We experimentally demonstrate self-trapping of light, as a result of plasmonic resonant optical nonlinearity, in both aqueous and organic (toluene) suspensions of gold nanorods. The threshold power for soliton formation is greatly reduced in toluene as opposed to aqueous suspensions. It is well known that the optical gradient forces are optimized at off-resonance wavelengths at which suspended particles typically exhibit a strong positive (or negative) polarizability. However, surprisingly, as we tune the wavelength of the optical beam from a continuous-wave (CW) laser, we find that the threshold power is reduced by more than threefold at the plasmonic resonance frequency. By analyzing the optical forces and torque acting on the nanorods, we show theoretically that it is possible to align the nanorods inside a soliton waveguide channel into orthogonal orientations by using merely two different laser wavelengths. We perform a series of experiments to examine the transmission of the soliton-forming beam itself, as well as the polarization transmission spectrum of a low-power probe beam guided along the soliton channel. It is found that the expected synthetic anisotropic properties are too subtle to be clearly observed, in large part due to Brownian motion of the solvent molecules and a limited ordering region where the optical field from the self-trapped beam is strong enough to overcome thermodynamic fluctuations. The ability to achieve tunable nonlinearity and nanorod orientations in colloidal nanosuspensions with low-power CW laser beams may lead to interesting applications in all-optical switching and transparent display technologies.
© 2018 Chinese Laser Press
The study of optical nonlinearities in plasmonic nanostructures and nanocomposites has attracted much attention in recent years [1–5]. As a result of strongly enhanced fields with subwavelength confinement and high sensitivity to the environment, plasmonic nanostructures exhibit unique nonlinear optical phenomena with potential applications in all-optical switching and modulation  and sensing . Among the plasmonic nanocomposite systems studied, colloidal suspensions of plasmonic nanoparticles are particularly interesting due to the possibility of manipulating these systems by mechanical, electrical, and optical methods. Previously, third-order optical nonlinearities in colloidal suspensions of gold nanoparticles of different shapes have been studied [8,9]. Self-focusing of a 532 nm laser beam and optical soliton has been demonstrated in plasmonic nanosuspensions of gold nanoparticles and core–shell particles . Furthermore, the propagating self-trapped laser beam forms a soliton channel, a self-induced waveguide, and the guidance of a low-intensity probe beam inside such a channel has also been observed [11,12].
In addition to optical nonlinearity, it may be possible to align gold nanorods using optical fields as suggested theoretically [13,14]. The collective alignment of a large quantity of gold nanorods in a liquid environment may lead to macroscopic anisotropic optical response and can find applications in information processing and display technologies. While ordering of an ensemble of rods has been demonstrated with techniques including applying electric fields [15–20], self-assembly based fabrication [21–23], the stretched-film method [24–26], and the electrospinning technique [27,28], so far only manipulation of individual plasmonic nanorods was demonstrated experimentally with optical traps [29–34]. Recently, we attempted to achieve orientational ordering of gold nanorods inside an optical soliton channel established by pumping a colloidal suspension of gold nanorods with a 532 nm laser beam . In the study, transmission as a function of the polarization direction of a linearly polarized low-intensity 1064 nm probe beam was measured, providing indirect evidence for the presence of nanorod ordering in the system. However, the input power of the probe beam was not fixed for different polarizations, which may complicate the interpretation of the experimental results. Furthermore, control of nanorod alignment via plasmonic resonant tuning remains elusive.
In this work, we study optical nonlinearity in suspensions of gold nanorods and explore the effect of the solvent environment (aqueous versus organic) on soliton formation. Toluene is chosen as the organic solvent here, motivated by previous reports of obtaining good alignment of gold nanorods in toluene by applying an electrical field [18,19]. The threshold power for soliton formation for both suspensions is measured as a function of wavelength. We then analyze the optical forces exerted on the nanorods and discuss their role in the formation of solitons. By analyzing the optical torque acting on the nanorods and associated rotational potential energy, we show theoretically that it is possible to align the nanorods inside a soliton channel, leading to wavelength-dependent orientations. Finally, we perform polarization transmission measurements of a low-power probe beam (at 1064 nm) guided along the soliton channel to obtain information about soliton-mediated anisotropic optical properties of the colloidal suspensions.
