article · Physical review. E
A theoretical framework based on Maxwell equations models the behaviour of dissipative light bullets propagating through nonlinear metamaterials. Described by a (3+1)-dimensional cubic-quintic complex Ginzburg-Landau equation, the formulation extends beyond the slowly varying envelope approximation to incorporate diffraction, dispersion, gain, loss, higher-order nonlinearities, and self-steepening effects. An investigation into modulational instability reveals that plane waves experience instability regardless of initial wave amplitude. Analytical evaluations using linear stability theory and direct numerical simulations of the Fourier space based on the Drude model demonstrate complete agreement across both normal and anomalous group-velocity dispersion regimes. The resulting instability manifests as complex localised wave patterns, including soliton clusters, multihump shapes, and dromion-like structures, driven by a balance between dispersive and nonlinear factors alongside specific self-steepening parameters.
Understanding how light pulses behave inside engineered metamaterials is fundamental to advancing optical physics. By establishing how light splits into localised, resilient waveforms such as solitons, this research clarifies the conditions needed to manage optical energy and control complex beam profiles over varying propagation distances without signal degradation.
The abstract does not indicate an application pathway, as the study focuses exclusively on theoretical derivations and numerical simulations of electromagnetic wave dynamics.
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Considering the theory of electromagnetic waves from the Maxwell's equations, we introduce a (3+1)-dimensionsal cubic-quintic complex Ginzburg-Landau equation describing the dynamics of dissipative light bullets in nonlinear metamaterials. The model equation, which is derived beyond the slowly varying envelope approximation, includes the effects of diffraction, dispersion, loss, gain, cubic, and quintic nonlinearities, as well as cubic and quintic self-steepening effects. The modulational instability of the plane waves is studied both theoretically, using the linear stability analysis, and numerically, using direct simulations of the Fourier space of the proposed nonlinear wave equation, based on the Drude model. The linear theory predicts instability for any amplitude of the primary wave. Also, in the linear stability analysis, self-steepening effects of different orders are confronted and one discusses their effects on the behavior of the gain spectrum under both normal and anomalous group-velocity dispersion regimes. Analytical results are equally confronted to direct numerical simulations and fully agree with the predictions from the gain spectra. Modulational instability is manifested by clusters of solitons and multihump and dromion-like structures, whose emergence and features depend not only on system parameters, such as the cubic and quintic self-steepening coefficients, but also on the propagation distance under a suitable balance between nonlinear and dispersive effects.
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DOI: 10.1103/physreve.102.042207
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