Related papers: Spectral Singularities with Directional Sensitivit…
In this paper we give a review on the computational methods used to characterize the complex singularities developed by some relevant PDEs. We begin by reviewing the singularity tracking method based on the analysis of the Fourier spectrum.…
Spontaneous symmetry breaking (SSB) occurs when modes of asymmetric profile appear in a symmetric, double-well potential, due to the nonlinearity of the potential exceeding a critical value. In this study, we examine SSB in a periodic…
Spontaneous symmetry breaking (SSB) and exceptional points (EPs) are often assumed to be inherently linked. Here we investigate the intricate relationship between SSB and specific classes of EPs across three distinct, real-world scenarios…
Nonlinear periodic systems, such as photonic crystals and Bose-Einstein condensates (BECs) loaded into optical lattices, are often described by the nonlinear Schr\"odinger/Gross-Pitaevskii equation with a sinusoidal potential. Here, we…
This paper studies singularity structures of the linear inviscid damping of two-dimensional Euler equations in a finite periodic channel. We introduce a recursive definition of singularity structures which characterize the singularities of…
In two dimensions, the standard treatment of the scattering problem for a delta-function potential, $v(\mathbf{r})=\mathfrak{z}\,\delta(\mathbf{r})$, leads to a logarithmic singularity which is subsequently removed by a renormalization of…
Conformal defects -- extended objects in conformal field theories -- carry localised excitations inherited from symmetry currents, known as the displacements and tilts. They capture the linear response of the defect to deformations of its…
The work is devoted to the self-action of laser beams propagating in the isotropic phase of a cholesteric liquid crystal near the transition temperature to the mesophase in a wide range of parameter values characterizing the nonlocality of…
We introduce a class of unidirectional lasing modes associated with the frozen mode regime of non-reciprocal slow-wave structures. Such asymmetric modes can only exist in cavities with broken time-reversal and space inversion symmetries.…
Speckle metrology exploits the high sensitivity of scattered fields to parameters of interest, yet this also leaves measurements vulnerable to unintended perturbations. Here we employ transmission matrix formalism to engineer light fields…
Despite the benefits that directional coupler based parity-time symmetric systems may offer to the field of integrated optics, the realization of such couplers relies on rather strict design constraints on the waveguide parameters. Here, we…
The interaction between a mobile discrete dark soliton (DDS) and impurities in one-dimensional nonlinear (Kerr) photonic lattices is studied. We found that the scattering is an inelastic process where the DDS can be reflected or transmitted…
We use beam tracing -- implemented with a newly-written code, Scotty -- and the reciprocity theorem to derive a model for the linear backscattered power of the Doppler Backscattering (DBS) diagnostic. Our model works for both the O-mode and…
Brewster-reflection of a post-paraxial optical beam at a plane dielectric interface unravels fundamentally significant optical singularity dynamics. We express the simulated field-component profiles of a Brewster-reflected post-paraxial…
The versatile and exactly solvable Scarf II has been predicting, confirming and demonstrating interesting phenomena in complex PT-symmetric sector, most impressively. However, for the non-PT-symmetric sector it has gone underutilized. Here,…
We prove existence, uniqueness and regularity of solutions of nonlocal heat equations associated to anisotropic stable diffusion operators. The main features are that the right-hand side has very few regularity and that the spectral measure…
For a general formulation of linearised hybrid inverse problems in impedance tomography, the qualitative properties of the solutions are analysed. Using an appropriate scalar pseudo-differential formulation, the problems are shown to permit…
In a neutral particle gas detector, the parallax error resulting from the perpendicular projection on the detection plane or wire of the radial particle trajectories emanating from a point like source (such as a scattering sample) can…
Optical nonlinearities typically require macroscopic media, thereby making their implementation at the quantum level an outstanding challenge. Here we demonstrate a nonlinearity for one atom enclosed by two highly reflecting mirrors. We…
Solitons are universal nonlinear excitations that appear in settings as varied as optics, water waves, and quantum gases [1-5]. While reduced models of soliton dynamics are well established, their validity and dynamical behaviour in…