2. EXPERIMENTAL SETUP
In a typical experiment, a cuvette with 5 mL of the nanorod solution (Nanopartz, Part #A12-50-800 for aqueous suspension and #E12-50-800-NPO-TOL for toluene suspension) is used in the optical path, as shown in Fig. 1. A continuous-wave (CW) laser beam of tunable wavelength is focused into the sample, driving the nanorods to form a soliton channel, and will be referred as the pump (soliton-forming) beam in this study. The input power of the pump beam can be varied from 0 to 1000 mW by a half-wave plate mounted on a step motor. The profile of the soliton beam is recorded with a CCD camera at the input and at the output when the beam exits from the sample. The power transmission of the soliton beam is measured for a range of wavelengths by recording both the input and output power. To measure the optical anisotropy of the soliton channel, a 1064 nm probe beam from a CW laser with a fixed power for different polarizations, which can be tuned by a polarizer placed before the dichroic mirror, is then guided through the soliton channel. Since the probe beam has a very low power and is at a wavelength that does not favor the nonlinear self-action of the beam, it will not interfere with the formation of a soliton by the pump beam. The power of the output probe beam after the sample is then measured with the use of a long-pass filter to remove the pump beam and a pinhole to exclude the probe beam that is outside the soliton channel. The formation of the soliton beam and the guidance of the probe beam along the soliton channel are also verified by recording their side-view images, as shown in the inset of Fig. 1.
3. RESULTS AND DISCUSSION
A. Solvent-Dependent Nonlinear Response
By sending a focused, linearly polarized 740 nm pump beam at varying input powers into a 1.25-cm-long cuvette of gold nanorods (average diameter 50 nm, average length 145 nm) suspended in water or toluene, we compare the nonlinear effects of gold nanorods in two different suspensions. The optical densities of the samples are matched by diluting the toluene solution (Part #E12-50-800-NPO-TOL) obtained from Nanopartz to the same as the aqueous solution (Part #A12-50-800). For both cases, when an input beam at 10 mW is applied [see Figs. 2(a) and 2(e)], an output beam exhibiting linear diffraction is observed [see Figs. 2(b) and 2(f)]. For the aqueous plasmonic solution, linear diffraction of the beam dominates for input pump power up to 50 mW. At an input pump power of 157 mW, nonlinear focusing starts to have an effect and the output beam size starts to decrease [see Fig. 2(c)] compared to the beam sizes at lower pump powers. The output beam size is further reduced with increasing pump power, and nonlinear self-trapping is observed at a pump power of 620 mW [see Fig. 2(d)], indicating the formation of a soliton beam. In the case of the toluene solution, nonlinear focusing starts to have an effect on the output beam profile for a pump power as low as 50 mW [see Fig. 2(g)]. However, at an input power of 157 mW, nonlinear self-trapping of the input beam to form a soliton is observed [see Fig. 2(h)], indicating a significant decrease in threshold power. We note that the ring structures in Fig. 2(h) are a result of thermal defocusing, which has been reported previously .
As seen from Fig. 2, the necessary input power needed to create a soliton is significantly different for the aqueous and toluene samples. Given that the dimensions of the gold rods and the input beam sizes [see Figs. 2(a) and 2(e)] are the same for the two types of samples, a possible explanation for the different level of optical nonlinearity observed here could be that water and toluene have different values of refractive index and viscosity, which can affect the motion of nanorods in the solvent. We have found that the values of nanorod polarizability and extinction cross section are similar for the aqueous and toluene suspensions due to the small difference in their refractive indices. On the other hand, viscosity affects the translational motion of the rods. Since the two solvents have very different values of viscosity, we believe the viscosity of the background medium plays a major role in determining the soliton threshold power and have provided a detailed analysis of the optical forces and their effect on optical nonlinearity in Section 3.C. Furthermore, while the exact mechanism is not yet clear, we believe viscosity also affects the rotational dynamics of the rods and the degree of nanorod alignment at equilibrium. More specifically, the viscosity of toluene reported in the literature is smaller than that of water, enabling the orientations of gold nanorods to be readily controlled by an external field [18,19].
