The optomechanical interaction between a plasmonic nanocavity and a gold nanorod through optical forces is demonstrated. It is revealed that strong localized plasmon resonance mode hybridization induced by a gold nanorod results in the resonance mode of the nanocavity splitting into two different plasmon resonance modes (bonding plasmon resonance mode and antibonding plasmon resonance mode). When the whole system (gold nanorod and gold nanocavity) is excited at the antibonding plasmon mode, the gold nanorod can receive an optical pushing force and be pushed away from the gold nanocavity. On the other hand, an optical pulling force acts on the gold nanorod and the gold nanorod can be trapped by the gold nanocavity when the plasmonic tweezers work at the bonding mode. The optical pulling force acting on the gold nanorod can be enhanced by two orders of magnitude larger than that of the same sized dielectric nanorod, which benefits from the strong resonant nearfield interaction between the gold nanorod and the gold nanocavity. More importantly, the shape and the position of the optical potential can be tuned by tailoring the wavelength of the laser used in the optical trapping, which can be used to manipulate the gold nanorod within a nanoscale region. Our findings have important implications for optical trapping, manipulation, sorting, and sieving of plasmonic nanoparticles with plasmonic tweezers.
© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
Optical tweezers, which can trap mesoscopic objects near the focus by the gradient force generated from a tightly focused laser beam, have been widely used in biology, biochemistry, and physics because of its unique capability of remote and noninvasive manipulation of mesoscopic object . Using conventional optical tweezers, micrometric dielectric particles [2,3], living cells [4,5], and plasmonic nanoparticles [6,7] can be trapped and manipulated, while trapping nanoobjects with conventional optical tweezers still remains challenging for the following reasons: First, the trapping volume of conventional tweezers is diffraction-limited; Second, high laser power is needed to create a gradient force large enough to overcome the prominent Brownian motion; Third, high power irradiation may lead to irreversible side-effects such as thermal or material damage on samples, especially on biological specimens. In recent years, advances in plasmonic nanostructures such as disks [8–10], dipole antennas [11–14], nanocavities [15,16], and antenna arrays [17,18] have been proved to be effective strategies to overcome these obstacles. Thanks to their capability of strong field localization and enhancement associated with localized surface plasmon resonance (LSPR), the trapping volume could be reduced beyond the diffraction limit. Consequently, for similar optical power, these nanostructures can generate a larger gradient force than that of conventional optical tweezers.
Among the variety of plasmonic nanostructures employed for optical trapping in the past few years, the plasmonic nanocavity—subwavelength apertures drilled in thin metal films—provides a very appealing alternative for trapping nanometric dielectric particles [14,19,20], magnetic nanoparticles , and biomolecules [22–27].In these experiments using plasmonic nanocavities, a new trapping mechanism has been observed that the trapping performance of the optical nanocavity can be improved by the trapped nanoobjects, the so called self-induced back-action (SIBA) effect, which can further reduce the optical power required in the optical trapping and suppress the thermal fluctuation and optical damage [15,28–30]. The underlying physics mechanism of SIBA effect is that the LSPR mode of the plasmonic nanocavity is perturbed by the trapped nanoobject, which leads to a reconfiguration and prominent enhancement of the intra-cavity electric field and the optical force experienced by the nanoobjects. A tiny shift to the long wavelength of the LSPR resonance wavelength of the whole system can be observed in these experiments when the trapped nanoparticle is confined at different positions of the plasmonic nanocavity. Quidant et al. demonstrated theoretically and experimentally that the optical potential of a plasmonic nanocavity can be tuned with the SIBA effect [31,32], which implies a potential of further enhancement of the trapping efficiency by utilizing the optomechanical interaction between a plasmonic nanocavity and the trapped nanoobject. Recently, Aporvari et al. showed numerically with finite-difference time-domain (FDTD) method that a dielectric nanowire can be trapped and rotated by using a plasmonic nanocavity .
