### Description

The subject of nanoscience is the preparation and investigation of structures well below one micron. The macroscopic properties of materials strongly alter, when the size is significantly reduced. Nanostructures are also very interesting in optics. Especially for metal-dielectric nanostructures with "unit cells" much smaller than the wavelength a large number of unexpected new phenomena are predicted like superlensing and cloaking. It is expected that with these so called Metamaterials new photonic devices with freely tuneable permittivity and permeability can be built. These theoretical approaches rely on the assumption of idealized effective optical parameters.

### Current Research Topics

- Plasmonics: optical investigations of random and ordered arrangements of nanoparticles
- Linear and nonlinear properties of metallic thin films close to the percolation threshold
- Dispersion engineering and metamaterials
- Active control of the optical properties of plasmonic structures
- Optical characterization of biological materials

## Recent Activities

The interaction of nanostructures, periodic or random, with polarized light creates very rich physics where scattering, diffraction and absorbance are linked to a variety of dispersive modes and coupling effects. Each of these excitations depends strongly on polarization, angle of incidence, azimuthal orientation of the sample and wavelength. The entire optical response can be obtained, independently from any model, by measuring the Mueller matrices at various k-vectors over a broad frequency range. This results in complex data hiding the underlying physics. Here we present a simple but versatile method to identify the physical properties present in the Mueller matrices. This method is applicable to a wide variety of photonic and plasmonic samples. Based on the simple example of a one-dimensional gold grating where the optical response is characterized not only by diffraction but also by a complex mixing of polarization, we present a very general procedure to analyse the Mueller matrix data using simple analytical tools. The calculated Mueller matrix contour plots obtained from an effective anisotropic layer model are completed by the presence of plasmonic modes, Rayleigh-Woods anomalies and the interband transition absorbance. A comparison of the so-constructed contour plots with the measured ones satisfactorily connects the optical properties of the grating to their physical origin. This straightforward procedure is very general and will be powerful for the analysis of complex optical nanostructures.

Meng Wang, Anja Löhle, Bruno Gompf, Martin Dressel, and Audrey Berrier*Physical interpretation of Mueller matrix spectra: a versatile method applied to gold gratings,*

Opt. Express **25**, 6983-6996 (2017).

Metallic nanostructures offer efficient solutions in polarization control with a very low thickness. In this report, we investigate the optical properties of a nano-fabricated plasmonic pseudo-depolarizer using Mueller matrix spectroscopic ellipsometry in transmission configuration. The depolarizer is composed of 256 square cells, each containing a periodically corrugated metallic film with random orientation. The full Mueller matrix was analyzed as a function of incident angle in a range between 0 and 20° and over the whole rotation angle range. Depolarization could be achieved in two visible wavelength regions around the short-range and long-range surface plasmon polariton frequencies, respectively. Furthermore, depolarization for circularly polarized light was 2.5 times stronger than that for linearly polarized light. Our results could work as a guidance for realizing a broadband high efficiency dielectric metasurface depolarizers.

L. Fu, A. Berrier, H. Li, P. Schau, K. Frenner, M. Dressel, W. Osten*Depolarization of a randomly distributed plasmonic meander metasurface characterized by Mueller matrix spectroscopic ellipsometry*

Optics Express **24**(24), 28056-28064 (2016).

The geometrical arrangement of metallic nanoparticles plays a crucial role on the optical response of nanoplasmonic samples due to particle-particle interactions. In this work, large-area, two-dimensional meta-glasses (random arrangements) and meta-crystals (periodic arrangements) made of identical metallic nanoparticles are investigated for three different particle densities of 5, 10, and 15 discs/μm2. A direct comparison between random and periodically ordered arrays is presented. The comparison clearly shows that the particle density has the largest influence on the extinction spectra for both periodic and random samples, and that for equal densities, the optical response away from diffraction effects is strikingly similar in both cases. The role of the radial density function and minimum particle distance is also determined. This study elucidates the role of the particle-particle interactions on the response of plasmonic nanoparticles and indicates how to control position and shape of the plasmonic resonance.

S. De Zuani, M. Rommel, R. Vogelgesang, J. Weis, B. Gompf, M. Dressel, and A. Berrier*Large-Area Two-Dimensional Plasmonic Meta-Glasses and Meta-Crystals: a Comparative Study*

Plasmonics, 2016, 10.1007/s11468-016-0397-9

GeSn as a group-IV material opens up new possibilities for realizing photonic device concepts in Si-compatible fabrication processes. Here we present results of the ellipsometric characterization of highly p- and n-type doped Ge0.95Sn0.05 alloys deposited on Si substrates investigated in the wavelength range from 1 to 16 μm. We discuss the suitability of these films for integrated plasmonic applications in the infrared region.

