Gratings with periods smaller than visible wavelengths in ambient white light will exhibit enhanced colors if the profile is designed so that resonant light interaction occurs in the visible range. Resonances have a frequency-selective influence to the grating diffraction inducing colors in transmittance and reflectance, respectively. Apart from the well-known surface-plasmon polariton excitations and cavity resonances, newly discovered resonances in TE-polarization can be exploited for colorizing wire-gratings, when simply illuminated by unpolarized white light. Colors can be laterally tuned by varying the grating profile. The capability of generating images by sub-wavelength gratings is exemplified by a metallic wire grating embedded in a plastic foil with a lateral variable modulation depth. This method for producing colored images is predestined for industrial mass production and will have ever more practical applications such as for security features.
© 2009 OSA
Structurally induced colors in nature have fascinated scientists for quite some time . A prominent example is the wing of the Morpho butterfly whose iridescent blue color primarily comes from light interference on a sophisticated double periodic structure [2,3]. Presently, there is a considerable interest by various industrial branches to present colors utilizing nanostructures rather than by pigmentation. Famous historical examples are the Roman Lycurgus cup (British Museum, London) and the stained glass windows at the Notre Dame cathedral in Paris whose colors are generated by excitation of surface plasmons on gold and silver nanoparticles, respectively. Colors arising from nanoparticles can be tuned by the size or by the shape of the particles [4,5]. Periodic structures, however, would have advantages for reproducing complete images: they could be inexpensively replicated by standard techniques, like hot embossing  or nanoimprint lithography [7,8]. Furthermore, their colors could be laterally varied very accurately down to the magnitude of a micrometer. This method even allows for images with a very high resolution to be easily displayed.
The discovery of enhanced transmission through a metallic film perforated with a subwavelength hole array  has attracted many researchers in the last decade to investigate the resonant process of transmissive periodic structures and potential applications [10–14]. Perforated silver films may exhibit the basic colors blue, green, and red in transmittance for certain periods and hole diameters, respectively [10,12]. Recently, nanostructures consisting of hole and slit arrays, respectively, surrounded by gratings have been suggested as plasmonic photon sorters [13,14]. These structures may generate different colors in transmittance for appropriate hole diameters, when they are illuminated by white light. But, they suffer from the following drawbacks: The effort in manufacturing, due to focused ion-beam milling is quite high and therefore limited to microscopic areas. Furthermore, the efficiency in light transmission is rather low. In practice the colors are probably only observable by the aid of a microscope. Therefore, it is rather unlikely that this kind of nanostructures will have any relevant impact on industrial color reproduction or to art in the near future.
2. Colored image by a sub-wavelength grating
In this paper, I will demonstrate how an image can be reproduced by a one-dimensional periodic nanostructure which is even suitable for cheap mass production. If a dielectric grating with a rectangular groove profile is evaporated with metal under a non-normal angle (non-conical case), a non-adjacent film will be deposited on the grating. For a near normal evaporation angle, it forms a wire grating with “Z” shaped wires as illustrated in Fig. 1(a). Note that the widths of the lower metallic stripes depend on the modulation depth of the grating: It becomes smaller for increasing depth. The electron micrograph in Fig. 1(b) shows the profile of a grating which was manufactured by this method. The period of this grating is d=330 nm. The dielectric lamellar structure with a groove depth of 300 nm and a width of the bars b=130 nm was replicated from a master, which was manufactured by electron beam writing. The bars are formed by UV resin lying on a thin plastic foil. The refractive index ν of these materials is approximately 1.5. This structure was then evaporated by aluminium under an angle Q=20° relative to the normal of the grating plane, forming a 60 nm thick metallic film on the plateaus, and an approximately 22 nm thick layer on one side of the dielectric lamellar structure. Finally, the grooves were filled with UV-resin and covered on the top with a plastic foil.
First, we numerically investigate the transmittance of the grating from Fig. 1(a) by means of a rigorous electromagnetic method . For the non-conical case, the diffraction of unpolarized light can be considered as a superposition of polarized light from both fundamental cases of polarization: TM-polarization, when the E-vector of the impinging light oscillates perpendicular to the wires, and TE-polarization, if the E-vector vibrates parallel to the wires. The calculated transmittance of both cases of polarization as well as the related power losses are shown in Fig. 2 for the visible wavelength range. In the numerical calculation, the data for complex refractive indices of metallic wires are used from Ref. 16. Furthermore, a non-dispersive refractive index of ν=1.5 was assumed for the surrounding plastics. In Figs. 2(a) and 2(c), the modulation depth of the grating was varied between 100 nm and 250 nm. Figures 2(b) and 2(d) illustrate the transmittance for a grating with a modulation depth of 150 nm and for various angles of incidence. Let us first discuss the light diffraction on gratings for TM polarization. The transmittance exhibits resonances in TM polarization which are shifted towards longer wavelengths for increasing modulation depths. Note that for these gratings, the basic resonance lies in the NIR region. These so-called cavity resonances emerge from interference of electromagnetic surface modes between the upper and the lower grating plane and were previously found for wire gratings with a rectangular profile . The resonator cavity is formed by the height of the modulated structure, equivalent to a Fabry-Perot interferometer. A dispersion of these resonances can be observed by varying the angle of incident light. The presently discussed gratings obviously show a lower dispersion than for slit gratings having a rectangular wire cross-section . Moreover, bear in mind that the plasma resonance of aluminium lies at around 830 nm which causes an increase of power losses in this wavelength regime.
