1. INTRODUCTION

Research on optically manipulating tiny fragile objects started with the works of Ashikin et al. in 1986 [1]. By using a highly focused laser beam, the produced optical force by a field gradient under momentum conservation can manipulate tiny objects in three-dimension in real time. This contactless and non-destructive approach inspired various novel applications [2–8] in biology, micro-manufacturing, and physical chemistry in subsequent decades. However, this traditional way then faced the first challenge in handling objects smaller than the diffraction limit. In this case, the field gradient became smooth relative to the sub-wavelength scale of the objects, which made its produced optical force insufficient for stable trapping. Even though one can increase the optical intensity to enlarge the field gradient, this action may bring extra thermal accumulations and damages to the trapped bio-object. The second challenge is the massive optical system configuration when using a focused laser beam. Fortunately, research [9] by Kawata et al. found that the evanescent field gradient of light propagation at the dielectric interface of the optical waveguide could also produce a similar optical force. This finding prompted the utilization of different photonic nanostructures [10–14] to realize on-chip optical tweezers in the near-field regime.

Among the utilized photonic nanostructures, some were capable of confining light in a volume smaller than the diffraction limit, thus overcoming the first challenge mentioned above. For example, in traditional dielectric-based structures, researchers can design nano slots [15,16] or photonic molecules with narrow gaps [14] to compress the optical field within an ultrasmall space, or shape the optical modes to have extremely sharp field gradients by artificial photonic lattices [17,18]. With proper cavity [14,16,17] or waveguide [19] designs, optical nano-tweezers based on dielectric structures have shown capabilities of efficient trapping, easiness in integration with photonic circuits, and the advantage of low optical loss (metal free).

On the other hand, various metallic nanostructures with localized surface plasmon resonance (LSPR) [20] are undoubtedly the other candidate in realizing efficient optical nano-tweezers. The most remarkable feature of the plasmonic structure is its easiness in producing LSPR hot spots near the structural surface, which have sharp and strong field gradients and are accessible for trapping targets. With the maturing of nanofabrication techniques in the last two decades, optical nano-tweezers based on different LSPR structures [12,21–36] have also bloomed. One of the important issues of this kind of device is how to enhance the produced optical force as well as lower its power consumption, which prevents the local thermal perturbation from the hot spot and damage to the targets. Modifications to the topologies of metallic nanostructures to enhance the LSPR fields inside based on lightning-rod [21–24,27,28,30,32,34], plasmon hybridization [25,31,32], or dimer effects [28] are common approaches in the field. However, these optimizations usually inevitably result in extremely delicate topological designs that need very fine control during the fabrication procedure [26,32,33]. In this paper, we significantly enhance the LSPR field via a different approach that can produce extra surface plasmon polariton (SPP) waves by additional meta-structures and couple them into the LSPR. Our presented design based on this idea can effectively enhance LSPR and reduce the power consumption for trapping without using an extremely delicate metallic topology.

2. EVOLVING THE LSPR MODE OF THE PLASMONIC BOWTIE APERTURE FOR STRONG OPTICAL TRAPPING

In LSPR nanostructures suitable for realizing optical nano-tweezers, the bowtie topology consisting of two triangles facing each other is well known for its extremely strong LSPR hot spot based on lightning-rod and dimer effects. In our previous work [24], we demonstrated a gold bowtie antenna on a ${\mathrm{SiN}}_x$ waveguide to manipulate the polystyrene (PS) microsphere. However, owing to the isolated structure of the bowtie antenna, the strong LSPR field within the gap is accompanied by significant heating simultaneously. This local heating results in thermal perturbation and affects the trapping stability near the trapping site. To compensate for the above weakness, the plasmonic bowtie aperture (PBA) [27,30] in Fig. 1(a) penetrating through a metallic layer became an alternative in realizing nano-tweezers in recent years. This kind of PBA structure can generate similar LSPR hot spots based on lightning-rod and dimer effects as well, where the unpatterned metal layer can further play the role of conducting the heat produced by the LSPR hot spot [33]. Such an idea of increasing system heat sinking by high thermal conductive substrates is also reported in optical tweezers based on different plasmonic [21,29] and dielectric [18] structures.

