  This paper proposes an isogeometric boundary element method (IGBEM) to solve
the electromagnetic scattering problems for three-dimensional doubly-periodic
multi-layered structures. The main concerns are the constructions of (i) an
open surface (between two layers) and (ii) a vector basis function with using
the B-spline functions. Regarding (i), we considered an algorithm to generate a
doubly-periodic open surface with the tensor product of the B-spline functions
of any degree. Regarding (ii), we employed the vector basis function based on
the B-spline functions, which was proposed by Buffa et al. (2010), and adapted
it to the underlying periodic problems so that it can satisfy the
quasi-periodic condition on the boundary of an open surface. The proposed IGBEM
worked for solving some numerical examples satisfactorily and proved the
applicability to plasmonic simulations.
