Ultrafast Reversal of the Ferroelectric Polarization

We report on the demonstration of ultrafast optical reversal of the ferroelectric polarization in ${\mathrm{LiNbO}}_3$. Rather than driving the ferroelectric mode directly, we couple to it indirectly by resonant excitation of an auxiliary high-frequency phonon mode with femtosecond midinfrared pulses. Because of strong anharmonic coupling between these modes, the atoms are directionally displaced along the ferroelectric mode and the polarization is transiently reversed, as revealed by time-resolved, phase-sensitive, second-harmonic generation. This reversal can be induced in both directions, a key prerequisite for practical applications.

Figure 1

(a) Harmonic energy potential $V_{\mathrm{IR}}(Q_{\mathrm{IR}})$ of the resonantly excited high frequency mode $Q_{\mathrm{IR}}$. (b) Double well potential $V(Q_P,Q_{\mathrm{IR}})$ along the ferroelectric mode $Q_P$. For finite amplitude of $Q_{\mathrm{IR}}$, the energy minimum of the equilibrium potential [$V_P(Q_P)$, dashed line] is first displaced and then destabilized as the amplitude of $Q_{\mathrm{IR}}$ exceeds a threshold (colored lines). (c),(d) Solution to the corresponding coupled equations of motion (see text). Following excitation of $Q_{\mathrm{IR}}$ with midinfrared pulses (orange), a force $F\propto Q_{\mathrm{IR}}^2$ displaces the ferroelectric mode $Q_P$ toward lower values. For above-threshold excitation of $Q_{\mathrm{IR}}$, the polarization reverses permanently. (e) Crystal structure of ferroelectric ${\mathrm{LiNbO}}_3$. Drawn are the hexagonal crystal axes. The Li an Nb sublattices are shifted against the oxygen octahedra (orange and green arrows), inducing a ferroelectric polarization $P_S$ along the $c$ axis. Further shown are schematics of the motions associated with the phonon modes $Q_{\mathrm{IR}}$ and $Q_P$. The ferroelectric mode $Q_P$ involves $c$-axis motions of the Nb and Li sublattices against the oxygen octahedra (orange and green arrows) and modulates the ferroelectric polarization.

Figure 2

(a) Carrier envelope phase stable 19 THz midinfrared pulses were used to excite the high frequency mode $Q_{\mathrm{IR}}$ shown in Fig. 1. The inset shows the Fourier transformation of the pulse. (b) Time-resolved second-harmonic intensity, normalized to its value before excitation. Following excitation, the second-harmonic intensity reduces before relaxing back. This drop increases with pump fluence. For all fluences above $60\mathrm{mJ}/{\mathrm{cm}}^2$, the second-harmonic signal vanishes, followed by a transient recovery before relaxing back to its equilibrium value.

Figure 3

(a) Experimental geometry for phase-sensitive measurements of the second harmonic. The time dependent second-harmonic signal from the excited ${\mathrm{LiNbO}}_3$ crystal was interfered with a reference second-harmonic field from an unexcited sample and measured with a CCD camera. The resulting interference pattern consisted of fringes on top of a Gaussian background, which was subtracted. (b) Time-resolved measurement of the interference fringes, integrated along the $x$ axis of the camera and normalized. The data show a transient phase change by 180° (sign reversal) between 0 and 200 fs. (c) Normalized interference fringes at $-200\mathrm{fs}$ and in the reversed polarization state at $+80\mathrm{fs}$.

Figure 4

Probe pulse polarization dependence of the second-harmonic signal at four time delays after excitation. The angles 0° and 90° denote a polarization of the 800 nm pulses along and perpendicular to the spontaneous polarization. The arrows indicate the time dependent amplitude and sign of the ferroelectric polarization for each time delay, determined from the measurements of Fig. 3. The solid lines are fits to the data using the ${\chi }^{(2)}$ tensor of ${\mathrm{LiNbO}}_3$.

Figure 5

(a) Time-resolved normalized ferroelectric polarization $P_S(\tau )/P_{S,0}$ following excitation of ${\mathrm{LiNbO}}_3$ with two opposite initial polarization states, as determined from the measurement of the SH intensity and the phase of the SH field. (b) Phase of the SH field derived from a sine fit to the interference pattern (see text).

Figure 6

(a) Normalized polarization at the peak of the time dependent signal ${[P_S(\tau )/P_{S,0}]}_{\text{peak}}$ as function of pump fluence. The three curves correspond to excitation with pulses at different frequencies. The polarization reverses for excitation above $60\mathrm{mJ}/{\mathrm{cm}}^2$ with 19-THz pulses, resonant with the $Q_{\mathrm{IR}}$ mode transverse optical frequency ${\omega }_{\mathrm{IR},\mathrm{TO}}$. (b) Pump pulse frequency dependence of the susceptibility to the excitation (blue dots, left axis), defined as the slope of linear fits to the fluence dependence of ${[P_S(\tau )/P_{S,0}]}_{\text{peak}}$, shown in Fig. 6. The solid line shows the extinction coefficient of ${\mathrm{LiNbO}}_3$ for comparison (right axis).