The dispersion of the peaks in absorption of Fig. 2(b) indicate that the here discussed grating structure also support the excitation of surface-plasmon polaritons (SPs) . The resonant maxima, however, lie very close beside the Rayleigh anomalies, for which the first diffracted order becomes evanescent. Both effects contribute to spectral absorption of incident light. The excitation of SPs damps the light transmission for the resonant wavelengths. Moreover, it is worth to mention that the resonance width of SPs is quite narrow for good conducting materials like aluminium in the visible wavelength range, too narrow for a significant colorizing of an incident white spectrum. Therefore, this effect will not contribute substantially for coloring of the here discussed grating structure.
It should be pointed out that cavity resonances cannot be interpreted by excitation of SPs. Let us recall the definition of SPs: Non-radiate surface waves which propagate along an interface between a metal and a dielectric with phase velocities less than that of light are denoted as SPs . Gratings are especially suitable for studying SPs, since the grating provides reciprocal lattice vectors as additional momentum for the matching of momenta in the excitation mechanism. The excitation process demands that the momentum relation between the impinging photons and the induced SPs is fulfilled. Otherwise, a physical model introducing quasi-particles would be questionable. Ebbesen et al.  forejudged that the enhanced transmission through sub-wavelength hole arrays is caused by the excitation of SPs, since their observed transmission maxima exhibited a dispersion similar to that of SPs on gratings. Hence, they were astonished in their paper that I found dips in transmission coincident with peaks in absorption, when SPs are excited on wire gratings [19,21]. Unfortunately, their statement caused a still persisting confusion in the literature [22–24]. SPs, however, fundamentally differ from cavity resonances: They cannot be excited by photons on a grating with a symmetric profile at normal incidence, since there is no momentum transfer from the impinging photon to a potential SP travelling along the grating plane. Moreover, a study of the electromagnetic near fields  would demonstrate clearly, if there is a strong energy flow along the grating surface arising from SPs. Finally, it is worth to mention that cavity resonances are still present in contrast to SPs, if the grating material becomes infinitely conducting.
Resonances also may occur for TE polarization. Figures 2(c) and 2(d) demonstrate that wire gratings exhibit enhanced transmission of TE polarized light for wavelengths approximately equal to that of the grating period. The sharp singularity at 495 nm coincides with the Rayleigh anomaly for which the diffracted light is redistributed to the remaining propagating orders. For increasing modulation depths, however, a second maximum in transmission becomes clearly distinguishable. This phenomenon of enhanced transmission for TE polarization can be explained by an electromagnetic resonance inside the spacing between the wires. The resonator length is formed by the width of the spacing. Hence, the position of the resonance maxima moves towards longer wavelengths for increasing modulation depth, i.e., increasing spacing in the metallic film. Note that the transmission maximum in Fig. 2(d) practically does not move for varying the angle of incidence. In contrast to the well-known anomalies like Rayleigh anomalies, cavity resonances or SP excitation in TM polarization, this type of resonance obviously does not exhibit any dispersion. Furthermore, it should be pointed out that the overall light transmittance of the visible spectrum is substantially higher in TE polarization than in TM polarization for this grating structure. This can be explained as light absorption on metallic wire gratings being distinctly lower for TE polarization than for TM polarization in the resonance domain. In TE polarization, the lower strength of the electromagnetic field on the metallic surface causes lesser power losses in the wires. Accordingly, the resonance in TE polarization yields an essential contribution for colorizing of white light.
