All-metal structures consisting of nanoprotrusions on a bulk silver layer are theoretically investigated and shown to have narrow near-perfect absorption peaks (>95%). Within the constraints of constant nanostructure height (50 nm) and pitch (250 nm), these peaks are tunable across the visible spectrum by adjusting the width and shape of the protrusion. The peaks are caused by localized surface plasmon resonances leading to dissipation on the surface of the protrusions. As the peaks occur in the visible range, they produce subtractive colors with high saturation, in accordance with Schrödinger’s rule for maximum pigment purity.
© 2015 Optical Society of America
Solutions of colloidal nanoparticles of silver and gold are known to support localized surface plasmon resonances. These optical resonances give rise to colors that are a function of the material, geometry, and size . On solid substrates, similar structures that are fabricated by lithographic means will scatter light and appear colorful when viewed under a darkfield microscope . When metallic nanostructures are suspended above a backreflector by a dielectric post, colors have been shown to appear in plain view, i.e. under brightfield illumination . Due to the excitation of local surface plasmon resonances (LSPR) instead of surface plasmon polaritons, individual nanodisk or nano-ellipse structures that exhibit different colors can be juxtaposed with each “pixel” occupying ~250 nm by ~250 nm, thus exhibiting non-diffractive colors that are angle independent. This nanostructure design has been used as a colorant for plastic consumer products , and in high-resolution color printing , color mixing , and polarization-sensitive color printing .
In this paper, we report numerical simulation results for an alternative nanostructure design that does not rely on isolated structures on dielectrics. This all-metal nanostructure design achieves near-perfect absorption with size- and shape-tunable resonances across the visible spectrum. The resonances occur at visible wavelengths and cause absorption peaks, thus producing the subtractive colors of cyan, magenta, and yellow (CMY). The reflectance at the absorption wavelengths is nearly zero and specific wavelengths are removed from the incident white light. E. Schrödinger had shown mathematically  that pigments of high “lightness”, or saturation in modern colorimetric nomenclature, must have reflectances of either zero or unity, with a maximum of two such transitions in the visible spectrum. In an attempt to create saturated plasmonic colors as viewed in brightfield illumination, we designed surfaces that approach this criterion for appropriate nanostructure geometries: the spectra exhibit single reflectance minima that approach zero and near-perfect reflectance at wavelengths away from the minima. In addition, these minima are tunable across the entire visible spectrum by varying the size and shape of the nanostructure.
The near-perfect absorption property of the all-metal nanostructure is interesting in its own right, and many designs of perfect absorbers have been widely studied. The physical mechanism for large absorption in plasmonic and multi-layered structures relies on a combination of index matching , Fabry-Perot-like cavities [9, 10], metasurfaces [11–13], gap plasmons [14–16], and absorption in lossy dielectrics . However, these designs invariably require layers of different materials, which increases fabrication time and cost. A significant challenge remains in obtaining single-mode resonance with near-perfect absorption across the visible spectrum using only nanostructured metal surfaces, i.e. without introducing dielectric films.
Within the constraints of constant nanostructure height (50 nm), pitch (250 nm), and material (Ag), our simulations show that changing the structure geometry allows the realization of near-perfect absorption across the visible spectrum. The structures also exhibit polarization-independent local plasmon resonances, and incidence-angle tolerance of ± 25 deg. Unlike previous studies of spectral-selective continuous metal surfaces where resonances were achieved within nano-trenches of varying depths , or non-resonant broadband absorption within ultra-sharp convex grooves , here narrow (~50 nm) resonances are achieved from individual nanostructures of equal height. The constraint of constant height enables structures to be fabricated with scalable patterning and etching processes, or direct imprinting into metal substrates . In addition to color printing, an all-metal design could have potential in high-temperature thermophotovoltaic applications and thermal emitters.
