arXiv subjects

Georg Maret

Publications and source records attributed to Georg Maret.

At least 19 recordsLinked to original sources

arXiv2024

Stealthy and hyperuniform isotropic photonic bandgap structure in 3D

In photonic crystals the propagation of light is governed by their photonic band structure, an ensemble of propagating states grouped into bands, separated by photonic band gaps. Due to discrete symmetries in spatially strictly periodic dielectric structures their photonic band structure is intrinsically anisotropic. However, for many applications, such as manufacturing artificial structural color materials or developing photonic computing devices, but also for the fundamental understanding of light-matter interactions, it is of major interest to seek materials with long range non-periodic dielectric structures which allow the formation of {\it isotropic} photonic band gaps. Here, we report the first ever 3D isotropic photonic band gap for an optimized disordered stealthy hyperuniform structure for microwaves. The transmission spectra are directly compared to a diamond pattern and an amorphous structure with similar node density. The band structure is measured experimentally for all three microwave structures, manufactured by 3D-Laser-printing for meta-materials with refractive index up to $n=2.1$. Results agree well with finite-difference-time-domain numerical investigations and a priori calculations of the band-gap for the hyperuniform structure: the diamond structure shows gaps but being anisotropic as expected, the stealthy hyperuniform pattern shows an isotropic gap of very similar magnitude, while the amorphous structure does not show a gap at all. The centimeter scaled microwave structures may serve as prototypes for micrometer scaled structures with bandgaps in the technologically very interesting region of infrared (IR).

physics.app-ph↗

arXiv2022

Crossover from renormalized to conventional diffusion near the 3D Anderson localization transition for light

We report on anomalous light transport in the strong scattering regime. Using low-coherence interferometry, we measure the reflection matrix of titanium dioxide powders, revealing crucial features of strong optical scattering which can not be observed with transmission measurements: (i) a subdiffusive regime of transport at early times of flight that is a direct consequence of predominant recurrent scattering loops, and (ii) a crossover to a conventional, but extremely slow, diffusive regime at long times. These observations support previous predictions that near-field coupling between scatterers prohibits Anderson localization of light in three-dimensional disordered media.

cond-mat.dis-nn↗

arXiv2019

Magnetic field effects on one-dimensional Anderson localization of light

Transport of coherent waves in multiple-scattering media may exhibit fundamental, non intuitive phenomena such as halt of diffusion by disorder called Anderson localization. For electromagnetic waves, this phenomenon was observed only in one and two dimensions so far. However, none of these experiments studied the contribution of reciprocal paths nor their manipulation by external fields. In order to weaken the effect of reciprocity of coherent wave transport on Anderson localization in one dimension (1D), we studied light propagation through stacks of parallel Faraday-active glass slides exposed to magnetic fields up to 18 Tesla. Measurements of light transmission statistics are presented and compared to 1D transfer-matrix simulations. The latter reveals a self-organization of the polarization states in this system leading to a saturation of the Faraday rotation-induced reciprocity breaking, an increase of the localization length, and a decrease of transmission fluctuations when reciprocity is broken. This is confirmed experimentally for samples containing small numbers of slides while for larger samples a crossover from a 1D to a quasi-1D transport regime is found.

physics.optics↗

arXiv2019

Tunable high-index photonic glasses

Materials with extreme photonic properties such as maximum diffuse reflectance, high albedo, or tunable band gaps are essential in many current and future photonic devices and coatings. While photonic crystals, periodic anisotropic structures, are well established, their disordered counterparts, photonic glasses (PGs), are less understood despite their most interesting isotropic photonic properties. Here, we introduce a controlled high index model PG system. It is made of monodisperse spherical TiO$_2$ colloids to exploit strongly resonant Mie scattering for optimal turbidity. We report spectrally resolved combined measurements of turbidity and light energy velocity from large monolithic crack-free samples. This material class reveals pronounced resonances enabled by the possibility to tune both the refractive index of the extremely low polydisperse constituents and their radius. All our results are rationalized by a model based on the energy coherent potential approximation, which is free of any fitting parameter. Surprisingly good quantitative agreement is found even at high index and elevated packing fraction. This class of PGs may be the key to optimized tunable photonic materials and also central to understand fundamental questions such as isotropic structural colors, random lasing or strong light localization in 3D.

