We theoretically investigate the photonic band gap in one-dimensional photonic crystals with a graded multilayer structure. The proposed structure constitutes an alternating composite layer （metallic nanoparticles embedded in TiO2 film） and an 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.
Two-dimensional double nanoparticle （DNP） arrays are demonstrated theoretically, supporting the interaction between out-of-plane magnetic plasmons and in-plane lattice resonances, which can be achieved by tuning the nanoparticle height or the array period due to the height-dependent magnetic resonance and the periodicity-dependent lattice resonance. The interplay between the two plasmon modes can lead to a remarkable change in resonance lineshape and an improvement on magnetic field enhancement. Simultaneous electric field and magnetic field enhancement can be obtained in the gap region between neighboring particles at two resonance frequencies as the interplay occurs, which presents “open” cavities as electromagnetic field hot spots for potential applications on detection and sensing. The results not only offer an attractive way to tune the optical responses of plasmonic nanostructure, but also provide further insight into the plasmon interactions in periodic nanostructure or metamaterials comprising multiple elements.
