Here, the improved exp(-Omega(eta))-expansion method and extended sinh-Gordon equation expansion method are being applied on (1+2)-dimensional non-linear Schrodinger equation (NLSE), optical metamaterials, with anti-cubic nonlinearity. Materials like photovoltaic-photorefractive, polymer and organic consists of spatial solitons and optical nonlinearities, which can be identified by seeking help from NLSE with anti-cubic nonlinearity. Abundant exact traveling wave solutions consisting of free parameters are established in terms of bright, dark, singular, kink-singular, and combined dark-bright soliton solutions. Various arbitrary constants obtained in the solutions help us to discuss the graphical behavior of solutions and also grants flexibility to formulate solutions that can be linked with a large variety of physical phenomena. Moreover, graphical representation of solutions are shown vigorously in order to visualize the behavior of the solutions acquired for the equation.