  We present an open geometry Fourier modal method based on a new combination
of open boundary conditions and an efficient $k$-space discretization. The open
boundary of the computational domain is obtained using basis functions that
expand the whole space, and the integrals subsequently appearing due to the
continuous nature of the radiation modes are handled using a discretization
based on non-uniform sampling of the $k$-space. We apply the method to a
variety of photonic structures and demonstrate that our method leads to
significantly improved convergence with respect to the number of degrees of
freedom, which may pave the way for more accurate and efficient modeling of
open nanophotonic structures.
