1. Introduction

Optical computing (optical information processing) has been an active research field over past seventy years [1], triggered by the considerable interests in developing future high-performance computers. Among various optical computing techniques, the design and investigation of nanophotonic chips for transporting and manipulating light information at nanoscales has attracted successive attentions [2,3]. Nanophotonic devices are the very fundamental functions in a photonic integrated circuit (PIC), which have led to a revolutionary development in many enchanting applications, such as artificial neural network [4], biomedical therapy [5], optical data storage [6], and quantum information processing [7]. Toward this end, researches have demonstrated various kinds of nanostructures that are made of plasmonic and dielectric materials, including optical waveguides [8], ring resonators [9], photonic crystal resonators [10], nanoapertures [11], and nanoantennas [12]. Plasmonics is perceived as the most encouraging candidate for the next generation of integrated on-chip technology [13,14]. In particular, using plasmonic nanoantennas, optical fields enhancement and confinement can be achieved with deeply subwavelength range, leading to strong light–matter coupling and with enhanced optical forces and potential energy [15]. Another reason for the use of plasmonics is its ease of integration with other photonic waveguides for optical information processing at nanoscales [16].

As predicted by Maxwell’s equations, light fields have linear momentum and thus can generate optical forces on tiny objects via momentum transfer [17–19]. Nanoantennas utilize optical forces to trap and manipulate small particles at relatively low incident intensities [20–22]. For the field of nanoscience, the on-chip ability to handle single nanoparticles at integrated devices is quite advantageous [23]. Various nanoparticles have been trapped, including polystyrene and silica beads [24], gold nanoparticles [25], proteins [26], λ-DNA [27], quantum dots [28], magnetic nanoparticles [29], and chiral nanoparticles [30], and their interactions with confined light fields are well studied. Followed by the early demonstration of optical trapping of 200 nm polystyrene beads in water using pairs of gold nanopillars in 2008 [31], a large number of theoretical and experimental works have been done with different geometries of nanoantennas (and not only for optical trapping), such as nanorods [32], gap dipole antennas [25], Yagi-Uda antennas [33], cross antennas [34], bowtie antennas [35], pairs of nanocylinders with outer rings [36], V-shaped antennas [37], and T-shaped antennas [38–40]. Among them, T-shaped nanoantennas provide fantastic optical properties and have been of particular interest. Coupled T-shaped nanoantennas have two key characteristics: strong light focusing capability in the nanometer slot and fine tunability by adjusting various parameters of the morphology of the structure [41]. Other properties reported include two resonances excitation and the polarization- and wavelength-based identification [41]. Traditionally, gold (Au) has been used as the material of choice in plasmonics because of its relatively good optical properties and chemical stability [42,43]. Advances in plasmonic materials investigation have pioneered in alternative materials with optical properties across a broad range of the optical spectrum such as aluminum [44], silver [45], copper [46], and titanium nitride [47]. Among them, copper (Cu) particularly has attracted significant attention owing to its good optical and plasmonic properties and abundant quantity [48]. Copper is comparably cheap, which is compatible with industry-standard fabrication processes, for instance, the complementary metal-oxide-semiconductor (CMOS) technology, and has been widely used in microelectronics. Another favorable attribute of Cu is its wide availability. More recently, the optical trapping of Cu nanoparticles using conventional free-space optical tweezers has been investigated [49]. It has also been demonstrated that plasmonic copper waveguides fabricated in a simple process can yield high mode confinement in the nanoscale range along with the long propagation distance [46]. These motivate us to demonstrate the optical trapping of nanoparticles based on a copper plasmonic platform. Nevertheless, the investigation of copper nanoantennas tends to fall behind other materials [43], essentially in the field of optical trapping and manipulation of nanostructures.