However, in the previous studies, only weak interactions between the trapped nanoobject and the photonic nanocavity have been considered, and the optical trapping of nanoobject is regarded as a dielectric perturbation to the dielectric background around the plasmonic nanocavity, which only leads to a tiny red-shift of the resonance frequency of the optical mode of the nanocavity. In fact, the spectral shape of the resonance mode of the nanocavity can be modified and reshaped by the hybridization of the resonance modes of the trapped nanoobject, especially for the case that there exists strong coupling between the trapped nanoparticle and the plasmonic nanocavity. In addition, though the trapping efficiency and ability of plasmonic tweezers can be improved prominently by using the LSPR of plasmonic nanostructures and the SIBA effect, the corresponding manipulation ability compared with conventional optical tweezers, such as trapping objects in different positions or moving nanoobjects in a nanoscale region, is suppressed due to the fixed near field distributions of the plasmonic nanostructures. In this paper, we discuss the optomechanical interaction of a plasmonic nanocavity and a plasmonic nanoparticle under the strong coupling interaction. The motion of the gold nanorod couples with the plasmonic nanocavity, which results in a strong LSPR modes hybridization between the gold nanorod and the plasmonic nanocavity. It is found that the LSPR resonance mode can split into bonding and antibonding plasmonic resonance modes due to the LSPR mode hybridization, which leads to tunable optical forces and reshaped trapping potentials exerted on the gold nanorod.
2. Physical model and numerical methods
The physical model proposed in our work is schematically depicted in Fig. 1(a). A subwavelength cylindrical nanoaperture with radius 100 nm milled in a 100-nm-thick gold thin film is chosen as the plasmonic nanocavity. Dielectric nanoparticles with a size smaller than 50 nm, such as polystyrene spheres, do not support resonant mode in the considered spectrum of the gold nanohole. In order to achieve a prominent modes-coupling, we choose a gold nanorod as the trapped nanoobject. It has been known that there exist two SPRs in gold nanorods, namely, the transverse SPR and the longitudinal SPR modes, which correspond to the collective oscillations of electrons along the short and longitudinal axes of gold nanorods, respectively. While the former remains nearly unchanged at ~520 nm, the latter is quite sensitive to the around dielectric environment. Furthermore, the longitudinal SPR can be tuned from the visible to the near infrared spectral region by varying the ratio of the length to the diameter, which provides a flexible means to engineer the optical modes coupling of the plasmonic nanocavity and the trapped nanoobject. The length and diameter of the gold nanorod studied in this paper are chosen to be 60 and 30 nm, respectively. The whole system (the nanoaperture and the gold nanorod) immersed in water (refractive index n = 1.33) is excited by using a plane wave with its k-vector normal to the nanocavity. The excitation polarization of the plane wave is set to be parallel to the longitudinal axis of the gold nanorod and the power intensity of the plane wave is set to be 10 mW/μm2.
We employ the three-dimensional finite-difference time-domain (3D-FDTD) method to model the optical mode coupling and optomechanical interaction of the gold nanoaperture and the gold nanorod . The dielectric permittivity for gold and its dispersion relation used in the calculations are taken from the experimental data of Johnson and Christy . The simulations are performed based on a discrete grid with a size of 1 nm to take a balance between accuracy and efficiency. Perfect match layers are used to truncate the modeling domain and avoid reflection from all boundaries. For the optical forces acting on the gold nanorod, a volumetric integration method proposed by Zakharian et al. is used . Once the electromagnetic fields distributions (both inside and outside the medium) have been calculated by using FDTD, the time-averaged net force acting on the mass center of the gold nanorod can be determined by
In practical optical trapping of rod-like nanoparticles such as gold nanorods , silver nanowires  and ZnO nanorods , optical torques will be exerted on these nanoparticles if the orientations of the rod-like nanoparticles lie a certain angle with the excitation polarization of the introduced laser. However, considering that these nanoparticles eventually can be trapped and lies along with the excitation polarization of the laser, we neglect this process and mainly focus on the optical forces and potentials acting on the gold nanorod.
