Far-field sub-wavelength imaging and focusing using a wire medium based resonant metalens

This is the second article in a series of two dealing with the concept of a ‘resonant metalens’ we introduced recently. This is a new type of lens capable of coding in time and radiating efficiently in the far-field region sub-diffraction information about an object. A proof of the concept of such a lens is performed in the microwave range, using a medium made out of a square lattice of parallel conducting wires with finite length. We investigate a sub-wavelength focusing scheme with time reversal and demonstrate experimentally spots with focal widths of λ/25. Through a cross-correlation based imaging procedure we show an image reconstruction with a resolution of λ/80. Eventually we discuss the limitations of such a lens which reside essentially in losses.     

The nonlocal elastomagnetoelectrostatics of disordered micropolar media

The interactions of electric, magnetic, and elastic subsystems in nonlinear disordered micropolar media that possess a bending–torsion tensor and an nonsymmetric strain tensor have been studied in the framework of phenomenological elastomagnetoelectrostatics. A system of nonlinear equations for determining the ground state of these media has been obtained by the variational method. It is shown that nonuniform external and internal rotations not only create elastic stresses, but also generate additional electric and magnetic fields, while nonuniform elastic stresses and external fields induce internal rotations. The nonlocal character of the micropolar media significantly influences elementary excitations and nonlinear dynamic processes.     

Diffusion in disordered media

Diffusion in disordered systems does not follow the classical laws which describe transport in ordered crystalline media, and this leads to many anomalous physical properties. Since the application of percolation theory, the main advances in the understanding of these processes have come from fractal theory. Scaling theories and numerical simulations are important tools to describe diffusion processes (random walks: the ‘ant in the labyrinth’) on percolation systems and fractals. Different types of disordered systems exhibiting anomalous diffusion are presented (the incipient infinite percolation cluster, diffusion-limited aggregation clusters, lattice animals, and random combs), and scaling theories as well as numerical simulations of greater sophistication are described. Also, diffusion in the presence of singular distributions of transition rates is discussed and related to anomalous diffusion on disordered structures.     

Diffusion in disordered media

Diffusion in disordered systems does not follow the classical laws which describe transport in ordered crystalline media, and this leads to many anomalous physical properties. Since the application of percolation theory, the main advances in the understanding of these processes have come from fractal theory. Scaling theories and numerical simulations are important tools to describe diffusion processes (random walks: the 'ant in the labyrinth') on percolation systems and fractals. Different types of disordered systems exhibiting anomalous diffusion are presented (the incipient infinite percolation cluster, diffusion-limited aggregation clusters, lattice animals, and random combs), and scaling theories as well as numerical simulations of greater sophistication are described. Also, diffusion in the presence of singular distributions of transition rates is discussed and related to anomalous diffusion on disordered structures.     

Dielectric resonances in disordered media

Binary disordered systems are usually obtained by mixing two ingredients in variable proportions: conductor and insulator, or conductor and super-conductor. They present very specific properties, in particular the second-order percolation phase transition, with its fractal geometry and the multi-fractal properties of the current moments. These systems are naturally modeled by regular bi-dimensional or tri-dimensional lattices, on which sites or bonds are chosen randomly with given probabilities. The two significant parameters are the ratio h = σ ₁/σ of the complex conductances, σ and σ ₁, of the two components, and their relative abundances p (or, respectively, 1 - p). In this article, we calculate the impedance of the composite by two independent methods: the so-called spectral method, which diagonalises Kirchhoff's Laws via a Green function formalism, and the Exact Numerical Renormalization method (ENR). These methods are applied to mixtures of resistors and capacitors (R-C systems), simulating e.g. ionic conductor-insulator systems, and to composites constituted of resistive inductances and capacitors (LR-C systems), representing metal inclusions in a dielectric bulk. The frequency dependent impedances of the latter composites present very intricate structures in the vicinity of the percolation threshold. In this paper, we analyse the LR-C behavior of compounds formed by the inclusion of small conducting clusters (“n-legged animals”) in a dielectric medium. We investigate in particular their absorption spectra who present a pattern of sharp lines at very specific frequencies of the incident electromagnetic field, the goal being to identify the signature of each animal. This enables us to make suggestions of how to build compounds with specific absorption or transmission properties in a given frequency domain. Received 16 August 2002 Published online 14 February 2003 RID="a" ID="a"e-mail: laurent.raymond@l2mp.fr RID="b" ID="b"e-mail: steffen.schaefer@l2mp.fr RID="c" ID="c"UMR CNRS 6137     

微球透镜对亚波长表面结构的显微成像研究

为了研究微球透镜对亚波长物体的成像特性,利用直径为3.4μm的二氧化硅微球透镜对刻录蓝光光碟的亚波长表面结构进行了显微成像实验,观察了不同排列方式和液体浸没深度下微球透镜的成像特性。实验结果表明:微球透镜在不同浸没深度下对亚波长表面结构具有放大作用,放大率为1.2~1.8倍,并且通过微球透镜的密排列,可以获得更大的视场;浸没液体深度增大时,图像的放大率减小,视场增大。基于时域有限差分的电场仿真表明,微球透镜可以将光场汇聚成半高全宽为260nm,纵向可持续几个微米的高强度光区域,引起强的背景散射,从而获得普通光学显微镜不能分辨的亚波长表面结构图像。     

The field-theoretic description of dynamics of interfaces in disordered media

The time evolution of an interface in a disordered media is described by using the propagator method. The method enables one to represent the perturbation expansions of different quantities characterizing the interface by means of diagrams which are familiar from the field theory. By the analysis of the divergences in the vicinity of the critical dimension d_c = 4 we found that the regularization of the theory demands the renormalization of the mobility and all moments of the disorder correlator excepting the zero one. The renormalization group (RG) calculations of the average velocity of the interface, the roughness, and the functional RG equation of the disorder correlator are presented to order ? = 4 - d. The latter coincides with the result obtained by D. S. Fisher in the equilibrium case. The RG equations have a pole at the value of the driving force, which coincides with the value of the threshold below which the interface becomes pinned as predicted by Bruinsma and Aeppli. The behavior of the mobility in the vicinity of the pole is discussed.     

