Plasmon enhancement of third-order nonlinear optical absorption of gold nanoparticles dispersed in planar oriented nematic liquid crystals

We report structural and nonlinear optical properties of 20 nm gold (Au) nanoparticles (NPs) that are dispersed in planar degenerate (non-oriented) and planar oriented nematic liquid crystals (LCs) (4′-Pentyl-4-biphenylcarbonitrile-5CB). Taking advantage of elastic forces in the planar oriented nematic LC, we aligned AuNPs parallel to the 5CB director axis. In the case of planar degenerate, 5CB is not aligned and has no preferred orientation, forcing the AuNPs to disperse randomly. Results show that the linear optical absorption coefficient for the planar oriented 5CB/AuNPs mixture is larger than the corresponding planar degenerate sample. The nonlinear absorption coefficients are greatly enhanced in planar oriented samples at relatively high concentrations which can be attributed to plasmon coupling between the aligned AuNPs. This study demonstrates the utility of LCs for developing the assembly of NPs with enhanced optical properties which may offer important insight and technological advancement for novel applications, including photonic nanomaterials and optoelectronic devices.


Introduction
Plasmonic nanomaterials exhibit strong light-matter interaction that can be controlled by the size, shape, and material composition of nanoparticles (NPs) [1,2]. In these systems incident light induces localized surface plasmon resonances (LSPR) on NPs, leading to fascinating and unique properties that have found applications in fields of medicine, biology, chemistry, photonics, and biomedical imaging and sensing [3][4][5][6][7][8][9][10][11][12]. In recent years, the rapid development of nanoscience and nanotechnology has enabled the synthesis of NPs from a wide variety of materials that include the fabrication of multi-nanoparticle structures and arrays [13][14][15][16]. Compared to single NP, the complex structure of NPs, such as NP dimer, can more strongly enhance the localized electric field, leading to further enhancement of near-field electric field [17]. However, the degree of enhancement depends on the spacing between NPs [3,18,19]. Sun et al developed an analytical model for the evaluation of filed enhancement in Au spheres dimer, relative to that can be obtained a single sphere showing enhancement in the gap of dimer increases when the gap size decreases [20]. In a follow-up study, however, they applied a self-consistent method to the dimer analysis and the result shows that the field cement stops increasing (becomes saturation) if the gap size reduces to a few nanometers (less than 10 nm) mainly due to the Landau Damping [21], suggesting spacing between NPs plays an important role in the field enhancement.
Interaction strength between the NPs and the dielectric medium also plays a role in the plasmon resonance. Several researchers have demonstrated that plasmon resonance shift, sensitivity, and optical response of noble metal NPs depend on size, shape, interparticle spacing, and the dielectric constant of the medium [22,23]. Fakhri et al studied graphene oxide-Au nanoparticles (GO-AuNPs) in different solvents and demonstrated that due to the nonlocal interaction, surrounding media could influence the nonlinear optical properties of GO-AuNPs [24]. When it comes to the host medium, soft materials such as liquid crystals (LCs) have become desirable systems to align NPs due to their elastic forces capable of controlling and assembling various classes of nanomaterials [25][26][27][28][29]. For example, it has been shown that metallic NPs inside nematic LCs can be oriented in a preferred direction, allowing us to exploit the optically induced collective LSPR and the corresponding changes in Freedericksz threshold, viscoelastic coefficients, and dielectric anisotropy of the samples [27].
Despite the growing body of work on complex nanoparticle structures and the exploitation of their plasmon coupling for a variety of applications, only a few studies are addressing the effect of plasmon enhancement on third-order nonlinear optical absorption for NPs in LCs. ZnS NPs doped nematic LCs mixture, the nonlinear optical absorption is shown to be concentration dependent [30]. Podoliak et al demonstrated that doping nematic LCs with small amounts of AuNPs can improve two-beam coupling gain and nonlinear refractive index coefficient [31]. Pezzi's group investigated aligned AuNPs in nematic LCs where they found photothermal sensitivities and their refractive index changed significantly when AuNPs were photoheated [32]. To this end, we carried out linear and third-order nonlinear optical studies of AuNPs dispersed in nematic LCs with various orientations to investigate the role of alignment on the plasmon enhancement. We used 4'-pentyl-4-biphenylcarbonitrile (5CB) LC (Frontier Scientific), to align 20 nm AuNPs endcapped with citrate ligands (NN-Labs, Citrate capped 20 nm gold nanocrystals, SPR peak at 524 nm, Molar extinction coefficient 9.21E + 08 M −1 cm −1 , and size dispersity: <12%) in a planar degenerate and planar oriented cells. Upon establishing the alignment of AuNPs, their third-order nonlinear optical absorption properties were studied using the conventional z-scan technique [33], while varying the AuNP concentration and laser repetition rate. Our results show the enhancement of nonlinear optical absorption through LSPR in the planar oriented cells.