B. Wavelength-Dependent Nonlinear Response
The creation of soliton beams in both water and toluene is verified over a wide range of wavelengths from 700 to 960 nm by examining the output profile of the soliton-forming pump beam. At each wavelength, similar to what is observed in Fig. 2, the output beam size decreases as the power of the pump beam increases, and the power corresponding to the smallest output beam size is recorded and is shown in Fig. 3(a) for a toluene suspension of gold nanorods. We find the soliton power varies between 40 and 185 mW for wavelengths ranging from 800 to 950 nm and reaches a minimum of 40 mW at 880 nm, indicating the strongest optical nonlinearity at this wavelength. We note a similar resonant behavior is observed for the aqueous suspension, except that the soliton powers are much higher () and the minimum power occurs around 790 nm.
The properties of the pump beam in the toluene solution are further explored by measuring the transmission spectra of the soliton beam at different input powers. The results are shown in Fig. 3(b). We find the transmission spectra are independent of the input power of the pump beam, and display a clear transmission minimum (extinction peak) at 880 nm, in good agreement with the predicted longitudinal surface plasmon resonance (LSPR) of gold nanorods in toluene [dashed line in Fig. 3(b)] and the measured white-light extinction spectrum [solid line in Fig. 3(b)]. Remarkably, the wavelength of maximum nonlinearity in Fig. 3(a) corresponds well to the minima in the transmission spectra in Fig. 3(b). In other words, the system exhibits strongest optical nonlinearity at the extinction peak.
C. Optical Forces and Plasmonic Resonant Nonlinearity
To understand the solvent- and wavelength-dependent behavior of solitons in suspensions of gold nanorods, we need to analyze the optical forces exerted on the rods. To do that, we have numerically calculated the polarizabilities for gold nanorods in toluene. The results are shown in Fig. 4(a). We find the real part of the polarizability along the short axis of a nanorod, , stays positive throughout the wavelength range [dashed line in Fig. 4(a)], but for the polarizability along the long axis, , its real part has a longitudinal surface plasmon resonance around 865 nm, so it can be positive or negative depending on the wavelength [solid line in Fig. 4(a)]. We have also performed similar calculations for gold nanorods in an aqueous suspension. The results are quite similar to those obtained for toluene suspensions, with the major difference being the shift of the LSPR to 790 nm.
Because of the wavelength-dependent polarizabilities, the optical forces acting on the nanorods in the suspension are different when pumped by a linearly polarized laser beam of different wavelengths. For particle size smaller than the incident wavelength (Rayleigh regime), the gradient force is related to the particle’s polarizability by [37–40]10,11,37]. On the other hand, for pump wavelengths above 865 nm, where the real parts of both and are positive, nanorods of both orientations will be attracted to the center of the beam. In both wavelength regimes, a higher refractive index can be effectively induced in the center of the beam under proper conditions, although all positive polarizabilities tend to develop unstable soliton propagation when the intensity-dependent nonlinearity is too high [37–39].4(b), the perpendicular extinction section is approximately 2 orders of magnitude smaller than the parallel one and displays a monotonic behavior for the wavelength region considered here. Thus, scattering and absorption experienced by the nanorods orientated parallel to the polarization of the pump beam are primarily responsible for the observed minimum in the transmission spectra of the pump beam shown in Fig. 3(b).
