Analysis of tunable bandgaps in liquid crystal-infiltrated 2D silicon photonic crystals

We present a theoretical study on two-dimensional photonic crystals composed of silicon and the E7 liquid crystal. We analyze how the optical axis orientation of the liquid crystal influences the photonic bands and bandgaps, for the case when the Maxwell equations can be decoupled into the TE and TM modes. We consider two different structures, a triangular lattice of E7 liquid crystal cylinders in a silicon background and a triangular lattice of silicon cylinders in an E7 liquid crystal background. The effect of the liquid crystal anisotropy on the geometry of the irreducible Brillouin zone allows us to propose a simplified way to calculate the photonic bandgaps. Results show that the bandgap width and center frequency have a 60° periodicity for both structures. Using the plane-wave expansion method, we determined the maximum bandgap and the optimal radius of the cylinders for each structure. Finally, for the second structure, we propose an optical switch with a 50% duty cycle. These structures can be applied to design tunable photonic devices.