Are these resonance effects capable to colorize unpolarized white light? To answer this question, the observed colors in transmission and reflectance, respectively, were evaluated numerically. To estimate the transmitted color, the emissivity spectrum of a standard light source D65 which represents the day-light spectrum and the spectral sensitivity function of the human eye have been convolved with the calculated transmittance spectrum of the grating. A detailed explanation of the numerical procedure for the color evaluation can be found in textbooks . Subsequently, the visual aspect produced by an illuminated object can be quantified by chromaticity coordinates. Figure 3(a) shows the CIE-1931 chromaticity diagram, wherein the colors are represented by the coordinates x and y. Note that only the colors inside the triangle can be displayed with a monitor screen. Then, the color coordinates of transmittance have been evaluated for a grating with parameters from Fig. 1. The trajectory in Fig. 3(a) which forms roughly a semi-circle, represents the colors which can be generated by varying the modulation depth from 70 nm to 250 nm. All colors inside the area surrounded by this curve can be produced by color mixing from the basic colors lying on that trajectory. Unfortunately, this grating structure is far away from covering the whole color space, the colors yellow and red are clearly underrepresented. As a consequence, we choose a master image for our experiment which does not include the whole color space. The painting “Doctor Gachet” from the Dutch impressionist Vincent van Gogh  appears suitable and will be used henceforward as a master for testing the color reproduction with a grating. The color coordinates of all pixels from that master image shown in Fig. 3(b) have been mapped into the chromaticity diagram as black points in Fig. 3(a). Since most of these points lie inside the trajectory, a reproduction of this image by means of a grating seems to be promising.
Now, four colors equivalent to four modulation depths of the grating were chosen for the color mixing: 90 nm, 130 nm, 180 nm, and 240 nm. The desired color is then mixed by the ratio of intensities, i.e., pixel areas, for these four basic colors. In practice, each color pixel of the image is formed by four subpixels of the basic colors. For the color reproduction by using a grating, each color pixel from the master image has to be attributed at the best to the disposable colors of the grating. Subsequently, this results in a map of laterally varying modulation depth within the grating area. Having done the color attribution, we are able to calculate the appearance of the image formed by such a grating with laterally variable modulation depth. Figure 3(c) illustrates the calculated transmitted colors of a grating with the above mentioned modulation, and the parameters from Fig. 1. The calculated image is formed by 416×500 color pixels. A comparison with Fig. 3(b) shows a good coincidence between the reconstructed image by means of the grating and the original image. Some remaining deviations arise from the limited color space and the matching of the hue.
3. Experimental verification
Finally, we manufactured gratings with laterally variable modulation depth based on above design. A grating with a constant groove depth of 300 nm was covered with photoresist. Then, the calculated modulation pattern was written into the photoresist by means of a laser-writer. Subsequently, a grating with lateral variable groove depth is formed after removing the exposed photoresist. This structure was replicated on plastic foils and evaporated with aluminium as described above. Figure 4 shows the transmittance through such a grating replica at normal incidence. The grating having a size of 20.8 mm×25.0 mm was illuminated by an unpolarized light source, equivalent to the day-light spectrum. The photograph was taken by means of a conventional digital camera. It emerges that this image matches quite well with the calculated design from Fig. 3(c).
Which advantage do images produced with the aid of this quite involved and sophisticated method have in contrast to conventional printing techniques? There are many features which makes such an image unique. This kind of image could store in it additional information due to its polarizing effects. An image formed by a grating structure looks different, when it is observed with a polarizer. Its colors change by observation from TM- to TE-polarization. Figure 5 shows the transmitted light through the same grating replica from above, but for polarized incident white light. It has to be mentioned that the shutter speed of the camera was adapted for each image individually, since light transmission is much lower for TM polarization than for TE polarization.
Even a polarization conversion effect can occur when such a constructed image is observed between two crossed polarizers. Figure 5(c) shows the transmitted light of the grating replica, when it is placed between the polarizers and its grating wires are oriented by an angle of 45° relative to the polarizing plane.
Furthermore, the colors may vary for different observation angles. For these reasons, such an image cannot be copied by a conventional color photocopier. Moreover, the pixel size of images stored in gratings could be made smaller than for conventional photographs. When taken together, such properties are very attractive for applications as security features.
In summary, a wire grating structure was presented which generates colors from incident unpolarized white light by exploiting resonant light interaction. Its color can be tuned by varying the modulation depth of the grating profile. New found resonances in TE-polarization essentially contribute to the coloring of the transmitted light. In contrast to the well-known resonances in TM polarization, these resonances do not exhibit any dispersion. Hence, the color will not change, when the angle of incidence is varied. This is a relevant feature for coloring, when a structure is illuminated by diffuse light, e.g. day-light conditions. It was demonstrated that a grating with laterally variable modulation depth can generate an image by color mixing from four basic colors. In a first attempt, a painting from Vincent van Gogh has been reproduced by a sub-wavelength wire grating showing that image in transmission. Furthermore, it was demonstrated that the colors of the image change, when the grating is illuminated by polarized light.
In practice, there are still a great many challenges, especially when designing structures which cover the whole color space and that must provide an efficient light throughput. Nevertheless, this would be a further example for sub-wavelength grating structures which may soon leave high level equipped laboratories and enter into the mass market.
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