If the gradient force plays the main role in the observed optical nonlinearity in suspensions of gold nanorods, we would expect smaller soliton powers at 800 and 940 nm, where the magnitude of the parallel polarizability reaches local maxima. Instead, we find the smallest soliton power occurs at a wavelength of around 880 nm [Fig. 3(a)], where the extinction cross section reaches a maximum. This suggests that the scattering and absorption forces may play an important role in the formation of solitons for the suspensions of gold nanorods studied here. As a result of the scattering and absorption forces, we expect the rods would be pushed forward with a longitudinal velocity proportional to the sum of the two forces and inversely proportional to the viscosity of the solvent medium:4(b)]. Thus, it is the longitudinal motion of the parallel rods that is responsible for the observed reduction in soliton power near the LSPR. By having the rods move at certain speeds, the concentration of parallel rods inside the soliton channel can be kept at a certain level, thus preventing excessive attenuation of the pump beam along the propagation direction. Compared with off-resonance wavelengths, the extinction cross section near the LSPR is largest, and therefore less power is needed to have the same longitudinal velocity. This is consistent with our observation that the smallest pump power is needed for soliton formation near the extinction peak. We note that it is possible that the velocity of the rods for wavelengths near the LSPR may have to be larger than for off-resonance wavelengths. As the rods move faster, they will spend less time moving across the channel, leading to a decrease in the concentration of parallel rods inside the channel. This will prevent significant attenuation of the pump beam along the propagation direction at the LSPR where the extinction cross section is greatest.
According to Eq. (3), the solvent can affect the velocity of the nanorods through the refractive index of the background medium, the extinction cross section, and the viscosity. The values of extinction cross sections near their respective LSPRs are similar for water and toluene, the refractive index of toluene (1.48) is slightly larger than that of water (1.33), and the viscosity of toluene ( at 25°C and 0.1 MPa)  is smaller than that of water ( at 25°C and 0.1 MPa) . Thus, a smaller pump power is needed in toluene suspensions than in water to generate the same longitudinal velocity, consistent with our observations.
D. Optical Torque and Nanorod Orientation
Next, we consider nanorod orientation inside the soliton-induced waveguide channel. Using finite element method simulations, we calculated the optical torque acting on individual nanorods and found that the nanorods inside the soliton channel tend to align themselves with respect to the polarization of the soliton beam. The rotational potential energy of a nanorod, , for an arbitrary orientation angle between the long axis of the rod and the polarization of the pump beam (the axis), is defined as5.
As shown in Fig. 5(a), the rotational potential energy is minimum at 90° for nanorods located at the focus of a 740 nm laser beam (solid line) with a power of 100 mW and a Gaussian beam radius of 10 μm. The depth of the potential well is about 3 times larger than , the thermal energy responsible for Brownian motion and disordering of nanorods. Therefore, for this pump wavelength, the torque has a tendency to keep the rods aligned perpendicular to the beam polarization, as schematically shown in Fig. 5(b). However, for a 960 nm laser beam, the minimum of the rotational potential energy occurs at 0° (dashed line), and thus the rods tend to align themselves parallel to the polarization of the pump beam [Fig. 5(b)]. As a result of the wavelength-dependent polarizability, the torque is also wavelength dependent. We find the rods tend to orient themselves parallel (perpendicular) to the direction of the pump polarization for wavelengths above (below) the LSPR, which is consistent with the preferred orientations obtained from analyzing the optical forces as discussed in Section 3.C.
E. Soliton-Mediated Anisotropic Optical Property
Because of the intrinsic anisotropic property of the nanorods, the different orientations of nanorods inside the soliton channel should result in synthetic anisotropic optical properties at the macroscopic scale. The anisotropic properties of the synthetic material created by the soliton beam can be characterized by measuring the polarization transmission spectrum of a probe beam linearly polarized at an angle of with respect to the polarization of the soliton beam (the axis) through the soliton channel. As a result of the difference between the refractive indices along the two principal axes ( and ) of the synthetic material, the output beam generally turns elliptically polarized after passing through the sample. This can be characterized by measuring the intensity transmitted through a polarizer placed after the sample as a function of the polarizer’s angle with respect to the axis, given by4(a)] and the Clausius–Mossotti relation:
To examine the ordering effects in nanorod suspensions as discussed above, we perform a series of polarization transmission measurements with a linearly polarized 1064 nm probe beam guided through the soliton channel (see Fig. 1 for the experimental setup). The input power of the probe beam is fixed at 5.0 mW, and the probe beam itself does not experience appreciable nonlinear self-action, so it will not interfere with the alignment of the rods in the suspensions since the soliton beam has a much higher input power. As a typical example, the measured transmission of the probe beam for a 740 nm pump beam at various powers is shown in Fig. 6. We see a threefold increase in transmission of the probe beam when the power of the pump beam is increased to achieve nonlinear self-trapping, indicating guidance of the probe beam by the soliton channel induced by the pump beam. However, a decrease in transmission for pump powers exceeding 150 mW is observed, since thermal defocusing starts to affect the formation of solitons and thus the guidance.
