Guillaume Bal

In this study we analyze the topological invariants and edge states of transverse magnetic wave propagation in continuum photonic systems at a finite-width interface between two gyrotropic materials with different magnetic biases. Where previous studies have almost exclusively considered sharp transitions between two different electromagnetic media, we consider the more general geometry where the magnetic field bias is allowed to vary arbitrarily in a finite-width interface between two bulk regions. We find that when the magnetic field bias varies continuously between the two bulk regions, the bulk edge correspondence (BEC) holds robustly with respect to well-defined Chern invariants. However, discontinuities in the magnetic field bias introduce new edge modes and anomalous high-wavenumber spectral effects which alter the BEC. We analyze these spectral alterations and define a new anomalous BEC in continuum photonic systems which includes contributions from topological invariants and discontinuities in magnetic field bias.

This paper concerns the inverse scattering problem of a topologically non-trivial waveguide separating two-dimensional topological insulators. We focus here on the Dirac system and contrast it to the topologically trivial Klein Gordon model. We show that a short-range perturbation can be fully reconstructed from scattering data in a linearized setting and in a finite-dimensional setting under a smallness constraint. We also provide a stability result in appropriate topologies. We then solve the problem numerically without any smallness assumption by means of a standard adjoint method and illustrate our theoretical findings with several numerical simulations.

This paper concerns the inverse scattering problem of a topologically non-trivial waveguide separating two-dimensional topological insulators. We consider the specific model of a Dirac system. We show that a short-range perturbation can be fully reconstructed from scattering data in a linearized setting and in a finite-dimensional setting under a smallness constraint. We also provide a stability result in appropriate topologies. We then solve the problem numerically by means of a standard adjoint method and illustrate our theoretical findings with several numerical simulations.

Wavefield speckle patterns are generated by interference of randomly scattered coherent light. In the weak-coupling regime of the Itô-Schrödinger paraxial model for long-distance wave propagation, we show the following multiscale character: a macroscopic envelope solves a deterministic diffusion equation while the local wavefield (the speckle) is described by a complex Gaussian process both in terms of spatial axial and lateral displacements as well as frequency and angular variations of the incident wavebeam. These results describe speckle patterns and corroborate chromato-spatial memory effects observed in laser light propagation through heterogeneous media.

Interference of randomly scattered classical waves naturally leads to familiar speckle patterns, where the wave intensity follows an exponential distribution while the wave field itself is described by a circularly symmetric complex normal distribution. Using the Itô–Schrödinger paraxial model of wave beam propagation, we demonstrate how a deterministic incident beam transitions to such a fully developed speckle pattern over long distances in the so-called scintillation (weak-coupling) regime.

This paper concerns the topological classification of continuous Hamiltonians that find applications in biased cold plasmas and photonics. Besides a magnetic bias, the Hamiltonians are parameterized by a plasma frequency and a fixed vertical wavenumber. Eight distinct phases of matter are identified as these parameters vary. When insulating gaps are shared by two such phases, asymmetric edge modes propagate along interfaces separating the two phases. Here we apply the notion of a bulk difference invariant (BDI) to this Hamiltonian, and show by numerical diagonalizations of interface Hamiltonians that after an appropriate regularization our BDI correctly predicts edge transport as described by a bulk edge correspondence (BEC). We also derive theoretical tools to compute the BDI and show the limitations of the BEC when the phase transition is too singular.

This paper concerns the propagation of high frequency wave beams in highly turbulent atmospheres. Using a paraxial model of wave propagation, we show in the long-distance weak-coupling regime that the wavefields are approximately described by a complex Gaussian field whose scintillation index is unity. This provides a model of the speckle formation observed in many practical settings. The main step of the derivation consists in showing that closed-form moment equations in the Itô–Schrödinger regime are still approximately satisfied in the paraxial regime. This is done via Duhamel expansions, under the assumption that the random medium has Gaussian statistics. The rest of the proof is then an extension of results derived in [G. Bal and A. Nair, Complex Gaussianity of Long-Distance Random Wave Processes, preprint, arXiv:2402.17107, 2024].