# Rapidly convergent quasi-periodic Green functions for scattering by arrays of cylinders—including Wood anomalies

@article{Bruno2017RapidlyCQ, title={Rapidly convergent quasi-periodic Green functions for scattering by arrays of cylinders—including Wood anomalies}, author={Oscar P. Bruno and Agustin G. Fernandez-Lado}, journal={Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences}, year={2017}, volume={473} }

This paper presents a full-spectrum Green-function methodology (which is valid, in particular, at and around Wood-anomaly frequencies) for evaluation of scattering by periodic arrays of cylinders of arbitrary cross section—with application to wire gratings, particle arrays and reflectarrays and, indeed, general arrays of conducting or dielectric bounded obstacles under both transverse electric and transverse magnetic polarized illumination. The proposed method, which, for definiteness, is…

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## References

SHOWING 1-10 OF 37 REFERENCES

### A new integral representation for quasi-periodic scattering problems in two dimensions

- Mathematics
- 2011

Boundary integral equations are an important class of methods for acoustic and electromagnetic scattering from periodic arrays of obstacles. For piecewise homogeneous materials, they discretize the…

### Efficient high-order evaluation of scattering by periodic surfaces: deep gratings, high frequencies, and glancing incidences.

- Computer ScienceJournal of the Optical Society of America. A, Optics, image science, and vision
- 2009

A superalgebraically convergent integral equation algorithm for evaluation of TE and TM electromagnetic scattering by smooth perfectly conducting periodic surfaces z=f(x) that produces solutions with full double-precision accuracy in single-processor computing times of the order of a few seconds.

### A Super-Algebraically Convergent, Windowing-Based Approach to the Evaluation of Scattering from Periodic Rough Surfaces

- Mathematics
- 2008

We introduce a new second-kind integral equation method to solve direct rough surface scattering problems in two dimensions. This approach is based, in part, upon the bounded obstacle scattering…

### Stable and efficient evaluation of periodized Green's functions for the Helmholtz equation at high frequencies

- Computer ScienceJ. Comput. Phys.
- 2009

### Efficient high-order evaluation of scattering by periodic surfaces: vector-parametric gratings and geometric singularities

- Computer Science
- 2010

This work introduces a highly accurate and efficient solver for problems of scattering by vector-parametric, possibly non-smooth one-dimensional periodic surfaces and produces solutions with full double-precision accuracy in single-processor computing times of the order of a few seconds.

### Rapidly convergent two-dimensional quasi-periodic Green function throughout the spectrum - including Wood anomalies

- MathematicsJ. Comput. Phys.
- 2014

### A fast, high-order algorithm for the solution of surface scattering problems: basic implementation, tests, and applications

- Computer Science
- 2001

The present algorithm can evaluate accurately in a personal computer scattering from bodies of acoustical sizes of several hundreds and exhibits super-algebraic convergence; it can be applied to smooth and nonsmooth scatterers, and it does not suffer from accuracy breakdowns of any kind.

### Solution of a boundary value problem for the Helmholtz equation via variation of the boundary into the complex domain

- MathematicsProceedings of the Royal Society of Edinburgh: Section A Mathematics
- 1992

Synopsis In this paper we deal with the problem of diffraction of electromagnetic waves by a periodic interface between two materials. This corresponds to a two-dimensional quasi-periodic boundary…

### Lattice sums and the two-dimensional, periodic Green's function for the Helmholtz equation

- Computer Science, MathematicsProceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences
- 2001

A new integral representation for lattice sums is described, and the results are compared with other techniques for evaluating similar quantities.

### The Green's Function for the Two-Dimensional Helmholtz Equation in Periodic Domains

- Mathematics
- 1998

Analytical techniques are described for transforming the Green's function for the two-dimensional Helmholtz equation in periodic domains from the slowly convergent representation as a series of…