Dynamics of Airy beams in nonlinear media

The dynamics of truncated Airy beams in optical media with Kerr nonlinearity is studied in the framework of the nonlinear Schrödinger (NLS) model. It is demonstrated that an intense Airy beam with zero total momentum can generate static solitons, as well as moving solitons. The parameters of these solitons are calculated using the Zakharov-Shabat scattering problem associated with the NLS equation. It is found that solitons take the main part of the initial power, while only a small fraction of the power is transformed into a self-accelerating linear packet. The threshold parameters of the Airy beam for the soliton formation are obtained. It is shown that the threshold for the formation of the first static soliton is also a threshold of the solitonless regime.

Figure 1

Dependence of the amplitude (solid lines) and velocity (dashed lines) of solitons, emerging from initial type-I TAB (3), on the amplitude $u_0$ for (a) $w_0=10$ and (b) $w_0=5.4$. Thick (thin) solid lines correspond to amplitudes of static (moving) solitons.

Figure 2

Dynamics of the type-I TAB (3) for $w_0=10$ and different initial amplitudes. (a) There are no solitons at $u_0=1$. (b) For $u_0=4$, there is one static soliton and two moving solitons. A self-accelerating linear packet exists in all cases. A thick dashed line is a trajectory $x=z^2/4$ of the truncated Airy beam in a linear medium [5].

Figure 3

Dependence of the total power of linear waves $E_L$ on the initial power $E_0$ for $w_0=10$. Vertical dashed lines correspond to the thresholds of static soliton creation. Numbers near lines correspond to the $n\text{th}$ threshold.

Figure 4

Same as Fig. 1, but for type-II TAB (4), and for (a) $w_0=10$ and (b) $w_0=5$.

Figure 5

Dynamics of the type-II TAB (4) for $w_0=10$ and different initial amplitudes. (a) One static soliton at $u_0=1$. (b) A two-soliton state for $u_0=2.5$. A thick dashed line is a trajectory $x=z^2/4$.

Figure 6

Threshold initial amplitudes for the formation of solitons versus the inverse of the truncation parameter $1/w_0$ for type-I TAB (3). Solid (dashed) lines are the thresholds for static (moving) solitons.

Figure 7

Same as Fig. 6, but for type-II TAB (4).