L. Augel, I.A. Fischer, F. Hornung, M. Dressel, A. Berrier, M. Oehme, J. Schulze*Ellipsometric characterization of doped Ge0.95 Sn0.05 films in the infrared range for plasmonic applications*

Opt. Lett. 41, 4398 (2016)

Metal−dielectric composites exhibit remarkable properties at the percolation threshold. A small variation of the filling factor can lead to a huge variation in the dc conductivity from an insulator-like to a metal-like behavior while the real part of the permittivity diverges. This behavior can, in principle, be described by percolation theories at low frequencies and by effective medium approximations at higher frequencies. These theories assume a random distribution of the metallic inclusions inside the insulating matrix. But what happens in ordered structures when the percolation is deliberately suppressed? Even though a simple, nanometer-wide scratch can deteriorate the dc conductivity of a thin metal film, can it influence the mirror-like reflectivity? To address this question, we perform a systematic ellipsometric investigation on nearly closed Au films interrupted only by a two-dimensional periodic mesh of 20 nm wide lines. These nanostructured films have metal filling factors close to unity, but exhibit no dc conductivity. In the infrared, they show an antireflective behavior that can be tuned through the mesh periodicity. Surprisingly, the optical response of these structures can be modeled quite well by simple effective medium approximations. Increasing the size of the squares leads to a tunable, diverging, real part of the permittivity: a maximum of the real part of the permittivity of 1420 is found for the largest investigated squares in this study.

S. De Zuani, M. Rommel, B. Gompf, A. Berrier, J. Weis, and M. Dressel*Suppressed Percolation in Nearly closed Gold Films*

ACS Photonics 3, 1109 (2016)

*The samples investigated in this study are 50nm thick gold wires made by electron beam lithography following the pattern corresponding to a Hilbert curve of order 9. They show an in-plane isotropic, metallic behavior while they have dielectric properties in the out-of-plane direction. The reflectance of these samples is almost flat in a wide spectral range and their optical properties can be tuned by acting on the wire thickness. *

Ultra-thin metal films exhibit an isotropic nearly frequency independent optical behavior, which theoretically can be tuned by their thickness. In practice however, below a certain critical thickness, the so-called percolation threshold, they undergo a metal-to-insulator transition, where the dielectric properties diverges. One way to overcome this problem is to look for continues metal structures with a homogeneous, isotropic and frequency independent behavior. Self-similar structures are promising candidates as non-periodic, non-resonant structures exhibiting a homogeneous, isotropic and frequency-independent effective optical response. Hilbert fractal curves in particular are self-avoiding, continuous curves, proposed for the first time by David Hilbert in 1891 as a particular geometry of a family of curves introduced by Giuseppe Peano in 1890, known as “FASS-curves” (space-**f**illing, self-**a**voiding, **s**imple and self-**s**imilar). Our experiments show that high-order Hilbert nanostructures of fractal order N = 9 exhibit a nearly frequency independent reflectance and an in-plane isotropic optical response. The response can be simulated in the framework of a simple Bruggeman effective medium approximation (BEMA) model with a limited number of parameters. High-order Hilbert structures can be considered as a “transparent in-plane metal”, which dielectric function is modified by the filling factor *f*, hence creating a tunable conductive effective metal with tailorable plasma frequency and variable reflectance without going through an insulator-to-metal transition.

S. De Zuani, T. Reindl, M. Rommel, B. Gompf, A. Berrier, and M. Dressel

ACS Photonics 2, 1719 (2015).

#### Optical anisotropies of single-meander plasmonic metasurfaces analysed by Mueller matrix spectroscopy

*The samples, made of a thin silver layer evaporated onto MF2 one-dimensional gratings, are operating in transmission. It transforms a linearly polarized beam into circularly polarized light. The dispersion diagram is characterized by a large, dispersive passband. The Mueller matrices reveal the excited modes as a coupling between the short range (SR) and the long range (LR) surface plasmon polaritons across the thin silver layer. The measured Mueller matrix data are used to calculate both the ellipticity and the optical rotation of the meander sample.*

The fascinating optical properties of metamaterials and metasurfaces are intrinsically wave-vector (**k**) dependent and spatial dispersion effects induce a complex optical response. We use Mueller matrix spectroscopic ellipsometry, providing both amplitude and phase information in the visible, is used in a large frequency and **k**-space range to characterize a plasmonic meander and assign the polarization effects to the microscopic plasmonic excitations of a metasurface. The measurement of Mueller matrices leads to a fundamental physical insight into the optical properties of the plasmonic meanders: the effect of closed-film resonant coupling is used for large polarization rotation and high transmission, and multiple optical functions are created within one compact design, which cannot be obtained by any natural crystal.

