Metamaterials have revolutionized the field of optics by enabling the manipulation of light in unprecedented ways. However, understanding the nonlinear optical properties of these materials is still a developing area. This study aims to investigate the nonlinear optical phenomena exhibited by engineered metamaterials. Using a combination of theoretical modeling and experimental validation, the research explores the interaction between intense light waves and the sub-wavelength structures of metamaterials. Our findings reveal significant enhancement in third-order nonlinear effects, such as self-focusing and optical Kerr effect, under specific material configurations. Through rigorous analysis, we demonstrate that these effects can be tuned by altering the structural parameters of the metamaterials, offering a new dimension of control over light behavior. The results not only provide deeper insights into nonlinear dynamics but also open up potential applications in developing advanced photonic devices. Conclusively, this study sheds light on the profound capabilities of metamaterials in nonlinear optics, paving the way for future research aimed at optimizing these materials for technological advancements.