Transmission spectra of a probe beam with polarizations perpendicular [crosses in Fig. 6(a)] and parallel [open circles in Fig. 6(a)] to the pump beam polarization are measured. No appreciable difference between the two transmittances is observed. The percentage difference between the two [see Fig. 6(b)] is within 2%, a result consistently observed during several repeated measurements. With a theoretically estimated value of for obtained assuming the rods were fully ordered and to be for our sample, we would expect the perpendicular transmittance to be 4.4 times greater than that for the parallel transmittance. The discrepancy between the theoretical expectation and the experimental observation can be attributed to two possible reasons: first, the rods are not fully aligned due to thermodynamic fluctuations caused by Brownian motion of the solvent molecules, and second, ordering probably occurs over a local region near the focus of the laser beam where the optical field is strong and does not extend along the entire beam path as a result of the expansion and attenuation of the pump beam. The pump beam intensity at the focus is strong enough for oriented rods to overcome thermal fluctuations; however, the intensity drops quickly along the lateral direction. The depth of the potential well becomes comparable to the thermal energy at a radius of 7.5 μm and is only 40% of the thermal energy at a radius equal to the beam radius of 10 μm. Therefore, it is unlikely that rods are fully ordered over the entire cross section of the pump beam. This can possibly reduce to a fraction of its value in the fully ordered case. As the pump beam propagates along the soliton channel, it also attenuates and expands. We estimate the beam size at output to be approximately 3 times its size at the focus. As a result, the laser beam intensity outside the focus region will not be strong enough to overcome thermal fluctuations to align the nanorods. This will cause the action length to be significantly smaller than the sample length, thus effectively reducing . Both scenarios will cause the transmission of the probe beam to be insensitive to its polarization. Assuming that becomes 3 times smaller than in the fully ordered case, and ordering only occurs over an action length of 500 μm (50 times the beam radius at the focus), we find the percentage difference between the perpendicular and parallel transmittances will be within 2%, a result consistently observed in our experiments. We want to point out that the conclusion drawn here does not match with that from our previous report , where an aqueous suspension of gold nanorods was pumped by a 532 nm laser beam and the polarization-dependent transmission of a probe beam appeared to be identified. After a careful examination of the previous results and a series of new experiments performed in the same setting, we found that the apparent polarization-dependent transmission was observed in experiments where the power of the probe beam input to the sample was not fixed when its polarization was adjusted with polarization optics. The underlying mechanism for this phenomenon is not quite clear, though, and we believe it may be related to interactions between the soliton beam and the probe beam. In any case, it is with no doubt that nanorods can be aligned by high electric fields [18–20], so the proposed scheme in Fig. 5(b) and associated anisotropic optical properties should be achievable with intense optical beams under appropriate conditions.
In summary, we have demonstrated self-focusing of light in colloidal suspensions of gold nanorods over a wide range of pump wavelengths and in different solvent environments. We find a much smaller power is needed for the formation of solitons at the longitudinal surface plasmon resonance of the rods, and the soliton formation power in toluene suspensions is also significantly less than that in aqueous suspensions. Our results suggest that the optical scattering and absorption forces play a major role in soliton formation. By analyzing the optical forces and torque acting on the gold nanorods, we show theoretically that it is possible to align the nanorods inside a soliton channel with wavelength-dependent orientations. A theoretical estimate for the resulting synthetic optical anisotropy inside the soliton channel is also provided, although the expected synthetic anisotropic properties are too subtle to be observed through polarization transmission measurements of a low-intensity 1064 nm probe beam guided along the soliton channel. The ability to achieve tunable soliton formation and control nanorod orientations in colloidal nanosuspensions with low-power CW laser beams can be used to produce polarization-dependent transmission, which may lead to interesting applications in all-optical switching and transparent display technologies.