Penetration of hot electrons through a cold disordered wire

We study a penetration of an electron with high energy E ≫ T through strongly disordered wire of length L ≫ a (a being the localization length). Such an electron can loose, but not gain the energy, when hopping from one localized state to another. We have found a distribution function for the transmission coefficient 풯. The typical 풯 remains exponentially small in L/a, but with the decrement, reduced compared to the case of direct elastic tunneling: $ \overline {\ln T} $ \overline {\ln T} ≈ 0.237 × 2L/a. The distribution function has a strong tail in the domain of anomalously high 풯; the average $ \overline T $ \overline T ∝ (a/L)² is controlled by rare configurations of disorder, corresponding to this tail.     

Local correlations of different eigenfunctions in a disordered wire

The correlation of the local density of states 〈ρ_ɛ(r ₁)ρ_{ɛ + ω}(r ₂)〉 in quasi-one-dimensional disordered wires in a magnetic field is calculated under the assumption that |r ₁ − r ₂| is much smaller than the localization length. This amounts to finding the zero mode of the transfer-matrix Hamiltonian for the supersymmetric σ model, which is done exactly by mapping to the three-dimensional Coulomb problem. Both the regimes of level repulsion and level attraction are obtained, depending on |r ₁ − r ₂|. We demonstrate that the correlations of different eigenfunctions in the quasi-one-dimensional and strictly one-dimensional cases are dissimilar. The text was submitted by the authors in English.     

Wave propagation in nonlinear disordered media

We analyze mechanisms and regimes of wave packet spreading in nonlinear disordered media. We discuss resonance probabilities, and predict a dynamical crossover from strong to weak chaos. The crossover is controlled by the ratio of nonlinear frequency shifts and the average eigenvalue spacing of eigenstates of the linear equations within one localization volume. We consider generalized models in higher lattice dimensions and obtain critical values for the nonlinearity power, the dimension, and norm density, which influence possible dynamical outcomes in a qualitative way.     

Bi-laplacian growth patterns in disordered media

Experiments in quasi-two-dimensional geometry (Hele-Shaw cells) in which a fluid is injected into a viscoelastic medium (foam, clay, or associating polymers) show patterns akin to fracture in brittle materials, very different from standard Laplacian growth patterns of viscous fingering. An analytic theory is lacking since a prerequisite to describing the fracture of elastic material is the solution of the bi-Laplace rather than the Laplace equation. In this Letter we close this gap, offering a theory of bi-Laplacian growth patterns based on the method of iterated conformal maps.     

Appearance of pseudo-band-gaps in a disordered quantum wire array

The density of states and the conductivity are calculated in lateral superlattices with disorder in the period within a self-consistent Born approximation. Although the potential loses its periodicity on average due to disorder, it leads to an opening up of a pseudo-band-gap and modifies the conductivity perpendicular to the superlattice even qualitatively, when the energy reaches the zone boundary.     

Dynamics of surface roughening in disordered media

In this paper the roughening of interfaces moving in inhomogeneous media is investigated by examining the corresponding stochastic differential equations using (i) numerical methods and (ii) dimensional analysis. We consider interface evolution equations where disorder is represented by quenched noise which can be both additive and multiplicative. Our main finding is that quenched noise leads to a new universality class as concerning the exponents δ and β describing respectively the spatial and temporal scaling of surface roughness. In particular, additive noise close to the pinning transition results in a behaviour with δ = 0.71 ± 0.08 and β = 0.61±0.06 up to a crossover time. These estimates are in very good agreement with the theoretical prediction and that we derive from a dimensional analysis of the equation. Furthermore, we argue that multiplicative noise is the appropriate choice to describe experiments where the interface between two flowing phases is considered. By numerically integrating the proposed equation we have obtained (i) surfaces remarkably similar to those observed in the experiments and (ii) a scaling of the surface width as a function of time with an exponent β = 0.65 being in an excellent agreement with the experimental value. In addition to the exponents we discuss other relevant features of the surfaces, including the scaling of the average velocity of the surface ν_a close to pinning and the non-trivial, power law distribution of waiting times and noise along the interface in the stationary regime.     

Pinning of cracks in two-dimensional disordered media

We study the statistics of crack pinning in two dimensions by experiments and simulations of directed polymers in random media. Mode I tensile tests on paper samples show a delocalization phenomenon as the notch length is varied if the fraction of cracks pinned to the notch is monitored. This is compared with the behavior of directed polymers in the presence of both an energetically favorable localized pinning center and bulk disorder. An analysis of the crack interface roughness indicates self-affine behavior with a roughness exponent ζ in the proximity of the minimum energy surface value 2/3. Received 4 April 2000 and Received in final form 10 October 2000     

Instabilities of waves in nonlinear disordered media

We develop a self-consistent theory of temporal fluctuations of a speckle pattern resulting from the multiple scattering of a coherent wave in a weakly nonlinear disordered medium. The speckle pattern is shown to become unstable if the nonlinearity exceeds a threshold value. The instability is due to a feedback provided by the multiple scattering and manifests itself in spontaneous fluctuations of the scattered intensity. The development of instability is independent of the sign of nonlinearity.