Mode analysis of 2D photonic quasicrystals based on an approximate analytic model

In this work, we have developed a semi-analytical model based on perturbation theory for evaluating optical properties of photonic quasicrystals. Although numerical techniques are being used for determining characteristics of photonic quasicrystals, it is believed that analytical studies based on approximations help us to understand the physical properties and treatment of the structure more easily. Towards that end, the use of perturbation method can be beneficial in approximating the photonic band structure and mode profile in photonic quasicrystals made of low dielectric contrast materials with high accuracy. It is shown that error incurred by the approximation through the perturbation method can be estimated to be a few percent, in comparison to the more accurate finite difference time domain method. In addition, the effect of variation in the dielectric contrast on the photonic band structure of 2D 12-fold photonic quasicrystal has been studied and it is presented that by decreasing dielectric contrast a smaller photonic band gap is obtained, which is interesting for optical communication devices.