physics.optics↗

arXiv2017

Resonant transport and near-field effects in photonic glasses

A fundamental quantity in multiple scattering is the transport mean free path the inverse of which describes the scattering strength of a sample. In this paper, we emphasize the importance of an appropriate description of the effective refractive index $n_{\mathrm{eff}}$ in multiple light scattering to accurately describe the light transport in dense photonic glasses. Using $n_{\mathrm{eff}}$ as calculated by the energy-density coherent potential approximation we are able to predict the transport mean free path of monodisperse photonic glasses. This model without any fit parameter is in qualitative agreement with numerical simulations and in fair quantitative agreement with spectrally resolved coherent backscattering measurements on new specially synthesized polystyrene photonic glasses. These materials exhibit resonant light scattering perturbed by strong near-field coupling, all captured within the model. Our model might be used to maximize the scattering strength of high index photonic glasses, which are a key in the search for Anderson localization of light in three dimensions.

cond-mat.dis-nn↗

arXiv2016

Mermin-Wagner fluctuations in 2D amorphous solids

In a recent comment, M. Kosterlitz described how the discrepancy about the lack of broken translational symmetry in two dimensions - doubting the existence of 2D crystals - and the first computer simulations foretelling 2D crystals at least in tiny systems, motivated him and D. Thouless to investigate melting and suprafluidity in two dimensions [Jour. of Phys. Cond. Matt. \textbf{28}, 481001 (2016)]. The lack of broken symmetries proposed by D. Mermin and H. Wagner is caused by long wavelength density fluctuations. Those fluctuations do not only have structural impact but additionally a dynamical one: They cause the Lindemann criterion to fail in 2D and the mean squared displacement not to be limited. Comparing experimental data from 3D and 2D amorphous solids with 2D crystals we disentangle Mermin-Wagner fluctuations from glassy structural relaxations. Furthermore we can demonstrate with computer simulations the logarithmic increase of displacements predicted by Mermin and Wagner: periodicity is not a requirement for Mermin-Wagner fluctuations which conserve the homogeneity of space on long scales.

cond-mat.stat-mech↗

arXiv2016

Can 3D light localization be reached in "white paint"?

When waves scatter multiple times in 3D random media, a disorder driven phase transition from diffusion to localization may occur [Anderson 1958 Phys. Rev. 109 1492-505; Abrahams et al 1979 Phys. Rev. Lett. 42 673-6]. In "The question of classical localization: A theory of white paint?" P.W. Anderson suggested the possibility to observe light localization in TiO$_2$ samples [Anderson 1985 Phil. Mag. B 52 505-9]. We recently claimed the observation of localization effects measuring photon time of flight (ToF) distributions [Störzer et al 2006 Phys. Rev. Lett. 96 063904] and evaluating transmission profiles (TP) [Sperling et al 2013 Nat. Photonics 7 48-52] in such TiO$_2$ samples. Here we present a careful study of the long time tail of ToF distributions and the long time behavior of the TP width for very thin samples and different turbidities that questions the localization interpretation. We further show new data that allow an alternative consistent explanation of these previous data by a fluorescence process. An adapted diffusion model including an appropriate exponential fluorescence decay accounts for the shape of the ToF distributions and the TP width. These observations question whether the strong localization regime can be reached with visible light scattering in polydisperse TiO$_2$ samples, since the disorder parameter can hardly be increased any further in such a "white paint" material.

cond-mat.dis-nn↗

arXiv2015

Discontinuous shear modulus determines the glass transition temperature

A solid - amorphous or crystalline - is defined by a finite shear modulus while a fluid lacks such. We thus experimentally investigate the elastic properties of a colloidal glass former near the glass transition: spectroscopy of vibrational excitations yields the dispersion relations of longitudinal and transverse phonons in the glassy state. From the long wavelength limit of the dispersion relation we extract the bulk and the shear modulus. As expected, the latter disappear in a fluid and we measure a clearly resolved discontinuous behaviour of the elastic moduli at the glass transition. This not only determines the transition temperature T_G of the system but also directly addresses recent discussions about elasticity during vitrification. We show that low frequency excitations in our system are plane waves such that continuum elasticity theory can be used to describe the macroscopic behaviour.

