Dissipative optical solitons

Dissipative solitons

“…For the theoretical description of VCSELs we refer to [332,333] and the recent article of Lugiato et al in [246]. From many of the experimental results on VCSELs we draw the conclusion that observed spots are type A non-vortex optical DSs in the sense of Section 1.…”

Topological three-dimensional dissipative optical solitons

“…We consider the propagation of quasi-monochromatic, nearly linearly polarized radiation with angular divergence close to the diffractive limit through a weakly nonlinear active (with laser amplification) medium (e.g. [3,4]). The electric fieldẼ is represented in the following form:…”

“…We assume that the radiation pulse duration exceeds the relaxation times of the centres (their response to the radiation is fast). Then, Maxwell's equations result, in the framework of the slowly varying envelope approximation, in the following governing equation [3,4,[6][7][8]:…”

“…Under condition (2.5), the trivial solution of equations (2.2) and (2.3), E = 0, is stable; otherwise, any bright localized solution of these equations would be unstable because of the field growth at the structure's periphery. Another restriction on the coefficients comes from the condition of bistability: the equation f nl (I hom ) = 0 should have a non-trivial solution with positive intensity I hom > 0 corresponding to the homogeneous balance of gain and loss [4]. For function f nl given by equation 2.4,…”

“…Solitons-particle-like, localized structures of fields in distributed nonlinear media and schemes-are one of the most exciting objects in nonlinear science. Although they exist both in conservative (without dissipation) and in dissipative optical systems [2][3][4], their features are very distinct: conservative optical solitons form families with continuously varying characteristics, including their shape and energy, whereas dissipative optical solitons are 'calibrated' and have a discrete spectrum of their main parameters for fixed parameters of the scheme. This difference results in much higher stability of dissipative optical solitons and in the possibility to generate almost arbitrary complex spatio-temporal localized structures.…”