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Understanding the ability of particles to maneuver through disordered environments is a central problem in innumerable settings, from active matter and biology to electronics. Macroscopic particles ultimately exhibit diffusive motion when…
Solutions of the wave equations for time-independent disordered media can exhibit Anderson localization where instead of wave propagation we observe their localization around different points in space. Photonic time crystals are spatially…
Optimal paths play a fundamental role in numerous physical applications ranging from random polymers to brittle fracture, from the flow through porous media to information propagation. Here for the first time we explore the path that is…
We consider a ring of identical or near identical coupled periodic oscillators in which the connections have randomly heterogeneous strength. We use the master stability function method to determine the possible patterns at the…
Topic of the thesis is a theoretical description of the ultracold atomic gases in one- and two-dimensional optical lattices in the presence of the disorder leading to the Anderson localization. The disorder is created by interaction of the…
We theoretically investigate light propagation and Anderson localization in one-dimensional disordered superlattices composed of dielectric stacks with graphene sheets in between. Disorder is introduced either on graphene material…
We show that fabrication imperfections in silicon nitride photonic crystal waveguides can be used as a resource to efficiently confine light in the Anderson-localised regime and add functionalities to photonic devices. Our results prove…
We study theoretically the spatial distribution of the polarizations in the array of resonant electromagnetic dipole emitters coupled to a one-dimensional waveguide. The ratchet effect manifests itself in the spatial asymmetry of the…
We discuss the scattering of photons from a three-level emitter in a one-dimensional waveguide, where the transport is governed by the interference of spontaneously emitted and directly transmitted waves. The scattering problem is solved in…
We propose the use of a left-handed material in an optical waveguide structure to reduce its thickness well below the wavelength of light. We demonstrate that a layer of left-handed material, added to the cladding of a planar waveguide…
We show how two-dimensional waveguide arrays can be used to probe the effect of on-site interaction on Anderson localization of two interacting bosons in one dimension. It is shown that classical light and linear elements are sufficient to…
Localized waves in disordered one-dimensional materials have been studied for decades, including white-noise and correlated disorder, as well as quasi-periodic disorder. How these wave phenomena relate to those in crystalline (periodic…
When gently placing a droplet onto a vertically vibrated bath, a drop can bounce without coalescing. Upon increasing the forcing acceleration, the droplet is propelled by the wave it generates and becomes a walker with a well defined speed.…
We experimentally study the effect of enhancement of localization in weak one-dimensional random potentials. Our experimental setup is a single mode waveguide with 100 tuneable scatterers periodically inserted into the waveguide. By…
We present a detailed numerical and theoretical analysis of the recently discovered phenomenon of coherent forward scattering. This effect manifests itself as a macroscopic interference peak in the forward direction of the momentum…
We demonstrate, by explicit construction, that a single band tight binding Hamiltonian defined on a class of deterministic fractals of the b = 3N Sierpinski type can give rise to an infinity of dispersionless, flat-band like states which…
We demonstrate Anderson localisation of visible light on a chip and report quality factors exceeding highly engineered two-dimensional cavities. Our results reverse the trend, observed so far, of the quality of disorder-induced light…
The propagation of light through samples with random inhomogeneities can be described by way of transmission eigenchannels, which connect incoming and outgoing external propagating modes. Although the detailed structure of a disordered…
Our study connects the physics of disordered integer-dimensional systems and regular self-similar objects by studying spectral properties of fractal agglomerates with tunable dimension. The latter is controlled by parameter $\alpha$ of the…
We examine the localized mode and the transmission of plane waves across a capacitive impurity of strength $\Delta$, in a 1D bi-inductive electrical transmission line where the usual discrete Laplacian is replaced by a fractional one…