WIAS Preprint No. 2726, (2020)

Radiation conditions for the Helmholtz equation in a half plane filled by inhomogeneous periodic material


  • Hu, Guanghui
  • Rathsfeld, Andreas

2010 Mathematics Subject Classification

  • 74J20 76B15 35J50 35J08


  • Half-space radiation condition, inhomogeneous medium, wave-mode expansion, scattering by grating, RCWA




In this paper we consider time-harmonic acoustic wave propagation in a half-plane filled by inhomogeneous periodic medium. If the refractive index depends on the horizontal coordinate only, we define upward and downward radiating modes by solving a one-dimensional Sturm-Liouville eigenvalue problem with a complex-valued periodic coefficient. The upward and downward radiation conditions are introduced based on a generalized Rayleigh series. Using the variational method, we then prove uniqueness and existence for the scattering of an incoming wave mode by a grating located between an upper and lower half plane with such inhomogeneous periodic media. Finally, we discuss the application of the new radiation conditions to the scattering matrix algorithm, i.e., to rigorous coupled wave analysis or Fourier modal method.

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