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Tuning nanoparticle electrodynamics by an optical-matter-based laser beam shaper Fan Nan, and Zijie Yan Nano Lett., Just Accepted Manuscript • DOI: 10.1021/acs.nanolett.9b01090 • Publication Date (Web): 23 Apr 2019 Downloaded from http://pubs.acs.org on April 24, 2019
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Tuning nanoparticle electrodynamics by an optical-matter-based laser beam shaper Fan Nan and Zijie Yan* Department of Chemical and Biomolecular Engineering, Clarkson University, Potsdam, New York 13699, United States
Abstract: Periodically modulated optical fields provide the perspective of tuning nanoparticle (NP) dynamics in colloidal suspension. Here, it is shown that the lateral interferometric optical field created by a chain of optically bound Au NPs (i.e., optical matter) can tailor the electrodynamic interactions among more Au NPs. The free-standing NP chain, which is assembled and confined by an auxiliary optical line, shapes the main trapping beam and guides the self-organization of Au NPs under an optimized polarization direction. We find that the NP chain can largely enhance the anisotropic optical binding interaction of two nearby NPs but suppress the anisotropic interaction of multiple NPs, leading to isotropic self-organization. The dynamics and structural transitions of the NPs are well reproduced in simulation by using a coupled finite-difference time-domain (FDTD)-Langevin dynamics approach. Our work provides a new dual-beam optical trapping and in situ laser beam shaping approach to study and control interparticle electrodynamic interactions among colloidal NPs.
Keywords: gold nanoparticles, chain structures, optical trapping, optical binding, interferometric optical field, self-assembly
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Colloidal particles, due to their easy visualization and slow dynamics compared with atoms and molecules, have been widely used to study various problems in statistical physics such as phase transition and self-assembly.1-6 Colloids are susceptible to optical forces,7-10 making it possible to tailor particle dynamics and arrangements using spatially modulated light.7,
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In particular,
when the periodicity of an optical pattern is commensurate to the mean particle distance, the periodic optical potential can induce disorder-to-order transitions.13-16. Interferometry techniques are commonly used to create such periodic optical potential.17, 18 For example, in a standing wave pattern of two interfering laser beams, reversible transitions between amorphous and crystalline phases are observed in colloidal assembly of polystyrene microparticles.16 These observations suggest that the balance between particle-particle and particle-potential interactions plays a key role in triggering colloidal phase transition in a potential landscape. Relevant experimental studies have been focused on colloidal microparticle systems.13-16, 19-21 Since particle-particle interactions are usually weak and the Brownian fluctuations are strong at nanometer scale, NP dynamics in periodic energy landscapes are mainly focused on studies of particle diffusion.22-24 Metallic NPs can interact strongly through interparticle forces induced by coherent laser scattering, a phenomenon known as optical binding.25, 26 Optical binding provides a novel way to drive disorder-to-order transition in colloidal metal NPs confined by extended optical fields,27-31 e.g., the fabrication of quasi-one-dimensional metamolecules in a smooth Gaussian beam.31 Modulated potential energy landscapes can significantly influence optical binding.17,
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Povinelli group investigated the behavior of strongly interacting Au NPs within a periodic array of optical traps generated by a photonic crystal template, where one-dimensional chains and twodimensional arrays could be selectively fabricated by tuning the lattice constant and lattice 2 ACS Paragon Plus Environment
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symmetry of the template.33 Very recently, we reported a strategy to create in-situ interferometric optical tweezers by illuminating single Ag nanowires deposited on glass substrates.34 However, the trapped NPs were not in the same plane with the Ag nanowires due to the electrostatic repulsion between charged surfaces of the substrates and NPs, thus the interferometric optical fields were not fully experienced by the NPs.34 Moreover, the modulated optical fields lack controllability and tunability because the Ag nanowires of varied sizes were just drop-casted on the substrates with random orientations. In this letter, we show that the free-standing and optically bound metal NP chains with tunable lengths35 are better candidates to generate controlled periodic potentials for studying dynamic selfassembly of metal NPs in a two-dimensional plane. In our experiments, an auxiliary optical line is used to