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We propose and demonstrate two methods for modal decomposition in multi-mode fibres. Linearly polarized modes propagating in a slightly multi-mode fibre are easily retrieved from intensity measurements at the fibre output surface. The first…
In this paper we propose methods for inference of the geometric features of a multivariate density. Our approach uses multiscale tests for the monotonicity of the density at arbitrary points in arbitrary directions. In particular, a…
The scattering parameter extraction method of metamaterial homogenization is reviewed to show that the only ambiguity is the one related to the choice of the branch of the complex logarithmic function (or the complex inverse cosine…
In the field of metamaterials, many intriguing phenomena arise from having a structure which is periodic in space. In time-dependent structures, conceptually similar properties can arise, which nevertheless have fundamentally different…
Mechanical metamaterials leverage geometric design to achieve unconventional properties, such as high strength at low density, efficient wave guiding, and complex shape morphing. The ability to control shape changes builds on the complex…
Nearly all practical applications of the theory of characteristic modes (CMs) involve the use of computational tools. Here in Paper 2 of this Series on CMs, we review the general transformations that move CMs from a continuous theoretical…
By means of Monte Carlo simulations we show that there are two qualitatively different modes of localization of classical waves in 1-{\em D} random periodic-on-average systems. States from pass bands and band edges of the underlying band…
Observations of pulsars across the radio spectrum are revealing a dependence of the characteristic scattering time ($\tau$) on frequency, which is more complex than the simple power law with a theoretically predicted power law index. In…
We develop a perturbative approach that allows one to study the surface scattering in quasi-1D waveguides with rough boundaries. Our approach is based on the construction of an effective ``bulk'' potential of a very complicated structure.…
As an example of thin composite layers we consider single and double grids of periodically arranged interacting wires loaded with a certain distributed reactive impedance. Currents induced to the wires by a normally incident plane wave are…
We examine characteristic properties of deterministic and stochastic diffusion in low-dimensional chaotic dynamical systems. As an example, we consider a periodic array of scatterers defined by a simple chaotic map on the line. Adding…
Using the time periodic ABCD parameters, an expression for the dispersion relation of space-time modulated structures is obtained. The relation is valid for general structures even when the spatial granularity is comparable to the operating…
A method of modelling the three-dimensional microstructure of random isotropic two-phase materials is proposed. The information required to implement the technique can be obtained from two-dimensional images of the microstructure. The…
In this paper, we develop a high order numerical method for the numerical solutions of scattering problems with slightly perturbed periodic surfaces in two dimensional spaces. Based on the regularity property introduced in Part I, the…
Metasurfaces are efficient and versatile electromagnetic structures that have already enabled the implementation of a wide range of microwave and photonic wave shaping applications. Despite the extensive research into metasurfaces, a…
This chapter is a pedagogical review of methods and results for studying wave propagation in one-dimensional complex structures. We describe and compare the tight-binding, scattering matrix, transfer matrix and Riccati formalisms. We…
The Random Coupling Model (RCM) is a statistical approach for studying the scattering properties of linear wave chaotic systems in the semi-classical regime. Its success has been experimentally verified in various over-moded wave settings,…
Surface-bound modes in metamaterials forged by drilling periodic hole arrays in perfect-conductor surfaces are investigated by means of both analytical techniques and rigorous numerical solution of Maxwell's equations. It is shown that…
Frequency domain spectroscopy allows an experimenter to establish optical properties of solids in a wide frequency band including the technically challenging 10 THz region, and in other bands enables metrological comparison between…
We study the scattering properties of $N$ identical one-dimensional localized $\mathcal{PT}$-symmetric potentials, connected in series as well as in parallel. We derive a general transfer matrix formalism for parallel coupled quantum…