cond-mat.soft↗

arXiv2015

Kibble-Zurek mechanism in colloidal monolayers

The Kibble-Zurek mechanism describes the evolution of topological defect structures like domain walls, strings, and monopoles when a system is driven through a second order phase transition. The model is used on very different scales like the Higgs field in the early universe or quantum fluids in condensed matter systems. A defect structure naturally arises during cooling if separated regions are too far apart to `communicate' (e.g. about their orientation or phase) due to finite signal velocity. This results in separated domains with different (degenerated) locally broken symmetry. Within this picture we investigate the non-equilibrium dynamics in a condensed matter analogue, a two-dimensional ensemble of colloidal particles. In equilibrium it obeys the so called Kosterlitz-Thouless-Halperin-Nelson-Young (KTHNY) melting scenario with continuous (second-order like) phase transitions. The ensemble is exposed to a set of finite cooling rates covering roughly three orders of magnitude. Along this process, we analyze the defect and domain structure quantitatively via video microscopy and determine the scaling of the corresponding length scales as a function of the cooling rate. We indeed observe the scaling predicted by the Kibble-Zurek mechanism for the KTHNY universality class.

cond-mat.soft↗

arXiv2015

Entropy and Kinetics of Point-Defects in Two-Dimensional Dipolar Crystals

We study in experiment and with computer simulation the free energy and the kinetics of vacancy and interstitial defects in two-dimensional dipolar crystals. The defects appear in different local topologies which we characterize by their point group symmetry; $C_n$ is the n-fold cyclic group and $D_n$ is the dihedral group, including reflections. The frequency of different local topologies is not determined by their almost degenerate energies but dominated by entropy for symmetric configurations. The kinetics of the defects is fully reproduced by a master equation in a multi-state Markov model. In this model, the system is described by the state of the defect and the time evolution is given by transitions occurring with particular rates. These transition rate constants are extracted from experiments and simulations using an optimisation procedure. The good agreement between experiment, simulation and master equation thus provides evidence for the accuracy of the model.

cond-mat.soft↗

arXiv2014

Spontaneous symmetry breaking in 2D: Kibble-Zurek mechanism in temperature quenched colloidal monolayers

The Kibble-Zurek mechanism describes the formation of topological defects during spontaneous symmetry breaking for quite different systems. Shortly after the big bang, the isotropy of the Higgs-field is broken during the expansion and cooling of the universe. Kibble proposed the formation of monopoles, strings, and membranes in the Higgs field since the phase of the symmetry broken field can not switch globally to gain the same value everywhere in space. Zurek pointed out that the same mechanism is relevant for second order phase transitions in condensed matter systems. Every finite cooling rate induces the system to fall out of equilibrium which is due to the critical slowing down of order parameter fluctuations: the correlation time diverges and the symmetry of the system can not change globally but incorporates defects between different domains. Depending on the cooling rate the heterogeneous order parameter pattern are a fingerprint of critical fluctuations. In the present manuscript we show that a monolayer of superparamagnetic colloidal particles is ideally suited to investigate such phenomena. In thermal equilibrium the system undergos continuous phase transitions according KTHNY-theory. If cooled rapidly across the melting temperature the final state is a polycrystal. We show, that the observations can not be explained with nucleation of a supercooled fluid but is compatible with the Kibble-Zurek mechanism.

cond-mat.soft↗

arXiv2014

Specific heat in two-dimensional melting

We report the specific heat $c_N$ around the melting transition(s) of micrometer-sized superparamagnetic particles confined in two dimensions, calculated from fluctuations of positions and internal energy, and corresponding Monte Carlo simulations. Since colloidal systems provide single particle resolution, they offer the unique possibility to compare the experimental temperatures of peak position of $c_N(T)$ and symmetry breaking, respectively. While order parameter correlation functions confirm the Kosterlitz-Thouless-Halperin-Nelson-Young melting scenario where translational and orientational order symmetries are broken at different temperatures with an intermediate so called hexatic phase, we observe a single peak of the specific heat within the hexatic phase, with excellent agreement between experiment and simulation. Thus, the peak is not associated with broken symmetries but can be explained with the total defect density, which correlates with the maximum increase of isolated dislocations. The absence of a latent heat strongly supports the continuous character of both transitions.

cond-mat.soft↗

arXiv2014

Inelastic scattering puts in question recent claims of Anderson localization of light

