A Bloch wave numerical scheme for scattering problems in periodic wave-guides
This work provides a novel numerical method for scattering problems in periodic waveguides, which is important for applications in photonics and wave propagation.
The paper presents a new numerical scheme for solving the Helmholtz equation in periodic waveguides, proving stability and demonstrating effectiveness on interfaces including negative refraction in photonic crystals.
We present a new numerical scheme to solve the Helmholtz equation in a wave-guide. We consider a medium that is bounded in the $x_2$-direction, unbounded in the $x_1$-direction and $\varepsilon$-periodic for large $|x_1|$, allowing different media on the left and on the right. We suggest a new numerical method that is based on a truncation of the domain and the use of Bloch wave ansatz functions in radiation boxes. We prove the existence and a stability estimate for the infinite dimensional version of the proposed problem. The scheme is tested on several interfaces of homogeneous and periodic media and it is used to investigate the effect of negative refraction at the interface of a photonic crystal with a positive effective refractive index.