The hybrid concept for realization of an ultra-thin plasmonic metamaterial antire fl ection coating and plasmonic rainbow

We report on the design, simulation, fabrication, and characterization of a novel two layer anti-reflective coating (ARC) based on a plasmonic metamaterial and a dielectric. Promoted by the strong material dispersion of the plasmonic metamaterial, our novel concept (called hybrid ARC) combines two possible arrangements for layers in an anti-reflection coating into a single structure; albeit at two different wavelengths. This, however, causes a broadband reduction of reflection that is less sensitive against oblique incidence when compared to traditional antireflective coatings. Furthermore, we show that the current metamaterial on a metal reflector can be used for the visualization of different coloration such as plasmonic rainbow despite its sub-wavelength thickness.

The nite reectivity from the interface of two disparate media with dispersive material properties is an obstacle that oen denies the design of efficient photonic and opto-electronic devices. 1 Traditionally, the problem can be diminished while incorporating anti-reection coatings (ARCs) 2 that are based on graded index layers, 3-6 gradient-index coatings, 7,8 or nanostructured textures. 9,10 However, these approaches usually suffer from one or multiple severe drawbacks such as a narrow spectral domain of operation, sensitivity against oblique incidence, complexity, or a lack of applicability to extremely thin lms. Here, we mitigate these problems by introducing and verifying a new class of ultrathin two-layer anti-reection coating with a metamaterial as the top and a dielectric material as the second layer; demonstrating therewith an entire novel concept named as "hybrid ARC". The key feature of this hybrid ARC is using (quasi) two arrangements for the dielectric layers in one design where the refractive indices ascend or descend in consecutive layers with a descending order, albeit at a different wavelength. This is only possible by exploiting the strongly dispersive character of metamaterials. High ARC performance on silicon substrate is shown to be possible by plasmonic nanocomposites with a strong dispersion in the permittivity around its plasmonic resonance. Below the plasmon resonance wavelength the layer acts as a traditional graded-index coating while it performs as a Fabry-Perot interferometer at longer wavelengths. This provides the opportunity to considerably lower the reection across a broad range of wavelengths with only a marginal angular sensitivity. Moreover, the hybrid concept can be applied on metals where the tunability of the plasmonic nanocomposite enables realization of plasmonic rainbow colors by a subwavelength coating.
The consideration of anti-reective coatings (ARCs) as being very important is justied from their integration in nearly all photonic devices. [11][12][13][14][15] Optical elements where they nd use range from ordinary lenses over any laser system up to advanced photonic devices for disruptive technologies. Traditional ARCs made from an individual non-absorbing layer can usually be optimized to operate perfectly at an isolated design wavelength. Then, the refractive index (RI) of the ARC (being directly linked to the square root of the permittivity for non-magnetic, homogenous, isotropic, local materials as considered here) has to be the geometric mean of the RIs of the materials on both sides of the respective interface from which the spurious reection is encountered, i.e. herein called a substrate and the incident medium. By no means of restriction, we consider in the following the RI of the substrate to be larger than the RI of the incident material (coating). The thickness of the ARC ought to be a quarter of the desired wavelength. However, and quite detrimental, the vanishing reectivity only occurs at normal incidence and only at the isolated design wavelength. Nevertheless, wider-band ARCs are possible by relying on innovative designs, 16,17 plasmonic and metamaterial layers 18,19 or multilayer coatings. 20 For instance, two-layer ARCs, 21 i.e. 'V' coat, could result in a wide-band ARC by a proper selection of lms. In such a case the RI of the top layer should be smaller than the second layer and each layer thickness shall equal a quarter of the desired wavelength. The rst suggestion for such a traditional arrangement of the layer materials is linked to the name of Lord Rayleigh; hence hereaer we call it the Rayleigh conguration. In fact, the order of the ARC lm is very crucial in such a technique and once the order of layers is inversed (i.e. low and high RI placing as the spacer and the top layer, respectively), the reection of the device increases and could even turn the substrate (in certain circumstances) into a mirror (Braggmirror). 