In this work, we demonstrate the optical trapping of single dielectric nanospheres (NSs) in a microfluidic water chip using a coupled T-shaped copper plasmonic nanoantenna at 1064 nm wavelength. The T-shaped Cu nanoantenna comprises two identical Cu elements separated by a 50 nm gap and each element is designed with two nanoblocks. The field enhancement results in optical fields to be confined in the spatial slot region via the excitation of localized surface plasmons (LSPs), which is in a Fabry–Perot cavity. Our nanoantenna is based on the metal-on-insulator platform. At the trapping wavelength employed here (λ = 1064 nm), Cu has a very similar permittivity as gold (ε_Cu = −49.34−4.93i and ε_Au = −48.45−3.6i) [50]. We present numerical simulations of the near-field distribution, optical force (via the Maxwell stress tensor method), temperature rise, and fluid velocity during the trapping process. We also demonstrate how the presence of an oxide layer of cupric oxide (CuO) and the heat sink silicon (Si) substrate influence the optical trapping properties of copper nanoantennas. By utilizing a water chamber and using an infrared trapping laser, we find that the near field features of the T-shaped Cu nanoantenna covered with an oxidized shell are comparable with the pure T-shaped Cu nanoantenna, and thus the effect of surface oxidation is trivial in the trapping. Our low-cost Cu device can provide the same level of optical trapping properties as that of gold and can be conveniently integrated into the lab-on-a-chip devices.

2. Simulation and results

As shown in Fig. 1(a), our coupled nanoantenna is composed of two identical T-shaped Cu nanostructures separated by a nanoscale gap (g = 50 nm). Each element is designed with a short nanoblock (length w = 200 nm, width t = 180 nm, height h = 200 nm) coupled with a long nanoblock perpendicularly (length l = 600 nm, width t = 180 nm, height h = 200 nm), forming the letter of “T”. The nanoantenna is situated on a glass substrate (n_glass=1.45) and the medium above Cu is water (n_water = 1.33). We perform finite element method simulations (FEM; COMSOL Multiphysics) of our Cu nanoantenna to evaluate its local field behaviors. In these simulations, the light illumination is from the water side (travelling in −z axis) and is an x-polarized plane wave (i.e., across the gap) at normal incidence with 1064 nm wavelength. The complex-valued relative permittivity of Cu is taken as ε_Cu = −49.34−4.93i, which is reasonable for the trapping laser wavelength here [50]. The origin of the xy-plane is set at the gap center and the plane of z = 0 is on the top surface of the glass layer. In Fig. 1(b), we display the electric field distribution of the very center of the Cu nanoantenna along the z-axis with an illumination intensity of I₀ = 0.5 mW/µm² for different gap sizes. The peaks represent the resonantly enhanced fields near the nanoantenna vertical bottom (z = 0) and top (z = 200 nm) surfaces, and the valleys around z = 100 nm represent the local minimum of the light fields inside the Fabry–Perot nanocavity. Within the gap region, the electric fields at the top edge along with Cu–water interface are smaller than the one along with Cu–glass interface since the refractive index of water is smaller than that of glass. At a fixed vertical position, the norm of the electric field increases as the gap is reduced. We also notice that there exist some drops around the bottom and top of the nanoantennas for some gap size cases. We think that these might result from the simulation error of mesh distribution in the COMSOL solver.

 

Fig. 1. (a) Schematic of the coupled T-shaped Cu nanoantenna on a glass substrate. The nanoantenna is illuminated with an x-polarized 1064 nm plane wave from the top. (b) Electric field profile along the z-axis with different gap sizes (I₀ = 0.5 mW/µm²). (c, d) EFE distribution for Cu nanoantenna with a 50 nm gap (x-polarized plane wave, 1064 nm). (c) z = 200 nm cross section. (d) y = 0 cross section. (e) EFE profile for two-block Cu nanoantenna with a 50 nm gap, plotted in the xz- and top cross sections. The scale bar is 200 nm in (c)–(e).

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We next show the simulated electric field enhancement (EFE) distributions on two cross sections through the nanoantenna (for g = 50 nm) as Figs. 1(c) and 1(d). The EFE is derived as the ratio of the norm of the total electric field (|E_tot|) over the norm of the incident plane wave electric field (|E₀|), respectively. In Fig. 1(c), we plot the EFE distribution in the z = 200 nm cross section, and in Fig. 1(d), we plot the EFE distribution in the y = 0 cross section. As expected, the region with the highest EFE is in the narrow gap region near the Cu surface through the excitation of the surface plasmons. It can be seen that our nanoantenna has a maximum EFE of ∼20.3 that is larger than that of the Au double nanohole aperture [11]. In Fig. 1(d), along with the vertical position, from the bottom surface of the nanoantenna to the center, the electric field intensity declines, and then begins to rise until the top surface of the nanoantenna. This potentially exerts a harmonic potential well on the trapped nanoparticle within the gap cavity. For comparison, we also simulate the EFE distributions for an Au (ε_Au = −48.45−3.6i at 1064 nm) [50] and a Si (n_Si = 3.553, k_Si = 0.0001 at 1064 nm) [51] coupled T-shaped nanoantennas on a glass substrate. Both nanoantennas have the same dimensions as that of the Cu nanoantenna and are illuminated under the same conditions and are covered by water. The results in xz-plane (not shown here) indicate a maximum EFE of ∼18.7 for the Au nanoantenna and a maximum EFE of ∼3.29 for the Si nanoantenna. In Fig. 1(e), we plot the EFE distributions for a two-block Cu nanoantenna with a 50 nm gap in the y = 0 cross section and z = 200 nm cross section. The color bar for the case of z = 200 nm cross section is not shown here. The nanoblocks have the same dimensions as that of the short blocks in the coupled T-shaped nanoantenna (length w = 200 nm, width t = 180 nm, height h = 200 nm, gap g = 50 nm), and no long blocks are included. It can be seen that the field enhancement is largest within the gap region and around the bottom of the nanoantenna (i.e., at the glass side). However, there has no potential barrier on the top surface of the nanoantenna and the maximum EFE is smaller than that of the coupled T-shaped nanoantenna.

