Ultrashort spatiotemporal optical solitons in quadratic nonlinear media: Generation of line and lump solitons from few-cycle input pulses

Abstract

To cite this version:and of stable lumps (for a quadratic medium with anomalous dispersion). Besides, a typical example of the decay of the perturbed unstable line soliton into stable lumps for a quadratic nonlinear medium with anomalous dispersion is also given.

Lump solutions to the Kadomtsev–Petviashvili equation

“…Evolution of lump solitons and their generation from few-cycle input pulses were numerically simulated by Minzoni and Smyth[24] and by Leblond, Kremer and Mihalache[25], respectively. Multiple lump solitons were characterized by the discrete 131 66 Contour plots of (2.21) at t = 1 with (a) = 0.3, (b) = 0.2, (c) = 0.1.…”

Pulse Propagation Models with Bands of Forbidden Frequencies or Forbidden Wavenumbers: A Consequence of Abandoning the Slowly Varying Envelope Approximation and Taking into Account Higher-Order Dispersion

“…It should be noticed that the value k p = −40, which we obtained from Figures 11 and 12, could also be obtained from Equations (31) and (32). If we define f (ω) = c 3 ω 3 − c 2 ω 2 , we can approximate S(ω) ∼ = i(1 + 2c 0 f (ω)), and therefore Equation (31) implies that λ b ∼ = −i/c 0 − i f (ω).…”

“…Let us consider, for example, the particular case when 1/40, 1/2 and 1/50. In this case the radicand (given in (32)) has the form shown in Figure 6. (14).…”

“…In more recent times completely different models have been proposed to describe ultra-short optical pulses, and the famous Kortweg-de Vries (KdV), modified KdV (mKdV) and sine-Gordon (sG) equations have been found useful for this purpose, as well as a combination of the last two of these equations [29,30]. Another two equations which have been useful to describe ultra-short spatiotemporal pulses are a two-dimensional sG equation [31] and a cubic generalized Kadomtsev-Petviashvili (cgKP) equation [32,33]. It is worth observing that in all these models (KdV, mKdV, sG, mKdV-sG, 2D-sG and cgKP) the temporal variable which appears in the equations is a delayed time (not the laboratory time), similar to the retarded time that appears in the standard NLS equation.…”

Spatiotemporal optical solitons in carbon nanotube arrays

“…[13], we used a powerful reductive perturbation technique or a multiscale analysis [14] to obtain a generic Kadomtsev-Petviashvili evolution equation governing the propagation of (2 + 1)-dimensional femtosecond spatiotemporal optical solitons, alias light bullets (LBs) [15,16] in quadratic nonlinear media beyond the slowly varying envelope approximation (SVEA). 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].…”