Spontaneous polarization in ultrasmall lithium niobate nanocrystals revealed by second harmonic generation

Nanocrystals of lithium niobate (LiNbO${}_3$) with diameters of between 5 and 50 nm were produced by a combination of sol-gel synthesis and wet-chemical etching. The phase purity and nearly spherical shape of the crystals were verified by transmission electron microscopy. Power and polarization dependences of the second harmonic signal of single nanocrystals reveal that the nanocrystals have the noncentrosymmetric point group $3m$ and that the second-order nonlinear optical coefficients known from the bulk material are fully present in all nanocrystals studied. The volume of the crystals is still the main source of frequency conversion and they are spontaneously polarized.

Figure 1

Experimental setup for second harmonic measurements. The laser delivers linearly polarized $1.0$-ns pulses at a 1064-nm wavelength. The polarization direction in the focal plane can be adjusted using a rotatable half-wave plate.

Figure 2

Polar plot of the calculated scalar $d_{\mathrm{m}}(\theta ,\varphi ,\psi )$ for certain sets of $\theta$ and $\varphi$. The angle $\psi$ is varied. A light polarization perpendicular to the crystal $c$ axis corresponds to $\varphi =90$°, while $\psi =\varphi =0^{\circ }$ corresponds to a light polarization parallel to the $c$ axis. Note that the minimum value for each curve is always the same $d_{\mathrm{m}}^{\min }$, while the maximum varies between 27 and $5.6$ pm/V. The average maximum is calculated via Eq. (9).

Figure 3

Angular dependent radiated intensity for point dipole antennas on a glass substrate, in the laboratory frame of reference. The pump light propagates parallel to the dashed arrow. The upper halfspace consists of air, the lower of glass, the shaded region marks the collection angle, $\gamma$ represents the angle between antenna and surface.

Figure 4

(a) TEM bright-field image of the AG batch. (b) Electron diffraction Debye-Scherrer pattern of crystals of M10. Reflection rings of LiNbO${}_3$ (ICDS database No. 28294) are outlined and indexed, indicating phase-pure LiNbO${}_3$. (c) High-resolution TEM image of H20. Crystal contours and some prominent lattice fringes are outlined in white.

Figure 5

Crystal size distribution for two batches, with lognormal fits shown as lines. The crystal size was determined by averaging the long and short axes. Batches: filled squares represent AG, which peaks at 25 nm and averages to 30 nm. Open triangles represent M30, which peaks at 9 nm and averages to 13 nm. Data are normalized to a cumulated probability of 1, and the statistical bin size is 2 nm.

Figure 6

(a) Mean crystal diameter versus etching time for three HF concentrations: open squares, 95 mM HF; filled squares, 180 mM HF; and open triangles, 335 mM HF. The lines are linear fits to the data. (b) Averaged crystal axis ratios for different etching treatments. Symbols are the same as in (a), and bars indicate the standard deviations of the axis ratio. The horizontal (orange) line at an 0.8 axis ratio is a guide for the eye.

Figure 7

(a) Overlain light microscopical image, in red scale with greatly enhanced contrast, and scanned SH response, in gray scale, of a typical sample. (b) Averaged polarization-dependent SH pulse energy for a crystal from batch M10 at $I=80$ GW/cm${}^2$ pump intensity. (c) Averaged SH pulse energy versus pump intensity for an AG crystal with minimum-conversion light polarization direction. The solid line illustrates the predicted $\propto$$I_{\mathrm{p}}^2$ curve with $d_{\mathrm{m}}=5.6$ pm/V and $r=28$ nm.

Figure 8

Polar plot of the averaged SH pulse energy of a crystal from batch M30. The thick (blue) line is a calculated prediction with $\theta ={65}^{\circ }\pm 5^{\circ }$ and $\varphi ={75}^{\circ }\pm 5^{\circ }$. The prediction curve was scaled via the minimum SH response.

Figure 9

(a) Averaged SH pulse energy versus crystal size in a semilogarithmic plot. The minimum (filled squares) and maximum (open triangles) polarization-dependent values are shown. The upper (blue) line shows the prediction using a pump intensity of $I=80$ GW/cm${}^2$ and $d_{\mathrm{m}}=12.9$ pm/V; the lower (orange) line uses $d_{\mathrm{m}}=5.6$ pm/V. (b) Calculated $d_{\mathrm{m}}$ versus average crystal size; line colors and symbols as in (a).

Figure 10

Occurrence probability of the sixth root of the SH pulse energy in M30: (a) At minimum conversion. The solid (orange) line was predicted using the measured crystal size distribution and $d_{\mathrm{m}}^{\min }=5.6$ pm/V. (b) At maximum conversion. The solid (blue) line was predicted, using the measured crystal size distribution and $d_{\mathrm{m}},{\mathrm{ave}}^{\max }=12.9$ pm/V. Filled squares and open triangles show the sixth roots of the respective measured SH pulse energies. The shaded region indicates where the crystal response is lower than the substrate response.