2. Results and discussion
We considered an all-metallic structure with silver nano-protrusions emerging from a bulk silver layer, as shown in the schematic in Fig. 1(a). Simulations were performed using a commercial finite-difference time domain (FDTD) solver (Lumerical FDTD Solutions) in order to calculate the reflectance, absorptance and electric/magnetic field distributions of each structure. A plane wave at normal incidence (negative z direction) was used as the light source, while field monitors placed above the structure and parallel to the xz plane were used to compare the incident and reflected power. A perfectly matched boundary condition was applied to the z-min and z-max boundaries, while a periodic condition was used for the x-min, x-max, y-min and y-max boundaries. The permittivity data for silver were obtained from Palik .
To avoid complications associated with grayscale patterning that creates structure with variable heights and profiles, we imposed the condition of structures with straight sidewalls and constant heights. These structures are amenable for fabrication by standard binary lithography processes. The nano-protrusions have a fixed height of 50 nm and are arranged in a square lattice of pitch 250 nm. Three different geometric designs were investigated, namely a circle, a square and a cross with equal-length arms. Here, the widths of the cross arms were fixed at 30 nm. For each shape, the lateral dimension (circular radius, square length and total cross length) was varied between 50 to 240 nm. Unlike grating structures, these geometries produce a polarization independent response at normal incidence, as the square and cross have 4-fold rotational symmetry, while the circle has an infinite rotational symmetry. Therefore, they respond identically to normal-incidence Transverse Electric (TE) and Transverse Magnetic (TM) polarizations of light.
2.1 Resonance mode and near-perfect absorptance
Schematics of the local surface plasmon resonance mode supported by these geometries are as shown in Fig. 1(b), an xz section through the protrusion. We expect the mode to create null net electric and magnetic fields at the metal surface to act as a perfect electric and magnetic mirror for enhanced absorption of light . The mode is characterized by its diametrically symmetrical charge distribution where the top horizontal surface and upper side wall of the protrusion has net positive charges on one half (x<0) and net negative charges on the other half (x>0). The distribution of charges is reversed at the base of the protrusion, such that the negative charges are on the x<0 half and the positive charges are on the x>0 half. Therefore, at the start of the resonance cycle, energy is stored in the capacitive form, i.e. a strong electric field parallel to the top surface of the protrusion in the + x direction, and another two strong electric field regions at the bottom corners of the protrusions. These fields are likened to that arising from two antiparallel dipoles that result in a dark mode. A quarter cycle later, these time varying electric fields generate magnetic fields above the top surface of the protrusion and adjacent to the side wall of the protrusion, with energy transferred into the inductive form, i.e. kinetic energy of the free electrons and magnetic fields . The magnetic fields point in the + y and -y directions respectively and have nearly equal strength, such that the net magnetic field averaged over the metal surface is almost zero, reminiscent of a magnetic mirror . A half-cycle later, the charge distributions and electric field distributions change signs, so the magnetic fields point in the opposite direction but attain the same magnitude, therefore they cancel each other out again. The all-metallic composition provides a conductive path for charges to flow easily from the protrusion into the substrate and vice versa.
The reflectance plots in the visible range (~400 nm to ~750 nm) for the three different geometries are summarized in Fig. 2(a). A common feature for all the individual spectra is the presence of a large prominent dip. At a sub-wavelength pitch of 250 nm, these structures are unable to support propagating plasmon modes in the visible spectrum. Instead, a localized plasmon resonance mode is responsible for the spectral dip. As a consequence of the excitation of local resonances, changes in the lateral dimensions (L) would result in a shift in the spectrum. As expected, we observe a red-shift in the reflectance minimum with increasing L. However, the shifts are insufficient to span the entire visible range for any single shape. For instance, the circles show resonances that shift only between 410 to 620 nm and correspond to yellow, orange, pink, violet and cyan colors, while the crosses have resonances spanning the longer wavelength range, between 465 to 710 nm, corresponding to the same colors with higher saturation. Thus, the reflectance minimum is tunable by simply controlling the lateral dimensions and geometries of the protrusion.
