Advertisement

Laplace Transform Methods and the Rayleigh Identity for an Array of Elliptical Cylinders

  • A. J. Reuben
  • J. G. Yardley
  • R. C. McPhedran
Conference paper
Part of the Solid Mechanics and Its Applications book series (SMIA, volume 91)

Abstract

For the purpose of determining the transport properties of a two dimensional array composite consisting of rotated elliptical cylinders the Laplace transform can be used to obtain rapidly convergent representations for both the field expansions and the static lattice sums. Furthermore, these representations can be used to derive interesting analytic results involving the elliptic analogue of Rayleigh’s famous conditionally convergent dipole sum.

Keywords

Effective Property Incident Field Elliptical Cylinder Conditional Convergence Quadrupole Field 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Yardley, J., G., McPhedran, R., C., Nicorovici, N., A. and Botten, L., C. (1999). Addition Formulas and the Rayleigh Identity for Arrays of Elliptical Cylinders. Phys. Rev. E, 60:6068–6080.CrossRefADSGoogle Scholar
  2. Yardley, J., G., Reuben, A., J. and McPhedran, R, C. Transport properties of Layers of Elliptical Cylinders. Proc. R. Soc. Lond. A. submittedGoogle Scholar
  3. Lu, S. (1994) J. Appl. Phys. 76:2641.ADSCrossRefGoogle Scholar
  4. Lord Rayleigh (1892). On the influence of obstacles arranged in rectangular order upon the properties of a medium. Phil. Mag., 34:481–502.zbMATHGoogle Scholar
  5. Andre Weil (1976). Elliptic Functions according to Eisenstein and Kronecker, 1976. Springer-Verlag.Google Scholar
  6. Botten, L., C., Nicorovici, N., A., Asatryan, A., A., McPhedran, R., C., de Sterke, C., M. and Robinson, P., A. (2000). Formulation for electromagnetic scattering and propagation through grating stacks of metallic and dielectric cylinders for photonic crystal calculations. Part 1: Method. Journal of the Optical Society of America AGoogle Scholar
  7. Botten, L., C., Nicorovici, N., A., Asatryan, A., A., McPhedran, R., C., de Sterke, C., M. and Robinson, P., A. (2000). Formulation for electromagnetic scattering and propagation through grating stacks of metallic and dielectric cylinders for photonic crystal calculations. Part 2: Properties and Implementation. Journal of the Optical Society of America AGoogle Scholar

Copyright information

© Kluwer Academic Publishers 2001

Authors and Affiliations

  • A. J. Reuben
    • 1
  • J. G. Yardley
    • 2
  • R. C. McPhedran
    • 2
  1. 1.Department of Applied PhysicsUniversity of Technology SydneyAustralia
  2. 2.Department of Theoretical Physics, School of PhysicsUniversity of SydneyAustralia

Personalised recommendations