Spatial Akhmediev breathers and modulation instability growth-decay cycles in a quadratic optical medium

We investigate the spatial nonlinear localization of light on a quasi-plane-wave background with a harmonic perturbation induced by modulation instability in a quadratic nonlinear optical medium. In particular, we demonstrate experimentally the excitation of deterministic Akhmediev breathers and thus the growth-decay dynamics of modulation instability in a ${\mathrm{LiNbO}}_3$ slab waveguide. The results should stimulate new interest in modulation instability, extreme events, turbulence, recurrence, and supercontinuum generation in quadratic nonlinear optics.

Figure 1

Experimental setup.

Figure 2

Normalized intensity distribution $I_1(x,I_{1\mathrm{P}})$ of the FF beam at the waveguide output: (a) measurement and (b) simulation, $T=287.5{}^{\circ }\mathrm{C}$, $\mathrm{\Delta }kL=113\pi$ at the ${\mathrm{TE}}_0$ resonance, modulation period 185 $\mu \mathrm{m}$, $m=0.6$.

Figure 3

Normalized intensity profiles $I_1\left(x\right)$ of the FF beam: (a) input spot, (b) waveguide output at $I_{1\mathrm{P}}=7\mathrm{W}/\mu \mathrm{m}$, (c) $I_{1\mathrm{P}}=95\mathrm{W}/\mu \mathrm{m}$, and (d) $I_{1\mathrm{P}}=215\mathrm{W}/\mu \mathrm{m}$ under the experimental conditions of Fig. 2. Black-solid lines indicate experimental and red-dotted lines numerical results.

Figure 4

Color-coded normalized intensity evolution of the growth-decay cycle of breathers with different spatial periods: (a) period 300 $\mu \mathrm{m}$, $m=0.6$, $T=285{}^{\circ }\mathrm{C}$; (b) period 133 $\mu \mathrm{m}$, $m=0.35$, $T=287.5{}^{\circ }\mathrm{C}$.

Figure 5

(a) Effective cubic nonlinearity $\gamma$. (b) Input intensity $I_{1\mathrm{P}}$ for the observation of the breather maxima at the waveguide output, modulation period 185 $\mu \mathrm{m}$, $m=0.6$ for red objects, $m=0.35$ for dark objects. Circles refer to measurements, solid lines to simulations. The dashed lines show analytical predictions from [31]. Dotted blue vertical lines indicate phase-matching temperatures for ${\mathrm{TE}}_0$ and ${\mathrm{TE}}_1$ resonances. The dashed blue vertical line indicates the temperature where the different nonlinear contributions cancel each other.