Efficient Bloch mode calculation of periodic systems with arbitrary geometry and open boundary conditions in the complex wavevector domain.

We show how existing iterative methods can be used to efficiently and accurately calculate Bloch periodic solutions of Maxwell's equations in arbitrary geometries. This is carried out in the complex-wavevector domain using a commercial frequency-domain finite-element solver that is available to the general user. The method is capable of dealing with leaky Bloch mode solutions, and is extremely efficient even for 3D geometries with non-trivial material distributions. We perform independent finite-difference time-domain simulations of Maxwell's equations to confirm our results. This comparison demonstrates that the iterative mode finder is more accurate, since it provides the true solutions in the complex-wavevector domain and removes the need for additional signal processing and fitting. Due to its efficiency, generality and reliability, this technique is well suited for complex and novel design tasks in integrated photonics, and also for a wider range of photonics problems.