A theoretical approach to optical properties of opal based Photonic Crystals

Summary form only given: If one wants to achieve a full control of light propagation and emission, three-dimensional photonic crystals (3D PhCs) are the most appropriate structures to deal with. Artificial opals are readily available 3D PhC as they can be produced with easy and low cost process, such as natural sedimentation or vertical deposition, and eventually infiltrated with high-index materials to obtain the so-called inverse opals. Bare opals consist of dielectric spheres arranged in a close-packed fcc lattice oriented along the [111] crystallographic direction. They present interesting features: photonic band gap formation, optical properties in the low- and high-energy regions, superprism effects and diffraction phenomena are just a few of the interesting issues to be studied in opal structures. A theoretical description of the optical properties including diffraction in the high energy region is difficult, also because of the partial overlap between consecutive layers of spheres along the [111] direction. In this work we present a theoretical approach to calculate optical spectra of opal PhCs. We mimic the actual opaline structure by subdividing each sphere in a set of cylinders whose axis are oriented along [111] direction. Cylinder parameters are optimized by minimizing the difference between the photonic band dispersion of the actual and model geometry, calculated by means of plane wave expansion. The optimized structure is then implemented in a scattering matrix code [following the method developed by Whittaker and Culshaw(1999)] in order to obtain the optical spectra. Results for bare opal optical spectra both in the low and in the high energy region are shown. In particular we analyse the dependence of diffraction intensity with respect to the layer number: we verify the existence of a "Pendellosung phenomenum", i.e. the periodic exchange of energy between two propagating beams inside the crystal. The method can also be applied to infiltrated opals - nd can be extended to calculate emission from opals containing active media