Army Research Office (ARO) (W911NF-15-1-0413); National Science Foundation (NSF) (PHY-1404510); National Key R&D Program of China (2017YFA0303800); National Natural Science Foundation of China (NSFC) (11504184).
1. M. Kauranen and A. V. Zayats, “Nonlinear plasmonics,” Nat. Photonics 6, 737–748 (2012). [CrossRef]
2. J. Butet, P.-F. Brevet, and O. J. F. Martin, “Optical second harmonic generation in plasmonic nanostructures: from fundamental principles to advanced applications,” ACS Nano 9, 10545–10562 (2015). [CrossRef]
3. A. S. Reyna and C. B. de Araújo, “High-order optical nonlinearities in plasmonic nanocomposites—a review,” Adv. Opt. Photon. 9, 720–774 (2017). [CrossRef]
4. N. C. Panoiu, W. E. I. Sha, D. Y. Lei, and G.-C. Li, “Nonlinear optics in plasmonic nanostructures,” J. Opt. 20, 083001 (2018). [CrossRef]
5. N. M. Litchinitser, “Nonlinear optics in metamaterials,” Adv. Phys. X 3, 1367628 (2018). [CrossRef]
6. G. A. Wurtz, R. Pollard, W. Hendren, G. P. Wiederrecht, D. J. Gosztola, V. A. Podolskiy, and A. V. Zayats, “Designed ultrafast optical nonlinearity in a plasmonic nanorod metamaterial enhanced by nonlocality,” Nat. Nanotechnol. 6, 107–111 (2011). [CrossRef]
7. M. Mesch, B. Metzger, M. Hentschel, and H. Giessen, “Nonlinear plasmonic sensing,” Nano Lett. 16, 3155–3159 (2016). [CrossRef]
8. Y. Hua, K. Chandra, D. H. M. Dam, G. P. Wiederrecht, and T. W. Odom, “Shape-dependent nonlinear optical properties of anisotropic gold nanoparticles,” J. Phys. Chem. Lett. 6, 4904–4908 (2015). [CrossRef]
9. M. Gordel, J. Olesiak-Banska, R. Kolkowski, K. Matczyszyn, M. Buckle, and M. Samoc, “Shell-thickness-dependent nonlinear optical properties of colloidal gold nanoshells,” J. Mater. Chem. C 2, 7239–7246 (2014). [CrossRef]
10. S. Fardad, A. Salandrino, M. Heinrich, P. Zhang, Z. Chen, and D. N. Christodoulides, “Plasmonic resonant solitons in metallic nanosuspensions,” Nano Lett. 14, 2498–2504 (2014). [CrossRef]
11. T. S. Kelly, Y.-X. Ren, A. Samadi, A. Bezryadina, D. N. Christodoulides, and Z. Chen, “Guiding and nonlinear coupling of light in plasmonic nanosuspensions,” Opt. Lett. 41, 3817–3820 (2016). [CrossRef]
12. A. S. Reyna and C. B. de Araújo, “Guiding and confinement of light induced by optical vortex solitons in a cubic-quintic medium,” Opt. Lett. 41, 191–194 (2016). [CrossRef]
13. J. Trojek, L. Chvátal, and P. Zemánek, “Optical alignment and confinement of an ellipsoidal nanorod in optical tweezers: a theoretical study,” J. Opt. Soc. Am. A 29, 1224–1236 (2012). [CrossRef]
14. J.-W. Liaw, W.-J. Lo, and M.-K. Kuo, “Wavelength-dependent longitudinal polarizability of gold nanorod on optical torques,” Opt. Express 22, 10858–10867 (2014). [CrossRef]
15. K. C. Chu, C. Y. Chao, Y. F. Chen, Y. C. Wu, and C. C. Chen, “Electrically controlled surface plasmon resonance frequency of gold nanorods,” Appl. Phys. Lett. 89, 103107 (2006). [CrossRef]
