Plasmonic Colour Printing by Light Trapping in Two-Metal Nanostructures

Structural colour generation by nanoscale plasmonic structures is of major interest for non-bleaching colour printing, anti-counterfeit measures and decoration applications. We explore the physics of a two-metal plasmonic nanostructure consisting of metallic nanodiscs separated from a metallic back-reflector by a uniform thin polymer film and investigate the potential for vibrant structural colour in reflection. We demonstrate that light trapping within the nanostructures is the primary mechanism for colour generation. The use of planar back-reflector and polymer layers allows for less complex fabrication requirements and robust structures, but most significantly allows for the easy incorporation of two different metals for the back-reflector and the nanodiscs. The simplicity of the structure is also suitable for scalability. Combinations of gold, silver, aluminium and copper are considered, with wide colour gamuts observed as a function of the polymer layer thickness. The structural colours are also shown to be insensitive to the viewing angle. Structures of copper nanodiscs with an aluminium back-reflector produce the widest colour gamut.

represents the mix of colour cones, while z(λ) represents the blue colour cone. In the visible, i.e. in the 400-700 nm region, all the curves have non-zero values. For each spectrum the corresponding CIE XYZ values can be obtained with the following formulas: = 100 ∫ ( ) ( ) ( ) The CIE XYZ values were linear transformed to RGB, in the form of fractional integers, ranging from The standard decoding gamma for sRGB is γ = 2.
2. An exponent of 2.4 is used, to compensate for the linear threshold region below 0.0031308. This transform returns fractional (0-1) sRGB values, which are multiplied by 255 and rounded to generate a set of three 8-bit numbers ranging from 0-255. sRGB values combine luminance and chromaticity of a colour. In colour vision, the luminance indicates how much luminous power will be detected by an observer of an object or surface from a particular angle of observation. The larger the luminance value of the colour, the higher the visibility of that colour under the observation conditions. Chromaticity is an objective quantitative measure of the quality of colour, and is independent of the luminance value of the object or surface being observed.
Chromaticity values represent all discernible different colours that can be perceived by humans using the three colour cones in the retina. High sRGB values indicate higher luminance values. For example, a sRGB of 255:4:4 indicates a predominantly red colour of maximum luminance, and so would be visible as a bright, pure red colour to the human eye. A value of 63:1:1 also represents a red colour of the same chromaticity (as the relative weighting is the same) but at a quarter of the luminance, and so would be visible as a darker red colour.
For the CIE xyY plots, the XYZ primaries can also be mapped with the following functions [4]: The Y value in the xyY is the Y primary in the CIE standard observer functions, and denoted luminance.
3. Calculated colour generation (sRGB) for different polymer thicknesses    reflectance in the spectral region between 400 and 550 nm is necessary for the generation of red and orange colours. In our nanostructures, the interaction between the plasmonic modes of the nanodisc arrays and the back reflector modes is the main mechanism responsible for the colour generation. At 450 nm and at 545 nm the light is trapped within the nanostructure, mostly at the nanodics air/ air polymer interface. Moreover, the electric fields exhibit multipolar character. Therefore, the reflectance is extremely low. As discussed in the main manuscript, the electric fields distributions around the nanoparticle exhibit dipolar character at 585 nm. The dipolar character of the localized nanodisc modes increases the reflectance in the red spectral region, and overlaps with the maximum of z(λ). At 625 nm, the light is completely trapped within the nanostructure, mostly in the polymer layer. However, the spectrally narrow feature at around 625 nm plays only a marginal role in the colour generation, due to the rather small spectral overlap with the redder tail of z(λ). The high reflectance above 700 nm does not spectrally overlap with the CIE XYZ 2° standard observer functions, and as expected is not crucial for the colour generation. For a better visualisation, the field distributions are displayed on the same scale. For the generation of green colours, a high reflectance between 500 and 550 nm is desirable. Additionally low reflectance in the spectral region between 400 and 500 nm and above 550 nm is necessary. At 450 nm and at 545 nm the back reflector modes are the main mechanism responsible for the relative high reflectivity. At 450 nm , the gold d-absorption reduces the reflectivity as well, which in this case is beneficial for the generation of green colours. The spectrally narrow feature at 585 nm overlaps with the maximum of z(λ). The extremely low reflectivity compensates the maximum of z(λ). Consequently, narrow feature at 585 nm is crucial for the generation of green colours. Green colour can be only generated with hybrid nanostructures with certain polymer thicknesses (100 nm and 280 nm), since this feature arises from both, the spectral and spatial overlap of the localized plasmonic modes of the nanodiscs and the local minima of the back reflector modes. In contrast, at 625 nm the reflectance seems dominated by the back-reflector mode, which at this wavelength exhibits a local maximum. Therefore, the reflectance is substantially higher at 625 nm, since the electric and magnetic fields couple now to the far field. Additionally, the electric and magnetic field amplitudes at 625 nm are smaller than at 585 nm, therefore the light trapping within the nanostructure is weaker, as discussed in the main manuscript. Although, some of the light is trapped within the nanostructure at 545 nm, 585 nm and 625nm, for thin films 60-80 nm, the reflectance seems dominated by the back-reflector modes. The electric and magnetic fields couple now to the far field, increasing the reflectance. Additionally, the electric fields distributions around the nanoparticle exhibit dipolar character at 585 nm. Fortunately, the plasmonic coupling between the nanodiscs and the Ag film distorts the dipolar character, and hence it weakens the coupling to the far field. For substantially thicker polymers (220 nm or 260 nm) the light trapping is more efficient especially at 545 nm. This minimum spectrally narrows (down to 35 nm) for nanodiscs heights between 80 nm and-100 nm and the reflectance drops down below 2%. Surprisingly, an increase of the disc height by 200 nm leads to similar spectral features as for nanodisc heights between 40 nm and 120 nm. However, the investigation of this apparent periodicity is beyond the scope of this paper.