 

Fig. 1. (a) Schematics of PBA and PBN, and (b) their structural parameter definitions. (c) Theoretical normalized electric fields $|E{|}^2/{|E_0|}^2$ of PBA ($T=0\mathrm{nm}$) and PBN ($T=60\mathrm{nm}$) along $xy$ and $xz$ planes. (d) For PBN with different $T$ from 0 to 100 nm, their produced theoretical $F_z$ acts on a PS sphere with a diameter of 100 nm.

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In Figs. 1(a) and 1(b), the silver PBA on a glass substrate has parameters of bowtie angle $\theta$, length $L$, height $H$, and gap $g$ of 90°, and 200, 100, and 30 nm. To explain our proposed design, we first explore the LSPR in PBA and its produced optical trapping force for a PS sphere in water by the 3D finite element method (FEM). In the simulation setup, the refractive indices of the glass substrate, surrounding water, and PS sphere are 1.45, 1.33, and 1.59, respectively. The dielectric function of silver is described by the Lorentz–Drude model [37,38]. At the wavelength of 1064 nm for exciting the devices, the corresponding permittivities ${\epsilon }_1$ and ${\epsilon }_2$ of silver are $-62.7$ and 1.17, respectively, while the permeability of silver in simulation is one. Here we choose silver as the metal layer instead of the widely used gold because of its higher thermal conductivity (420 W/mK) than that of gold (315 W/mK). In Fig. 1(c), the theoretical electric fields of LSPR along $xy$ and $xz$ planes show concentrated distributions at the tips on both the top and bottom sides of PBA owing to the lightning-rod effect. These hot spots with a sharp gradient can efficiently produce a trapping force for the PS microsphere.

However, we need only one side of the PBA structure to trap the target; thus, the hot spot on the other side is redundant. Therefore, we leave a silver layer with thickness $T$ between PBA and the glass substrate, which forms a design of a plasmonic bowtie notch (PBN), shown in Figs. 1(a) and 1(b). In this design, the presence of the underlying silver layer eliminates the bottom silver/dielectric aperture pattern of PBA. In this case, the screening effect by the bottom silver layer will push the induced charges upward [39] and concentrate most of the LSPR fields at the tips on the top side of PBN, as shown by the theoretical electric field distribution in Fig. 1(c). This enhanced LSPR hot spot undoubtedly can produce stronger light–matter interactions than in PBA. Also, because of the comparable size of the LSPR mode and trapping target, the plasmonic tweezers usually involve self-induced back-action (SIBA) [40,41], where the trapping target will affect or enhance the LSPR mode and plays a role of self-enhancing during the trapping process. However, the SIBA phenomenon is different in different plasmonic structures by particle size and accessibility to the plasmonic hot spot. In our paper, although it is not obvious, the field distributions in Fig. 1(c) still show slight enhancements within the spheres, which implies the existence of SIBA in our PBA and PBN designs.

To validate the trapping capability of our design, we use the comprehensive Maxwell stress tensor (MST) [42] in FEM to calculate the force of trapping the PS sphere along different directions. In this method, we first calculate the LSPR field distribution of the PBN with the particle existence and then use the MST to calculate the corresponding trapping forces at different positions, whose calculation thus includes the SIBA phenomenon of the nanoparticle in plasmonic tweezers. The MST describes the vectorial surface density of optical force provided by the field gradient on the nanoparticle. In a Cartesian coordinate, each component of the time-averaged MST can be expressed as

