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Diffusion-driven patterns appear on curved surfaces in many settings, initiated by unstable modes of an underlying Laplacian operator. On a flat surface or perfect sphere, the patterns are degenerate, reflecting translational/rotational…

It is common for dispersion curves of damped periodic materials to be based on real frequencies versus complex wavenumbers or, conversely, real wavenumbers versus complex frequencies. The former condition corresponds to harmonic wave motion…

The scattering of light impacts sensing and communication technologies throughout the electromagnetic spectrum. Overcoming the effects of time-varying scattering media is particularly challenging. In this article we introduce a new way to…

This work discusses the homogenization analysis for diffusion processes on scale-free metric graphs, using weak variational formulations. The oscillations of the diffusion coefficient along the edges of a metric graph induce internal…

We investigate, theoretically and experimentally, the evolution of a paraxial beam propagating in free space when its initial transverse structure is characterized by an asymmetric Gaussian modulation combined with an entire function.…

We study two-dimensional wave propagation in materials whose properties vary periodically in one direction only. High order homogenization is carried out to derive a dispersive effective medium approximation. One-dimensional materials with…

We suggest a novel concept of diffraction management in waveguide arrays and predict the existence of discrete gap solitons that possess the properties of both conventional discrete and Bragg grating solitons. We demonstrate that both the…

A new approach to the modeling of nonfree particle diffusion is presented. The approach uses a general setup based on geometric graphs (networks of curves), which means that particle diffusion in anything from arrays of barriers and pore…

Knowing the dispersion regime (normal vs anomalous) is important for both an isolated waveguide and a waveguide array. We investigate by the Finite Element Method the dispersion properties of a LiNbO3 waveguides array using two techniques.…

We present a theoretical and experimental study of light transport in disordered media with strongly heterogeneous distribution of scatterers formed via non-scattering regions. Step correlations induced by quenched disorder are found to…

This work is concerned with optical imaging in strongly diffusive environments. We consider a typical setting in optical coherence tomography where a sample is probed by a collection of wavefields produced by a laser and propagating through…

This paper concerns the reconstruction of properties of narrow laser beams propagating in turbulent atmospheres. We consider the setting of off-axis measurements, based on light detection away from the main path of the beam. We first model…

We experimentally study the transport prop- erties of dipolar and fundamental modes on one di- mensional (1D) coupled waveguide arrays. By carefully modulating a wide optical beam, we are able to effec- tively excite dipolar or fundamental…

Using quantum theory, we study the propagation of an optical field in an inhomogeneous dielectric, and apply this scheme to traveling optical fields in a waveguide. We introduce a field-atom interaction Hamiltonian and derive the refractive…

Waveguide arrays offer enormous potential to design circuit elements essential to fabricate optical devices capable to processing information codified by light. In this work we study the existence and stability of localized beams in one…

The recent interest in the imaging possibilities of photonic crystals (superlensing, superprism, optical mirages etc...) call for a detailed analysis of beam propagation inside a finite periodic structure. In this paper, an answer to the…

We study propagation of light in nonlinear diffraction-managed photonic lattices created with arrays of periodically-curved coupled optical waveguides which were fabricated using femtosecond laser writing in silica glass, and titanium…

Since the early works[1-4] on the so-called nondiffracting waves (called also Localized Waves), a great deal of results has been published on this important subject, from both the theoretical and the experimental point of view. Initially,…

We investigate light propagation through materials with periodically modulated gain/loss profile in both transverse and longitudinal directions, i.e. in material with two-dimensional modulation in space. We predict effects of…

While diffusion models excel at generating high-quality images from text prompts, they struggle with visual consistency when generating image sequences. Existing methods generate each image independently, leading to disjointed narratives -…