5CB/AuNP sample preparation
Spherical AuNPs of diameter 20 nm stabilized with citrate ligands in an aqueous solution (purchased from NNCrystal) are dried under a slow airflow to eliminate water. The dry NPs are then dispersed in an ethanol solution and added to the 5CB. The solvent was then evaporated under a slow airflow at 60°C overnight. Finally, the samples were vacuum-dried at the same temperature for one hour to eliminate any residual solvent. The samples were used immediately after the dispersion of NPs to avoid the formation of big aggregates.
The 5CB/AuNPs are then injected in prefabricated planar cells (planar oriented and planar de-generate). These cells are prepared as follows: two glass plates (25 × 20 × 1.0 mm, Fisher brand), initially cleaned with water and acid, are coated with a monolayer of 3 wt% poly-vinyl alcohol (PVA) solution (90 wt% water + 10 wt% ethanol), then placed in an oven for 1 h at 110°C to crosslink the PVA. For planar orientation, the PVA films are rubbed with cloth along one direction to impose the anchoring. Two PVA-treated slides were assembled by keeping the rubbing direction parallel to each other. A 100 μm Mylar spacer is placed between two glass plates to fix the cell thickness. The cell is then sealed with optical glue. Finally, the 5CB/AuNP mixture is loaded into the cell by capillarity while heating the 5CB to the isotropic phase to avoid the elasticity and aggregation of NPs. The presence of citrate ligands on the surface of the NPs helps to disperse them uniformly in the mixture. Similar steps were performed to prepare planar degenerate samples except not rubbing the PVA.

Z-scan setup
A frequency-doubled Nd:YAG laser (Continuum Minilite II, 532 nm, 3-5 ns pulse width, 55 μm beam waist) is focused on the LCs cells using a 20 mm focal length lens. The LCs cell is placed on a translation stage (Thorlabs NRT 150) and is moved freely through the focal region. An optical detector (Newport 818-SL) is used to record the transmittance. Incident laser energy is measured by a Coherent FieldMax Laser Power/Energy meter. The transmittance of the sample is recorded as the translation stage is moved in steps of 5 mm. The movement of the translation stage and the data collection is controlled by a LabView routine. All the z-scan experiments were carried out at the intensity of 1.86 × 10 12 W m −2 . Figure 2 shows the schematic of the arrangements and alignments of AuNPs in 5CB and their associated brightfield optical microscopy images (figures 2(b) and (e)). Uniform field distribution in these images indicates that the NPs are well dispersed in the 5CB. The black spots in these two images are LCs defects near the surface of the cells, due to the non-perfect layer of PVA. These spots disappeared when the sample is heated, and the LCs transitioned into the isotropic phase; reappeared at a different position after the sample is cooled down back to the nematic phase. Figures 2(c) and (f) are the corresponding images observed under cross-polarization. Light can still be observed due to the birefringence of the LCs and the change of light polarization when it propagates through the nematic director in the degenerate cell with no certain direction alignment (figure 2(c)), whereas for the oriented sample (figure 2(f)), the cell is completely dark when it's easy axis is aligned with one of the polarizers, which indicates that the molecules of LCs are perfectly oriented. Figure 2(a) exemplifies a degenerate cell where there is no preferred orientation of the 5CB director axis, and hence random dispersal of the AuNPs. Figure 2(d) illustrates the aligned 5CB director axis in a preferred direction due to the rubbing, as it happens in the planar oriented cell.