The above process inspires us to push extra plasmons into a specific region to enhance the LSPR by modifying the metallic/dielectric structure. Therefore, we herein propose the design of periodic curved grooves (CGs) [43] placed outside the PBN, as shown in Fig. 2(a). These periodic grooves can produce extra SPP waves, while their curved shapes couple the produced SPP wave into the PBN region. Figure 2(a) defines the parameters of CGs including their numbers $N$, periodicity $P$, depth d, width w, and angle $\theta$. First, for the CGs with $N$, $d$, $P$, $w$, and $\theta$ of 2, 100, 670, 250 nm, and 90°, respectively, the two valleys of the theoretic reflection spectrum in Fig. 2(b) correspond to band edges of ${\omega }^{+}$ and ${\omega }^{-}$ of the surface plasmon photonic bandgap [44]. Their theoretical mode profiles in electric fields in Fig. 2(b) show that the ${\omega }^{+}$ band concentrates more plasmons in the central region. To couple this produced SPP wave into the PBN, we design the PBN with $\theta$, $L$, $H$, and $g$ of 90, 300, 100, and 30 nm, respectively. Its theoretical reflection spectrum in Fig. 2(b) has a valley corresponding to LSPR, which shows good wavelength alignment of the ${\omega }^{+}$ band with the CGs. Figure 2(c) shows the theoretical electric field distributions of LSPR in PBN with PBN-CGs and without CGs. Along the bowtie gap [white dotted line in Fig. 2(c)], the SPP coupling by CGs brings 10 times maximum-field over that without CGs, and the $F_z$ produced by this enhanced LSPR hot spot to trap a 100 nm PS sphere in water is 3.2 times stronger [$>8\text{nN/}({\text{W/}\mathrm{\mu }\mathrm{m}}^2)$] than that using PBN without CGs, as shown in Fig. 2(d).

 

Fig. 2. (a) Schematic of silver PBN-CGs on a glass substrate and definitions of the structural parameters. (b) Theoretical reflection spectra of PBN and CGs. The insets show the theoretical electric field distributions corresponding to ${\omega }^{+}$ and ${\omega }^{-}$ band edges of the surface plasmon photonic bandgap. (c) (Left) Theoretical normalized electric field distributions of LSPR in PBN-CGs and PBN, and (right) their maximum electric field distributions crossing the gaps. (d) Produced $F_z$ by PBN-CGs and PBN when trapping a 100 nm PS sphere.

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To further enhance the resulted trapping force, we study the effects given by different parameters of CGs individually in simulation, where the PBN has constant $\theta$, $g$, $L$, and $H$ of 90°, 30, 300, and 100 nm, respectively. First, for CGs with fixed $N$, $d$, and $T$ of 2, 100, and 60 nm, respectively, Fig. 3(a) shows the maximum normalized electric fields under different $P$ and $w$. For each variation in $w$ or $P$, we can obtain the optimized $P$ or $w$ with local maximum field intensity caused by maximized SPP coupling between CGs and PBN. This SPP coupling maximization is determined mainly by its wavelength alignment with LSPR in PBN. In Fig. 3(b), for those $P$ and $w$ with wavelengths ranging from 1060 to 1075 nm [corresponding to LSPR in PBN, represented by the shadow region in Fig. 3(b)], they apparently have locally maximized electric fields, as shown in Fig. 3(a). The results of the electric fields in Fig. 3(a) directly reflect the $F_z$ variation shown in Fig. 3(c) in trapping a 100 nm PS sphere. For CGs with $P=670\mathrm{nm}$ and $w=250\mathrm{nm}$, we can obtain a maximum $|F_z|>8\mathrm{nN}/(\mathrm{W}/{\mathrm{\mu m}}^2)$.

 

Fig. 3. For PBN-CGs with different $w$ and $P$, their theoretical (a) normalized electric fields, (b) wavelengths, and (c) $|F_z|$ for trapping a 100 nm PS sphere. (d) For PBN-CGs with different $d$ from 40 to 140 nm, the theoretical $|F_z|$ for trapping a 100 nm PS sphere. The insets show the normalized electric field distributions of LSPR in PBN-CGs with $d=40$ and 90 nm. (e) For PBN-CGs with different $N$ from zero (PBN) to six, the theoretical $|F_z|$ for trapping a 100 nm PS sphere. The insets show the normalized electric field distributions of LSPR in PBN-CGs with $N=0$, 2, 4, and 6.