3. Results and discussion
3.1 Plasmonic resonance modes hybridization of nanocavity and gold nanorods
Let us first examine the evolution of the scattering spectrum of the plasmonic nanoaperture when the gold nanorod approaches the center of nanoaperture from different directions. In this case, three representative moving directions of the gold nanorod are considered: both are that the gold nanorod, which is placed in a X-Y plane with a distance of h = 35 nm above the upper surface of the gold film, moves towards the center of the nanocavity along with X and Y direction (the blue dashed line arrow shown in Figs. 1(a) and (b)), respectively; The third direction is that the gold nanorod moves towards and passes through the center of the nanoaperture along with Z direction (the blue dashed line arrow shown in Fig. 1(c)). It should be noted that the longitudinal axis of the nanowire lies on the X-Y plane which is parallel to polarization direction of the incident light. In Figs. 1(d)-(f), we present the dependence of the scattering spectra of the whole system on the distance d of the gold nanorod from the center of the nanocavity along the three representative directions. It can be noted that the single-peak shaped scattering spectrum gradually splits into a two-peak shaped spectrum when the gold nanorod approaches the center of the nanocavity, which is totally different from that presented in previous research where only weak interaction can be induced when nanoparticles are trapped by the plasmonic tweezers [10,12,16,31]. As mentioned in the Section 2, some dielectric nanoparticles with size smaller than 50 nm cannot support any resonant mode around the resonant wavelength of the gold nanohole. Therefore, only shift of resonant wavelength of the plasmonic tweezers can be observed when these nanoparticles are trapped by plasmonic tweezers.
Basically, the splitting originates from the near field coupling interaction between the gold nanorod and the nanoaperture, which is analogous to that of electron states in diatomic molecules where the interaction of two atoms causes a splitting of the degenerate atomic levels into bonding and antibonding orbitals. For the coupling of plasmonic resonance modes, the plasmonic resonance mode splits into two new resonance modes: the lower energy bonding plasmonic resonance mode and the higher energy antibonding plasmonic resonance mode. In order to confirm the two new plasmonic resonance modes, we have calculated the charge distributions of the gold nanorod and the nanoaperture at the resonance wavelengths when the gold nanorod is placed above the center of the nanocavity. A plasmon mode hybridization picture is utilized to illustrate the formation of the bonding mode and the antibonding mode , as shown in Fig. 2. One can clearly see from Fig. 2(b) that the dipolar gold nanorod plasmon resonance (1) at λ = 675 nm (shown with red arrow in upper panel of Fig. 2(a)) interacts with the bonding dipolar nanoaperture plasmon resonance (2) at λ = 740 nm (shown with red arrow in lower panel of Fig. 2(a)). The strong near field interaction between the two dipolar plasmon modes results in two hybridized plasmon resonance (shown with red arrows in middle panel of Fig. 2(a)). A lower energy plasmon resonance at λ = 781nm is a bonding state (4) composed of antisymmetric aligned bonding dipolar states of the gold nanorod and the nanocavity. The corresponding higher energy plasmon antibonding state (3) at λ = 643 nm is a symmetric combination of the bonding dipolar states of the gold nanorod and the nanocavity. It can be apparently seen from Figs. 1(d), (e) and (f) that the strength of the plasmon hybridization depends on the distance of gold nanorod from the nanoaperture. As the distance increases, the interaction between the gold nanorod and nanoaperture decreases gradually.
3.2 Tunable optical forces and potentials
We now examine the evolution of the optical forces and the optical potential imposed on the gold nanorod when the gold nanorod move towards the center of the nanoaperture along with the three representative directions shown in Figs. 1(a)-(c). When the gold nanorod approaches the center along with X direction, as shown in Fig. 1(a), the optical force acting on the gold nanorod is dominated by x-component Fx and z-component Fz. The y-component Fy of the optical force is negligible due to the symmetry of the structure. In Figs. 3(a) and (b), we present the dependence of Fx and Fz on the positions of the gold nanorod at λ = 643 nm and λ = 781 nm which correspond to the antibonding and bonding modes, respectively. It can be obviously seen that the gold nanorod receives pushing forces (direction pointing to the outside of the gold nanohole) at λ = 643 nm due to the repulsive interaction of the same kind of polarization charges shown in Fig. 2(b) (3), which means that the gold nanorod can be pushed away from the nanocavity under the irradiation of the laser with wavelength at λ = 643 nm. On the contrary, under the excitation of a laser with a wavelength at λ = 781 nm corresponding to the bonding mode of the whole system, we can see that optical pulling forces (direction pointing to the center of the gold nanohole) acting on the gold nanorod originate from attractive interplay of opposite polarization charges shown in Fig. 2(b) (4), which indicates that the gold nanorod can be pulled into the gold nanocavity. It should be pointed out that though Fx can reach a zero-force point when the gold nanorod is located in the position 35 nm above the center of the nanoaperture the gold nanorod cannot be trapped at the position due to a large longitudinal optical pulling force acting on the gold nanorod.