Results and discussion
The elastic forces of the LCs force the AuNPs to assemble into linear chains forming dimers along the easy axis of 5CB. Upon excitation, free electrons in the AuNPs oscillate in the direction of the electric field polarization, inducing field enhancement around AuNPs. In the planar degenerate sample, dimers are formed, but are randomly oriented as seen in figure 2(a). Thus, their contribution to plasmon enhancement is limited. But in the planar oriented sample, as AuNPs form dimers parallel to the electric field polarization, the electric field gets further amplified in the gap of the AuNPs, as shown in the inset of figure 2(d). Figure 3(a) shows the plot between the α 0 versus concentration for all the samples while figure 3(b) illustrates the variation of normalized α 0 /α 05CB . Compared to the pure 5CB, the absorbance of the planar oriented samples is higher and increased linearly with AuNP concentration. For the case of planar degenerate, although the absorbance is higher than the pure 5CB sample, they are lower than the corresponding planar oriented samples. According to the spec sheet, the plasmon resonance of AuNPs is ∼524 nm. When dimers are formed, the resonance peak could shift to a longer wavelength, resulting in the increase of absorbance in the oriented samples.
The nonlinear optical studies are carried out using the open-aperture z-scan technique for all the AuNP concentrations. All the samples show reverse saturable absorption property-absorption increases as fluence is increased, as shown in figure 4. According to the band theory, free electrons in AuNPs absorb the laser energy and undergo either interband transition or intraband transition, resulting in a reverse saturable absorption behavior [34]. Third-order nonlinear absorption coefficient, β is obtained for all the samples I 0 is on axis light intensity, L being sample thickness, z 0 is Rayleigh range by equation (πω 2 0 )/λ, where ω 0 and λ beam waist and wavelength of the laser source, respectively. α 0 is the linear absorption coefficient. Figures 3 and 5 show that both α 0 and β values, respectively, for the 5CB/AuNP mixture are higher than the pure 5CB sample. This observation is consistent with the previously published theory on plasmonic enhancement of linear and nonlinear processes [35,36]. In the presence of AuNPs, the optical fields E ω around the vicinities of AuNPs are enhanced by a factor where is the average incident excitation field, which is proportional to the Q-factor of the LSPR of NPs, resulting in enhancement of linear absorption and third-order nonlinear processes that scale with F 2 and F 4 , respectively, in close proximities of the AuNPs. Given the fact that AuNPs are sparsely dispersed in LCs, we can introduce the effective fill factor f and estimate the enhancement of the linear absorption and the third-order nonlinearity as (1 + fF 2 ) and (1 + fF 4 ), respectively. It is not difficult to see that the enhancement for the third-order nonlinear process is stronger than that of linear process as has been previously pointed out plasmonic enhancements are in general always stronger for inefficient processes such as Raman scattering and two-photon absorption [37]. This is indeed what we have observed in figure 5 where the enhancement of third-order nonlinear coefficient β is consistently stronger than that in figure 3 for the linear absorption α 0 .
For AuNP concentrations less than 0.025 wt%, β is about the same for the corresponding planar oriented and planar degenerate samples. However, for concentrations greater than 0.025 wt%, the β values of planar oriented samples are ∼2.5 times higher than the corresponding planar degenerate samples. Aside from the increasing fill factor that contributes to the increased enhancement, the possibility of these AuNPs form coupled NP dimers also increases, in the case of oriented AuNPs shown in figure 2(d), when plasmonic dimers are formed, the incident light with its polarization along the line that runs through the two AuNPs sphere centers forming the dimer will be able to induce even stronger optical field in the gap of AuNP dimer than in the vicinity of an isolated AuNP [3]. Obviously, for the AuNPs dispersed in planar degenerate LCs as shown in figure 2(a), such an alignment is not likely to occur, as a result, we observed a consistent increase of plasmonic enhancement for the third-order nonlinearity in the oriented AuNP samples with the increase of AuNP concentration, but no such clear trend is observed in the degenerate samples.
Another important factor to consider is the enhancement of nonlinear absorption. From figure 3 it is evident that α 0 increased with AuNP wt% in the case of planar oriented samples. In order to estimate the enhancement of third-order nonlinear absorption we calculated β Au /β 5CB (figure 5). Once again, we see the enhancement when the wt% of AuNPs in 5CB is greater than 0.025, and that too, in the case of planar oriented samples only. Not much difference is observed at relatively low concentrations, and in degenerate samples. When 0.05 wt% of AuNPs are added to the planar degenerate 5CB, β is increased by 1.5 times. However, due to plasmon enhancement, the β is increased by 4 times in the planar oriented samples.
Cumulative thermal effects are commonly observed in nematic LCs under nanosecond laser illumination. High pulse repetition rates may heat the 5CB and change their thermooptical properties. To assess its effect on our samples, we performed z-scan studies by keeping the laser energy the same but changing the laser pulse repetition rates at 2 Hz, 5   Hz, and 10 Hz. The comparison graph is shown in figure 6. Results indicate that by increasing repetition rates from 2 Hz to 10 Hz, β values decrease among all samples, indicating that cumulative thermal effects can influence the orientation of the LCs director. At high repetition rates, the laser may strongly influence the structure and state of LCs which can change the alignment of AuNPs, affecting the nonlinearity of samples.