A. Berrier, B. Gompf, L. Fu, T. Weiss, H. Schweizer

Phys. Rev. B **89**, 195434 (2014)

*The real part of the dielectric constant ɛ _{1} obtained at 1 cm^{-1} is strongly varying as function of film thickness. At the percolation threshold, ɛ_{1} shoots up and reaches values above 100. This project aims at linking the evolution of the second harmonic generated (SHG) signal to the position of the percolation threshold. The SHG from the samples is excited by a laser and is experimentally collected with a collecting lens and a photomultiplier. When comparing the raw SHG signal and the dielectric constant ɛ_{1} obtained at 1 cm^{-1} as a function of the film thickness around the main peak, we can see that the SHG peaks at the percolation threshold. The black solid line is a guide to the eye. The red solid line corresponds to a fit of the experimental data.*

When a metal is evaporated onto an insulating substrate and the metal filling factor is gradually increased, the coalescence between initially isolated metallic nanoparticles results in the formation of clusters. Close to the percolation the metallic particles form an almost closed film with almost touching particles and the insulator-metal phase transition occurs. The optical conductivity of such ultrathin metal films is dominated by two contributions: a Drude component starting at the percolation threshold in the low-frequency range and by localized surface plasmons polaritons in the near-infrared region, which red shift with increasing film thickness. When the inter particle distance decreases, very large field enhancements are expected. The interplay of both components leads to a dielectric anomaly in the infrared region with a maximum of the dielectric constant at the insulator-to-metal transition. We investigate gold film thicknesses from few nm (well below the percolation threshold) to 60 nm where the gold film is closed, varying the film thickness in order to accurately achieve the thickness where the percolation threshold takes place. We observe an increase of the second harmonic signal which sharply peaks around the dielectric anomaly corresponding to the insulator-to-metal transition. The large second harmonic optical nonlinearities are attributed to the strong local field enhancement caused by the interplay of localized plasmons and the transition to electron delocalization at the percolation threshold.

S. De Zuani, T. Peterseim, A. Berrier, B. Gompf, M. Dressel

Appl. Phys. Lett. **104**, 241109 (2014).

*Silver nanoparticle-PDMS composites can be made to be metallic (hence displaying a negative permittivity value, as illustrated in point A). Their appearance is shiny. When these flexible samples are isotropically stretched, the total volume of the PDMS increases and therefore the filling factor of the Ag nanoparticles in the PDMS decreases. This induces a variability of the permittivity, which can be controlled from the metallic regime into the dielectric regime, through the percolation threshold.*

Tunable metal/dielectric composites are promising candidates for a large number of potential applications in electronics, sensor technologies and optical devices. Here we systematically investigate the dielectric properties of Ag-nanoparticles embedded in the highly flexible elastomer poly-dimethylsiloxane (PDMS). As tuning parameter we use uniaxial and biaxial strain applied to the composite. We demonstrate that both static variations of the filling factor and applied strain lead to the same behavior, i.e., the filling factor of the composite can be tuned by application of strain. In this way the effective static permittivity ε_{eff} of the composite can be varied over a very large range. Once the Poisson’s ratio of the composite is known, the strain dependent dielectric constant can be accurately described by effective medium theory without any additional free fit parameter up to metal filling factors close to the percolation threshold. It is demonstrated that, starting above the percolation threshold in the metallic phase, applying strain provides the possibility to cross the percolation threshold into the insulating region. The change of regime from conductive phase down to insulating follows the description given by percolation theory and can be actively controlled.

P. Gaiser, J. Binz, B. Gompf, A. Berrier, and M. Dressel

Nanoscale **7**, 4566-4571 (2015).