16. W. Ahmed, E. S. Kooij, A. van Silfhout, and B. Poelsema, “Quantitative analysis of gold nanorod alignment after electric field-assisted deposition,” Nano Lett. 9, 3786–3794 (2009). [CrossRef]
17. P. Zijlstra, M. van Stee, N. Verhart, Z. Gu, and M. Orrit, “Rotational diffusion and alignment of short gold nanorods in an external electric field,” Phys. Chem. Chem. Phys. 14, 4584–4588 (2012). [CrossRef]
18. J. Fontana, G. K. B. da Costa, J. M. Pereira, J. Naciri, B. R. Ratna, P. Palffy-Muhoray, and I. C. S. Carvalho, “Electric field induced orientational order of gold nanorods in dilute organic suspensions,” Appl. Phys. Lett. 108, 081904 (2016). [CrossRef]
19. S. Etcheverry, L. F. Araujo, G. K. B. da Costa, J. M. B. Pereira, A. R. Camara, J. Naciri, B. R. Ratna, I. Hernández-Romano, C. J. S. de Matos, I. C. S. Carvalho, W. Margulis, and J. Fontana, “Microsecond switching of plasmonic nanorods in an all-fiber optofluidic component,” Optica 4, 864–870 (2017). [CrossRef]
20. M. Maldonado, L. de Souza Menezes, L. F. Araujo, G. K. B. da Costa, I. C. S. Carvalho, J. Fontana, C. B. de Araújo, and A. S. L. Gomes, “Nonlinear refractive index of electric field aligned gold nanorods suspended in index matching oil measured with a Hartmann–Shack wavefront aberrometer,” Opt. Express 26, 20298–20305 (2018). [CrossRef]
21. Q. Liu, Y. Cui, D. Gardner, X. Li, S. He, and I. I. Smalyukh, “Self-alignment of plasmonic gold nanorods in reconfigurable anisotropic fluids for tunable bulk metamaterial applications,” Nano Lett. 10, 1347–1353 (2010). [CrossRef]
22. K. C. Ng, I. B. Udagedara, I. D. Rukhlenko, Y. Chen, Y. Tang, M. Premaratne, and W. Cheng, “Free-standing plasmonic-nanorod superlattice sheets,” ACS Nano 6, 925–934 (2012). [CrossRef]
23. Q. Liu, Y. Yuan, and I. I. Smalyukh, “Electrically and optically tunable plasmonic guest-host liquid crystals with long-range ordered nanoparticles,” Nano Lett. 14, 4071–4077 (2014). [CrossRef]
24. C. J. Murphy and C. J. Orendorff, “Alignment of gold nanorods in polymer composites and on polymer surfaces,” Adv. Mater. 17, 2173–2177 (2005). [CrossRef]
25. J. Pérez-Juste, B. Rodriguez-Gonzalez, P. Mulvaney, and L. M. Liz-Marzan, “Optical control and patterning of gold-nanorod-poly(vinyl alcohol) nanocomposite films,” Adv. Funct. Mater. 15, 1065–1071 (2005). [CrossRef]
26. J. Li, S. Liu, Y. Liu, F. Zhou, and Z.-Y. Li, “Anisotropic and enhanced absorptive nonlinearities in a macroscopic film induced by aligned gold nanorods,” Appl. Phys. Lett. 96, 263103 (2010). [CrossRef]
27. K. E. Roskov, K. A. Kozek, W. C. Wu, R. K. Chhetri, A. L. Oldenburg, R. J. Spontak, and J. B. Tracy, “Long-range alignment of gold nanorods in electrospun polymer nano/microfibers,” Langmuir 27, 13965–13969 (2011). [CrossRef]
28. H. Zhang, Z. Hu, Z. Ma, M. Gecevičius, G. Dong, S. Zhou, and J. Qiu, “Anisotropically enhanced nonlinear optical properties of ensembles of gold nanorods electrospun in polymer nanofiber film,” ACS Appl. Mater. Interfaces 8, 2048–2053 (2016). [CrossRef]
