# Scattering in periodic waveguide: integral representation and spectrum decomposition

@article{Zhang2019ScatteringIP, title={Scattering in periodic waveguide: integral representation and spectrum decomposition}, author={Ruming Zhang}, journal={arXiv: Analysis of PDEs}, year={2019} }

Scattering problems in periodic waveguides are interesting but challenging topics in mathematics, both theoretically and numerically. Due to the existence of eigenvalue, the unique solvability of such problems is not always guaranteed. To obtain a unique solution that is physically meaningful, the limiting absorption principle (LAP) is a commenly used method. LAP assumes that the limit of a family of solutions of scattering problems with absorbing material converges, as the absorbing parameter…

## One Citation

### Numerical methods for scattering problems in periodic waveguides

- Mathematics, Computer ScienceNumerische Mathematik
- 2021

New numerical methods for scattering problems in periodic waveguides are proposed and based on the Limiting Absorption Principle, which does not need the LAP process during numerical approximations, thus a standard error estimation is easily carried out.

## References

SHOWING 1-10 OF 30 REFERENCES

### A Floquet-Bloch Transform Based Numerical Method for Scattering from Locally Perturbed Periodic Surfaces

- Mathematics, Computer ScienceSIAM J. Sci. Comput.
- 2017

A new numerical method is introduced and analyzed to simulate scattering from locally perturbed periodic structures based on the Bloch transform to give convergence analysis and error bounds for a Galerkin discretizatio...

### A radiation condition arising from the limiting absorption principle for a closed full‐ or half‐waveguide problem

- Mathematics
- 2018

In this paper, we consider the propagation of waves in a closed full or half waveguide where the index of refraction is periodic along the axis of the waveguide. Motivated by the limiting absorption…

### The Limiting Absorption Principle for a Periodic Semi-Infinite Waveguide

- MathematicsSIAM J. Appl. Math.
- 2011

A small absorption is introduced to regularize the problem of an elliptic boundary value problem in a semi-infinite, straight waveguide containing a periodic material distribution and it is proved that the solutions converge locally in $H^1$.

### Evaluation of scattering operators for semi-infinite periodic arrays

- Mathematics
- 2009

Periodic arrays are structures consisting of geometrically identical subdomains, usually named periodic cells. In this paper, by taking the Helmholtz equation as a model, we consider the definition…

### Variational Approach in Weighted Sobolev Spaces to Scattering by Unbounded Rough Surfaces

- MathematicsSIAM J. Math. Anal.
- 2010

Well-posedness of this variational formulation in an energy space with weights is proved, which extends previous results in the unweighted setting to more general inhomogeneous terms in the Helmholtz equation.

### Numerical Simulation of Waves in Periodic Structures

- Physics
- 2008

In this work we improve and extend a technique named recursive doubling procedure developed by Yuan and Lu [J. Lightwave Technology 25 (2007), 3649-3656] for solving periodic array problems. It turns…

### Riesz bases and Jordan form of the translation operator in semi-infinite periodic waveguides

- Mathematics
- 2010

### Exact boundary conditions for time-harmonic wave propagation in locally perturbed periodic media

- Mathematics
- 2009

### An overview of periodic elliptic operators

- Mathematics
- 2015

The article surveys the main techniques and results of the spectral theory of periodic operators arising in mathematical physics and other areas. Close attention is paid to studying analytic…

### Absolute Continuity in Periodic Waveguides

- Mathematics
- 2002

We study second order elliptic operators with periodic coefficients in two‐dimensional simply connected periodic waveguides with the Dirichlet or Neumann boundary conditions. It is proved that under…