Symmetry-breaking instability of quadratic soliton bound states

We study both numerically and experimentally two-dimensional soliton bound states in quadratic media and demonstrate their symmetry-breaking instability. The experiment is performed in a potassium titanyl phosphate crystal in a type-II configuration. The bound state is generated by the copropagation of the antisymmetric fundamental beam locked in phase with the symmetrical second harmonic one. Experimental results are in good agreement with numerical simulations of the nonlinear wave equations.

Figure 1

Quadratic soliton bound state corresponding to a total power of 29 kW as calculated numerically from Eqs. (1) with the experimental parameters given in the text. Shown are amplitude profiles of (a) $U_o$, (b) $U_e$, and (c) $V_e$ and their corresponding phase profiles [(d), (e), and (f), respectively].

Figure 2

Simulated output intensity profiles of the three interacting waves after 2 cm of propagation of (a) the numerical bound-state solution of Fig. 1; (b) the same initial conditions as in (a) but in the linear regime (low power) and in the absence of initial phase slope in the $x$ direction; (c) the same as in (b) but at soliton power.

Figure 3

Simulated intensity profiles in the $y$ direction (resulting from integration in $x$) of the beams corresponding to a total power of 20 kW. The red (bottom bold), magenta (bottom), and blue (upper) lines represent $U_o$, $U_e$, and $V_e$, respectively. (a) Input $z=0$ cm, (b) $z=0.5$ cm, (c) $z=2$ cm, and (d) $z=5$ cm.

Figure 4

Experimental setup. $\lambda /2$ stands for the half-wave plate. $L_x$ and $L_y$ are cylindrical lenses with focal length of 150 mm in the $x$ direction and 80 mm in the $y$ directions, respectively. ${\mathrm{P}}_1$ and ${\mathrm{P}}_2$ are the phase plates. FF and SH are imaged using distinct imaging systems with synchronized CCD cameras.

Figure 5

Experimental intensity profiles of $U_o,$ $U_e$, and $V_e$ in the first, second, and third column, respectively. (a) Input condition, (b) output in the low-power regime, (c,d) output at soliton power $\approx 60$ kW showing both the soliton bound state and its symmetry breaking, and (e) output at soliton power but with an unfavorable FF and SH phase relation.

Figure 6

Statistical study of the soliton symmetry-breaking process: (a) input beam, 66 laser shots; (b) output in the low-power regime, 87 laser shots; (c) output in the soliton regime, 159 shots.