This study emphasizes a unique contribution as we investigate the dimensionless version of the perturbed stochastic NLSE within an optical metamaterial-designed coupler. We employ Kudryashov’s sextic-power law nonlinearity to present this formulation, and, for the first time, we introduce multiplicative white noise using the Ito interpretation. This study aims to bridge the gap in understanding the influence of stochastic effects on optical metamaterials and offers valuable insights for future research in this field. The methods introduced include enhancements to Kudryashov’s approach and extensions to the modified sub-ODE technique. These methodologies are leveraged to derive a wide array of solutions, such as bright, dark, singular, and combined solitons, with some solutions presented using Jacobi and Weierstrass elliptic functions. The effectiveness of these methods in addressing various nonlinear partial differential equations is demonstrated through the results. The study further delves into how random noise impacts optical solitons and analyzes soliton behavior when subjected to different conditions. It is observed that white noise plays a crucial role in the formation of optical solitons within the coupler and that these solitons demonstrate highly dispersive properties under specific scenarios. These insights are pivotal for designing and innovating optical metamaterials for diverse technological uses.