Spatiotemporal instability and optical filament formation in metamaterials

\n\nThis study investigates the spatiotemporal instability in artificial metamaterials, with a focus on generating ultrashort pulses or light filaments. We identify the parametric regions where the metamaterial exhibits spatiotemporal instability, enabling the generation of ultrashort pulses. Our approach involves modeling nonlinear pulse propagation in the metamaterial using a (3+1)-dimensional nonlinear Schrödinger equation and performing a standard linear stability analysis to explore the spatiotemporal instability. Leveraging the engineering freedom to tailor the material parameters, we numerically demonstrate the generation of ultrashort pulses through spatiotemporal instability.\n