Quantitative spectral analysis of electromagnetic scattering. II: Evolution semigroups and non-perturbative solutions

@article{Zhou2022QuantitativeSA,
  title={Quantitative spectral analysis of electromagnetic scattering. II: Evolution semigroups and non-perturbative solutions},
  author={Yajun Zhou},
  journal={ArXiv},
  year={2022},
  volume={abs/2110.06092}
}
  • Yajun Zhou
  • Published 12 October 2021
  • Mathematics
  • ArXiv
We carry out quantitative studies on the Green operator Ĝ associated with the Born equation, an integral equation that models electromagnetic scattering, building the strong stability of the evolution semigroup {exp(−iτ Ĝ )|τ ≥0} on polynomial compactness and the Arendt– Batty–Lyubich–Vũ theorem. The strongly-stable evolution semigroup inspires our proposal of a nonperturbative method to solve the light scattering problem and improve the Born approximation. 

Figures from this paper

1 2 O ct 2 02 1 QUANTITATIVE SPECTRAL ANALYSIS OF ELECTROMAGNETIC SCATTERING
  • Mathematics
  • 2021
We perform quantitative spectral analysis on the Born equation, an integral equation for electromagnetic scattering that descends from the Maxwell equations. We establish norm bounds for the Green

References

SHOWING 1-10 OF 45 REFERENCES
Integral equation methods in scattering theory
Preface to the Classics Edition Preface Symbols 1. The Riesz-Fredholm theory for compact operators 2. Regularity properties of surface potentials 3. Boundary-value problems for the scalar Helmholtz
One-parameter semigroups for linear evolution equations
Linear Dynamical Systems.- Semigroups, Generators, and Resolvents.- Perturbation and Approximation of Semigroups.- Spectral Theory for Semigroups and Generators.- Asymptotics of Semigroups.-
Trace ideals and their applications
Preliminaries Calkin's theory of operator ideals and symmetrically normed ideals convergence theorems for $\mathcal J_P$ Trace, determinant, and Lidskii's theorem $f(x)g(-i\nabla)$ Fredholm theory
Analytical light-scattering solution for Chebyshev particles.
TLDR
A modification of the T-matrix method that allows for fast calculations of scattering properties of particles with irregular shapes and can provide rapid particle-size and refractive index averaging in a particle ensemble is developed.
Inverse Acoustic and Electromagnetic Scattering Theory
Introduction.- The Helmholtz Equation.- Direct Acoustic Obstacle Scattering.- III-Posed Problems.- Inverse Acoustic Obstacle Scattering.- The Maxwell Equations.- Inverse Electromagnetic Obstacle
Extinction and scattering by soft spheres.
On the basis of an approximate relation, the Mie series are replaced by new ones, which can be summed exactly with the aid of various modified and generalized forms of the addition theorem for
Computational Electrodynamics the Finite-Difference Time-Domain Method
TLDR
This paper presents background history of space-grid time-domain techniques for Maxwell's equations scaling to very large problem sizes defense applications dual-use electromagnetics technology, and the proposed three-dimensional Yee algorithm for solving these equations.
The discrete dipole approximation : An overview and recent developments
TLDR
A review of the discrete dipole approximation (DDA), which is a general method to simulate light scattering by arbitrarily shaped particles, is presented, taking the viewpoint of a general framework based on the integral equations for the electric field.
Effect of finite terms on the truncation error of Mie series.
TLDR
An improved formula is obtained, which includes the number of terms needed for determining the scattering cross section within a prescribed relative error, using extended precision computation for a wide range of commonly used size parameters and indices of refraction.
...
1
2
3
4
5
...