A close inspection of Fz presented in Fig. 3(a) shows a weak optical pulling force acting on the gold nanorod as the gold nanorod approaches the edge of the nanoaperture. It implies there are two underlying mechanisms to determine the optical forces acting on the gold nanorod with plasmonic tweezers: one is the gradient force induced by the LSPR of the gold nanocavity  and the other is the enhanced gradient force induced by the coupling of gold nanorod and the plasmonic nanoaperture. In this case, the coupling between the gold nanorod and the gold nanoaperture can be neglected because of the long distance between the gold nanorod and the nanocavity, and the optical force mainly originates from the gradient force induced by the significantly enhanced electric field gradient of the gold nanoaperture. However, when the gold nanorod passes through the edge of the gold nanoaperture and moves into the coupling region of the nanoaperture, the repulsive interaction gradually dominates the dynamics of the gold nanorod. Consequently, one can see obviously from Fig. 3(a) that the gold nanorod receives a prominent optical pushing force due to the repulsive interaction of the same kind of polarized charges, which pushes the gold nanorod away from the nanoaperture.
In order to clarify the effect of the plasmonic resonance modes hybridization on the optical pulling force acting on the gold nanorod, we calculate the scattering spectrum and optical forces imposed on a dielectric nanorod (refractive index n = 2, such as ZnO nanowires) with the same size as that of the gold nanorod shown in Figs. 3(c) and (d). In contrast with the case of gold nanorod, the profile of the scattering spectrum remains unchanged and the maximum resonant wavelength shift of the plasmonic nanoaperture caused by the dielectric nanorod is less than 1nm even when the dielectric nanorod is placed at the position 35 nm above the center of the nanoaperture. This result indicates that the fluctuation introduced by the dielectric nanorod to the field distribution and the LSPR mode of the gold nanoaperture can be neglected and the optical forces acting on the dielectric nanorod mainly originate from the localized gradient electric field. Comparing the results of Fig. 3(b) with Fig. 3(d), one can see that the optical pulling forces acting on the gold nanorod are about 20 times larger in X direction and 30 times larger in Z direction than those acting on the dielectric nanorod in both directions , which means that the near-field interaction between the trapped nanoobject and the plasmonic tweezers would induce giant enhancement of the optical forces imposed on the trapped nanoobject.
Basically, in practical experiments, the trapping of a gold nanorod with plasmon tweezers is a dynamic interaction process, as shown in Figs. 1(d), (e) and (f), which indicates the trapping of the gold nanorod can be modified by the coupling of the two plasmonic nanostructures. For this purpose, we calculate the optical forces acting on the gold nanorod when the gold nanorod approaches the gold nanoaperture under the irradiation of laser lines with different wavelengths around 781 nm (the bonding state), as shown in Fig. 4. Figure 4(a) presents Fx as a function of distance d and wavelength. For the cases of λ > 781 nm, we can see the X component of the optical force acting on the gold nanorod increases gradually when the gold nanorod approaches the nanoaperture. After reaching the maximum, it reaches an equilibrium state at the center of the nanoaperture. However, for λ < 781 nm, the X component of the optical force imposed on the gold nanorod is tuned gradually by the coupling of the gold nanorod with different parts of the nanoaperture. When the wavelength is switched to 731 nm, it can be seen that Fx drops abruptly to 0 pN at the edge of the gold nanoaperture after reaching the maximum. As the gold nanorod further approaches the center of the nanoaperture, the gold nanorod receives an opposite force to its moving direction. From the Fz shown in Fig. 4(b), we can conclude that the gold nanorod can be pulled down and held on the edge of the nanoaperture under the assistant of the gold film. Figure 4(c) shows the optical trapping potential in X direction as a function of λ. It can be seen that the trapping potential at λ < 751 nm splits gradually into two narrow optical trapping potentials, which implies that the gold nanorod can be confined in different positions of the nanoaperture by tuning the wavelength of the laser.
