Ultrahigh resolution and color gamut with scattering-reducing transmissive pixels

While plasmonic designs have dominated recent trends in structural color, schemes using localized surface plasmon resonances and surface plasmon polaritons that simultaneously achieve high color vibrancy at ultrahigh resolution have been elusive because of tradeoffs between size and performance. Herein we demonstrate vibrant and size-invariant transmissive type multicolor pixels composed of hybrid TiOx-Ag core-shell nanowires based on reduced scattering at their electric dipolar Mie resonances. This principle permits the hybrid nanoresonator to achieve the widest color gamut (~74% sRGB area coverage), linear color mixing, and the highest reported single color dots-per-inch (58,000~141,000) in transmission mode. Exploiting such features, we further show that an assembly of distinct nanoresonators can constitute a multicolor pixel for use in multispectral imaging, with a size that is ~10-folds below the Nyquist limit using a typical high NA objective lens.


Supplementary Note 1. Role of Ag films in resonant transmission through hybrid nanoresonators
To illustrate the role of the top Ag layer, we present the calculated scattering efficiency and full-wave simulations for three simple scenarios: a bare opaque Ag substrate, a nanoresonator without the top Ag coating on the Ag substrate, and a hybrid nanoresonator on the Ag substrate.
Detailed structures are illustrated in the index profiles in Supplementary Fig. 2b. As displayed in Supplementary Fig. 2a, the bare Ag substrate does not scatter whereas the bare nanoresonator scatters over the wavelength range of interest. However, the hybrid nanoresonator with a 30nmthick top Ag layer produces a sharp decrease in the scattering intensity at a resonant wavelength (633 nm). To further visualize the dramatically reduced backscattering of the hybrid nanoresonator, the z-component of the electric field under planar illumination is calculated at off-resonant (550 nm) and resonant (633 nm) wavelengths and compared with that of the bare Ag substrate and bare nanoresonator. One can see that the bare Ag substrate reflects all incident waves without any scattering, and that the bare nanoresonator scatters waves, observable through wave interference patterns in the air. The hybrid nanoresonator, on the other hand, shows minimal backscattering at the resonant wavelength (633 nm), in contrast to the scattering behavior of the off-resonant wavelength (550 nm). Here, the Ag coating introduces a dipole moment opposite to that of the internal dipole moment in the TiOx, but equal in strength.
Therefore the net dipole moment is nulled, cancelling the scattering. We can visualize the strong internal dipolar response as seen in the field distribution.
The bottom Ag film plays the simple role of effectively converting the reduced backscattering from an opaque Ag substrate into narrowband transmission through the hybrid nanoresonator.
To demonstrate this, we present three scenarios with a thin Ag film on glass: a bare Ag thin 4 film, an open aperture in the thin film, and a hybrid nanoresonator on the thin film.
The Ag film thickness needs to be thin enough so that the hybrid nanoresonator can locally transmit light at resonance, but also sufficiently thick enough to ensure an optically opaque background for enhanced pixel contrast. We find that at an optimized thickness of 20 nm, transmission is sufficiently reduced for a bare Ag layer, while the hybrid nanoresonator resonantly transmits at a wavelength similar to the one observed for reduced backscattering described above (Supplementary Fig. 2c). Full wave simulations give some more insight into this picture. Because of dramatically reduced scattering, the hybrid nanoresonator effectively appears invisible to the incoming wave, and therefore behaves as a transparent aperture that gives rise to propagating wavelets in the transmitted region. In fact, this is analogous to the scenario where a plane wave hits an aperture of identical size to the hybrid nanoresonator, in the Ag film, as can be seen in Supplementary Fig. 2b. The bottom Ag layer therefore ensures light at resonance to transmit through by contributing to the formation of a dipolar resonance that makes the nanoresonator transparent. The enhanced transmission for increased thickness also suggests improved cancellation of the internal (TiOx) and outer (Ag) dipole moments in each hybrid nanoresonator. However, as the thickness is increased over 30 nm, the Ag shell becomes more optically opaque causing the absolute zeroth order transmission to drop. 6 We additionally visualized Ez to clearly depict the resonantly enhanced transmission and reduced backscattering for the hybrid nanoresonator array with varying Ag shell thickness.
With the exception of the bare nanoresonators, all hybrid nanoresonators give rise to strong contrast in field amplitudes between glass and air at resonant wavelengths (middle column).
The transmission is optimized for a 30 nm-thick top Ag shell.