22,23 We wish to call such an arrangement in the following the reverse-Rayleigh conguration. Note that the in the reverse-Rayleigh conguration at least two reection dips surround the central reection peak. 24 Recently, a new class of ARCs has been introduced, specically for metallic substrates where the coating acts as an absorbing element to reduce the light reection. In such a conguration, the reection drops not only due to the interference 25 but also by exploiting the absorbing character of the coating combined with losses in the metallic substrate. [26][27][28][29][30][31][32][33][34] The strong optical attenuation through the highly absorbing coating or the strong resonant behavior in layers 29 gives rise to low reection from the metal substrate, although the thickness of the coating is much less than the wavelength of light. This concept works well on gold lms which could sustain a plasmonic response under certain conditions as well as a broad intrinsic absorption (i.e. minimum reection) in the visible range because of interband transition. The question arises whether this concept is equally applicable to semi-conductors as the substrate material. It is known that semi-conductors like silicon exhibit strongly dispersive material properties that complicate the design of efficient ARCs. Therefore, it remains a challenge to perceive an ARC that operates over the entire range of the visible and near-IR for semi-conductors. 35 Here, we introduce an ultra-thin bi-layer coating as an ARC. The key-feature of our coatings is the use of a material with a high RI for the layer that faces the incident medium, i.e. the top layer. Moreover, the thicknesses of all involved layers are considerably thinner than a half or even a quarter of a wavelength. By a systematic analysis we show that an excellent anti-reection performance is possible. While demonstrating the concept in the rst stage with a pair of dielectric materials possessing only a weak dispersion, i.e. TiO 2 /SiO 2 , we exploit the strong dispersive nature of metamaterials in the second stage to demonstrate the hybrid-concept and eventually achieve a broadband ARC with only a marginal angular sensitivity.
The metamaterial we will use consists of an ultrathin plasmonic nanocomposite made from ultra-ne metallic nanoparticles (diameter D < 5 nm (ref. 26)). Fig. 1a and b show the cross-sectional and top view TEM images of the sample. It is apparent that the particles' diameters are around 5 nanometers and they are randomly distributed in the matrix. It possesses a dispersive permittivity with a Lorentzian prole centered at the particle plasmon resonance. The homogenous isotropic metamaterial is characterized by a strongly dispersive RI that takes high values at long wavelengths and small values at short wavelengths, taken with respect to the particle plasmon resonance. Such a material can therefore benecially be used to perceive an ARC that combines the reverse-Rayleigh and the Rayleigh ARC in the same structure, albeit at different wavelengths. Therefore, we call this structure a "Hybrid-Antireection" structure. We postulate that the broadband anti-reection performance of the presented metamaterial is facilitated by the anomalous material dispersion around the plasmon resonance. The dispersive refractive index of the composite varies in a way that at wavelengths longer than the resonance the coating serves in a reverse-Rayleigh conguration but at smaller wavelengths the composite's RI is smaller than the second layer and hence the Rayleigh condition is satised. In other words, by overlapping the reection dip of the traditional ARC with that of a Fabry-Perot interferometer, the corresponding reection dip of our two layer coating is very broad despite its low thickness. This unique dispersive RI of the presented metamaterial leads to the opportunity to observe a hybrid wide-band ARC encompassing the Rayleigh/reverse-Rayleigh congurations. Full wave electro-magnetic simulations of the metamaterial verify that it acts as a homogenous medium rather than an ensemble of plasmonic absorbers. This entails their description in terms of effective material properties which paves the way to consider such a structure in the design of many high efficient ARC devices.
To start with, we consider a bi-layer ARC where the top layer facing air as the incident medium is an ultrathin lm of a high RI material. With the nal device in mind, the thickness is chosen to be 20 nm. This adheres to the desire to have an ultrathin and compact ARC. We leave here the exact value of the RI as a free parameter. The second layer shall be made from a low RI material. Silicon dioxide is selected as the low RI lm since it is a common material in silicon industry and it can be either deposited or grown on the silicon substrate with good adhesion. We leave as a degree of freedom the thickness of this layer. In such a scheme, the substrate, i.e. silicon wafer, has the highest RI in the stack.
To identify on analytical grounds the conditions where the ARC operates optimal, a thin-lm transfer matrix technique is applied to calculate the reection. Results are shown in Fig. 1c. There, the reectivity at a design wavelength (in this case at 600 nm) is calculated depending on the RI of the top layer and the thickness of the SiO 2 layer. It is apparent that the reection is suppressed for a rather high value of RI of the ultrathin top layer and a thin SiO 2 layer. To suppress reectivity at longer design wavelengths, the RI should be approximately the same but the thickness of the SiO 2 layer should be slightly increased. However, it can always be assured that the reection can be reduced to a negligible quantity, even though the coating is subwavelength in its thickness, i.e. far below the quarter of the design wavelength.
