Absorbing boundary condition for Bloch-Floquet eigenmodes

We present an absorbing boundary condition for electromagnetic frequency domain simulations of photonic crystals and metamaterials. This boundary condition can simultaneously absorb multiple Bloch-Floquet eigenmodes of a periodic crystal, including both propagating and evanescent modes. The photonic crystal or metamaterial in question can include lossy, active, anisotropic and even bi-anisotropic inclusions. The absorbing boundary condition is dependent on an orthogonality condition for Bloch-Floquet eigenmodes, a generalized version of which is presented here. We test this absorbing boundary condition numerically and present the results.