In order to understand the tunable feature of the optical force, we investigate the electric field distributions when the distances d between the gold nanorod and the center of the nanoaperture are 200 nm, 100 nm, and 0 nm and the wavelength of the laser are λ = 781 nm and λ = 731 nm, respectively, as shown in Fig. 5. For comparison, we only show the electric filed distributions in X-Y section that is 10 nm apart from the upper surface of the gold film. The left panel and the right panel of Fig. 5 show the two cases with λ = 731 nm and 781 nm, respectively. One can clearly see that only intrinsic LSPR modes (dipole modes) are excited when the gold nanorod is far from the gold nanoaperture (d = 200 nm) either at λ = 731 nm or at λ = 781 nm, as shown in Figs. 5(a) and (d). Most of the energy is localized in both rims of the nanoaperture along the polarization of the laser. For these cases, the optical forces exerted on the gold nanorod mainly originate from the gradient of the localized field of the nanoaperture, as shown in Fig. 3(a). As the gold nanorod further approaches the nanoaperture, we can notice that the distributions of the localized electric field are modified, and the localized field has been significantly enhanced due to the coupling interaction of gold nanorod and the nanoaperture. When the gold nanorod is localized on the edge of the nanoaperture, the field mainly is confined in the gap between the gold nanorod and the left rim of the nanoaperture at λ = 731 nm, as shown in Figs. 5(b) and (e). As a result, it can be seen from Fig. 4(a) that the gold nanorod can be pulled down on the edge of the nanoaperture. As the gold nanorod is placed on the center of the nanoaperture, the distribution of the field of the whole system recombines into a symmetric bonding mode, as shown in Figs. 5(c) and (f). For this case, the gold nanorod receives a total optical pulling force pointing to the center of the nanoaperture, as shown in Fig. 4(b). It should be emphasized here that the localized fields are enhanced in some degree when the gold nanorod is localized on the edge of the nanoaperture at λ = 781 nm. The enhancement of localized field results in a small dip (around d = ± 90 nm) in the Fx curve and an abrupt increase of Fz when the gold nanorod passes the edge of the nanoaperture, as shown in Figs. 4(a) and (b).
So far, we discuss the optical force acting on the gold nanorod when the gold nanorod moves to the center of the nanoaperture along with X direction. In this moving direction, the gold nanorod can only be confined on the left edge or the right edge of the nanoaperture by using the laser with λ = 731 nm under the supporting of the upper surface of the gold nanofilm. However, as mentioned above, for excitation of laser with λ = 781 nm, although Fx exerted on the gold nanorod can reach zero-force point at the center of the gold nanoaperture, the gold nanorod can be pulled in the nanoaperture due to the longitudinal pulling force Fz. In order to estimate the trapping effect of the gold nanorod in the Z direction, we calculate the optical force acting on the gold nanorod when the gold nanorod approaches the nanoaperture along the Z direction. In this case, the optical force exerted on the gold nanorod is dominated by the optical pulling force along the Z direction Fz. The Y and X components of the optical force are negligible due to the symmetry of the structure. In Fig. 6, we present the dependence of Fz and the optical potential on the position of gold nanorod at λ = 731, 751, 771 and 791 nm. One can clearly see from Fig. 6(a) that the gold nanorod receives an optical restorting force pointing to center of the nanoaperture, which means that the gold nanorod could be trapped into the aperture under the irradiation of the lasers with these wavelengths. An interesting phenomenon which can be observed in Fig. 6(a) is that the trapping positions of the gold nanorod can be tuned from about dz = 0 nm at λ = 791 nm to dz = 55 nm at λ = 731 nm, which can also be obviously manifested as the shift of the bottom of the optical potential in Fig. 6(b). The result mainly originates from the different resonant mode coupling interactions between the gold nanorod and the gold nanocavity. When the gold nanorod moves towards the center of the gold nanohole along with X direction, the coupling interaction happens between the gold nanorod and the upper surface of the gold nanohole. However, for the case that the gold nanorod approaches and goes through the gold nanohole along with Z direction, the coupling interaction exists not only between the gold nanorod and the upper surface of the nanohole but also between the gold nanorod and the lower surface of the gold nanohole, which means that the gold nanorod will receive two opposite restoring forces in Z direction when the gold nanorod is placed in the gold nanohole. The gold nanorod can only be trapped when both opposite restoring forces cancel each other, which is manifested the zero-force points in Fig. 6(a). It can be clearly seen from Fig. 6 that the zero-force point can be modulated by tuning the coupling interaction between the gold nanorod and the gold nanoaperture. Therefore, we can manipulate and position the gold nanorod in a nanoscale region of the nanoaperture by choosing the laser with appropriate wavelength in practical optical trapping experiments.