fabricate a NP chain as illustrated in Figure 1a. Another extended laser beam, which has the same wavelength but orthogonal polarization to that of the auxiliary optical line, is used to create the interference fringes from the NP chain and confine multiple metal NPs in a twodimensional space. Thus, the loosely confined NPs and tightly trapped chain are in the same trapping plane. Most importantly, this dual-beam system is totally different from the previous cases where standing wave optical line traps were generated by a reflecting substrate28 or gold nanoplate mirror.32 The intensity modulation direction is perpendicular to the trapping plane in those standing wave traps and the NPs are always immersed in one of the interference fringes. By introducing lateral interferometric optical fields, two competing processes appear in our system: the alignment of NPs along the interference fringes (particle-potential interaction) and self-assembly of chain structures perpendicular to the interference fringes (anisotropic and long-range particle-particle interaction). We find that when the polarization direction of the trapping beam is along the orientation of the NP chain, the light intensity is the strongest in the far field and the periodicity of 3 ACS Paragon Plus Environment
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the interference fringes matches well with the optical binding separations of metal NPs. Consequently, in a two-NP system, we observe a dominant particle-particle interaction, which leads to the formation of a rigid dimer oriented perpendicular to the interference fringes, and the interparticle interactions are largely enhanced by the NP chain. However, in a multi-NP system, the two competing processes result in suppression of anisotropic interparticle interactions and development of isotropic self-organization of the NPs. Our results provide a novel strategy to investigate dynamic NP self-assembly in a two-dimensional space and reveal the perspective of tuning NP electrodynamics in periodic optical potentials. Details of our experiment setup are illustrated in Figure S1. Briefly, a polarizing beamsplitter cube is used to generate two beams (denoted as the auxiliary and trapping beams, respectively) from a continuous-wave laser (λ = 800 nm). To fabricate tunable free-standing NP chains with high spatiotemporal stabilities, the auxiliary beam is shaped into an optical line trap using a spatial light modulator.35 At the same time, the trapping beam spot is expanded to ~ 13 µm in diameter, which overlaps with the auxiliary beam and allows confining multiple NPs in the x-y plane near a coverslip surface.30 Because the optical path difference of the two beams is much larger than the coherent length (2.4 mm at 40 GHz linewidth) of the 800 nm continuous-wave laser, there is no coherence between the auxiliary and trapping beams.
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Figure 1. Enhanced NP trapping with spatially structured potential generated by a onedimensional optically bound NP chain. (a) Schematic of the experiment setup with two linearly polarized laser beams. One is shaped into an optical line for assembly of a NP chain, and the other is expanded into a broad Gaussian beam to trap NPs and probe the trapping potentials near the chain. The centers of two laser beams are separated by ~1.5 µm along y-axis. (b) Calculated intensity distributions of the electric fields created by a single Au NP and a chain of four Au NPs (150 nm in dia., interparticle separations of ~600 nm). The NPs are immersed in water and illuminated by a plane wave of λ = 800 nm with linear polarization along the chain. (c) Calculated trapping (binding) potential wells for an isolated Au NP induced by the single Au NP (blue line) and NP chain (red line), respectively. (d) Measured trajectories and probability density (ρd) distributions of the y-positions of the isolated Au NP in the interferometric optical fields. The trajectories of the NPs in each plot are obtained from 1400 dark-field images. 5 ACS Paragon Plus Environment
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The calculated intensity distributions of light around a single Au NP and a chain with four Au NPs (150 nm in dia.) are presented in Figure 1b, which clearly show several interference fringes with anisotropic spatial character in the far fields (similar to the optical pattern generated by the longitudinal surface plasmon modes of a single Ag nanowire34). The single Au NP scatters more strongly in the direction perpendicular to the light polarization, leading to clear interference fringes. The fringes are broadened and enhanced as four Au NPs self-organized into chain. Accordingly, it is expected that in the trapping beam, both the trajectories and potential energies of the confined NPs could be largely tailored by the chain structures. To verify this conjecture, we calculate the potential energies of a single Au NP in these interferometric optical fields. The simulation model assumes the position of the