Nonlocal Surface-Wave Solitons

We demonstrate, experimentally and theoretically, surface-wave solitons occurring at the interface between a dielectric medium (air) and a nonlinear material with a very long-range nonlocal response. These surface solitons are always attracted toward the surface, and unlike their Kerr-like counterparts, they do not exhibit a power threshold.

Figure 1

(a) Sketch of a 1D surface soliton with its boundary conditions for the temperature. (b) Calculated width (FWHM) of a 1D surface soliton as a function of the 1D optical power density. (c),(d) Profile of a 1D surface soliton at high and low optical power, respectively. (e) 1D surface soliton for $n_1-n_2=2\times {10}^{-5}$; the low index contrast at the boundary supports surface solitons with a significant part of their optical power residing in the linear medium.

Figure 2

(a) Sketch of a 2D surface soliton, with its boundary conditions for the temperature. (b) 2D surface soliton for $n_1-n_2=0.8$. (c) 2D surface soliton for $n_1-n_2=2\times {10}^{-5}$.

Figure 3

Simulated propagation of (a) a surface soliton launched at its stationary position ($x_0$) with 5% noise, and (b) a beam of the same power launched $30\mu \mathrm{m}$ away from the stationary position. In the latter case, the beam forms a soliton oscillating about the stationary position.

Figure 4

The temperature profile induced by a surface soliton launched at ($x_1\ne x_0$, $y=0$) ($x_0,0$ being the center point of the surface soliton under the respective parameters). (a) The asymmetric cross sections of the temperature profile, taken in the $x$ direction, for a 1D soliton [marked by $T_{1\mathrm{D}}(x)$], and for a 2D soliton $T_{2\mathrm{D}}(x,y=0)$. In both cases, there is a net force pushing the beam toward the insulating interface at $x=d=0.05$. (b) The symmetric cross section (taken in the $y$ direction) of the temperature profile induced by the 2D soliton launched at ($x_1,0$).

Figure 5

Experimental photographs taken at the input and output faces of the sample, along with the respective calculated trajectories (top view) of the soliton. (a) A 2D surface soliton launched at its stationary position ($x_0,0$). (b),(c) A 2D surface soliton launched 22 and $35\mu \mathrm{m}$ to the left of ($x_0,0$). All the trajectories of (a)–(c) converge to the same output position, and the beams emerge as a surface soliton, at the close proximity of the insulating interface. (d) A 2D soliton launched $65\mu \mathrm{m}$ to the left of ($x_0,0$) moves toward the interface, but cannot converge to the proximity of ($x_0,0$) within the finite propagation length in our sample. (e) At low power, the input beam of (a) broadens considerably, and its intensity is modulated by interference with reflections from the interface, as shown in (e).