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For CGs with fixed $N$, $w$, $P$, and $T$ of 2, 250, 670, and 60 nm, respectively, Fig. 3(d) shows the theoretical $F_z$ under different $d$ for trapping a 100 nm PS sphere. When $d$ increases from 40 to 90 nm, $|F_z|$ monotonically increases with $d$ because the elongated groove sidewall induces more plasmon for coupling into the PBN. The theoretical electric field distributions in CGs with $d$ of 40 and 90 nm in the insets of Fig. 3(d) clearly show this phenomenon. However, when $d$ becomes deeper than 100 nm, the scattering of the SPP wave by the grooves becomes significant [45], thus reducing the plasmon coupling into PBN and decreasing $|F_z|$. In Fig. 3(d), CGs with $d$ of 90 to 100 nm show optimized $|F_z|>8\mathrm{nN}/(\mathrm{W}/{\mathrm{\mu m}}^2)$. The wavelength of CGs within this $d$ range also aligns well with that of LSPR in PBN [1060–1075 nm, shadow region in Fig. 3(d)]. Considering the feasibility in our fabrication, $d$ will be the same as $H$ (100 nm) in the following study.

Also, for CGs with fixed $d$, $w$, $P$, and $T$ of 100, 250, 670, and 60 nm, respectively, Fig. 3(e) shows theoretical $F_z$ under different $N$ for trapping a 100 nm PS sphere. In Fig. 3(e), it is easy to understand that the increase in $N$ will induce more plasmon coupling into the PBN and produce enhanced $F_z$. However, when $N$ becomes larger than four, extra scattering induced by more CGs will reduce the plasmons coupled into PBN and degrade $F_z,$ even though their wavelength in Fig. 3(e) (shadow region) still aligns with the LSPR in PBN. The theoretical electric field distributions of PBN-CGs with $N=0-6$ in the insets of Fig. 3(e) clearly validate the above discussions. When $N=4$, we can obtain an enhanced $|F_z|$ value as strong as $12.5\mathrm{nN}/(\mathrm{W}/{\mathrm{\mu m}}^2)$.

To confirm the trapping capability of the above optimized PBN-CGs, we use the comprehensive MST method in 3D FEM to calculate the optical trapping force ($F_x$, $F_y$, $F_z$) and potential ($U_x$, $U_y$, $U_z$) in three dimensions for trapping a 100 nm PS sphere in Figs. 4(a)−4(c). In the simulation, we calculate the optical potential by integrating the produced force for the PS sphere at different positions. In these figures, the PBN-CGs can individually produce potentials larger than $5\times {10}^4{k}_{B}T/(\mathrm{W}/{\mathrm{\mu m}}^2)$ near the PBN region along with all directions, where $k_B$ and $T$ represent the Boltzmann constant and system temperature, respectively. These potential values mean that we need only a power lower than $0.2\mathrm{mW}/{\mathrm{\mu m}}^2$ to overcome the Brownian motion ($>10k_{B}T$) and reach stable trapping in fluidics. Also, for comparison, we also calculate the trapping force and optical potential produced by PBN without CGs, as shown in Figs. 4(a)−4(c). The significant differences in trapping force and potential between PBN and PBN-CGs clearly indicate the enhancements produced by CGs.

 

Fig. 4. Theoretical trapping force and optical potential for a 100 nm PS sphere in water by the optimized PBN-CGs along (a) $x$ ($F_x$, $U_x$), (b) $y$ ($F_y$, $U_y$), and (c) $z$ directions ($F_z$, $U_z$). For comparison, the corresponding results by PBN without CGs are also shown in (a)–(c).

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3. MANUFACTURING PROCESS

To realize the above PBN-CG design, the manufacturing procedure in Fig. 5(a) starts from depositing a silver layer with a thickness of $T$ on a glass substrate by e-gun evaporation (step A). It is followed by spin-coating negative resist (ma-N2403, MicroChem) for electron-beam lithography on the silver layer (step B). We then define the PBN-CG patterns on the resist (step C) and deposit another silver layer with a thickness of H (step D) on the patterned resist. Afterward, lifting off the patterned resist forms the PBN-CGs structure (step E) shown in Fig. 2(a). The insets of Fig. 5(a) show the top view and zoom-in scanning electron microscope (SEM) images of finished PBN-CGs with $N$, $w$, $P$, $g$, and $L$ of 4, 230, 690, 30, and 310 nm, respectively. Also, we confirm the parameters $H$ and $d$ ($\sim 110\mathrm{nm}$) from the atomic force microscope (AFM) image of the trench mark manufactured on the same sample in Fig. 5(b). Figure 5(c) shows the reflection spectrum of the above PBN-CGs in air via a reflectance measurement system. The valley in Fig. 5(c) corresponds to the enhanced LSPR in PBN-CGs, which agrees well with the simulation result also shown in Fig. 5(c).