7.
Calculated reflectance spectra of nanodisc arrays for discs with 125 nm, 150 nm and 150 nm diameter  For the generation of blue colours, a high reflectance between 400 and 500 nm is desirable.
Additionally low reflectance in the spectral region above 500 nm is necessary, as early discussed. The experimental spectra show these characteristics, while the calculated show higher reflectance and more defined features. The high reflectance in the green and red region in the calculated spectra results in a colour closer to the center of the CIE plot ( Figure S10), while the experimental colour is closer to the blue primary. Although we attribute the differences mainly to variation in the thickness and surface roughness of the polymer layer, as well as to shape and size variation of the fabricated nanodiscs across the arrays. Additionally, the area underneath the discs could have been overexposed due to the close spacing of the nanoparticles. As a consequence, the nanodiscs could be embedded in the polymer. The comparison of the simulated spectra for different embedding depth of the nanodiscs with the experimental data ( Figure S11) suggest that this hypothesis is right. The calculated spectra for nanodiscs embedded 20 nm in the polymer film match the experimental spectra in the blue region, while the calculated spectra for nanodiscs embedded only 5 nm in the polymer are closer to the experimental values in the red spectral region. Consequently, one could conclude that the overexposure of the polymer area underneath the disc is not homogeneous and hence there is a gradient the polymer layer height underneath the nanodiscs.

Figure S13
Calculated reflectance spectra of nanodisc arrays for discs with diameters of 175 nm and 100 nm in height. The nanodiscs could be embedded in the polymer to some extent, due to overexposure.
Low reflectance in the spectral region between 400 and 550 nm is necessary for the generation of red and orange colours. For the thicker sample, the well defined features above 625 nm observed in the calculated spectra play only marginal roles in the colour generation, due to the rather small spectral overlap with the redder tail of z(λ). Especially the spectrally narrow feature at around 680 nm does not spectrally overlap substantially with the red CIE XYZ 2° standard observer functions and as expected is not crucial for the colour generation. Therefore, the calculated colours are close to the experimental observations.
Figure S12 (a) shows the dependence of the observed features at around 680 nm to variations of 5 nm in the thickness of the polymer layer as well as the spectra obtained from averaging the reflectance spectra for the three thicknesses. The nanodisc diameter is fixed to 175 nm. Figure S12 (b) shows the dependence of the observed features at around 680 nm to variations in the nanodiscs diameter and the spectra obtained from averaging the reflectance spectra for the six diameters. The polymer layer thickness is fixed to 195 nm.

Figure S14
(a) Polymer thickness dependence and (b) Au Nanodisc diameter dependence: Calculated reflectance spectra of nanodisc arrays for discs with diameters ranging from 160 nm to 190 nm.
The spectrally narrow features above 625 nm are highly dependent on the disk diameter, in contrast to the spectrally narrow feature at 585 nm ( Figure S9). As discussed previously, the spectrally narrow features arise from the interaction of localized plasmonic modes of the nanodiscs with the thin film modes, i.e., the spectral overlap with the minima in reflectance of the back-reflector. For thinner polymer films, i.e., 100 nm, the local minima and the local maxima in reflectance of the back-reflector are spectrally broader (cf. Figure S3) than the local minima and the local maxima observed for thicker polymer films, i.e, 180-200 nm (cf. Figure S4). Consequently, the spectral position of the spectrally narrow features above 625 nm observed for thicker films is strongly sensitive to changes in the spectral positions of the localized nanosdisc resonances, i.e., the red shifts of the resonances as the disc diameter is increased.
9. Calculated colour generation (sRGB) by a Cu nanodisc -Al back-reflector hybrid nanostructure as a function of polymer thickness.