Stability of few-cycle light bullets in nonlinear metamaterials beyond the slowly varying envelope approximation

This letter explores stable few-cycle light bullets in nonlinear metamaterials beyond the slowly varying envelope approximation. Using a (3+1)-dimensional cubic-quintic complex Ginzburg-Landau equation, the letter explores solitonic behaviors of light bullets in materials with a negative refractive index under the few-cycle regime. The analysis involves a Lagrangian variational approach designed for dissipative nonlinear systems and utilizes direct numerical simulations to demonstrate the possibility of stable light bullets forming in metamaterials and corroborate the stability analysis. Based on the stability conditions for the system parameters using the Routh-Hurwitz criterion, optimal values of the cubic and quintic self-steepening effects promote stable propagation of light bullets, while an imbalance may lead to collapse. These findings suggest that combining few-cycle light bullets with metamaterial-based optics may enable new possibilities for ultrafast and nonlinear optics.