The field, charge and power distribution at the resonant mode responsible for this dip in reflectance is shown in Fig. 3. As described previously, the electric field and magnetic fields in the structure at the resonant frequency are driven by the incoming light and oscillate in time. The left column shows that the electric field is concentrated around the top and bottom circumference of the protrusion, while in the middle column, the magnetic field is concentrated directly above the top surface and adjacent to the side walls of the protrusion. Note that the magnetic field has a larger spatial distribution than the electric field, as the magnetic field does not decay as rapidly with the distance from the surface of the protrusion. Furthermore the magnetic field distribution has an imperfect cancellation of the magnetic fields, i.e. lower magnitude at the top of the protrusion in the case of imperfect absorption (bottom row). In the right column, we can see that electromagnetic power is mostly absorbed at the circumference of the top surface of the protrusions and partially at the circumference of the base. This power absorption by the structure causes a dip in the reflection spectrum, as no power is reflected back at the resonance wavelength. This fundamental mode exists for the circular, square and cross-shaped protrusions.
The effects of additional scattering losses in real metals, and a protective coating are investigated next. Loss was quantified by adding a damping factor before the scattering frequency in the Drude-Lorentz model for permittivity, We simulated a worst case scenario corresponding to an extreme case of damping with . Fitting values for Ag were. Figure 4(a) shows a plot of the absorptances for three representative geometries (90 nm diameter circle, 110 nm wide square and 210 nm long cross) reproduced from Fig. 2(b) with the corresponding plots for higher metal losses. Redshifting, peak broadening, and lowering of the absortance were most pronounced for the cross geometry.
We simulated the effect of a 2 nm protective coating of Al2O3, which has been shown to be effective in preventing tarnishing of Ag nanostructures . As expected, the addition of a dielectric with a higher refractive index than air on the surface of the structure resulted in a redshift in the resonances as shown in Fig. 4(b). The effect of higher metallic losses and a protective coating on the color are shown in the panel in Fig. 4(c), illustrating that these effects can enhance the color saturation.
2.2 Subtractive colors
The reflectance and absorption spectra of the all-metal structures are reminiscent of those of pigments , which produce subtractive colors by absorbing light of certain wavelengths and reflecting the rest. Thus, the structures can also be expected to produce a wide range of colors by color mixing strategies . In order to determine the colors produced, the Commission Internationale de l'Eclairage (CIE) 1931 xyz chromaticity coordinates were calculated from the reflectance spectra R using the equations and , where S is the spectral power distribution of the illuminating light source, and is the color matching functions. Similar equations to (1) and (2) are used to find y and z. X, Y and Z are called the tristimulus values and can also be transformed to the standard red green blue (sRGB) color space, which is the standard for color displays.
Figure 2(c) is a plot of the chromaticity for the circular, square and cross-shaped structures, with the sRGB color approximations. The chromaticity coordinates of monochromatic colors form a horseshoe-shaped locus which bounds all other mixed colors. This region of points represents the set of colors that can be observed by the human eye, otherwise known as the gamut. Points lying on the locus are fully saturated as they are monochromatic, while points lying close to (⅓, ⅓) are white-like and faint. The chromaticity locus of structures for each shape marks out a large angular displacement of almost 2π around (⅓, ⅓) and thus the generated colors span a large range of hues.
The chromaticity coordinates of the square protrusions are closer to the boundaries of the CIE color space compared to the coordinates of the circular and cross-shaped protrusions. Therefore, the colors produced by the square protrusions are the most saturated of the three geometries studied. Schrödinger showed mathematically that the most saturated pigments are obtained when two criteria are fulfilled in its reflectance spectrum: (1) the reflectance takes only two values, 0 or 1, and (2) one or two step changes occur in the reflectance . Physical systems are unable to exhibit the binary spectral response of the first condition. However, a rule of thumb would be to achieve as large a modulation in the reflectance spectra as possible. In our context, it suggests that reflectances should be as close to 0 as possible at resonance. Criterion 2 suggests that we would do better with structures that support a single resonant mode within the visible spectrum.
