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

Abstract

By using a reductive perturbation technique applied to a two-level model, a generic twodimensional sine-Gordon evolution equation governing the propagation of femtosecond spatiotemporal optical solitons in Kerr media beyond the slowly-varying envelope approximation is put forward. 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 waveforms. In contrast to the case of quadratic nonlinearity, the light bullets oscillate in both space and time, and are therefore not steady-state lumps.

Spatiotemporal soliton solution to generalized nonlinear Schrödinger equation with a parabolic potential in Kerr media

“…To date, Sine-Gordon equation (SGE) [15,16], complex Ginzburg-Landau equation (CGLE) [17][18][19], nonlinear Schrödinger equation (NLSE) [20][21][22][23] have been extensively proposed to theoretically study the characteristics and propagation stability of STSs. For instance, Leblond et al proposed a reductive perturbation technique applied to 2D SGE to govern the propagation of femtosecond STSs in Kerr media [24]. For solving these equations, plenty of methods have been developed, such as Hirota bilinear method [25], Darboux transformation [26], variational method [27,28], and F-expansion method [29][30][31][32].…”

Spatiotemporal optical solitons in carbon nanotube arrays

“…The collapse of ultrashort spatiotemporal pulses in cubic (Kerr-like) media was also studied by using the multiscale analysis beyond the SVEA, and it was obtained from the Maxwell-Bloch equations for two-level atoms a generic cubic generalized Kadomtsev-Petviashvili nonlinear evolution equation [17]. Ultrashort LBs described by the two-dimensional sine-Gordon (2DsG) equation, obtained by using the multiscale analysis in the short-wave approximation for a cubic (Kerr-like) nonlinear medium, were studied recently [18], and it was shown that robust few-cycle LBs may form, oscillating in both space and time, that is, two-dimensional breathers.…”

Femtosecond nanometer-sized optical solitons

“…Light bullets, first discussed in the context of collapsing, intense light pulses [10] in nonlinear bulk media, offer a way to achieve spatiotemporal confinement by using a strong nonlinear interaction with a medium that can counterbalance linear effects of diffraction and dispersion [11,12]. Unfortunately, the localization of these self-confined bulk light bullets, multidimensional spatiotemporal solitons, is orders of magnitude larger in size than the wavelength.…”