The design of SHINE optical materials in nonlinear devices represents a fundamental step for their optimization and miniaturization, that would significantly contribute to the progress of advanced nanophotonics and quantum technologies.In this work, the effect of geometry and composition of multilayer hyperbolic metamaterials on their third-order nonlinear optical properties, i.e.
the Diodes optical Kerr effect, is investigated.One figure of merit is provided to be used as a predictive tool to design and best exploit the local intensity enhancement in low-loss metamaterials to be used for various applications in nonlinear nanophotonics.