According to the calculated reection contour (Fig. 1c), a high RI material which suitably matches the required RI is TiO 2 (its average RI in the visible region is 2.4 (ref. 36)). The oxide lms were prepared by sputtering of a dielectric target (namely SiO 2 or TiO 2 ) and the thicknesses were measured with a pro-lometer. Based on the simulation, 20 nm TiO 2 layer and a 50 nm SiO 2 coated on silicon could realize low reection at 570 nm. Indeed, the fabricated stacks with the mentioned geometry and thicknesses provide a broad reection reduction with a reection minimum at 570 nm wavelength for silicon as shown in Fig. 1d which agrees well with simulation. By resorting to a traditional order for the layers, i.e. an ordinary Rayleigh conguration where the materials are arranged in the ascending order of their RI, it was observed that the reection minimum occurs at 410 nm [ Fig. 1d (inset)], in agreement with Rayleigh's postulation but it does not vanish totally since its thickness is far below the quarter-wavelength which is required for anti-reectivity.
It can be seen that the ARC in the Rayleigh conguration is spectrally narrower than the reverse-Rayleigh conguration and its remaining reection almost doubled. However, since those results might be affected by experimental uncertainties, we would like to stress the major advantage of the reverse-Rayleigh concept that can be better appreciated while comparing the angular dependency of both congurations (i.e. Rayleigh and reverse-Rayleigh). The average reection at higher incidence angles for the case of the Rayleigh conguration is almost twice the intensity of a similar lm but in reverse order (Fig. 2a). In fact, the reection drop considerably red-shis upon changing the geometry from traditional to the reverse-one which proves that the performance of ultra-thin reverse-Rayleigh ARC is more promising for an operation in the visible spectrum.
The more pronounced reection drop and red-shi of the curve in reverse-Rayleigh compared to the Rayleigh conguration can be well explained by interference. 37 In principle, destructive interference of the direct reected light and the light reected at consecutive interfaces requires a phase accumulation of p by the wave traversing the layers back and forth. This easily explains the dogma on using quarter wavelength layers with a small RI as the rst (top) layer. However, in the case of a top-lm with high RI (reverse-Rayleigh), the light which travels through the low RI layer and the reected wave have a p phase difference 38 which ends up with a destructive interference. In other words, in the case of a top-lm with high RI, p phase accumulation comes for free as the impinging light reected at the various interfaces experiences p-0-p phase shis. The phase difference of the incoming and reected light in the cavity is 39   Nevertheless, neither ARC based on reverse-Rayleigh concept nor Rayleigh provide the desired properties of a wide-band ARC (i.e. whole solar spectrum range) owing to high reection that appears at short and long wavelengths of the visible for both congurations. Additionally, for shiing the reection dip to NIR, increasing the layer thickness and/or using a high RI material is needed. Note that there are only a limited number of materials with high refractive index which could fulll the required RI contrast for the reverse-Rayleigh conguration.
In our opinion, and from technological point of view, the eld is revolutionized if a coating is used that would enable both Rayleigh and reverse-Rayleigh congurations simultaneously, at different wavelengths though. Suppressing the reections at multiple wavelengths would automatically enable a broadband ARC based on ultrathin lms. However, this requires the use of strongly dispersive materials in the design of the ARC. Ideally, the geometrical dispersion that degrades the anti-reection action beyond the target wavelength in an ARC design where non-dispersive materials are used has to be compensated by a suitable material dispersion. This perfect balancing, however, requires an anomalous dispersion in the material properties, which is always accompanied by absorption. Nonetheless, motivated by the recent work on ARC coatings on metals using weakly absorbing materials, 29 we may conclude that if the ARC coating is sufficiently thin and contains ultrane plasmonic nanoparticles, the absorption might not be detrimental. To evaluate the potential of this idea, we sought out a way to design a new concept for a coating that considers articial materials (metamaterial) in their design that possesses a strong chromatic anomalous dispersion.
