Soliton wave analysis using FDTD approach applied to Maxwell equations on tin oxide

Soliton waves are self-reinforcing solitary waves that maintain their shape while traveling at a constant velocity, making them particularly useful in numerous optical applications. This research focuses on observing the phenomenon of soliton waves in tin dioxide (SnO2) to model the propagation of electromagnetic waves in both spatial and time domains. The FDTD method is well-suited for this type of study because it allows for the numerical analysis of electromagnetic wave propagation by solving Maxwell's equations over discrete time and space grids. One of the primary challenges in simulating wave propagation in materials like SnO2 is accounting for dispersive effects and nonlinearities. Therefore, this study aims to augment the FDTD approach with Z-transformation techniques, allows for an efficient formulation of dispersive and nonlinear effects, thus enhancing the computational efficiency and accuracy of the simulations. The simulation results show that soliton waves can form in the optical material of SnO2 when an electric field exceeding 0.8 V/m is applied. The formation of soliton waves in SnO2 is primarily attributed to the nonlinear properties of the material. The simulation demonstrates that SnO2 exhibits significant nonlinear behavior conducive to soliton formation. The dispersive properties of SnO2 also play a crucial role in the formation and stability of soliton waves. Dispersive effects can cause wave packets to spread out, but in the presence of nonlinearity, these effects can be balanced, forming stable solitons. In conclusion, this study provides a foundational understanding of soliton wave formation in SnO2, highlighting its potential for various optical applications