Rotational Bloch Boundary Conditions and the Finite-Element Implementation in Photonic Devices

Abstract

This article described the implementation of rotational Bloch boundary conditions in photonic devices using the finite element method (FEM). For the electromagnetic analysis of periodic structures, FEM and Bloch boundary conditions are now widely used. The vast majority of recent research, however, focused on applying Bloch boundary conditions to periodic optical systems with translational symmetry. Our research focused on a flexible numerical method that may be applied to the mode analysis of any photonic device with discrete rotational symmetry. By including the Bloch rotational boundary conditions into FEM, we were able to limit the computational domain to the original one periodic unit, thus enhancing computational speed and decreasing memory consumption. When combined with the finite-element method, rotational Bloch boundary conditions will give a potent tool for the mode analysis of photonic devices with complicated structures and rotational symmetry. In the meantime, the degenerated modes we calculated were consistent with group theory. Overall, this study expands the numerical tools of studying rotational photonic devices, and has useful applications in the study and design of optical fibers, sensors, and other photonic devices.