Accordingly, we consider a plasmonic nanocomposite of tiny metallic nanoparticles embedded in a dielectric host as a metamaterial with the required highly dispersive refractive index. The properties of the nanocomposite can be tuned by many parameters which constitute a great degree of freedom. They constitute an extraordinary material platform with many intriguing advantages. The fabrication of these nanocomposites is based on self-assembly processes using sputter techniques, which is well established, [40][41][42] and they can be deposited on a large surface in a short time and at low costs (for more details see the Methods section).
This metamaterial derives its unique properties from the excitation of localized plasmon polaritons in the metallic nanoparticles. 43 The nanoparticles are sufficiently small and arranged sufficiently dense, such that the material can be considered as effectively homogenous and isotropic. The material is characterized by a Lorentzian resonance in the effective permittivity which is centered at the plasmon resonance wavelength. Due to the isotropy of the material and the vanishing of any magnetic response, the permittivity uniquely denes the effective refractive index. The material can be perceived as a strongly dispersive dielectric with some nite absorption in resonance.
It is known that, with lling fractions for the metallic nanoparticles between 20% and 40%, the effective properties cannot be derived from canonical effective medium theories such as Clausius-Mossotti. 44 Instead, we used nite-difference time-domain (FDTD) simulations of a sufficiently large supercell and calculated the dispersive complex reection and transmission coefficient 45 (cf. Methods section). From these coefficients effective properties were retrieved for the composite. These parameters were aerwards fueled into a thin-lm transfer matrix technique to simulate all quantities of interest. Selected congurations were equally simulated by the FDTD method to cross-check the predictive power of the effective properties. Identical results were always predicted, justifying the treatment of the nanocomposite as an effective medium (for more details see the Methods section). The dispersive RIs of the nanocomposites with different lling factors are shown in Fig. 2c. It is apparent from this dispersion graph that at resonance the absorption is maximal and the real part of the RI undergoes anomalous dispersion. At wavelengths longer than the resonance wavelength the material is characterized by a large RI (large permittivity) and hence would be suitable to serve in the reverse-Rayleigh conguration as the top material (n top > n spacer ). In contrast, at wavelengths smaller than the resonance wavelength, the medium is characterized by a rather small RI (small permittivity) and accordingly would be appropriate to be used in the Rayleigh conguration as the top material (n top < n spacer ). Therefore, plasmonic nanocomposites can be considered as the hybrid ARC that meets the condition of both Rayleigh and reverse-Rayleigh geometries resulting in a broad-band ARC coating.
We demonstrate the hybrid concept by coating a polished silicon wafer with a 20 nm silver-silicon dioxide nanocomposite separated from the substrate by a thin layer (50 nm) of silicon dioxide as shown schematically in Fig. 2d. Such a stack gives rise to the realization of a black silicon with a homogeneous ultrathin layer coating. Fig. 3a shows the reection spectra of 20% and 30% nanocomposites deposited on 50 nm SiO 2 coated silicon and the inset is the true color photograph of the sample with 30%, which looks black indeed.
Angular reectance measurement of the coating with 30% lling factor (Fig. 3b) shows the marginal angular and polarization dependency of the plasmonic hybrid ARC. 46 More details on the angular behavior, 33 especially for the angular domain that is not shown here, can be found in the literature. 26 The spectra possess two main dips in the reection spectra. The small wavelength dip is attributed to the graded AR (i.e. in analogue to a conguration where 50 nm SiO 2 is deposited atop of 20 nm TiO 2 (cf. Fig. 1d (inset))) and the second reection dip originates from the destructive interference of the reected eld (i.e. in analogy with the TiO 2 lm atop of SiO 2 (cf. Fig. 1d (black curve))).
In spite of the expected wavelength shis of the antireection dips [cf. Fig. 3b (inset)], one peak at 450 nm (i.e. where the plasmon of the nanocomposite arise) is also revealed that is invariant against the angle of incidence and hence we attribute it to the plasmon resonance of the composite. Indeed, the wavelength of the peak remains unchanged by angle variation, which conrms the localized nature of the (particle plasmon) resonance.
