Electromagnetic metamaterials are artificial media consisting of periodic microstructures engineered on a length scale much smaller than the wavelength of an incident electromagnetic wave. These materials possess remarkable linear and nonlinear optical properties, beyond those of naturally occurring materials. It is possible to engineer a plasma metamaterial by combining the generation of a plasma with these periodic structures, leveraging the electromagnetic properties of a plasma to produce a metamaterial with a tunable electromagnetic response. Plasma metamaterials have recently been implemented in the lab and exotic linear behavior has been verified. However, the nonlinear electromagnetic properties of plasma metamaterials remain largely unexplored. In this work, we investigate the nonlinear optical process of stimulated Raman scattering (SRS) in a plasma metamaterial. We have generalized the theory describing SRS to incorporate a Drude-type magnetic response, producing novel predictions for the qualitative behavior and growth rate of the instability in such a metamaterial. This theory identifies a parameter window for SRS which is inaccessible within a normal plasma medium. We demonstrate that the instability growth rate predicted by the generalized theory matches that which is measured in simulation. We also investigate the effect of losses within a plasma metamaterial on SRS, and discuss the implications of these findings for observing this unusual regime of SRS in the laboratory.

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