Of the three geometries studied, the square is the most promising in terms of color saturation, as the reflectance spectra for the square protrusions with widths between 90 nm and 230 nm almost satisfy the Schrodinger criteria. On the other hand, for the circular protrusions, their reflectance minima do not reach 0, except when the width is between 70 nm and 90 nm, so the reflectance spectra fail to satisfy criterion 1 and the colors are expected to be faint. The reflectance spectra of the cross-shaped protrusions do not satisfy criterion 2, as another dip appears at short wavelengths when the arm length exceeds 150 nm, which means that four transitions occur in the reflectance.
To investigate if the resonance modes in the nanoprotrusions have an SPP component, we performed simulations for the circular protrusion over a range of periods. Figure 5(a) shows the dependence of the reflectance on the period of the structure, for circular protrusions with a width of 150 nm and a height of 50 nm. When the period is small (between 250 nm and 390 nm), there are two reflection minima bands, respectively centered at wavelengths of 300 nm and 450 nm. The first band is due to absorption in silver, while the second band corresponds to the local surface plasmon resonance mode. However, another reflection minimum band centered at a wavelength of 400 nm starts to develop as the period increases above 390 nm, and is representative of a SPP mode, which satisfies the condition , for the first order diffraction of the 2D array, i.e. m = 1 and n = 0, and and are the relative permittivities of the metal and vacuum respectively. On the other hand, the LSPR mode is independent of pitch, as indicated by the dashed vertical line. At a pitch of ~430nm, the SPP mode causes an avoided crossing. At larger pitches, the SPP mode is seen as a sharp feature that is distinct from the LSPR mode.
Figure 5(b) shows the change of reflectance with source angle for a period of 250 nm and the same protrusion geometry as in Fig. 5(a). In addition, we looked at angle-dependent reflectance for the square and cross geometries in Figs. 5(c) and 5(d). As the structures with small periods do not exhibit SPP modes, their reflectance spectra are expected to have low angular dependence. Figure 5(b) confirms this prediction, as the two reflection minima at wavelengths of 300 nm and 450 nm for planar incidence retain the same central wavelength and width for oblique incidence of up to 25 degrees for all geometries.
One drawback of the all-metal protrusion structures is that the colors produced exclude the majority of the green hues. Saturated green subtractive colors are difficult to manufacture, as the blue and red wavelengths should be eliminated via two absorption peaks. For the geometries, sizes and period studied, only one large absorption peak exists in the visible range, so saturated green hues were not created. Furthermore, given the design constraint of a constant height and vertical sidewalls, it remains to be explored if pseudo-random geometries could produce black color. Nonetheless, randomly roughened and vertically tapered metal surfaces have proven effective in achieving black color [19,26]. In future, arrays of mixed protrusions will be investigated to explore the possibility of generating two absorption peaks and creating green subtractive color.
In conclusion, we have presented an all-metal structure of nanoprotrusions on a bulk substrate that exhibit large absorption in the visible spectrum, which corresponds to a saturated subtractive color. These structures could simplify the fabrication of plasmonic color surfaces through electroplating or direct nanoimprinting into bulk metal. Three geometries of protrusion – circle, square and cross – and eleven widths – 50nm to 240 nm – were simulated and compared. Using circles and squares for the short wavelengths, and crosses for the longer wavelengths allows us to achieve near perfect absorptance peaks across the visible spectrum. A wide spectrum of subtractive colors are produced in the structures, with some variations in saturation and hue with the geometry chosen.
The cross-shaped protrusions have the additional property that the reflectance minima are very low at less than 0.05 and therefore could be used as near-perfect absorbers. The circular and square protrusions also have very low reflectance minima for small protrusion widths, so by selecting the right geometry and size, it should be possible to produce absorption peaks that span the entire visible range. We expect that similar results can be obtained in other metals such as aluminum and gold, though at different dimensions.
We would like to acknowledge funding support from the Institute of Materials Research and Engineering, the Agency for Science, Technology and Research (A*STAR), Singapore University of Technology and Design and the National Research Foundation.
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