Theoretical study on the photonic band gap in one-dimensional photonic crystals with graded multilayer structure

We theoretically investigate the photonic band gap in one-dimensional photonic crystals with a graded multilayer structure. The proposed structure is constituted of the alternating composite layer (metallic nanoparticles embedded in TiO₂ film) and the air layer. Regarding the multilayer as a series of capacitance, effective optical properties are derived. The dispersion relation is obtained with the solution of the transfer matrix equation. With a graded structure in the composite layer, numerical results show that the position and width of the photonic band gap can be effectively modulated by varying the number of the graded composite layers, the volume fraction of nanoparticles and the external stimuli.