Adaptive FEM Solver for the Computation of Electromagnetic Eigenmodes in 3D Photonic Crystal Structures

Photonic crystals (PhCs) are structures composed of different optical transparent materials with a spatially periodic arrangement of the refractive index [Joa95, Sak01]. Propagating light with a wavelength of the order of the periodicity length of the photonic crystal is significantly influenced by multiple interference effects. The most prominent effect is the opening of photonic bandgaps, in analogy to electronic bandgaps in semiconductor physics or atomic bandgaps in atom optics. Due to the fast progress in nano-fabrication technologies PhCs can be manufactured with high accuracy and with designed materials and geometrical properties. This allows for the miniaturization of optical components and a broad range of technological applications, like, e.g., in telecommunications [MBG04]. The properties of light propagating in PhCs are in general critically dependent on different system parameters, like the geometry of the device and the refractive indices of the present materials. Therefore, the design of photonic crystal devices calls for simulation tools with high accuracy, speed and reliability. In this paper we present a fast and flexible finite-element-solver for the calculation of Bloch-type eigenmodes of PhCs.