The interplay between nonlinear effects and Anderson localization in disordered optical fibres1 has recently attracted great interest, and it is important in the action of random lasers in which closed multiple scattering loops have enhanced intensity. As optical nonlinearities in TiO2 can give valuable information on the nature of light transport in strongly scattering powders, we studied these effects in an extended experimental and theoretical investigation (to be published). Now, Scheffold and Wiersma have ...

cond-mat.dis-nn↗

arXiv2013

Self-organized defect strings in two-dimensional crystals

Using experiments with single particle resolution and computer simulations we study the collective behaviour of multiple vacancies injected into two-dimensional crystals. We find that the defects assemble into linear strings that propagate through the crystal in a succession of rapid one-dimensional gliding phases and rare rotations, during which the direction of motion changes. At both ends, strings are terminated by dislocations with anti-parallel Burgers vectors. By monitoring the separation of the dislocations, we measure their effective interactions with high precision, for the first time beyond spontaneous formation and annihilation, and explain the double-well form of the dislocation interaction in terms of continuum elasticity theory. Our results give a detailed picture of the motion and interaction of dislocations in two dimensions and enhance our understanding of topological defects in two-dimensional nano-materials.

cond-mat.stat-mech↗

arXiv2013

Two-dimensional melting under quenched disorder

We study the influence of quenched disorder on the two-dimensional melting behavior by using both video-microscopy of superparamagnetic colloidal particles and computer simulations of repulsive parallel dipoles. Quenched disorder is provided by pinning a fraction of the particles. We confirm the occurrence of the Kosterlitz-Thouless-Halperin-Nelson-Young scenario with an intermediate hexatic phase. While the fluid-hexatic transition remains largely unaffected by disorder, the hexatic-solid transition shifts towards lower temperatures for increasing disorder resulting in a significantly broadened stability range of the hexatic phase. In addition, we observe spatio-temporal critical(-like) fluctuations consistent with the continuous character of the phase transitions.

cond-mat.soft↗

arXiv2012

Comparison of 2D melting criteria in a colloidal system

We use super-paramagnetic spherical particles which are arranged in a two-dimensional monolayer at a water/air interface to investigate the crystal to liquid phase transition. According to the KTHNY theory a crystal melts in thermal equilibrium by two continuous phase transitions into the isotropic liquid state with an intermediate phase, commonly known as hexatic phase. We verify the significance of several criteria based on dynamical and structural properties to identify the crystal - hexatic and hexatic - isotropic liquid phase transition for the same experimental data of the given setup. Those criteria are the bond orientational correlation function, the Larson-Grier criterion, 2D dynamic Lindemann parameter, the bond-orientational susceptibility, the 2D Hansen-Verlet rule, the Löwen-Palberg-Simon criterion as well as a criterion based on the shape factor of Voronoi cells and Minkowski functionals. For our system with long range repulsion, the bond order correlation function and bond order susceptibility works best to identify the hexatic - isotropic liquid transition and the 2D dynamic Lindemann parameter identifies unambiguously the hexatic - crystalline transition.

cond-mat.soft↗

arXiv2012

Glass elasticity from particle trajectories

Using positional data from video-microscopy of a two-dimensional colloidal system and from simulations of hard discs we determine the wave-vector-dependent normal mode spring constants in the supercooled fluid and glassy state, respectively. The emergence of rigidity and the existence of a displacement field in amorphous solids is clarified. Continuum elastic theory is used in the limit of long wavelengths to analyze the bulk and shear modulus of this amorphous system as a function of temperature. The onset of a finite static shear modulus upon cooling marks the fluid/solid transition. This provides an opportunity to determine the glass transition temperature $T_g$ in an intuitive and precise way.

cond-mat.soft↗

arXiv2009

Ultra-fast quenching of binary colloidal suspensions in an external magnetic field

An ultra-fast quench is applied to binary mixtures of superparamagnetic colloidal particles confined at a two-dimensional water-air interface by a sudden increase of an external magnetic field. This quench realizes a virtually instantaneous cooling which is impossible in molecular systems. Using real-space experiments, the relaxation behavior after the quench is explored. Local crystallites with triangular and square symmetry are formed on different time scales and the correlation peak amplitude of the small particles evolves nonmonotonically in time in agreement with Brownian dynamics computer simulations.

cond-mat.soft↗