Gold nanoparticle liquid crystal composites as a tunable nonlinear medium

We investigate the nonlinearity of a liquid crystal cell doped with gold nanoparticles by considering their selective absorption. Such nonlinearities are promising for optical processing applications and optical limiters. Systems displaying thermal nonlinearities are particularly attractive as the maximum nonlinearity may occur in the absence of an applied field and additionally this nonlinearity can be controlled by the reorientation of the liquid crystal. We show that there exists a theoretical optimum concentration of absorbers, which maximizes the nonlinearity. Further we show that the nonlinearity of the system can be tuned by the reorientation of the liquid crystal host, with the nonlinearity decreasing from $9\times 10{}^{-5}$ ${\mathrm{cm}}^2{\mathrm{W}}^{-1}$ to zero by the application of a magnetic field of the order of 0.01 Tesla. This allows a fine control of the diffraction efficiency and, in principle, many other nonlinear effects.

Figure 1

Schematic diagram of the diffraction efficiency experimental setup used in Ref. [21] to measure the thermal nonlinearity of the liquid crystal gold nanoparticle suspensions. In the configuration considered in this paper the polarizations of the pump and probe beams are parallel to the liquid crystal director which is in the $\widehat{\mathit{y}}$ direction.

Figure 2

A plot of the theoretical and experimental values for the diffraction efficiency for a range of intensities. The modeling parameters are as listed in Table 1 with the exception of of the pump and probe absorption coefficients which have values of 390 ${\mathrm{cm}}^{-1}$ and 276 ${\mathrm{cm}}^{-1}$ respectively. The experimental curve is the line of best fit from Ref. [21].

Figure 3

A plot of the theoretical and experimental values for the diffraction efficiency for a range of grating spacings. The modeling parameters are as listed in Table 1 with the exception of of the pump and probe absorption coefficients which have values of 390 ${\mathrm{cm}}^{-1}$ and 276 ${\mathrm{cm}}^{-1}$ respectively. The experimental curve is the line of best fit from Ref. [21].

Figure 4

A plot of the nonlinear coefficient against the absorption coefficient at the pump wavelength. With the exception of ${\alpha }_p$ the modeling parameters are listed in Table 1.

Figure 5

A plot of the diffraction efficiency of a gold nanorod suspension with varying aspect ratios and for a range of probe wavelengths. With the exception of ${\lambda }_{\mathrm{probe}}$ and the aspect ratio, the modeling parameters are listed in Table 1.

Figure 6

A plot of the magnetic field dependent absorption of a liquid crystal cell doped with gold nanospheres and gold nanorods. All parameters as listed in Table 1.

Figure 7

Plot of the effects that the magnetic field induced reorientation has on $n_2$. F2: Effect on birefringence. The dashed blue curve is the plot of $n_2$ computed assuming that $T=T(x,z)$ in Eq. (9), but $T=T_a$ in Eq. (17). F3: Effect of the director parameters. The solid green curve is the plot of $n_2$ computed assuming that $T=T_a$ in Eq. (9), but $T=T(x,z)$ in Eq. (17). All parameters as listed in Table 1. The inset shows a magnification of the effect of the director parameters (F3) highlighting the sign change of the nonlinearity.

Figure 8

Plot of the nonlinear coefficient $n_2$ against the applied magnetic field for: the gold nanorod suspension (dashed red line), the nanosphere suspension (solid green line) including factors F1–F3 and, for comparison, the nanosphere suspension neglecting F1 (dashed and dotted blue line). In the latter case α is no longer a function of the applied magnetic field H. All parameters as listed in Table 1.