Ultrashort light bullets described by the two-dimensional sine-Gordon equation

TL;DR

This paper derives a two-dimensional sine-Gordon equation to describe ultrashort light bullets in Kerr media, demonstrating through simulations that these solitons are stable, oscillatory, and do not collapse, unlike in long-wave approximations.

Contribution

It introduces a novel 2D sine-Gordon model for femtosecond optical solitons beyond the slowly varying envelope approximation.

Findings

No collapse occurs for ultrashort light bullets in the model.

Stable, oscillatory (2+1)D light bullets can form from few-cycle inputs.

Light bullets differ from steady-state lumps by oscillating in space and time.

Abstract

By using a reductive perturbation technique applied to a two-level model, this study puts forward a generic two-dimensional sine-Gordon evolution equation governing the propagation of femtosecond spatiotemporal optical solitons in Kerr media beyond the slowly varying envelope approximation. Direct numerical simulations show that, in contrast to the long-wave approximation, no collapse occurs, and that robust (2+1)-dimensional ultrashort light bullets may form from adequately chosen few-cycle input spatiotemporal wave forms. In contrast to the case of quadratic nonlinearity, the light bullets oscillate in both space and time and are therefore not steady-state lumps.