To demonstrate the tunability of the hybrid ARC coating and meanwhile to gain more understanding about the role of plasmon in the observed phenomena, the effect of the spacer layer on the optical responses was examined. Keeping the top layer thickness and composition constant while increasing the thickness of SiO 2 from 50 nm to 100 nm, a red-shi of the reverse-Rayleigh as well as Rayleigh antireection dips was observed (Fig. 3c). This behavior is in good agreement with our simulation (Fig. 3d) which shows that an increase of the spacer results in a broad ARC in NIR (800-900 nm) for the case of the reverse-Rayleigh conguration. On the other hand, ARC performance of the graded conguration (small wavelength regime) in the hybrid is deteriorated by thickening the spacer layer. Indeed, the origin of the mentioned high reection with a thicker inter-layer could be attributed to two phenomena; rstly the constructive interference of the incident and the reected light, and secondly, the spectral overlap of the plasmonic resonance of the nanocomposite and the Rayleigh antireection dip. Such an overlap occurred because of the red-shi of the Rayleigh originated dip via thickening of the spacer layer.
Indeed, integrating the plasmonic structure as a hybrid ARC coating provides an additional degree of freedom for tuning the performance of the ARC coating. In other words, by using the hybrid plasmonic ARC, the designer can reach the desired optical properties not only by alteration of the layer thickness but also by adjusting the lling factor (RI) and type of the metallic constituents of the nanocomposite. Generally, the performance of the hybrid ARC depends on the contrast of the RIs between the layers. At the wavelengths where the top layer shows higher RI, the reverse-Rayleigh condition is satised but the traditional Rayleigh would be realized once the top lm possesses the lower RI in the stack. The presented plasmonic anti-reector shows such a low and tunable reectivity due to the extreme dispersive RI of the metamaterial (cf. Fig. 2c), which has been shown formerly. [47][48][49][50] The RI of the nanocomposite with 40% lling factor changes from 0.9 up to 3.15 from small to long wavelengths. In other words, the relative RI changes of the host matrix before and aer embedding of the nanoparticles can vary from À30% to +140%.
In fact, the tunability of the plasmon resonance and correspondingly the reection change 29 by changing the lling factor of the nanocomposite provide the possibility for the coloring of metals using our hybrid concept. Fig. 4a shows a true photograph of samples of 25 nm SiO 2 coated gold lm which is covered with 20 nm gold-SiO 2 nanocomposite with a variety of lling factors, creating a spectrum of colors including yellow, orange, blue and green. The colors originated from the different reection drops associated with each lling factor demonstrating the potential of the hybrid concept for realization of plasmonic rainbow colors. 51 Note that demonstration of various colors on the silicon substrate is not possible under the same conditions (i.e. constant thickness of layers while varying the lling factor). It seems that, the surface plasmon of the gold lm (which is absent on silicon) in parallel with the hybrid ARC contributes to the rainbow colors.
We believe that the hybrid concept could pave the way for new highly efficient ARCs for a variety of applications ranging from photovoltaics 52 and optics to solar absorbers and stealth technology 53,54 as well as other elds where high reection is undesired. But for energy applications, not only the low reectance rather high transmission is desired. Calculation showed that the light transmission into the substrate (silicon) is enhanced by using the plasmonic coating. Fig. 4b shows the light absorbed by silicon (i.e. light transmitted into silicon) by means of current plasmonic coating. The light reaching the substrate is apparently increased through the coating, which shows the potential of such an approach for energy harvesting purposes. However, the preliminary results on photocurrent measurements of presented coating on p-silicon showed some current loss that we attributed to the poor interface of the prepared lms which acts as the sites for electron-hole recombination. Nevertheless, a more sophisticated design is required to better explore the role of the present ARC for electron-hole generation which is beyond the scope of this manuscript.

Conclusions
In summary, we demonstrated a new concept for antireection coatings and experimentally showed an ultra-thin tunable plasmonic anti-reector by using a routine technique of MEMS/ NEMS technology. The developed hybrid ARC, which is based on a continuous plasmonic medium, acts as a consolidation of the graded-index and interferometer (reverse-Rayleigh) providing a wide-band reection drop throughout the visible spectrum. Due to the simplicity of our production approach, the concept can be further extended to other substrates/applications where broadband ultra-thin anti-reective coatings are required.

