Light Meets Water in Nonlocal Media: Surface Tension Analogue in Optics

Shallow water wave phenomena find their analogue in optics through a nonlocal nonlinear Schrödinger (NLS) model in $2+1$ dimensions. We identify an analogue of surface tension in optics, namely, a single parameter depending on the degree of nonlocality, which changes the sign of dispersion, much like surface tension does in the shallow water wave problem. Using multiscale expansions, we reduce the NLS model to a Kadomtsev-Petviashvili (KP) equation, which is of the KPII (KPI) type, for strong (weak) nonlocality. We demonstrate the emergence of robust optical antidark solitons forming $Y$-, $X$-, and $H$-shaped wave patterns, which are approximated by colliding KPII line solitons, similar to those observed in shallow waters.

Figure 1

A $Y$-type interaction for $2{\kappa }_1={\kappa }_2=1$ and ${\lambda }_1=3{\lambda }_2=\frac{1}{4}$.

Figure 2

$X$-type interactions. Top: Short stem for ${\kappa }_1={\kappa }_2=\frac{1}{2}$ and ${\lambda }_1=-{\lambda }_2=\frac{2}{3}$. Middle: Intermediate stem for ${\kappa }_1={\kappa }_2=\frac{1}{2}$, ${\lambda }_1=-\frac{1}{4}-{10}^{-2}$, and ${\lambda }_2=\frac{3}{4}$. Bottom: Long stem for ${\kappa }_1={\kappa }_2=\frac{1}{2}$ and ${\lambda }_1=-{\lambda }_1+{10}^{-10}=\frac{1}{2}$.

Figure 3

An $H$-type interaction with $2{\kappa }_1={\kappa }_2=1$, ${\lambda }_1=\frac{1}{2}-{10}^{-7}$, and ${\lambda }_2=0$.

Figure 4

A typical lump solution with $a=0$, $b=1$.