Mueller matrix study of the dichroism in nanorods dimers: rod separation effects

We have studied the optical response of chiral metastructures composed of a disordered array of couples of plasmonic Au nanorods helically piled along the vertical direction. The fabrication is based on the use of multiaxial and multimaterial evaporation of the different metastructure building blocks through nanohole masks. From the analysis of the Mueller Matrix elements of the system, obtained both experimentally and from dedicated numerical simulations in forward and backward illumination conditions, we have been able to determine the linear and circular dichroic response of the system, as well as to sort out the optical anisotropy and intrinsic circular dichroism contributions to the circular differential extinction. We have also analyzed the dependence of the optical properties as a function of the angle between the rods and of the thickness of the dielectric separator. The study of quasiplanar as well as three-dimensional structures allows unraveling the role played by interactions between the constituting building blocks and, in particular, the distance between rods. We have experimentally and theoretically observed a decrease of the circular dichroic contribution and a change of the optical anisotropic contribution when the structures evolve from non-planar to planar. © 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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Fabricatio
The model str mask is as fol substrates (pr CaF 2 rod is d rod. Finally, a solvents favo disordered arr that is control can be varied evaporated fr deposition pro Fig Despite its versatility, the described fabrication method presents some intrinsic shortcomings that condition the actual choice on dimensions for the different elements, and on whose existence one must be aware. One of the drawbacks is the limitation in controlling of the spatial arrangement of the structures. Although it is possible to precisely stack the structures, the planar spacing is difficult to manage. The most relevant disadvantage is the gradual reduction of the diameter of the nanoholes in the mask, due to the accumulated material during deposition at oblique incidence [27]. As a consequence, the final elements in the metastructure are narrower and, for the same substrate oscillation span, shorter. This gradual hole diameter reduction also limits the total amount of deposited material and consequently the total height of the metastructure. As a consequence, the typical dimensions when the deposited heights of the different elements of the metastructure are 12nm Au/6nm CaF 2 /12nm Au/3 nm Ti/0.5mm BK7 result to be: (i) widths and lengths are 95 nm and 235 nm for the bottom rod and are 75 nm and 220 nm for the top rod, (ii) diameters of 20nm thick CaF 2 pillars are 135nm and 100nm, respectively.