We next display numerical predictions of the temperature rise in the vicinity of the nanoantenna and the thermal-induced fluid convection field [11,52] when it is illuminated at an intensity of I₀ = 0.5 mW/µm². We consider three nanoantennas: the coupled T-shaped nanoantenna designs made of Cu, Au, and Si with the same dimensions on a glass substrate. All nanoantennas are covered by water and illuminated at normal incidence with an x-polarized 1064 nm plane wave. The thermal conductivities in the simulations are set to be κ_Cu = 401 WK⁻¹m⁻¹, κ_Au = 317 WK⁻¹m⁻¹, and κ_Si = 148 WK⁻¹m⁻¹ for Cu, Au, and Si, respectively [53]. Some key results are provided in Fig. 2. In Figs. 2(a) and 2(b), we show the power dissipation density in the nanoantenna’s center plane (i.e., z = 100 nm cross section). It can be seen that a majority of the power dissipation is compressed very close to the surface of the Cu nanoantenna (same for Au and results not shown here), and for the situation of Si, a majority of the power dissipation is subjected within the individual T letters. It should be emphasized that the peak values of the scale bars are quite different [Fig. 2(a): ∼10¹⁶ W/m³ and Fig. 2(b): ∼10¹² W/m³]. The steady-state temperature increase profiles are depicted as Figs. 2(c) and 2(d). The peak temperature rises for all cases occur on the surfaces of nanoantennas. In Fig. 2(c), the simulation predicts the peak temperature increase is ∼14.3 K on the plotted center plane for the Cu nanoantenna. The peak temperature increase for the Au nanoantenna on the same plane takes a value of ∼12 K. Figure 2(d) shows the simulation for the Si nanoantenna with the peak value being only ∼0.04 K. Our simulations (not shown here due to page limits) predict a maximum buoyancy-driven fluid velocity of ∼3.3 nm/s for Cu, ∼2.7 nm/s for Au, and ∼8.8 pm/s for Si in the 15 μm thick water chamber. They are very weak and have a negligible dedication to the trapping process. It can be seen that the plasmonics-assisted responses produced by the Cu and Au nanoantennas are quite similar due to the comparable optical and thermal properties. However, in terms of the price and fabrication cost, we find that the Cu nanoantenna surpasses the Au nanoantenna. Thus, the Cu nanoantenna acts as a more cost-efficient optical trapping device than the Au nanoantenna.

 

Fig. 2. Heat power dissipation density around (a) a Cu nanoantenna on a glass substrate, and (b) a Si nanoantenna on a glass substrate. Temperature increase profile (for steady-state) around (c) Cu nanoantenna and (d) Si nanoantenna, both on a glass substrate. Panels (a)–(c) are plotted in the center plane (z = 100 nm) and panel (d) is plotted in the xz-plane (I₀ = 0.5 mW/µm²). The values in (d) are magnified by 100 for better display. The scale bar is 200 nm in (a)–(d). The chamber height is 15 μm.