Finally, we also consider the case that the gold nanorod approaches the nanoaperture along the Y direction, as shown in Fig. 7. In this case, the gold nanorod only receives optical forces in Y and Z directions due to the symmetry of the nanoaperture. The dependences of Fy and Fz on positions of gold nanorod at λ = 731, 751, 771, and 791 nm are demonstrated in Figs. 7(a) and (b). We can see that the evolution of forces is similar to that of the case that the gold nanorod approaches the nanoaperture along X direction. However, a close inspection of Fig. 7(a) shows that the transverse force Fy drop to 0 pN in positions closer to the edge of the nanoaperture than the case of moving along X direction, which implies that the coupling between the gold nanorod and the edge of the nanoaperture mainly determines the optomechanics of the gold nanorod. In addition, the gold nanorod also receives a strong longitudinal force Fz which pulls the gold nanorod down to the edge of the gold nanoaperture. With the supporting of the edge of the nanoaperture, the gold nanorod can also be confined on the edge of the nanoaperture. It should be pointed out that the value of longitudinal force Fz in Fig. 7(b) is a little different from that presented in Fig. 4(b) when the gold nanorod lies on the center of the gold nanoaperture, which originates from the calculation discrepancy induced by using different simulation domains in three representative directions as mentioned in the Section 2.
In conclusion, we investigate the optomechanical interaction between a plasmonic nanoparticle and a plasmonic tweezers in the optical trapping of a gold nanorod with a plasmonic nanocavity. Due to the strong dipolar plasmonic modes coupling between the gold nanorod and the plasmonic nanocavity, the LSPR mode of the whole system splits into antibonding and bonding modes which induce an optical pushing force and an optical pulling force acting on the gold nanorod. Considering the optical trapping of gold nanorod by using a plasmonic nanocavity, we mainly focus on the attractive force acting on the gold nanorod. It is found that the optical trapping force exerted on the gold nanorod can be enhanced by two orders compared with the same sized dielectric nanorod with the same nanoaperture corresponding to the case without coupling between the trapping nanoobjects and the nanocavity. More importantly, the plasmonic hybridization of the gold nanorod and the gold nanocavity can be modulated by the coupling of the gold nanorod with different parts of the gold nanocavity. By calculating the distance dependence of force spectra of the gold nanorod at different resonance modes, we reveal that the gold nanorod can be trapped in different positions of the gold nanohole. The results presented in this work can shed light on the dynamic interaction among plasmonic nanostructures with different shapes and sizes. The new trapped mechanism we proposed may find potential applications, for example, the gold nanocavity can be used to sieve and accumulate the plasmonic nanoparticles with uniform size by tuning the interaction between the nanoparticles and the gold nanocavity. Other applications, such as preparation of some special plasmonic nanostructures for sensing or enhancing the surface enhanced Raman scattering (SERS) signal in nanoscale region, can also be realized by trapping and confining the plasmonic nanorods at different positions in the plasmonic nanocavity.
National Natural Science Foundation of China (NSFC) (No.11774099); Natural Science Funds for Distinguished Young Scholar of Guangdong Province (Grant No. 2014A030306005); Natural Science Foundation of Guangdong Province (Grant Nos. 2016A030313398); Foundation for High-level Talents in Higher Education of Guangdong Province; Development Program for Outstanding Young Teachers in Guangdong University; Science and Technology Program of Guangzhou (Grant No. 201607010176); Visiting Scholar Project of China Scholarship Council; Special Funds for the Cultivation of Guangdong College Students Scientific and Technological Innovation (Grant No. pdjh2016b0075); Student's Platform for Innovation and Entrepreneurship Training Program (Grant Nos. 201610564481 and 201710564501).
