Fractal media-based distributed Bragg reflectors
We investigate the optical property of a distributed Bragg reflector (DBR) based on alternating layers of air and fractal thin films. Each fractal thin film layer of the DBR has the same fractal dimension. Using the transfer matrix method (TMM), we calculate the reflectivity of the DBR. Our calculations show that lowering the fractal dimension of the fractal thin film layers of the DBR effectively amplifies the overall reflectivity. We also observe that fractal media based DBRs produce a photonic bandgap. The photonic bandgap of these DBRs widens depending on the dimension of the fractal thin film layers. We show that fractal media based DBRs exhibit a higher reflectivity and a relatively wide photonic bandgap compared to integer media based DBRs. Given these properties of higher reflectivity and photonic bandgap, the results imply that fractal media based DBRs are better reflectors than integer media based DBRs.