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Green’s function, lattice sums and rayleigh’s identity for a dynamic scattering problem

  • R. C. McPhedran
  • N. A. Nicorovici
  • L. C. Botten
  • Bao Ke-Da
Part of the The IMA Volumes in Mathematics and its Applications book series (IMA, volume 96)

Abstract

We have recently exhibited expressions for Green’s functions for dynamic scattering problems for gratings and arrays, expressed in terms of lattice sums. We have also discussed new ways to evaluate these sums, and how their use in Green’s function forms leads naturally to Rayleigh identities for scattering problems. These Rayleigh identities express connections between regular parts of wave solutions near a particular scatterer, and irregular parts of the solution summed over all other scatterers in a system. Here, we will discuss these ideas and techniques in the context of the problem of the scattering of a scalar wave by a singly-, doubly-and triply-periodic lattices of perfectly conducting obstacles. We will discuss expressions for lattice sums which can be integrated arbitrarily-many times to accelerate convergence, computationally-efficient Green’s function forms, and the appropriate Rayleigh identities for these problems. We will also discuss the long-wavelength limit, in which the dynamic identity tends to the static identity in a mathematically-interesting way.

Keywords

Helmholtz Equation Reciprocal Lattice Neumann Series Spherical Bessel Function Poisson Summation Formula 
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.

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Copyright information

© Springer Science+Business Media New York 1998

Authors and Affiliations

  • R. C. McPhedran
    • 1
  • N. A. Nicorovici
    • 1
  • L. C. Botten
    • 2
  • Bao Ke-Da
    • 3
  1. 1.Department of Theoretical PhysicsSchool of Physics, University of SydneyAustralia
  2. 2.School of Mathematical SciencesUniversity of Technology SydneyAustralia
  3. 3.Department of PhysicsPeking UniversityBeijingPeople‘s Republic of China

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