*Tetradymites such as Bi _{2}Se_{3} are composed of stacks of quintuple atomic layers kept together by van der Waals bonding. The tensorial permittivity is extracted by modelling the spectroscopic ellipsometry data of a Bi_{2}Se_{3} crystal measured with a Woollam variable angle spectroscopic ellipsometer in the range between 0.6 and 4.3 eV. The permittivity shows the hyperbolic behavior of the topological insulator.*

Hyperbolic media exhibit unparalleled properties, e.g, as light absorbers in photovoltaics and photonics, as superlenses in far-field imaging, as subwavelength light concentrators in nanolithography, or as novel materials in emission engineering. With the advent of optical metamaterials, deliberate design of material properties became possible. However, inadvertent variability in fabrication techniques and other factors limit performance characteristics of man-made hyperbolic materials. Here, we draw attention to a class of natural hyperbolic materials, the tetradymites. From generalized spectroscopic ellipsometry we extract the dielectric tensor components and find hyperbolic behavior in Bi_{2}Se_{3} and Bi_{2}Te_{3} in the near-infrared to visible spectrum. Previously, natural hyperbolic media were known only in the far-infrared spectral range. As possible applications of tetradymites we discuss superlenses for near-field microscopy and far-field iso-index filters. Solid solutions of tetradymites are likely tuneable in operational wavelength from the infrared to the visible, complementing hyperbolic metamaterials

M. Esslinger, R. Vogelgesang, N. Talebi, W. Khunsin, P. Gehring, S. de Zuani, B. Gompf, K. Kern

ACS Photonics, **1**, 1285 - 1289 (2014)

*Divergence of the static dielectric constant (obtained at 1cm ^{-1}) as a function of nominal film *

*thickness d for Au on Si/SiO2. The solid lines below and above the critical thickness dc corresponds to*

*ε*

*(d)~(6.4nm-d)*

^{-1}and*ε*

*(d)~(6.7nm-d)*

^{-1}, respectively.Although for many applications closed metal films as thin as possible are desired, the dielectric properties of percolating metal films around the insulator-to-metal transition are not well understood. Thick continuous films show a behaviour similar to bulk material and can therefore be well described by the Drude model when corrections for size effects are considered. With decreasing thickness the films become granular, and below the percolation threshold the metallic behaviour disappears. In principle one can try to model the optical properties of semi-continuous films by effective medium approximations (EMA), but it was shown that these theories fail around the metal-to-insulator transition. We investigate ultrathin metal films at and around the percolation threshold (film thickness 3 to 10nm) in an extremely broad spectral range from dc up to 35.000cm^{-1} (285nm). Combining spectroscopic ellipsometry, Fouriertransform infrared spectroscopy and dc measurements the dielectric properties of the films can be described over the whole frequency range by Kramers-Kronig consistent effective dielectric functions. The optical conductivity of the films is dominated by two contributions: a Drude-component starting at the percolation threshold in the low frequency range and by plasmons in the near-infrared region, which shift own in frequency with increasing film thickness. The interplay of both components leads to a dielectric anomaly in the infrared region with a maximum of the dielectric constant at the insulator-to-metal transition. Here values of ε_{1}>100 can be obtained. This dielectric anomaly allows one in principle to tune the dielectric properties of these granular films over a very broad range.

*Small holes in an ultrathin metal film can obscure the view.** Right figure: Electron micrograph of the perforated Au film; Left figure: Scheme of the sampl*e

The observation of Ebbesen et. al. that the presence of a subwavelength hole array in a thick opaque metal film can lead to an extraordinary high optical transmission has triggered a huge number of publication. At our institute we investigate the transmission through ultrathin semitransparent metal films. In opposite to the investigation on thick film, in the case of semitransparent films, the closed film can be used as reference. For these nanostructured films we found exact the opposite behaviour: less light is transmitted through the perforated film compared to the closed metal film; the additional holes obscure the view. We investigate thin Au films only a few nanometer thick, pierced with subwavelength holes by electron beam lithography or optical interference methods. The holes have diameters between 150nm and about 500nm and are ordered in arrays with periodicities between 200nm and 600nm. These samples are characterized by spectroscopic ellipsometry and Fourtransform-IR spectroscopy over a very wide frequency range from the far-infrared to UV. The perforated metal films exhibit strong absorption in the visible and near-infrared.

This additional absorption, which is not observed on normal metals, is a direct consequence of the hole array, and depend in a first approximation only on the periodicity of the array and not on the hole diameter. The array enables the collective excitation of metal electrons, so called plasmons, which can not be exited by light in closed metal films. These plasmons show a strong dispersion leading to k-dependent optical properties of the nanostructures, which can not be described by complex anisotropic dielectric functions anymore.

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