References and links
8. M. Righini, A. S. Zelenina, C. Girard, and R. Quidant, “Parallel and selective trapping in a patterned plasmonic landscape,” Nat. Phys. 3(7), 477–480 (2007). [CrossRef]
9. M. Righini, G. Volpe, C. Girard, D. Petrov, and R. Quidant, “Surface plasmon optical tweezers: tunable optical manipulation in the femtonewton range,” Phys. Rev. Lett. 100(18), 186804 (2008). [CrossRef] [PubMed]
11. R. A. Nome, M. J. Guffey, N. F. Scherer, and S. K. Gray, “Plasmonic interactions and optical forces between Au bipyramidal nanoparticle dimers,” J. Phys. Chem. A 113(16), 4408–4415 (2009). [CrossRef] [PubMed]
14. A. N. Grigorenko, N. W. Roberts, M. R. Dickinson, and Y. Zhang, “Nanometric optical tweezers based on nanostructured substrates,” Nat. Photonics 2(6), 365–370 (2008). [CrossRef]
15. M. L. Juan, R. Gordon, Y. Pang, F. Eftekhari, and R. Quidant, “Self-induced back-action optical trapping of dielectric nanoparticles,” Nat. Phys. 5(12), 915–919 (2009). [CrossRef]
17. B. J. Roxworthy, K. D. Ko, A. Kumar, K. H. Fung, E. K. C. Chow, G. L. Liu, N. X. Fang, and K. C. Toussaint Jr., “Application of plasmonic bowtie nanoantenna arrays for optical trapping, stacking, and sorting,” Nano Lett. 12(2), 796–801 (2012). [CrossRef] [PubMed]
18. A. E. Cetin, A. A. Yanik, C. Yilmaz, S. Somu, A. Busnaina, and H. Altug, “Monopole antenna arrays for optical trapping, spectroscopy, and sensing,” Appl. Phys. Lett. 98(11), 111110 (2011).
19. J. Berthelot, S. S. Aćimović, M. L. Juan, M. P. Kreuzer, J. Renger, and R. Quidant, “Three-dimensional manipulation with scanning near-field optical nanotweezers,” Nat. Nanotechnol. 9(4), 295–299 (2014). [CrossRef] [PubMed]
21. H. Xu, S. Jones, B. C. Choi, and R. Gordon, “Characterization of individual magnetic nanoparticles in solution by double nanohole optical tweezers,” Nano Lett. 16(4), 2639–2643 (2016). [CrossRef] [PubMed]
24. A. A. Al Balushi, A. Zehtabi-Oskuie, and R. Gordon, “Observing single protein binding by optical transmission through a double nanohole aperture in a metal film,” Biomed. Opt. Express 4(9), 1504–1511 (2013). [CrossRef] [PubMed]
28. M. L. Juan, M. Righini, and R. Quidant, “Plasmon nano-optical tweezers,” Nat. Photonics 5(6), 349–356 (2011). [CrossRef]
30. C. Chen, M. L. Juan, Y. Li, G. Maes, G. Borghs, P. Van Dorpe, and R. Quidant, “Enhanced optical trapping and arrangement of nano-objects in a plasmonic nanocavity,” Nano Lett. 12(1), 125–132 (2012). [CrossRef] [PubMed]
31. P. Mestres, J. Berthelot, S. S. Aćimović, and R. Quidant, “Unraveling the optomechanical nature of plasmonic trapping,” Light Sci. Appl. 5(7), e16092 (2016). [CrossRef]
32. L. Neumeier, R. Quidant, and D. E. Chang, “Self-induced back action optical trapping in nanophotonic systems,” New J. Phys. 17(12), 123008 (2015). [CrossRef]
34. Z. Huang, Q. Dai, S. Lan, and S. Tie, “Numerical study of nanoparticle sensors based on the detection of the two-photon-induced luminescence of gold nanorod antennas,” Plasmonics 9(6), 1491–1500 (2014). [CrossRef]
35. P. B. Johnson and R. W. Christy, “Optical constants of the Noble metals,” Phys. Rev. B 6(12), 4370–4379 (1972). [CrossRef]
37. 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(13), 2075–2077 (2006). [CrossRef] [PubMed]
38. 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(1), 268–273 (2010). [CrossRef] [PubMed]