 

Fig. 5. (a) Fabrication flowchart of PBN-CGs and its top-view and zoom-in SEM images. (b) AFM image of the manufactured trench mark on the same sample. (c) Measured and theoretical reflection spectra of the PBN-CGs in air.

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4. EXPERIMENT RESULTS OF OPTICAL TRAPPING WITH REDUCED POWER CONSUMPTION VIA PBN-CGS

To observe the optical manipulation performed by the PBN-CGs, we mount the sample in a homemade microfluidics chamber and fill the chamber with a mixed solution of 0.005% 1 μm PS spheres and 1% surfactants to prevent the PS spheres aggregation. We should clarify that we use a larger sphere size in experiments for the easiness of observing the trapping sphere. As the required power consumption increasing exponentially proportional to particle size is known in the field, there would be a similar trapping force enhancement trend for different trapping particle sizes. With the system shown in Fig. 6(a), we focus a near-infrared (NIR) laser beam (with $\lambda =1064\mathrm{nm}$) with $x$ polarization onto the PBN-CGs using a $50\times$ objective lens for exciting the LSPR. The focused laser spot size is 12 μm in diameter, estimated via the CCD image without the NIR filter, as shown in the inset of Fig. 6(a). The CCD camera records the movement with the time of the PS near the PBN-CGs during optical manipulation. The screenshots of the video (Visualization 1) in Fig. 6(b) illustrate the procedure of trapping and releasing a single PS sphere by the PBN-CGs. After turning on the NIR laser (at $t=0\mathrm{s}$), a nearby PS sphere gradually comes closer to the PBN-CGs and is eventually trapped in the PBN region at $t=30\mathrm{s}$. After 30 s of stable trapping, turning off the NIR laser will rapidly release the PS sphere from the PBN region owing to the Brownian motion in fluidics. In the above stable trapping operation, the illuminating laser intensity is as low as $25\mathrm{\mu W}/{\mathrm{\mu m}}^2$, which corresponds to a required power of 9 μW on the trapping site.

 

Fig. 6. (a) Schematic of the optical system for observing the optical manipulation performed by PBN-CGs. The optical images of PBN-CGs at different time points when trapping/releasing (b) a single (Visualization 1) and (c) multi-PS spheres (1 μm) (Visualization 2). (d) Optical images of PBN at different time points when trapping/releasing a single PS sphere (1 μm) (Visualization 3). (e) Optical images of PBN-CGs at different time points when trapping/releasing a single dye-doped PS sphere (500 nm) (Visualization 4). (f) Positions of the trapped dye-doped PS sphere recorded in 10 s by the CCD camera. Most of them lie within the shadow region encircled by $U_x$ and $U_y$, which defines the trapping site of silver PBN-CGs.

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Moreover, it is also possible to trap more than one PS sphere if we extend the duration of laser excitation. The screenshots of the video (Visualization 2) at different time points in Fig. 6(c) prove this operation. Once we turn on the NIR laser, we can observe that the first, second, and third PS spheres come close to the PBN-CGs in sequence and are trapped by PBN at different time points $t$ of 27, 82, and 130 s. However, the incident power here is the same as that used in trapping a single PS sphere. Therefore, within the trapping duration, trapping the three PS spheres is actually like juggling balls, instead of trapping them simultaneously, which is the typical feature of the SIBA phenomenon [40]. When we turn off the NIR laser, all the PS spheres rapidly drift away. Also, the above long-term stable trapping means that there is no significant heat accumulation during the trapping process. This is attributed to the low power consumption by the enhanced force by LSPR in PBN-CGs, as well as the high thermal conductivity of the silver layer beneath the PNB.

