Study of Bragg scattering in the presence of dipole-dipole interaction in plasmonic nanohybrids

We have developed a theory of the Bragg scattering for metallic nanohybrid made of an ensemble of metallic nanorods doped in a substrate. The substrate can gas, liquid or solid. An external laser field is applied to study the Bragg scattered light. The photons from the incident laser interact with the surface plasmons od nanorods and produce surface plasmon polaritons (SPPs). The incident laser field also induced dipoles in the ensemble of nanorods and they interact with each other via the dipole-dipole interaction (DDI). We have developed a theory for Bragg scattering for metallic nanohybrids using the coupled-mode formulism based on Maxwell’s equation in the presence of SPP and DDI fields. It is found that the theory of Bragg scattered depends on the susceptibility induced by the SPP and DDI fields. We used the quantum mechanical density matrix method to calculate the susceptibility. An analytical expression of the Bragg scattered light intensity is obtained. These expressions can be useful for experimental scientists and engineers who can used them to compare their experiments and make new types of plasmonic devices. Next, we have compared our theory with the experiment data for a nanohybrid made of ensemble of Au-nanoris doped in water. We found a good agreement between theory and experiments. We have also performed the numerical simulations to study the effect of SPP and DDI fields on the Bragg intensity. We have predicted an enhancement the Brag intensity due to the SPP and DDI couplings. The enhancement is due to the two extra scattering mechanisms of the SPP and DDI polaritons with acoustic phonons. We have also found that the one peak in the Bragg intensity can be split int many peaks due the SPP coupling, DDI coupling and phase factor. The splitting is due the Bragg factor appearing in the theory, and it includes the coupling of the incident laser, SPP and DDI electric fields with of acoustic phonons. The enhancement effect can be used to fabricate new types of nanosensors. Similarity, splitting phenomenon can be used to fabricate new types nanoswitches where one peak can be considered as the OFF position and many peaks can be considered as the ON position.