Temperature dependence of the nonlinear optical response of smectic liquid crystals containing gold nanorods

The present study is devoted to the investigation of the nonlinear optical properties of a smectic liquid crystal doped with gold nanorods. Using the $Z$-scan technique, we investigate the changes in the optical birefringence of a homeotropic sample upon laser exposure, considering the configurations of normal and oblique incidence. Our results reveal that the birefringence variations may be governed by distinct physical mechanisms, depending on the relative angle between the far-field director and the wave vector of the excitation laser beam. In particular, we observe that the position dependence of the far-field transmittance exhibits different behaviors as the incidence angle is changed, indicating that distortions in the beam wavefront may be associated with the thermal lens phenomenon or an optically induced reorientation of the nematic director. The temperature dependence of the nonlinear refractive and absorptive coefficients is investigated close to the smectic-$A$–nematic phase transition. A detailed analysis of the interplay between smectic order and plasmon resonance is performed, thus unveiling the capability of plasmonic liquid crystal to be used in optical devices.

Figure 1

Extinction spectra of a homeotropic 8CB sample containing gold nanorods at distinct temperatures: $T=309$ K (black solid line), corresponding to the nematic phase, and $T=302$ K (red dashed line), corresponding to the smectic-$A$ phase. Notice that the transversal and longitudinal plasmon bands are highly sensitive to the sample temperature, indicating that the nematic and smectic ordering play an important role in the mean alignment of anisotropic guest particles. The inset shows a TEM image of the gold nanorods dispersed in the liquid crystal host.

Figure 2

Normalized $Z$-scan transmittance of a homeotropic sample of 8CB containing gold nanorods (gray circles), for different incidence angle: (a) $\varphi =0^{\circ }$ (normal incidence) and (b) $\varphi =5^{\circ }$ (oblique incidence). The sample temperature was fixed at 309 K, well above the smectic-$A$–nematic transition temperature. Red solid and blue dashed lines correspond to the best-fit curves using SB and TL models, respectively. Notice that the functional form of the normalized transmittance is strongly sensitive to the incidence angle, indicating that the birefringence changes are governed by different physical mechanisms.

Figure 3

Temperature dependence of nonlinear refractive index $n_2$ for a homeotropic 8CB sample containing gold nanorods. The dashed line is shown to guide the eyes. Notice that the nonlinear refractive index exhibits a pronounced increase in the vicinity of the nematic–smectic-$A$ phase transition.

Figure 4

Normalized $Z$-scan transmittance of 8CB doped gold nanorods at different temperatures: $T=302$ K (gray circles) and $T=305$ K (white squares). The $Z$-scan measurements were carried out in the configuration of a fully open aperture. The blue and red lines correspond to the best fits using Eq. (3).

Figure 5

Temperature dependence of the nonlinear absorption coefficient $\beta$ of homeotropic 8CB samples doped with gold nanorods. The dashed line is shown to guide the eyes. Notice that the nonlinear absorption coefficient tends to a constant value well below the nematic–smectic-$A$ transition temperature, reflecting the ordering degree of nanorods inside the smectic host as the temperature is reduced.