Scattering from periodic arrays of cylinders by Dirichlet-to-Neumann maps

A simple and efficient numerical method for computing the transmission and reflection spectra of periodic arrays of cylinders is developed. For each unit cell containing a cylinder, only the wave field on the edges of the unit cell is computed. For multilayered structures, a marching scheme based on a pair of operators is developed

[1]  P. Robinson,et al.  Calculation of electromagnetic properties of regular and random arrays of metallic and dielectric cylinders. , 1999, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[2]  Jean-Paul Hugonin,et al.  Algorithm for the rigorous coupled-wave analysis of grating diffraction , 1994 .

[3]  Daniel Maystre,et al.  Multicoated gratings: a differential formalism applicable in the entire optical region , 1982 .

[4]  K. Yasumoto,et al.  Accurate analysis of two-dimensional electromagnetic scattering from multilayered periodic arrays of circular cylinders using lattice sums technique , 2004, IEEE Transactions on Antennas and Propagation.

[5]  Ya Yan Lu,et al.  The Riccati method for the Helmholtz equation , 1996 .

[6]  D. Felbacq,et al.  Scattering by a random set of parallel cylinders , 1994 .

[7]  R. McPhedran,et al.  Bloch mode scattering matrix methods for modeling extended photonic crystal structures. I. Theory. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[8]  J. Allen Cox,et al.  Mathematical studies in rigorous grating theory , 1995 .

[9]  P. Lalanne,et al.  Highly improved convergence of the coupled-wave method for TM polarization and conical mountings , 1996, Diffractive Optics and Micro-Optics.

[10]  P A Robinson,et al.  Formulation for electromagnetic scattering and propagation through grating stacks of metallic and dielectric cylinders for photonic crystal calculations. Part I. Method. , 2000, Journal of the Optical Society of America. A, Optics, image science, and vision.

[11]  Neumann series and lattice sums , 2005 .

[12]  Y. Lu.  A fourth-order Magnus scheme for Helmholtz equation , 2005 .

[13]  T. Gaylord,et al.  Diffraction analysis of dielectric surface-relief gratings , 1982 .

[14]  Ya Yan Lu,et al.  One-Way Large Range Step Methods for Helmholtz Waveguides , 1999 .

[15]  Haijun Wu,et al.  Adaptive finite-element method for diffraction gratings. , 2005, Journal of the Optical Society of America. A, Optics, image science, and vision.

[16]  K. Sakoda.  Numerical analysis of the interference patterns in the optical transmission spectra of a square photonic lattice , 1997 .

[17]  Stephanos Venakides,et al.  Boundary Integral Calculations of Two-Dimensional Electromagnetic Scattering by Photonic Crystal Fabry-Perot Structures , 2000, SIAM J. Appl. Math..

[18]  Lifeng Li.  Formulation and comparison of two recursive matrix algorithms for modeling layered diffraction gratings , 1996 .

[19]  K. Yasumoto,et al.  Analysis of Two-Dimensional Electromagnetic Crystals Consisting of Multilayered Periodic Arrays of Circular Cylinders , 2005 .

[20]  T. Gaylord,et al.  Analysis and applications of optical diffraction by gratings , 1985, Proceedings of the IEEE.

[21]  Lifeng Li,et al.  New formulation of the Fourier modal method for crossed surface-relief gratings , 1997 .