Supplementary Note 2. Period dependent optical characteristics of nanoresonators
We consider excessively large periods (i.e., 1000 nm) to explore the response of single elements.
Although the transmission decreases for larger periods as expected since the nanoresonator coverage decreases ( Supplementary Fig. 5b), we emphasize an important aspect of this study in that the spectral position of the transmission peak stays fixed regardless of period and that the absolute transmission can be passively controlled (Supplementary Fig. 5c and d).
We also highlight the strong spatial confinement of the fundamental cavity mode as another important and useful feature of the hybrid nanoresonator for achieving ultrahigh DPIs.
Supplementary Fig. 5b shows the tightly confined spatial profile of the fundamental mode in all three hybrid nanoresonators. As described above in the previous comment, the Ag coating assists in tightly confining light at resonance. One can see that the spectral peak shift is not significant up to the period where the two resonators make contact (dashed lines in Supplementary Fig. 5b and c). Larger peak deviations can be observed for the blue pixels due to increased coupling between weakly confined dipolar modes, caused by the thinner Ag coatings on the sidewalls. Once the period fall below the lateral size of the nanoresonator (i.e., adjacent resonators merge), enhanced coupling can be observed that dramatically redshifts the spectral peak. At the limit where the nanoresonators have merged into a three-layer film (Ag-TiOx-Ag), the spectral peak converges to that of a planar Fabry-Perot resonator.

Supplementary Note 3. Non-plasmonic color filtering mechanism
A few key distinctions from grating-type SPP-based filters can be identified. First, the filtering mechanism is enabled when the electric field of the incoming light is s-polarized, as shown in Figure 1a and Supplementary Fig. 6a. This guarantees the absence of SPPs in the filtering mechanism because the electric fields are aligned parallel to the metallic interface. In fact, for the given structural design, the filtering function is lost or largely degraded when the white light source is p-polarized ( Supplementary Fig. 6b). Furthermore, one can further see that the excited mode profiles do not represent that of surface plasmons, as the field is peaked in the middle of the nanowire rather than at the metal-TiOx interface, as seen in Figure 1d. Moreover, since the filtering mechanism is not based on SPP interference, the periodicity does not control the color tunability.

Supplementary Note 4. Tunable gamut through the resist closure effect
In order to access the limits of sRGB colors, the spectral transmission peak position within the entire visible range (400~700 nm) must be sensitive to changes in the fabricated nanoresonator size. In our studies the fundamental resonance of the nanoresonator was used as it permits filtering at the smallest dimensions. To fully access the visible range, the fundamental mode profile must vary in size but maintain its spatial symmetry, suggesting that the TiOx core should vary in both lateral and vertical dimensions. We employed a 'resist closure effect' in the TiOx evaporation process to achieve this goal ( Supplementary Fig. 7a).
Supplementary Fig. 7b describes the nanowire width-height relation for different amounts of evaporated TiOx measured from cross-sectional images of the pixels. The total amount of evaporated TiOx was quantified in terms of its thickness without the resist closure effect, equivalently expressed as the TiOx film thickness. We fabricated three pixel sets with TiOx film thicknesses of 68, 92, and 115 nm, denoted as L (low-), M (middle-) and H (high thickness) pixel sets, respectively, to provide width-height relations for variable amounts of deposited TiOx. Polynomials were fitted onto each set of data points to model the evolution of nanowire shape from triangle to trapezoid. One can observe that at wide groove widths, the TiOx nanowire height asymptotically approaches that of the TiOx film (described by the dotted lines) as the groove width is too large for the resist closure effect to be significant. However, for narrow widths similar to or less than the deposited TiOx film thickness, the groove can close prematurely, resulting in a triangular TiOx nanowire of height shorter than that of the film.
These two effects increase the degree of nonlinearity in the dependence of nanowire height on width, especially for larger amounts of deposited TiOx, as can be observed from Supplementary   Fig. 7b. 13 Different width-height trends give rise to different width-resonance characteristics including spectral range. Supplementary Fig. 7c illustrates the calculated transmission through a nanoresonator as a function of wavelength and width for the three pixel sets, based on models derived from polynomial fits of Supplementary Fig. 7b. Each model included a bare Ag background of fixed area in order to maintain consistent transmission efficiencies among nanoresonators of different widths. For comparison, a reference pixel set with no resist closure effect is also considered. In this case, the nanowire height was set to be invariable at 92 nm, corresponding to the film thickness of the M-pixel set. For the reference model and L-pixel set, exhibiting little or no variation in nanowire height, the spectral range of resonances is found to be limited to ~200 nm. This narrow range results from the inability of the enlarged resonant mode profiles formed with longer wavelengths to be accommodated within the vertical dimension of the nanowire. However, with variation in nanowire height as shown by the M and H-pixel sets, the spectral range can be expanded to more than 300 nm.

Definition of the sRGB gamut coverage:
The sRGB gamut coverage is defined as the ratio between the area of a polygon with vertices defined by the pixel chromaticities and the full sRGB triangle area. The pixel chromaticities are derived from their absolute transmission spectra. An identical approach can also be found in Ref. 1 (Light Sci. Appl. 2017, 6, e17043). 1 If the polygon extends outside the sRGB triangle, it is truncated and only the area within the sRGB triangle is considered.