scattering object (e.g., a single NP or a NP chain orientated along the x-axis) is fixed while that of another isolated Au NP varies along the y-axis. The sign of the calculated optical forces oscillates between positive (repulsive) and negative (attractive) as the separation increases, leading to a series of equilibrium positions of the NP (where the total force is zero and restoring force exists around this position; see Figure S2). However, the optical trapping strength for a single NP saturates when the chain has four or more NPs (Figure S2). As two representative examples, Figure 1c compares the potential energy of the isolated Au NP (by integrating the optical force over the position) at ~ 1.65 µm away from another single Au NP and a chain of 4 NPs, respectively. The corresponding experimental results are shown in Figure 1d. The left column shows the trajectories of the NPs, in which the stably trapped NPs are marked with gray color and the loosely confined single NP is marked with blue or red color. The single NP’s trajectories clearly reproduce the interference fringes of the optical field, and the lateral confinement of the NP is largely enhanced by the chain 6 ACS Paragon Plus Environment
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of 4 NPs. The right column of Figure 1d shows the corresponding probability density (ρd) distributions of the NP’s y-positions. These results agree well with our calculations.
Figure 2. Tunable lateral confinement of a single Au NP with different polarization directions. (a) Calculated intensity distributions of the electric fields around a chain formed by 7 Au NPs with different polarization directions. (b) The corresponding optical forces exerted on a single Au NP as a function of the separation between the NP (150 nm in dia.) and the chain. (c) Measured probability density (ρd) distributions of the NP’s y-positions with different polarization angles.
The free-standing NP chains can act as tunable scattering objects for optical trapping. Figure 2a shows the calculated intensity distributions of the electric field around a 7-NP chain with different polarization directions, defined by the angle θ relative to the x-axis. In the near field, the electric fields are strongly confined near the surface of the NPs with all polarization directions. When θ = 90°, dumbbell‐like electromagnetic (EM) spots are generated at the middle of adjacent 7 ACS Paragon Plus Environment
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NPs, which is different from the EM field created by a metal nanowire (the electric field is strongly confined near its surface and no localized EM spots appear away from the surface34). Therefore, the NP chain offers another degree of freedom to guide the formation of quasi-two-dimensional structures caused by these localized EM spots36 (see Figure S3). Additionally, the enhanced interference fringes around the termini of the chain could guide the assembly of a much longer chain. As θ decreases from 90° to 0°, the interference fringes around the termini of the chain and the dumbbell‐like EM spots become weak, yet the intensities of the interference fringes increase along y-axis (with y > 1 µm). In the experiments, a half-wave plate is used to change the polarization directions of two laser beams, therefore the polarization directions of the beams are always perpendicular to each other. It is worth noting that the NP chain can scatter light from both the auxiliary and trapping beams, and the loosely confined NPs can scatter light from the trapping beam. For simplicity, we denote the three types of scattering as Ach, Tch and Tnp, respectively. It is the interference of scattering Tch with the incident trapping beam that leads to spatial gradients in the lateral plane. We find that the scattering light Tnp has negligible feedback on the chain in the auxiliary beam (Figure S4). The scattering Ach also has negligible influence on the NPs in the trapping beam when the polarization angle of the trapping beam is small (e.g., θ = 0° as examined in Figure S5). However, as θ increases, the influence of scattering Ach on the loosely confined NPs becomes more significant (e.g., θ = 60° and 90°, see Figure S6). Figure 2b presents the calculated optical forces exerted on a single Au NP as it continuously moves away from the NP chain with different polarization angles. The optical forces include the contributions from both the auxiliary beam and the trapping beam. When θ = 90°, no equilibrium position exists. As θ decreases, several equilibrium positions appear, and the amplitudes of the optical forces are largely increased. The θ-dependent probability density 8 ACS Paragon Plus Environment
