Control of strong-field ionization in ferroelectric lithium niobate: Role of the spontaneous polarization

We report the control of tunnel ionization in lithium niobate (${\mathrm{LiNbO}}_3$) using phase-controlled two-color laser fields. Through a macroscopic observable of high contrast, we disclose the crucial contribution of the microscopic spontaneous polarization of the ferroelectric material to the ionization rate: as the relative two-color phase is varied, the ablated area of ${\mathrm{LiNbO}}_3$ is modulated by 35% when the laser and crystal polarization directions are parallel. Rotating the sample by ${180}^{\circ }$ around the laser propagation axis leads to an out-of-phase modulation. We use a two-band model to highlight the key contribution of the material's spontaneous polarization for the symmetry breaking of the ionization rate. Our results open new perspectives for the direct control of ionization dynamics in solids by tailoring the electric field of femtosecond laser pulses.

Figure 1

(a) Sketch of the experimental setup. A laser field composed of the superposition of a fundamental frequency $\omega$ ($\lambda =1800$ nm) and its second harmonic $2\omega$ ($\lambda =900$ nm) is employed to ablate the surface of ${\mathrm{LiNbO}}_3$ samples just above the threshold fluence. The relative two-color phase $\varphi$ is adjusted by translating a motorized wedge in a direction perpendicular to the laser propagation axis and the beam is focused onto the crystal with an off-axis parabolic mirror. A fast ceramic motor stage ensures single-shot ablation by translating the sample in a direction parallel to its surface. The laser polarization and the $c$ axis of the crystal are oriented vertically. After a first ablation series, the sample is rotated by ${180}^{\circ }$ and the procedure is repeated. (b) Waveform representation of the electric field for $\varphi =0,\frac{\pi }{2},\pi$ [Eq. (1)]. The direction of the peak field with respect to the $c$ axis of ${\mathrm{LiNbO}}_3$ changes every $\mathrm{\Delta }\varphi =\pi$.

Figure 2

Single-shot ablated area as a function of the relative two-color phase for $\theta =0^{\circ }$ (solid blue) and $\theta ={180}^{\circ }$ (dashed orange). Each data point is averaged over ten measurements and the standard deviation is shown.

Figure 3

Determination of the spontaneous polarization. The ablated area as a function of 1800-nm field fluence (logarithmic scale) is shown. An ablation threshold of $0.51\mathrm{J}/{\mathrm{cm}}^2$ is retrieved from the fit. Dashed lines show the interpolated fluences for the maximal and minimal crater area in Fig. 2 from which a spontaneous polarization of $0.06\mathrm{C}/{\mathrm{m}}^2$ is retrieved.

Figure 4

Two-band model calculations. The conduction band (CB) population as a function of the relative two-color phase $\varphi$ is shown for $\theta =0^{\circ }$ and $\theta ={180}^{\circ }$. The two orientations correspond to a sign reversal of the spontaneous polarization that is either parallel or antiparallel to the laser peak electric field. Different values are compared: $P_s=\pm 0.05\mathrm{C}/{\mathrm{m}}^2$ (green squares and purple line), $P_s=\pm 0.1\mathrm{C}/{\mathrm{m}}^2$ (blue circles and orange crosses), and $P_s=0\mathrm{C}/{\mathrm{m}}^2$ (black dots). While a sign reversal leads to a $\pi$ phase shift of the modulation, the frequency is doubled when $P_s=0\mathrm{C}/{\mathrm{m}}^2$ (black dots, right scale).