Assessment of gamuts by other groups and ours:
To build the scatter plot, we extracted the chromaticities from color diagrams of reported by other groups, and calculated their areal coverage. Some of these color diagrams were reported from multiple samples sharing the same design principle and strategy as described in Ref. 2 (Sci. Rep. 2017, 7, 40649), 2 rather than from a single sample. Therefore, to be consistent, and to assess the largest possible gamut coverage offered by each design principle, we applied the above approach of Ref. 2 to all reported gamuts as shown in Figure 3c.
For a fair comparison of our gamut coverage with those of other groups, we applied the same assessment approach as described above-involving three samples (L, M, and H pixel sets). The uniform and vibrant spectral responses over the entire visible range result in a wide-area polygon sharing large portions of the sRGB triangle borders and recording one of the largest sRGB gamut coverages (74.1% (± 0.9%)).
For practical purposes, we also added to the scatter plot the gamut coverage of a single sample-that of the M-pixel set. The M-pixel set alone is able to achieve a sRGB gamut coverage of ~69%, which is still considered as one of the largest in transmission mode.

Technical notes:
1. To achieve the maximum possible gamut area, chromaticities need to reside furthest away from the color diagram center. However, in some cases, certain chromaticities may reside closer to the center than its adjacent neighboring chromaticities. This is especially true for the purple color, which cannot be produced through a single transmission peak. For systems that cannot produce this color, including its chromaticity can decrease the gamut area. We can dispel such a possibility with our system because any missing point between two adjacent chromaticities can be created through a linear combination of the two hybrid nanoresonators. We introduce a purple pixel (denoted as the blue rhombus) in the M-pixel set as shown in Supplementary Fig.   9b, to illustrate this concept. With or without the purple pixel, the gamut coverage stays consistent. Such pixels, for instance, may produce highly saturated blue colors, but desaturated red colors, resulting in an elongated chromaticity polygon in the CIE diagram. In this case, even though the gamut coverage value itself can be large due to the saturated blue colors, such designs are still incapable of rendering vivid red colors. This can function as a significant deteriorating factor in achieving high-resolution hyperspectral/multispectral imaging at all visible wavelengths.
We emphasize that, in our study, vibrant red, green and blue primaries can be accessed, preventing the color polygon from being severely skewed or distorted. Both the size (~74% of sRGB gamut coverage) and the shape of the achieved color space satisfy the ideal criterion for accomplishing hyperspectral/multispectral imaging over all visible wavelengths.

Supplementary Note 6. Demonstration of linearity
As shown in Supplementary Fig. 10a, we designed a series of pixels labeled from 1 to 7, composed of different ratios of two distinct nanoresonators with widths (colors) of 100 (blue) and 340 nm (red). The dotted box represents the smallest repeating unit. SEM images portraying representative regions of the fabricated pixel are shown in the bottom panel.
We can define the basis functions of our system as the measured transmission spectra of the full single color pixels, represented by the solid curves in Supplementary Fig. 10b and c for the blue and red colors, respectively. The dotted curves represent different weighting coefficients multiplied to the basis function. The superposition principle can be demonstrated by comparing the measured transmission spectrum from a dual color pixel from either one of the 2 to 6 pixel combinations shown in Supplementary Fig. 10a with the linearly combined basis functions multiplied by the corresponding weighting coefficients. For example, the mixing ratio for the blue and red nanoresonators for pixel 2 is 3:1, corresponding to a weighting coefficient of 0.75 to 0.25, respectively. For pixel 2 to be a linear system, the measured transmission spectrum must be equivalent to the addition of basis functions of the blue and red pixels multiplied by 0.75 and 0.25, respectively. Supplementary Fig. 10d shows that indeed the two curves are equivalent within an experimental range of error, establishing the linearity of the nanoresonators. Measured transmission spectra of the 2, 3, 4, 5, and 6 dual-color pixels (solid line) and linearly combined spectra from the two basis functions each multiplied by the corresponding weighing coefficients (dotted lines).

Supplementary Note 9. Transmission response of color pixels with hybrid nanoresonators of different lengths
We simulated the transmission of hybrid nanoresonators as a function of nanoresonator lengths from 0.5 µm to infinity, when the nanoresonator width is 100 nm and interspacings between neighboring nanoresonators in both axis are 150 nm under plane wave and Gaussian beam illumination ( Supplementary Fig. 16). As the aspect ratio of the nanowire decreases, the response deteriorates, as contributions from the edges increase. Gap-plasmonic responses can also appear leading to loss of spectral purity or color saturation.
Although degraded compared to the case of a long aspect-ratio nanoresonator, the transmitted response at a nanoresonator length of 0.5 µm (aspect ratio 5:1) still retains the overall spectral form, with the transmission maximized at the resonant wavelength (~ 490 nm). Such unchanging spectral characteristics at different nanoresonator lengths are also observed under a high numerical aperture. This shows that the packing density in the transversal direction can be increased, but at the expense of reduced intensity and sRGB gamut coverage.