Fabrication
All depositions were carried out in a cylindrical vacuum chamber, which was primarily evacuated to 10 À6 mbar. We used an RF magnetron for sputtering of SiO 2 and a DC magnetron sputter source for silver and gold. Both sources were oriented in reverse directions relative to the sample holder at 50 angle to the substrate plane. All the coating was done while the rotatable sample holder was spinning in order to end up with a uniform thickness and composition (details in ref. [40][41][42]. In order to keep the lling factor below the percolation threshold, the deposition rate of the metal was adjusted to be less than that of the dielectric during co-deposition. In other words, to avoid the coalesce of nanoparticles in the matrix, i.e. the formation of fractal aggregates of NPs, the deposition rate of SiO 2 was set to be 10 nm s À1 while the rate of silver was adjusted to be around 3 nm s À1 . However, for the creation of the plasmonic rainbow, the mentioned constrain was actually not necessary. Therefore, the gold deposition rate was varied between 3 and 13 nm s À1 . This enabled us to fabricate a gold nanocomposite with a wider range of lling factors (below and above the percolation threshold). Nevertheless, we increased the rate of deposited gold only to an extent such that we avoid the formation of a continuous gold lm instead of particles. By formation of a gold lm no localized plasmon resonance would appear which has to be avoided. From the nal TEM investigation data we could eventually observe that the particles do not coalesce and they are mainly spherical which further simplied the theoretical modeling (see Simulation).
The thickness of the lms was measured with a prolometer (Dektak 8000 surface prole measuring system) and the thickness of dielectric was further measured with an ellipsometer (M2000 (J.A. Woollam Co., Inc.)). Optical properties of the samples at normal incidence were measured with a UV/vis/NIR spectrometer (Lambda900, Perkin Elmer). For transmission measurements, the base line was collected by measuring the empty compartment (i.e. air considered as the reference) while for reection measurements, the mirror provided by the company was used. To extract the absolute value of reection, the measured reection spectra of the samples were normalized to the tabulated data of the mirror provided by the manufacturing company (PerkinElmer). In all types of measurements, the scan step was xed to 4 nm and the base line was collected twice by a full sweep across the spectral domain of interest while the integration and acquisition times were kept constant.
Polarization-dependent and variable angle spectroscopic Ellipsometry reection measurements of the lms was carried out with J.A. Woollam Co., Inc. M2000 UI (spectroscopic ellipsometer) with a dual lamp system with deuterium and Quartz Tungsten Halogen (QTH) lamps as light sources (data provided by LOT catalogue Europe). The angle sweep step was selected to be 5 or 10 and the angle variation from 45 to 85 was performed. In order to have a comparable study and achieve the best signal-to-noise, 5 second acquisition time was applied for all experiments. Accordingly, the measurement did not take more than few seconds. For analyzing the data, CompleteEASE® soware package provided by the company was used.
Simulations FDTD simulations were made with an in-house developed code on a sufficiently large cluster. 45 The simulated structure compares entirely to the experimental geometry. For this purpose a random arrangement of spherical metallic nanoparticles with a diameter corresponding to the mean diameter as extracted from the TEM samples has been generated. The lling fraction has been adjusted according to the experimental values and we only enforced an isolation of all spherical nanoparticles, i.e. their interpenetration has been excluded. The spatial domain considered in the simulation was 100 nm Â 100 nm in lateral directions. In these directions periodic boundaries were enforced to eventually mimic an innitely extended space. The chosen spatial domain was sufficiently large to exclude any notable effect from the periodicity. In the propagation direction the sequence of layers and their respective thicknesses have been considered in full analogy with the experimental situations. Permittivity of SiO 2 has been taken as non-dispersive and equal to 2.25. Permittivity of gold was taken as tabulated in the literature 55 but with an additional correction term to accommodate the nite and small size of the nanoparticles. 56 The intrinsic dispersion of the material has been fully taken into account by performing at each wavelength an individual simulation and adjusting the free parameters in a Drude model to provide a material with the respective properties at the considered wavelength. Spatial discretization in the FDTD was 1 nm and perfectly matched layers were used in the propagation direction. To retrieve the effective properties the complex reection and transmission coefficients have been extracted from the FDTD simulations and a parameter retrieval has been applied. 57 projects EL 554/1-1 and SFB 677 (C1,C9). M.E. would like to thank the Initiative and Networking Fund of the Helmholtz Association (grant no. VH-NG-523) for providing the nancial base for the start-up of his research group. The authors also gratefully acknowledge Dr U. Schürmann and Prof. Kienle for TEM measurements. This work was supported by the German Federal Ministry of Education and Research (PhoNa) and by the Thuringian State Government (MeMa). We thank Karsten Verch (http://www.karstenverch.com) for his artistic view of the concept in Fig. 2d.