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distributions of the loosely confined NP’s y-positions are shown in Figure 2c (see Figure S7 for their trajectories). When θ = 90°, the NP experiences a very weak interferometric optical field, thus the probability density of its y-position is dominated by the center of the trapping beam (which is set at ~1.5 µm along y-axis and the center of the auxiliary beam is set at 0). As θ decreases, the interferometric optical field becomes stronger and the distribution curve is much narrower with its center position shifts to ~1150 nm. These results agree well with our simulations. Moreover, subwavelength manipulations may be achieved by using the plasmonic fields of these free-standing NP chains to introduce opto-thermoelectric fields near the NP surfaces.4, 37, 38
Figure 3. Enhancing optical binding interaction in a NP dimer orientated perpendicular to the interference fringes. (a) Measured trajectories of a NP dimer without (I) and with (II-IV) interferometric optical fields created by a single (II), five (III) and seven (IV) Au NPs. The trajectories of the NPs in each plot are obtained from 1400 dark-field images. (b) The corresponding measured angular probability density distributions as a function of the interparticle separation of the dimers. 9 ACS Paragon Plus Environment
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The distances between the antinodes of the interference fringes generated by the NP chains are ~ 600 nm, which match the interparticle separations of optically bound metal NPs.27 We find that the optical binding interactions of a NP dimer can be enhanced by the interferometric optical fields. Figure 3a shows the trajectories of a dimer in the trapping beam without (I) and with (II to IV) periodic potentials. To evaluate the optical binding strength in the dimer structure, we measure its angular probability density distributions as a function of the interparticle separation (Figure 3b). Two optically bound NPs prefer to be separated by discrete distances equal to integer multiples of the trapping laser’s wavelength in the liquid (~ 600 nm), and along the direction perpendicular to the light polarization (90°). In the absence of the interferometric optical field (I, without scattering objects and the trapping beam is on), the angular probability density distribution shows two regions located at the first (~600 nm) and second (~1200 nm) optical binding separations. However, in the presence of the interferometric optical fields (II-IV), the distributions only show a single peak located at the first optical binding separation and 90°, and the probability density increases as the chain length increases. In a homogeneous optical field, the dimer unit experiences no net force and the optical binding energy can be treated as the trapping potential created by one NP on the other. However, in an inhomogeneous optical field created by other scattering objects, especially when the modulated potential gradient is along the orientation of the dimer, net force is applied on the dimer.39 In this case, the pure optical binding interaction in a dimer unit is difficult to describe. Therefore, we resort to dynamic simulations using a coupled FDTD-Langevin dynamics approach. We assume that the acceleration of any NP is negligible in the overdamped limit, thus its motion follows the simplified 2D Langevin equations: 𝐹(𝒓) +𝜂(𝑡) = 𝛾 𝑑𝒓/𝑑𝑡, 10 ACS Paragon Plus Environment
(1)
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where F(r) is the optical force acting on the NP at position r = (x, y), γ is the friction coefficient given by Stokes' law (γ = 6πνR, where ν and R are the dynamic viscosity of the medium and radius of the NP, respectively), and η(t) is the random (white noise) force. F(r) is calculated by the FDTD simulations, and η(t) obeys a normal distribution with the mean of zero and standard deviation of 1.1×10−22 N/(W/m2), and the direction is randomly chosen between −π and π. The positions of the NPs are evolved using customized scripts in Lumerical FDTD.30, 40 All NPs are illuminated by a plane wave (λ = 800 nm) in water. As two representative examples, we simulate the trajectories of a dimer without and with a 7-NP chain and calculate their angular probability density distributions as a function of the interparticle separation (Figure S8). These calculations also agree well with our experiment data, suggesting a reliable simulation method to study particle-particle and particlepotential interactions in multiple NPs. The chain length affects the strength of interparticle interactions between 2 NPs as revealed by Figures 3, it also determines the effective area of the interference field for self-organization of multiple NPs. Without the scattering objects, the NPs tend to form long chain structures as shown in Figure 4a-I. However, when a chain with 8 NPs is trapped by the auxiliary beam, the NPs (in the trapping beam) are more likely to self-organize in to hexagonal lattices or short (dimer) chains (Figure 4a-II). These observations clearly reveal two competing processes for a multi-NP system inside a lateral interferometric optical field: the alignment of NPs along the interference fringes and anisotropic self-assembly of chain structures perpendicular to the interference fringes (the competition also exists in a three-NP system, see Video S1).