Results and discussion
The optical properties of the samples have been studied using a spectroscopic ellipsometer (SE, M200Fi J. A. WoollamCo.) in transmission mode at normal incidence in the 400-1600 nm spectral range. In spectroscopic ellipsometers with PCSA configuration of the optical elements (polarizer, compensator, sample and analyzer), the elements of row 4 of the Mueller matrix (m 41 , m 42 , m 43 and m 44 ) cannot be obtained due to the lack of a second compensator [28]. From symmetry considerations, we have used a valid method based on measurements with sample illumination from the metastructures side (Front-F) or from the substrate side (Back-B) [29,30]. This allows, for example, to discern the different contributions of the system to the circular differential extinction [26,31]. The sample was mounted on a rotational stage which allows changing the in-plane orientation of the sample. Following this procedure it is possible to obtain the Mueller Matrix Elements (MME) of the system [28,32], containing full information about different optical aspects of the system [33,34]. As schematically indicated in the left of Fig. 2, in transmission mode, the element m 12 is directly related to the absorption difference for light that is polarized parallel or perpendicular to the x-axis (m 12 = (I X -I Y )/2, linear dichroism (LD)). On the other hand, m 13 is related to the difference in the absorption of light polarized parallel and perpendicular to an axis rotated 45 degrees with respect to the x-axis, x'-axis, (m 13 = (I X' -I Y' )/2, linear dichroism at 45° (LD')). Finally, m 14 is related to the difference in transmission for left-and right-handed circularly polarized light (m 14 = (I R -I L )/2 or circular differential extinction (CDE)). The measured MME are normalized to the element m 11 , which is the total transmission intensity of the sample [28]. In Fig. 2 we show the measured MME for three fabricated structures, namely single Au nanorods with CaF 2 pillars symmetrically positioned at both sides of the rods, and complete Au rod dimers at 45° and −45 degrees respectively with 6 nm thick CaF 2 dielectric rods separating them. SEM images for individual structures are also shown. For the experimental determination of the MME, the samples were carefully aligned in the plane so that the long axes of the Au rods close to the substrate were oriented along the y-axis.
For the single Au rod layer (left-hand column), the y-polarized light only excites the resonance along the principal axis of the rod, which is located at a lower energy than the corresponding for the short axis (only excited using x-polarized light). Therefore, the m 12 element has a sigmoidal spectral shape, with a negative dip centered at the position of the long axis resonance of the rod and a positive peak at the position of the short axis resonance. On the other hand, light polarized along x' or y' axes excites, in equal footing, long and short axes resonances and, as a consequence, the m 13 values for all the wavelengths are zero. The same occurs for the circular differential extinction value, m 14  mmetry of depend on is system nation of c circular dichroism (CD in ). It is known that, in complex systems with small anisotropies where these two effects (optical anisotropy and intrinsic circular dichroism) coexist, it is possible to separate their contributions to the CDE by carrying out forward and backward experimental measurements, since these two magnitudes behave differently for forward and backward illumination [26,33]. The experimentally measured circular differential extinction can be decomposed in the intrinsic circular dichroism and optical anisotropy components (CDE = CD in + OA) where 14 It is worth noticing that the Eq. (1) is a valid approximation in the range of values of CDE that we are studying. The real values of the CDE can be extracted from the differential Mueller matrix elements [31,[35][36][37]. It should be mentioned that the sources of the optical anisotropy are the preferential in plane ordering of the structures in the array configuration, as well as effects to the overlapping dimer. Therefore, it is possible to apply this methodology thanks to the correlated orientation of all the rods dimers between each other provided by the specific fabrication technique. This would not be possible in systems presenting a random orientation of rod dimers, such as those obtained by chemical methods, where the anisotropic contribution to the circular differential extinction cancels out [10].
In the left column of Fig. 3 we present the spectral dependence of m 14 for forward and backward illumination for both types of dimers. As it can be observed, the forward and backward spectra of these layers are different, highlighting the presence of the two contributions. On the other hand, comparing the spectra of the two samples they are, both for forward and backward illumination, mirror images of each other (Figs. 3(a) and 3(d)), due to their opposite twist sign. As mentioned before, with this kind of measurements, the two contributions (optical anisotropy and intrinsic circular dichroism) to the circular differential extinction can be obtained, and the results are shown in Figs. 3

(b) and 3(e) and in Figs. 3(c)
and 3(f). As it can be observed, the spectral shape of the two contributions is different: the intrinsic circular dichroism contribution (CD in ) has a sigmoidal like shape, whose sign depend on the relative arrangement of the dimers, whereas the optical anisotropy contribution (OA) consists of a broad peak, whose sign also depends on the twist. Minor differences on the spectral dependencies of these magnitudes for both dimers are due to the lack of perfect morphological reproducibility in the fabrication of these mirror structures.  he CDE as the ero intrinsic C CD in retains its he last conside the optical an resenting also a anar case, the anges in the si ith the dimer w and optical an ond. Qualitativ duced by the th tropy compone inor contributio ature of the f uly reproducin n l A g s e distance D signal. s spectral ered case, nisotropy an abrupt coupling ign of the with 6 nm nisotropy vely, the heoretical ent, good on of the fabricated ng all the existing morphological details is a great challenge. For example, it is worth noticing that, since in the modeling all interfaces are crisp and defect free, the CD in keeps governing the CDE down close to the planar case. In the experimental case the spacer free system already shows an almost vanishing the intrinsic CD contribution, which we attribute to the natural fabrication constrains, such as porosity, misalignments (especially in the height of the auxiliary pillars) that largely affects the CD in and tends to increase the optical anisotropy.

Conclusions
We have fabricated Au nanorod dimers helically stacked with different relative orientations and separation between them using a single deposition run technique. We have addressed the dependence of their linear and circular dichroism performing a careful analysis of the Mueller Matrix Elements obtained from both experimental measurements and dedicated FDTD numerical simulations. We have shown that there is a nearly proportional increase of the intrinsic circular dichroic contribution, and a dramatic change of the optical anisotropic part when departing from the planar situation. These findings highlight that the contributions to circular differential extinction can be controlled by carefully acting on the morphology of the sample.