STUDIES OF PHOTONIC CRYSTALS WITH PLANE-WAVE EXPANSION METHOD - Virgus, Yudistira
In this Thesis, we numerically investigate the band structure of photonic crystals with plane-wave expansion method based on earlier works. We also compare the result for one-dimensional photonic crystals with the analytical result from transfer matrix method. First, we analyze the optical properties of multilayer periodic structures, one-dimensional photonic crystals, by means of Bloch’s theorem and transfer matrix method. We focus on how to calculate the band structure of the systems analytically and show that there are photonic band gaps, i.e., a range of frequencies where no electromagnetic waves can propagate within the crystal. Such structures have been studied in great details because the structure response can be derived analytically, for example using standard transfer matrix method, and thus do not require powerful computational techniques. Furthermore, these results are easily tested since such structures can be easily fabricated with standard methods. Next, we analyze the band structure of photonic crystals using plane-wave expansion method. This numerical method is based on the Fourier expansion of the electromagnetic field and the dielectric function. Generally, it involves intensive computations with thousands of plane waves. We use MATLAB to implement the plane-wave expansion method. First, we try to calculate the band structure of one-dimensional photonic crystal with this method and compare its results with the analytical result. Furthermore, two-dimensional photonic crystal will be studied using the plane-wave expansion method. Finally, we investigate a two-dimensional photonic crystal with a defect using a supercell approach. By introducing a defect to the crystal structure, the utility of photonic crystals is enhanced because the creation of localized frequency states within the photonic band gap. We also investigate the electric-field patterns of the defect modes that appear within the photonic band gap.