance, respectively.
To conclude, we report a dielectric resonant metasurface with highly enhanced color saturation and large period-tolerant property by taking advantage of an a-Si:H nanodisk array with rectangular lattice. By separately altering the periods along the x- and y-axes, high-performance CMY color pixels are realized to feature the transmission spectra with high efficiency up to 91% at non-resonance along with the near-zero dip at resonance. The transmission spectra and output colors of the proposed CMY pixels upon the periods in both x- and y-axes are entirely investigated and compared with the color pixels based on the square lattice of a-Si:H nanodisks. It is convinced that the proposed color pixels based on the rectangular lattice offer the transmission spectra and output colors with lower dependence on the variation in one of the pitches than the square lattice does for variations in its period. The period-tolerant colors are further verified by calculating the excitation purity of the color pixels. Moreover, the proposed color pixels are anticipated to give rise to a relaxed angle tolerance, especially for yellow and magenta pixels. Meanwhile, stable output colors with consistent hue and high saturation can be provided by the magenta and cyan pixels for the incident polarization angle ranging from 0-90°. The yellow pixel can still enable the consistent hue but suffers from the degradation of color saturation with varying the incident polarization angle owing to the relatively large lattice asymmetry. By analyzing the E-field distributions in the x-z plane, the strong suppression in the transmission is predominately attributed to the ED and MD resonances excited by the individual nanodisk when the wavelength of RA is smaller than the wavelength of the nanodisk resonance. Once the RA wavelength becomes comparable to the wavelength of the nanodisk resonance, the lattice resonance arising from the dipole coupling between periodically arranged nanodisks starts to play a vital role, resulting in a sharply narrowed and period-tuned transmission spectrum. With the aid of the excitation of this lattice resonance, the transmission spectrum with high suppression ratio at 455nm, corresponding to the high-saturation yellow color pixel, is successfully achieved. The proposed high-performance color pixels tremendously facilitate their practical application in highly efficient, compact display/imaging devices.
National Natural Science Foundation of China (61604060, 61805101, 61905091); Natural Science Foundation of Shandong Province (ZR2017JL027, ZR2018BF025, ZR2019BF013); China Postdoctoral Science Foundation (2018M632605).
The authors declare no conflicts of interest.
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