29. M. Pelton, M. Liu, H. Y. Kim, G. Smith, P. Guyot-Sionnest, and N. F. Scherer, “Optical trapping and alignment of single gold nanorods by using plasmon resonances,” Opt. Lett. 31, 2075–2077 (2006). [CrossRef]
30. C. Selhuber-Unkel, I. Zins, O. Schubert, C. Sönnichsen, and L. B. Oddershede, “Quantitative optical trapping of single gold nanorods,” Nano Lett. 8, 2998–3003 (2008). [CrossRef]
31. L. Tong, V. D. Miljković, and M. Käll, “Alignment, rotation, and spinning of single plasmonic nanoparticles and nanowires using polarization dependent optical forces,” Nano Lett. 10, 268–273 (2010). [CrossRef]
32. P. V. Ruijgrok, N. R. Verhart, P. Zijlstra, A. L. Tchebotareva, and M. Orrit, “Brownian fluctuations and heating of an optically aligned gold nanorod,” Phys. Rev. Lett. 107, 037401 (2011). [CrossRef]
33. J. Do, M. Fedoruk, F. Jäckel, and J. Feldmann, “Two-color laser printing of individual gold nanorods,” Nano Lett. 13, 4164–4168 (2013). [CrossRef]
34. Z. Li, W. Mao, M. S. Devadas, and G. V. Hartland, “Absorption spectroscopy of single optically trapped gold nanorods,” Nano Lett. 15, 7731–7735 (2015). [CrossRef]
35. Y.-X. Ren, T. S. Kelly, C. Zhang, H. Xu, and Z. Chen, “Soliton-mediated orientational ordering of gold nanorods and birefringence in plasmonic suspensions,” Opt. Lett. 42, 627–630 (2017). [CrossRef]
36. R. Karimzadeh, “Spatial self-phase modulation of a laser beam propagating through liquids with self-induced natural convection flow,” J. Opt. 14, 095701 (2012). [CrossRef]
37. R. El-Ganainy, D. N. Christodoulides, C. Rotschild, and M. Segev, “Soliton dynamics and self-induced transparency in nonlinear nanosuspensions,” Opt. Express 15, 10207–10218 (2007). [CrossRef]
38. R. El-Ganainy, D. N. Christodoulides, E. M. Wright, W. M. Lee, and K. Dholakia, “Nonlinear optical dynamics in nonideal gases of interacting colloidal nanoparticles,” Phys. Rev. A 80, 053805 (2009). [CrossRef]
39. W. Man, S. Fardad, Z. Zhang, J. Prakash, M. Lau, P. Zhang, M. Heinrich, D. N. Christodoulides, and Z. Chen, “Optical nonlinearities and enhanced light transmission in soft-matter systems with tunable polarizabilities,” Phys. Rev. Lett. 111, 218302 (2013). [CrossRef]
40. L. Novotny and B. Hecht, “Forces in confined fields,” in Principles of Nano-Optics (Cambridge University, 2006), Chap. 13, pp. 427–428.
41. Q. Zhan, “Trapping metallic Rayleigh particles with radial polarization,” Opt. Express 12, 3377–3382 (2004). [CrossRef]
42. P. M. Hansen, V. K. Bhatia, N. Harrit, and L. Oddershede, “Expanding the optical trapping range of gold nanoparticles,” Nano Lett. 5, 1937–1942 (2005). [CrossRef]
43. F. J. V. Santos, C. A. Nieto de Castro, J. H. Dymond, N. K. Dalaouti, M. J. Assael, and A. Nagashima, “Standard reference data for the viscosity of toluene,” J. Phys. Chem. Ref. Data 35, 1–8 (2006). [CrossRef]
44. J. W. P. Schmelzer, E. D. Zanotto, and V. M. Fokin, “Pressure dependence of viscosity,” J. Chem. Phys. 122, 074511 (2005). [CrossRef]