Resonance-free regions for diffractive trapping by conormal potentials

Resonance Free Domains for Non-Analytic Potentials

Analytic continuation and resonance-free regions for Sturm-Liouville potentials with power decay

Let us write λ = z, where 0 ≤ arg z < π when 0 ≤ arg λ < 2π. Then (1. 3) implies that there is a solution ψ(x, z) of (1. 1) such that ψ(x, z) ∼ exp(izx), ψ′(x, z) ∼ iz exp(izx) (1. 4) as x → ∞, and ψ(x, z) is analytic in z for im z > 0 [7, Theorem 1.9.1]. Then ψ(x, z) is the Weyl L2(0,∞) solution of (1. 1) when λ is non-real and it forms the basis of the Weyl-Titchmarsh spectral theory of (1. 1...

Diffractive optical devices produced by light-assisted trapping of nanoparticles.

One- and two-dimensional diffractive optical devices have been fabricated by light-assisted trapping and patterning of nanoparticles. The method is based on the dielectrophoretic forces appearing in the vicinity of a photovoltaic crystal, such as Fe:LiNbO3, during or after illumination. By illumination with the appropriate light distribution, the nanoparticles are organized along patterns desig...

Power-dependent switching of nonlinear trapping by local photonic potentials.

We study experimentally and numerically the nonlinear scattering of wave packets by local multisite guiding centers embedded in a continuous dielectric medium as a function of the input power and angle of incidence. The extent of trapping into the linear modes of different sites is manipulated as a function of both the input power and the angle of incidence, demonstrating power-controlled switc...

The Calderón Problem for Conormal Potentials, I: Global Uniqueness and Reconstruction

The goal of this paper is to establish global uniqueness and obtain reconstruction, in dimensions n ≥ 3, for the Calderón problem in the class of potentials conormal to a smooth submanifold H in R. In the case of hypersurfaces, the potentials considered here may have any singularity weaker than that of the delta function δH on the hypersurface H ; in general, these potentials correspond to cond...