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Title: Solitons in Split Ring Resonator based Metamaterials with Higher Order Nonlinearity
Authors: Sharma, Neeraj
Supervisor: Jana, Soumendu
Keywords: Soliton;Nonlinear Dynamics;Metamaterial;Split-ring-resonator;Higher order nonlinearity
Issue Date: 5-Jun-2024
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 Schrodinger equation or modified nonlinear Schrodinger equation. And consequently solved by Lagrangian variational method based analytical method as well as split-step Fourier method and Runge–Kutta method based numerical methods. Stable compound dissipative solitons are found in cubic-quintic nonlinear media with multi-photon absorption and diffusion for a given set of parameters. Since the generation and stabilization conditions have been determined in a generic form, those fit any given material. The interaction dynamics of the dissipative solitons for various initial separations and phases of the participating soliton, ultimately resulting in soliton switching. Notably, it is found that a weak soliton beam has the ability to control a strong soliton beam. A simple approach has been undertaken to stabilize soliton in a two-dimensional hybrid metamaterial featuring split-ring resonator arrays on a graphene layer. This approach is so fundamental and direct that it can be applied to stabilize solitons in other media, too. Soliton is formed in SRR-based nonlinear metamaterials, wherein higher-order effects, namely, third-order diffraction, self-steepening and Raman scattering, are prominent. Both self-steepening and Raman scattering cause a transverse shift of the pulse; however, the former causes a greater shift. These soliton pulses are robust against perturbation; only the transverse shift decreases marginally with increasing perturbation. The interaction dynamics demonstrate the typical periodic oscillations along with some deformation due to self-steepening and Raman scattering. Breather-like diffraction-managed soliton solitons are found in a periodic array of metamaterials having alternate positive and negative diffraction. The initial beam energy required for the generation of diffraction-managed soliton is determined across diverse metamaterial array configurations. The approach enables the production of high-energy beams through the utilization of diffraction-managed metamaterial arrays. The stability zones for diffraction-managed solitons are identified. Most of the solitons presented in this thesis are robust against the randomness of the system parameters up to a certain extent. The findings of the thesis can be used as a guideline for further experimental observation of solitons and soliton-based devices in different types of metamaterials.
Appears in Collections:Doctoral Theses@SPMS

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