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Figure 4. Tailoring NP electrodynamics in a multi-NP system by periodic optical potential. (a) Representative dark-field images of the NP assemblies (I) without and (II) with the influence of a chain consisting of eight Au NPs. (b) Measured angular probability density distributions as a function of the separation of any two NPs without and with the influence of a NP chain. The data are extracted from the motions of loosely confined NPs in 1400 frames. (c) The corresponding simulated angular probability density distributions as a function of the separation of any two particles. The light polarization direction is along the x-axis.
We further investigate the spatial arrangements of multiple NPs in the trapping beam by measuring the separations and orientations of all pairs of NPs without and with the influence of the NP chain. The corresponding probability density distributions as a function of the orientation 12 ACS Paragon Plus Environment
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and separation of any two particles are shown in Figure 4b. In the absence of a chain, the probability density distribution of 12 loosely confined NPs shows similar characteristics with that of multiple Ag NPs owing to the long-range optical binding interactions.30 However, the distribution changes in the presence of a chain: (i) at the first optical binding separation, the orientation of any two NPs shows a significant preference along 0° and ±60° (the ρd at ±90° decreases); (ii) at the second optical binding separation, new orientations appear at ±30°; (iii) the formation probability of any two NPs at the third and fourth optical binding separation drastically decreases at ±90°. These results strongly suggest the suppression of optical binding anisotropy along the potential modulation direction, namely, the periodic spatial potential leads to phase transition from one-dimensional structures to quasi-two-dimensional structures. In order to understand why lateral interferometric optical field can tailor optical binding interactions among multiple NPs, dynamic simulations of an electrodynamically coupled NP system (12 Au NPs under thermal fluctuations) are performed without and with a stationary chain of 8 Au NPs. The simulated trajectories are shown in Video S2, which clearly reproduce the assembly processes in the experimental system. Additionally, the simulated probability density distributions of the 12 NPs (Figure 4c) also agree well with our experiment results. In summary, we have shown that a free-standing optical matter structure can be used as a novel laser beam shaper to tailor the electrodynamic interactions among colloidal metal NPs. The interference fringes created by a NP chain impose a periodic trapping potential onto the NPs in the cross-section of a laser beam, which can be easily tuned by changing the laser polarization direction. In particular, the optical binding strength in a dimer structure increases as the chain length increases, and a longer chain can create an extended scattering field, which effectively guides the assembly of multiple NPs into different configurations. These observations are well 13 ACS Paragon Plus Environment
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described by electrodynamics simulations using a 2D Langevin equation. Our results provide a novel strategy to manipulate mesoscale interparticle interactions in structured optical fields, which will benefit the studies of phase transition behavior and on-demand construction of reconfigurable photonic devices with designed functionalities.
ASSOCIATED CONTENT Supporting Information The Supporting Information is available free of charge on the ACS Publications website at Methods and additional figures (PDF) Optical trapping of 3 Au NPs in the presence of a NP chain. (AVI) Simulated trajectories of 12 Au NPs with and without a NP chain. (AVI)
AUTHOR INFORMATION Corresponding Author *E-mail:
[email protected] ORCID Fan Nan: 0000-0002-0786-4974 Zijie Yan: 0000-0003-0726-7042 Notes The authors declare no competing financial interest.
