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Complex periodic structures inherit spectral properties from the constituent parts of their unit cells, chiefly their spectral band gaps. Exploiting this intuitive principle, which is made precise in this work, means spectral features of…
Resonant scattering of plane waves by a periodic slab under conditions close to those that support a guided mode is accompanied by sharp transmission anomalies. For two-dimensional structures, we establish sufficient conditions, involving…
A statistical model is used to determine how stochastic fluctuations in the intensities of orthogonal polarization modes contribute to the modulation and depolarization of pulsar radio emission. General expressions for the distributions of…
While flat metasurfaces are intensively studied, theoretical modelling of conformal metasurfaces appears to be exceptionally challenging where it demands accurate analysis of the metasurface geometry. Here, it is shown how numerical…
We use a lattice Green function approach to study the stationary modes of a linear/nonlinear (Kerr) impurity embedded in a periodic one-dimensional lattice where we replace the standard discrete Laplacian by a fractional one. The energies…
We study differential forms invariant under a finite reflection group over a field of arbitrary characteristic. In particular, we prove an analogue of Saito's freeness criterion for invariant differential 1-forms. We also discuss how…
Feedback in cellular processes is typically inferred through cellular responses to experimental perturbations. Modular response analysis provides a theoretical framework for translating specific perturbations into feedback sensitivities…
Some basic properties of nonradiating systems are considered. A simple connection is established between the existence of residual electromagnetic potentials and the current density spectrum of the system. The properties of specific…
Linear response theories in the continuum capable of describing continuum spectra and dynamical correlations are presented. Our formulation is essentially the same as the continuum random-phase approximation (RPA) but suitable for uniform…
There are limits of validity of classical constitutive laws such as Fourier and Navier-Stokes equations, phenomena beyond those limits have been experimentally found many decades ago. However, it is still not clear what theory would be…
A theory based on the superposition principle is developed to uncover the basic physics of the wave behavior in a finite grating of N unit cells. The theory reveals that bound states in the continuum (BICs) of infinite quality factor…
We consider, both theoretically and experimentally, the excitation and detection of the localized quasi-modes (resonances) in an open dissipative 1D random system. We show that even though the amplitude of transmission drops dramatically so…
Classically, any structure for a signature $\Sigma$ may be completed to a model of a desired regular theory $T$ by means of the chase construction or small object argument. Moreover, this exhibits $\mathrm{Mod}(T)$ as weakly reflective in…
We investigate the effective properties (conductivity, diffusivity and elastic moduli) of model random composite media derived from Gaussian random fields and overlapping hollow spheres. The morphologies generated in the models exhibit low…
We conjecture that chaotic resonance modes in scattering systems are a product of a conditionally invariant measure from classical dynamics and universal exponentially distributed fluctuations. The multifractal structure of the first factor…
The peculiarities of defect modes and reflection spectra of chiral photonic crystals (CPC) with an isotropic defect for various thicknesses of the defect layer was investigated. The peculiarities of the spectra of photonic density of the…
One way of studying a relational structure is to investigate functions which are related to that structure and which leave certain aspects of the structure invariant. Examples are the automorphism group, the self-embedding monoid, the…
The rigorous solution to the grating diffraction problem is a cornerstone step in many scientific fields and industrial applications ranging from the study of the fundamental properties of metasurfaces to the simulation of photolithography…
We study bandstructure properties of periodic optical systems composed of lossy and intrinsically dispersive materials. To this end, we develop an analytical framework based on adjoint modes of a lossy periodic electromagnetic system and…
The trigonometric Ruijsenaars-Schneider model is diagonalized by means of the Macdonald symmetric functions. We evaluate the dynamical density-density correlation function and the one-particle retarded Green function as well as their…