Related papers: Inverse problems for nonlinear Maxwell's equations…
In this paper we prove stability estimates of logarithmic type for an inverse problem consisting in the determination of unknown portions of the boundary of a domain in $\mathbb{R}^n$, from a knowledge, in a finite time observation, of…
We study the inverse problems for the second order hyperbolic equations of general form with time-dependent coefficients assuming that the boundary data are given on a part of the boundary. The main result of this paper is the determination…
The lack of available table-top extreme ultraviolet (XUV) sources with high enough fluxes and coherence properties have limited the availability of nonlinear XUV and x-ray spectroscopies to free electron lasers (FEL). Here, we demonstrate…
We discuss a time-harmonic inverse scattering problem for a nonlinear Helmholtz equation with compactly supported inhomogeneous scattering objects that are described by a nonlinear refractive index in unbounded free space. Assuming the…
We consider the following perturbed polyharmonic operator $\Lc(x,D)$ of order $2m$ defined in a bounded domain $\Omega \subset \mathbb{R}^n, n\geq 3$ with smooth boundary, as \begin{equation*} \Lc(x,D) \equiv (-\Delta)^m +…
Nonlinear ultrasound imaging leverages harmonic wave generation to enhance contrast and spatial resolution beyond the capabilities of conventional linear techniques. This behavior is commonly modeled by the Westervelt equation, which…
Negative refractive index materials have attracted significant research attention due to their unique electromagnetic response characteristics. In this paper, we employ the complementing boundary condition to establish rigorous a priori…
In this paper, we will study increasing stability in the inverse source problem for the Helmholtz equation in the plane when the source term is assumed to be compactly supported in a bounded domain $\Omega$ with sufficiently smooth…
In this paper, we study forward problem and inverse problem for the fractional magnetic Schrodinger equation with nonlinear electric potential. We first investigate the maximum principle for the linearized equation and apply it to show that…
Recent experiments and calculations in topological semimetals have observed anomalously strong second-order optical nonlinearity, but yet whether the enhancement also occurs at surfaces of topological semimetals in general remains an open…
Second-order nonlinear optical responses, including photogalvanic effect (PGE) and second harmonic generation (SHG), are important physical phenomena in nonlinear optics. The PGE (SHG) related to linearly and circularly polarized light are…
We theoretically consider magnetization dynamics in a ferromagnetic slab induced by the magnetic field of a strong femtosecond laser pulse. The longitudinal geometry, in which the initial magnetization lies in both the plane of incidence…
The article considers the nonlinear inverse problem of identifying the material parameters in viscoelastic structures based on a generalized Maxwell model. The aim is to reconstruct the model parameters from stress data acquired from a…
We consider the initial-boundary value problem for systems of quasilinear wave equations on domains of the form $[0,T] \times \Sigma$, where $\Sigma$ is a compact manifold with smooth boundaries $\partial\Sigma$. By using an appropriate…
We consider the time-harmonic acoustic wave scattering by a bounded {\it anisotropic inhomogeneity} embedded in an unbounded {\it anisotropic} homogeneous medium. The material parameters may have discontinuities across the interface between…
We show that the nonlinear optical response reflects sensitively the electronic structure of transition-metal surfaces and interfaces. $d$ and $s$ electrons may contribute rather differently to the second harmonic generation (SHG) signal.…
We study the second harmonic generation (SHG) in a suspension of small spherical particles confined within a slab, assuming undepleted pump and applying (i) single scattering approximation and (ii) diffusion approximation. In the case (i),…
Second harmonic generation has been applied to study lattice, electronic and magnetic proprieties in atomically thin materials. However, inversion symmetry breaking is usually required for the materials to generate a large signal. In this…
Third-harmonic generation (THG) is a key nonlinear optical process for ultrafast imaging, terahertz (THz) signal generation, and symmetry-sensitive probes, often dominating in centrosymmetric materials where lower-order responses vanish.…
This paper provides a theoretical foundation for some common formulations of inverse problems in wave propagation, based on hyperbolic systems of linear integro-differential equations with bounded and measurable coefficients. The…