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ACKNOWLEDGMENTS This material is based upon work supported by the National Science Foundation under Grant No. 1610271. The authors also acknowledge support from the W. M. Keck Foundation Research Program. REFERENCES 1. Poon, W. Science 2004, 304, 830–831. 2. Manoharan, V. N. Science 2015, 349, 1253751. 3. Poon, W.; Pusey, P.; Lekkerkerker, H. Physics World 1996, 9, 27–34. 4. Lin, L.; Zhang, J.; Peng, X.; Wu, Z.; Coughlan, A. C. H.; Mao, Z.; Bevan, M. A.; Zheng, Y. Sci. Adv. 2017, 3, e1700458. 5. Fan, J. A.; Wu, C.; Bao, K.; Bao, J.; Bardhan, R.; Halas, N. J.; Manoharan, V. N.; Nordlander, P.; Shvets, G.; Capasso, F. Science 2010, 328, 1135–1138. 6. Gong, J.; Newman, R. S.; Engel, M.; Zhao, M.; Bian, F.; Glotzer, S. C.; Tang, Z. Nat. Commun. 2017, 8, 14038. 7. Löwen, H. J. Phys.: Condens. Matter 2001, 13, R415–R432. 8. Grier, D. G. Nature 2003, 424, 810–816. 9. Dholakia, K.; Reece, P.; Gu, M. Chem. Soc. Rev. 2008, 37, 42–55. 10. Ashkin, A. Phys. Rev. Lett. 1970, 24, 156–159. 11. Jenkins, M. C.; Egelhaaf, S. U. J. Phys.: Condens. Matter 2008, 20, 404220. 12. Evers, F.; Hanes, R. D. L.; Zunke, C.; Capellmann, R. F.; Bewerunge, J.; Dalle-Ferrier, C.; Jenkins, M. C.; Ladadwa, I.; Heuer, A.; Castañeda-Priego, R.; Egelhaaf, S. U. Eur. Phys. J. Spec. Top. 2013, 222, 2995–3009. 13. Bechinger, C.; Brunner, M.; Leiderer, P. Phys. Rev. Lett. 2001, 86, 930–933. 14. Chowdhury, A.; Ackerson, B. J.; Clark, N. A. Phys. Rev. Lett. 1985, 55, 833–836. 15. Loudiyi, K.; Ackerson, B. J. Phys. A 1992, 184, 1–25. 16. Wei, Q. H.; Bechinger, C.; Rudhardt, D.; Leiderer, P. Phys. Rev. Lett. 1998, 81, 2606– 2609. 17. Burns, M. M.; Fournier, J.-M.; Golovchenko, J. A. Science 1990, 249, 749–754. 18. Chiou, A. E.; Wang, W.; Sonek, G. J.; Hong, J.; Berns, M. W. Opt. Commun. 1997, 133, 7–10. 19. Strepp, W.; Sengupta, S.; Nielaba, P. Phys. Rev. E 2001, 63, 046106. 20. Capellmann, R. F.; Khisameeva, A.; Platten, F.; Egelhaaf, S. U. J. Chem. Phys. 2018, 148, 114903. 21. Sarmiento-Gómez, E.; Rivera-Morán, J. A.; Arauz-Lara, J. L. Soft Matter 2018, 14, 3684– 3688. 22. Albaladejo, S.; Marqués, M. I.; Scheffold, F.; Sáenz, J. J. Nano Lett. 2009, 9, 3527–3531. 23. Albaladejo, S.; Marqués, M. I.; Sáenz, J. J. Opt. Express 2011, 19, 11471–11478. 24. Luis-Hita, J.; Sáenz, J. J.; Marqués, M. I. ACS Photonics 2016, 3, 1286–1293. 25. Burns, M. M.; Fournier, J.-M.; Golovchenko, J. A. Phys. Rev. Lett. 1989, 63, 1233–1236. 26. Dholakia, K.; Zemánek, P. Rev. Mod. Phys. 2010, 82, 1767–1791. 15 ACS Paragon Plus Environment
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