For comparison, we also perform optical trapping by PBN without CGs under the same setup. We can observe the trapping and release of a single PS sphere by turning on and off the NIR laser (Visualization 3), as shown by the screenshots at different time points in Fig. 6(d). However, in this operation, the required incident laser intensity of $88\mathrm{M}\mathrm{W}/{\mathrm{m}}^2$ (corresponding to a required power of 32 μW on the trapping site) is over three times higher than that required in PBN-CGs. This result directly points out that we can significantly reduce the power consumption for trapping the same particle using PNB by simply adding CG structure.

Furthermore, we also use the same silver PBN-CGs to trap a smaller single PS sphere with a size of 500 nm in diameter. Because the PS sphere size is close to the diffraction limit, we dope the chemical dyes on it and excite it by a green laser, shown in Fig. 6(a), for observation during the manipulation procedure. From the screenshots of the recorded video (Visualization 4) at different time points in Fig. 6(e), we can observe the trapping and releasing of a single PS sphere via silver PBN-CGs by turning on and off the NIR laser. The required laser intensity of $37\mathrm{M}\mathrm{W}/{\mathrm{m}}^2$ (corresponding to a required power of 14 μW on the trapping site) for this operation is significantly lower than those required for trapping single particles with similar sizes via the previously reported c-shaped [25], spiral [26], and bowtie apertures [27,30], and V-shaped antenna [34]. We should note that this intensity/power value is even lower than that of PBN without CGs for trapping a 1 μm PS sphere. Therefore, this result again confirms the remarkable feature of reducing trapping power consumption by adding our proposed CGs.

To further confirm the stability of the above trapping, we use ImageJ software to analyze all the images during the trapping procedure captured by the CCD camera with a 30 frames per second frame rate. Figure 6(f) shows the recorded coordinates of the trapped PS sphere positions in 10 s. According to this position distribution, we can estimate the spatial variance $\mathrm{Var}(r)$ to calculate the trapping stiffness $k_r$ defined by $k_{B}T/\mathrm{Var}(r)$. The resulting trapping stiffnesses along $x$ ($k_x$) and $y$ ($k_y$) directions are 0.02 and 0.1 fN/nm, respectively. These values approximately agree with the optical potential widths of $U_x$ and $U_y$, which makes most of the recorded positions distribute within the region encircled by $U_x$ and $U_y$ shown in Fig. 6(f).

5. CONCLUSION

In this paper, based on the idea of coupling more plasmons to enhance the LSPR in metallic nanostructures, we evolve the traditional PBA to the PBN structure and further to PBN with CGs. Via theoretical studies of the effects on LSPR in PBN given by different parameters of CGs, the force for trapping a PS sphere with a diameter of 100 nm of the optimized silver PBN-CGs design shows 11 times enhancement over that of traditional silver PBA structure. Such a design provides an approach to greatly enhance LSPR fields without extremely delicate metallic topologies and structures. Using the silver PBN-CGs realized by our nanofabrication technique, stably trapping a single PS sphere with a diameter of 1 μm in experiments requires an illumination intensity of only $25\mathrm{\mu W}/{\mathrm{\mu m}}^2$. This value is significantly lower than the required intensity using PBN without CGs ($88\mathrm{\mu W}/{\mathrm{\mu m}}^2$), and this silver PBN-CG is also capable of trapping more than one PS sphere in our demonstration. Even for trapping a smaller PS sphere with a diameter of 500 nm, the required illumination intensity is only $37\mathrm{\mu W}/{\mathrm{\mu m}}^2$, which is even lower than that by PBN without CGs for trapping a 1 μm PS sphere. The above experimental results evidently show that the idea of adding CGs in PBN herein can effectively reduce the power consumption for trapping particles without using extremely delicate metallic topologies. Therefore, we believe our presented design would be very suitable for realizing efficient optical nano-tweezers. Based on this idea of adding meta-structures, we believe there is potential to properly combine any suitable SPP wave generating structures (e.g., plasmonic waveguides) with LSPR structures to realize highly efficient nano-tweezers in the plasmonic circuit on-chip.