ABSTRACT

Since scattering problems are inherently set in unbounded domains, the boundary conditions at infinity for the wave field—commonly referred to as radiation conditions—form an essential component of the mathematical formulation. Radiation conditions can both eliminate non-physical numerical solutions and truncate the computational domain, thereby providing a basis for analyzing the effectiveness and convergence of algorithms. The speaker will begin by reviewing classical radiation conditions, including the Sommerfeld condition, the Rayleigh expansion condition, and the angular spectrum representation condition. This will be followed by an introduction to novel radiation conditions developed for scattering problems in periodic structures with local perturbations. In particular, a constraint condition derived from the Limiting Absorption Principle will be presented. Combined with the classical Rayleigh expansion, this constraint yields a new radiation condition that guarantees the uniqueness of the solution for scattering by bi-periodic structures supporting bound states in the continuum.