Making beam splitters with dark soliton collisions

We show with numerical simulations that for certain simple choices of parameters, the waveguides induced by colliding dark solitons in a Kerr medium yield a complete family of beam splitters for trapped linear waves, ranging from total transmission to total deflection. The way energy is transferred from one waveguide to another is similar to that of a directional coupler, but no special fabrication is required. Dark soliton beam splitters offer potential advantages over their bright soliton counterparts: Their transfer characteristics do not depend on the relative phase or speed of the colliding solitons; dark solitons are generally more robust than bright solitons; and the probe peaks at nulls of the pump, enhancing the signal-to-noise ratio for probe detection. The last factor is especially important for possible application to quantum information processing.

Figure 1

(top) The pump signal, a dark soliton collision, using the analytical solution of Eq. (1) from Blow and Doran [20]. The velocity parameters are ${\lambda }_1=0.0$ and ${\lambda }_2=0.04$. (bottom) The corresponding probe signal for the case when the pump and probe equations have the same constants ($\kappa =1$), illustrating zero cross talk [14, 16].

Figure 2

(top to bottom) The probe signal in the same induced waveguide for the cases $\kappa =1.5,2$, and $2.5$.

Figure 3

The intensity of the probe signal (as seen from above) for $\kappa =12$.

Figure 4

The relative energy transmission of the dark-soliton beam splitter as a function of $\kappa$.

Figure 5

Full transfer of a captured wave, corresponding to the case $\kappa =2$, for waveguides resulting from soliton collisions at different speeds. (top) Relative speed (${\lambda }_2-{\lambda }_1$ in [20]) is 0.015, instead of 0.04; (bottom) relative speed is 0.12.

Figure 6

The effect of a junction on the second-degree modal function $u_{21}$. In this example, ${\kappa }_1=2/3$, ${\kappa }_2=2$, and the modal function $u_{21}$ is totally deflected.

Figure 7

The effect of a junction on an equal superposition of the second-degree modal functions $u_{21}$ and $u_{22}$. In this example, ${\kappa }_1=1/3$, ${\kappa }_2=1$, and the modes are separated, with only $u_{22}$ being deflected.