The square Thue–Morse tiling for photonic application

L. Moretti, V. Mocella
2008 Philosophical Magazine  
The photonic properties of a two-dimensional photonic aperiodic crystal based on the Thue-Morse substitutional sequence were investigated theoretically. Differently from the traditional photonic quasicrystals based on the Penrose tiling, these structures were obtained by removing the lattice points from a square arrangement, following the inflation rules emerging from the Thue-Morse sequence. The resulting structure does not exhibit the typical translational symmetry of a photonic crystals. In
more » ... articular, it is well known that the Thue-Morse sequence has a singular continuous Fourier transform. This property was transferred directly on the two-dimensional Thue-Morse photonic aperiodic crystal represented by an array of pillars in air. The electromagnetic field distribution can be described as a quasi-localized state, with characteristics lying between the localized states, corresponding to the defect state in a photonic crystal, and the Bloch states, as in case of the eigenmode in a photonic crystal. The photonic bandgap formation was explored as a function of pillar radius. Furthermore a preliminary investigation of the defect behaviour in square Thue-Morse tiling was carried out. The electric field in the defect state revealed to be strictly localized in the defect pillar. These structures provide interesting properties which could be used to design novel optical devices.
doi:10.1080/14786430802047076 fatcat:rsm7bntd2ne3dpytjkuofxpigm