Solitons in Split Ring Resonator based Metamaterials with Higher Order Nonlinearity

Abstract

Metamaterials and soliton are the two sought-after topics since the last century. Metamaterials offer some exclusive, apparently unnatural, yet extraordinarily beneficial phenomena. On the other hand, soliton, which is generated using the nonlinearity of the media, comes with a plethora of potential applications besides its strong, wide, and deep theoretical base. This thesis aims to combine these two branches, i.e., metamaterials and nonlinearity-induced soliton in order to reap the benefits of the advantages of both of them. While various types of metamaterials have been explored for soliton generation, and diverse solitons have been identified, limited attention has been paid towards higher-order nonlinearity. Even though the relative value of higher-order nonlinearity might be considerably smaller than the commonly considered lowest-order nonlinearity, its significance lies in the cumulative effects it exerts, especially in certain materials like metamaterials. Furthermore, harnessing higher-order nonlinearity, if appropriately employed, could give rise to intriguing phenomena. The presence of higher-order nonlinearity not only plays a pivotal role in the dynamics and stability of solitons but can also be leveraged for the advancement of smart devices. Precisely, this thesis presents the soliton generation in split ring resonator (SRR) based metamaterials having higher-order nonlinearity. Different types of nonlinearities have been used, namely, cubic-quintic nonlinearity and saturable nonlinearity. The effects of higher-order terms, namely, third-order diffraction, multiphoton absorption, self-steepening, and Raman scattering, have been considered. Soliton has been found in all the cases, however, with delicate stability conditions. Such conditions have been determined and numerically verified. The dynamics of the solitons, both spontaneous and interactive, have been portrayed. The theoretical investigation on the generation and stabilization of the soliton model is developed using the nonlinear