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Here we determine the optical forces generated by our T-shaped Cu nanoantenna to regard its use as nanotweezers for the optical trapping of nanoparticles at a reference intensity of I₀ = 1 mW/µm². We use the Maxwell stress tensor (MST) method to calculate the time-averaged forces on the surface of the nanoparticle [54]. The nanoparticle we chose here is the polystyrene (PS) nanosphere (n_NS = 1.6) because it has been widely used for various biological applications. The results are depicted as Fig. 3. In Fig. 3(a), we show the vertical force F_z on the NS (30 nm diameter) as a function of its vertical center position z_center. We also consider a T-shaped Au nanoantenna with the same dimensions on a glass substrate for comparison. Owing to the similarity of the near-field profiles, the force distributions display similar characteristics. It can be seen that for z_center < 100 nm (nanoantenna midpoint), the NS is pulled close to the glass surface with F_z being negative, and for 110 nm < z_center < 180 nm, the NS is pulled close to the nanoantenna top surface with F_z being positive, and for z_center > 190 nm, the NS is attracted into the nanoantenna with F_z being negative again. This reveals that the vertical forces guide NSs to around the top and bottom edges of the nanoantenna where the intensities reach the maximum, i.e., hotspots. As long as the forces are large enough, NSs can be trapped at the edges to interact with the enhanced local fields, and move around the intrinsic Fabry–Perot cavity. Since the optical forces from linear momentum transfer in figures are larger than tens of femtonewtons [11,36], NSs can be optically trapped by the designed device. Also, the electric double-layer coating of the nanoparticle is expected to have the beneficial effect on their trapping behaviors [36]. The location of the nanoantenna’s midpoint thus represents an unstable equilibrium position. In Fig. 3(b), we show the transverse force F_x and vertical force F_z on the 100 nm NS depending upon its center location outside of the nanoantenna along the x-axis (y_center = 0, z_center = 260 nm, i.e., 10 nm distance to the Cu–water interface). It could be emphasized that F_x is negative for x_center > 0 and F_x is positive for x_center < 0. This indicates that the NS experiences a restoring force along the x-direction when it is moving outside of the nanoantenna. For the range of positions considered, the negative values of F_z again verify that the NS is attracted into the nanoantenna. In Fig. 3(c), we plot the vertical force F_z on the PS NS versus its diameter at a fixed position (x_center = y_center = 0, z_center = 260 nm). It can be visualized that the optical force increases with the NS diameter, which is also anticipated from the dipole approximation. In Fig. 3(d), we plot the vertical force F_z on the 30 nm NS versus its refractive index at a fixed position (x_center = y_center = 0, z_center = 210 nm). It can be seen that the NS with a larger refractive index experiences a stronger optical force.

 

Fig. 3. MST optical forces on a single NS for I₀ = 1 mW/µm². (a) Optical force F_z vs. vertical position over the gap (d = 30 nm, x_center = y_center = 0). (b) F_x and F_z vs. NS center position along x-axis (y_center = 0, z_center = 260 nm). (c) F_z vs. NS diameter (x_center = y_center = 0, z_center = 260 nm, n = 1.6). (d) F_z vs. NS refractive index (x_center = y_center = 0, z_center = 210 nm, d = 30 nm).

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We also explore the effect of the oxidization on the optical properties of our T-shaped Cu nanoantenna. The structure of thin dielectric copper oxides layers is usually formed on the metallic Cu due to the air exposure [48]. Spontaneous formation of cupric oxide (CuO) and cuprous oxide (Cu₂O) results in changes in plasmonic properties and the dielectric functions of them are quite similar [55]. For this purpose, we assume that our T-shaped Cu nanoantenna is covered with an oxidized shell of CuO (n_CuO = 2.63) with varying thickness. A cross section of the simulated EFE distribution through the nanoantenna is shown in Fig. 4. When Cu oxidizes, it swells, hence, in our FEM simulations, we assume that half thickness of the CuO shell is derived from the Cu nanoantenna owing to the oxidation, and the other half thickness is taken from the oxide layer swelling [49]. In Fig. 4(a), we consider a 4 nm shell that includes the oxidation of 2 nm and an additional swelling of 2 nm, for this reason, the gap is 46 nm. The maximum EFE here is ∼16.8 in the plotted plane, which is a little smaller than that of the pure Cu nanoantenna without oxidization [see Fig. 1(d)]. In Fig. 4(b), we consider a 10 nm shell, including a 5 nm oxidation and a 5 nm swelling, hence, the gap is reduced to be 40 nm. The maximum EFE in this case is ∼8.86, which is approximately half of the pure Cu nanoantenna. It can be seen that the thin CuO layer has a weak influence on the local field properties, and the thick CuO layer leads to a noticeable change of optical properties. However, we argue here that this oxidization effect is not important in optical trapping. First, the optical trapping experiment is performed in water (rather than in air) and in room temperature, the oxygen content is decreased and the oxidation rate is relatively low. Second, based on investigations of optical trapping of Cu nanoparticles and their oxides [49], it has been suggested that the Joule heating from light absorption might cause the melting or ablation of the formed oxidized layer and recover the physical and chemical properties of the pure Cu. As a result, the optical trapping using a Cu nanoantenna indicates only minimal oxidation of the nanoantenna’s surface. We also notice that the optical trapping of Cu nanoparticles near the plasmon wavelength can significantly modify the trapping characteristics because the real part of Cu polarizability changes significantly within this wavelength range [49]. However, we employ 1064 nm infrared wavelength for trapping, which is far beyond the plasmon resonance.

