The optoelectronic properties of nanoscale systems such as carbon nanotubes (CNTs), graphene nanoribbons and transition metal dichalcogenides (TMDCs) are determined by their dielectric function. This complex, frequency dependent function is affected
by excitonic resonances, charge transfer effects, doping, sample stress and strain, and surface roughness. Knowledge of the dielectric function grants access to a materials transmissive and absorptive characteristics. Here we introduce the dual scanning near field optical microscope (dual s-SNOM) for imaging local dielectric variations and extracting dielectric function values using a mathematical inversion method. To demonstrate our approach, we studied a monolayer of WS$_2$ on bulk Au and identified two areas with differing levels of charge transfer. Our measurements are corroborated by atomic force microscopy (AFM), Kelvin force probe microscopy (KPFM), photoluminescence (PL) intensity mapping, and tip enhanced photoluminescence (TEPL). We extracted local dielectric variations from s-SNOM images and confirmed the reliability of the obtained values with spectroscopic imaging ellipsometry (SIE) measurements.
Crystals of plasmonic metal nanoparticles have intriguing optical properties. They reach the regimes of ultrastrong and deep strong light-matter coupling, where the photonic states need to be included in the simulation of material properties. We prop
ose a quantum description of the plasmon polaritons in supercrystals that starts from the dipole and quadrupole excitations of the nanoparticle building blocks and their coupling to photons. Our model excellently reproduces results of finite difference time domain simulations. It provides detailed insight into the emergence of the polariton states. Using the example of a face centered cubic crystals we show that the dipole and quadrupole states mix in many high symmetry directions of the Brilouin zone. A proper description of the plasmon and plasmon-polariton band structure is only possible when including the quadrupole-derived states. Our model leads to an expression of the reduced coupling strength in nanoparticle supercrystals that we show to enter the deep strong coupling regime for metal fill fractions above $0.8$. In addition to the plasmon-polariton energies we analyse the relative contributions of the dipole, quadrupole, and photonic states to their eigenfunctions and are able to demonstrate the decoupling of light in the deep strong coupling regime. Our results pave the way for a better understanding of the quantum properties of metallic nanoparticle supercrystals in the ultrastrong and deep-strong coupling regime.
Polariton-based devices require materials where light-matter coupling under ambient conditions exceeds losses, but our current selection of such materials is limited. Here we measured the dispersion of polaritons formed by the $A$ and $B$ excitons in
thin MoS$_2$ slabs by imaging their optical near fields. We combined fully tunable laser excitation in the visible with a scattering near-field optical microscope to excite polaritons and image their optical near fields. We obtained the properties of bulk MoS$_2$ from fits to the slab dispersion. The in-plane excitons are in the strong regime of light-matter coupling with a coupling strength ($40-100,$meV) that exceeds their losses by at least a factor of two. The coupling becomes comparable to the exciton binding energy, which is known as very strong coupling. MoS$_2$ and other transition metal dichalcogenides are excellent materials for future polariton devices.
Structured light are custom light fields where the phase, polarization, and intensity vary with position. It has been used for nanotweezers, nanoscale imaging, and quantum information technology, but its role in exciting optical transitions in materi
als has been little examined so far. Here we use group theory to derive the optical selection rules for nanosystems that get excited by structured light. If the size of the nanostructure is comparable to the light wavelength, it will sample the full beam profile during excitation with profound consequences on optical excitations. Using nanooligomers as model nanosystems, we show that structured light excites optical transitions that are forbidden for linearly polarized or unpolarized light. Such dipole forbidden modes have longer lifetimes and narrower resonances than dipole allowed transitions. We derive symmetry-adapted eigenmodes for nanooligomers containing up to six monomers. Our study includes tables with selection rules for cylindrical vector beams, for beams with orbital angular momentum, and for field retardation along the propagation direction. We discuss multi-photon processes of nonlinear optics in addition to one-photon absorption. Structured light will unlock a broad range of excitations in nanooligomers and other nanostructures that are currently inaccessible to optical studies.
In 2002, Benjamin Jourdain and Claude Martini discovered that for a class of payoff functions, the pricing problem for American options can be reduced to pricing of European options for an appropriately associated payoff, all within a Black-Scholes f
ramework. This discovery has been investigated in great detail by Soren Christensen, Jan Kallsen and Matthias Lenga in a recent work in 2020. In the present work we prove that this phenomenon can be observed in a wider context, and even holds true in a setup of non-linear stochastic processes. We analyse this problem from both probabilistic and analytic viewpoints. In the classical situation, Jourdain and Martini used this method to approximate prices of American put options. The broader applicability now potentially covers non-linear frameworks such as model uncertainty and controller-and-stopper-games.
Raman spectroscopy is a powerful tool for characterizing the local properties of graphene. Here, we introduce a method for evaluating unknown strain configurations and simultaneous doping. It relies on separating the effects of hydrostatic strain (pe
ak shift) and shear strain (peak splitting) on the Raman spectrum of graphene. The peak shifts from hydrostatic strain and doping are separated with a correlation analysis of the 2D and G frequencies. This enables us to obtain the local hydrostatic strain, shear strain and doping without any assumption on the strain configuration prior to the analysis. We demonstrate our approach for two model cases: Graphene under uniaxial stress on a PMMA substrate and graphene suspended on nanostructures that induce an unknown strain configuration. We measured $omega_mathrm{2D}/omega_mathrm{G} = 2.21 pm 0.05$ for pure hydrostatic strain. Raman scattering with circular corotating polarization is ideal for analyzing strain and doping, especially for weak strain when the peak splitting by shear strain cannot be resolved.
Multiferroicity in LiCu2O2 single crystals is studied using resonant soft x-ray magnetic scattering, hard x-ray diffraction, heat capacity, magnetic susceptibility, and electrical polarization. Two magnetic transitions are found at 24.6 K (T1) and 23
.2 K (T2). Our data are consistent with a sinusoidal spin structure at T2<T<T1 and with a helicoidal spin structure at T<T2 giving rise to ferroelectricity. Surprisingly, above T2 the correlation lengths of the spin structures increase as the temperature increases with dramatic changes of ~42% along the c-axis. Our results demonstrate the interplay of the geometrical frustration and the electronic and magnetic polarizations.
A new setup for doping helium nanodroplets by means of laser ablation at kilohertz repetition rate is presented. The doping process is characterized and two distinct regimes of laser ablation are identified. The setup is shown to be efficient and sta
ble enough to be used for spectroscopy, as demonstrated on beam-depletion spectra of lithium atoms attached to helium nanodroplets. For the first time, helium droplets are doped with high temperature refractory materials such as titanium and tantalum. Doping with the non-volatile DNA basis Guanine is found to be efficient and a number of oligomers are detected.