 

Fig. 4. EFE distribution and zoom-in of gap region for T-shaped Cu nanoantenna covered with a CuO layer, plotted in the xz-plane. (a) CuO thickness is 4 nm. (b) CuO thickness is 10 nm. Scale bar: 200 nm.

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Finally, we investigate the effect of the integrated heat sink function on the near-field distribution and temperate rise of our T-shaped Cu nanoantenna at an intensity of I₀ = 0.5 mW/µm². Adding a Si underneath layer influences the EFE and the temperature distribution in the water medium nearby [36,56]. The use of Si is inspired by its low cost, low light absorption, and the existence of mature fabrication technologies. Since Si has a much higher thermal conductivity than that of water and glass (κ_Si = 148 WK⁻¹m⁻¹, κ_water = 0.58 WK⁻¹m⁻¹, κ_glass = 1 WK⁻¹m⁻¹) [53], the heating yielded by optical absorption is readily conducted into the Si substrate, rather than into the water. In the simulation, Cu nanoantenna and Si film both act as heat sources. To compare the effect of the Si film thickness, we present the EFE distributions of the nanoantenna with a 50 nm height and a 100 nm height Si films as Figs. 5(a) and 5(b). It can be seen that the region with the highest EFE is in the gap area near the nanoantenna’s top surface only, i.e., Cu–water interface. The strong reflection between Si and water weakens the hotspot strength around the bottom of the nanoantenna. It can also be seen that with the Si substrate, the nanoantenna has a peak EFE value that is approximately half of the original Cu nanoantenna without Si substrate [see Fig. 1(d)]. Figures 5(c) and 5(d) plot the corresponding temperature rise profile in different cross sections through the Cu nanoantenna with the Si film. The maximum temperature rise on the Cu surface when a 50 nm Si substrate is used is ∼2.55 K, and the maximum temperature rise is ∼1.97 K for a 100 nm Si substrate. Thus, the integration of a Si substrate reduces the peak temperature rise by a factor of 5.6 (for a 50 nm Si film) and 7.3 (for a 100 nm Si film).

 

Fig. 5. (a, b) EFE profile for Cu nanoantenna with Si film substrate, plotted in the xz-plane. (a) Si film thickness is 50 nm. (b) Si film thickness is 100 nm. (c, d) Steady-state temperature rise distribution. (c) Cu nanoantenna with 50 nm Si film, plotted in the xz-plane. (d) Cu nanoantenna with 100 nm Si film, plotted in the xz-plane and center plane. Light intensity is I₀ = 0.5 mW/µm² in (c)&(d). The scale bar is 200 nm in (a)–(d).

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3. Conclusion

In conclusion, we demonstrate a coupled T-shaped Cu plasmonic nanoantenna for the optical trapping of single dielectric nanoparticles and investigate its plasmonic and optical properties interacting with an infrared trapping laser. The electric field enhancement (and thus the optical force), temperature rise, and induced fluid velocity it provides are quite similar in comparison to those provided by the Au nanoantenna design. Cu is cheap and compatible with standard microelectronic fabrication technologies. Large local field enhancements mean that low incident power can be utilized. In addition, we show that the oxidization effect on the Cu surface has a weak influence on trapping characteristics compared to the pure Cu nanoantenna, and the Si heat sink substrate can reduce the temperature rise in water. Our results verify that the coupled T-shaped Cu nanoantennas are robust as nanophotonic devices for optical information manipulation at nanoscales. They could also be used to manipulate and investigate single quantum emitters and small molecules. Beyond this, we anticipate a multitude of topics of Cu nanostructures could be performed for the future optical computer investigation and lab-on-a-chip application.