Achiral nanoparticle trapping and chiral nanoparticle separating with quasi-BIC metasurface

Na Liu; Shutao Wang; Jiangtao Lv; Jinqing Zhang

doi:10.1364/OE.497432

1. Introduction

In recent years, optical trapping technique has been widely used in biology and medicine due to their ability to trap microscale and nanoscale particles while simultaneously measuring forces and positions. The development of this technique can be traced back to 1986 when Ashkin et al. first used a focused laser beam to trap particles [1]. However, the inherent diffraction limit of light makes it difficult to focus on the subwavelength volume, which poses a great challenge to trap particles at low power. Additionally, the trapping capability decreases rapidly with the shrinking of the particle sizes for a given laser power, which greatly restricts the application of optical tweezers [2]. To address these challenges, plasmonic metallic nanostructures have been proposed for particle trapping because they can concentrate light efficiently, creating highly sensitive nanoregions that interact strongly with matter and can be used to detect very small amounts of molecules through changes in their optical response [3,4]. Many varieties of plasmonic tweezers have been investigated to produce the trapping potential wells required to trap, detect and identify nanoscale objects including nanoholes [5], bowtie notch [6,7], nanopillar [8], and dimers [9]. For example, Zhao et al. [5] proposed an optical technique to sort chiral specimens using coaxial plasmonic apertures. Results demonstrate that selective trapping of enantiomers can be achieved with circularly polarized illumination. Verschueren et al. [6] introduced a bowtie-shaped gold plasmonic nanoaperture, and the results showed that translocations of single DNA molecules can be optically detected. However, despite the proven effectiveness of plasmonic nanotweezers in trapping subwavelength nanoparticles, the nanoradiative absorption resulting from the intrinsic loss of the metals naturally limits the Q-factor of the resonance and leads to high temperatures [10]. When using plasmonic tweezers to trap biological objects, the excessive rise in temperature can have adverse effects on the measurements of these objects, such as denaturation of trapped chiral particles, and can affect the accuracy of the results.

On the other hand, BICs have been studied as a promising alternative for manipulating light at the subwavelength scale and enhancing the interaction between light and matter [11]. Originally reported by von Neumann and Wigner in 1929, BICs are discrete non-radiative bound states that coexist within a continuum spectrum of spatially extended states. They are formed through destructive interference between leaky modes and exhibit an infinite Q-factor [12,13]. However, in practice, due to the finite extent of structures, material absorption, and other external perturbations, a quasi-BIC resonance with a sharp peak and finite Q-factor is present [14]. For example, Koshelev et al. [15] revealed that metasurfaces created by seemingly different lattices of meta-atoms with broken in-plane symmetry can generate quasi-BICs with a sharp high-Q resonance of ${10^5}$. Li et al. [16] reported the properties of symmetry-protected BIC in highly symmetric nanodisks and demonstrate their transformation into quasi-BICs with high Q-factor resonators through the removal or addition of parts from the edge. Zhou et al. [17] introduced broken geometry symmetry in a dielectric metasurface, transforming BICs into a quasi-BICs with high Q-factor of $3.16 \times {10^9}$. Such high-Q resonances around a BIC point have gained increased attention for constructing ultra-sharp transmission/reflection spectra, resulting in a huge near-field enhancement and various promising applications [18–20]. In addition, the general idea of BIC-enhanced generational of optical force and torque has been numerically and experimentally demonstrated with a dielectric metasurface, which can be applied in various scenarios such as metavehicles [21], lightsails in space [22,23], and optical trapping of nanoparticles. For example, Wang et al. [24] proposed an all-dielectric nanotweezer using quasi-BIC mode to trap nanoparticles with a radius of 10 nm. Yang et al. [25] reported on the optical trapping process in a dielectric quasi-BIC system. Qin et al. [26] achieved wavelength and polarization tuning of optical/torque directions by changing the asymmetry of the two-bar structure. Wang et al. [27] systematically studied and compared the optical trapping capability of three mainstream optical resonances that can be supported by all-dielectric nanostructure arrays for the first time. The results show that the Fz can reach -135 pN/mW with a 50 nm diameter PS sphere. Compared with plasmonic metasurfaces, BICs based metasurfaces have the strengths of smaller dissipation, lower thermal conductivity, and also much stronger magnetic resonances [28]. These features are especially important for the nano-optical trapping of biological specimens without detrimental photoinduced heating effects present in plasmonic systems [25]. Furthermore, Chen et al. [29] introduced metasurfaces governed by BICs for enhancing the sensitivity of circular dichroism (CD) spectroscopy. It is clear that the structure based on quasi-BIC modes has a broad research prospect. However, the above examples do not clearly discuss and differentiate the chiral nanoparticles, and the potential of direct chirality manipulation using BIC symmetry breaking remains unexplored. Notably, although Levanon et al. [30] studied symmetry-breaking metasurfaces made of amorphous silicon nanodisks, they only discuss the angular transmission response, and the corresponding trapping performance is unclear. Therefore, further studies are needed.

Motivated by the above discussions, in this paper, we propose and numerically demonstrate novel methods for trapping, detecting, and identifying nanoscale particles based on silicon elliptical tetramer dielectric metasurfaces. We start by designing a metasurface with a symmetric tetramer structure, which produces an electric field of high intensity at the gap tips, creating a favorable region for light-particle interaction. This makes it an exceptional optical tweezer platform for trapping achiral nanoparticle, achieving a maximum optical trapping of -19 pN/100 mW and -35 pN/100 mW when trapping an achiral nanoparticle with a radius of 10 nm at P1 and P2, respectively. The corresponding trapping potential wells moving along the x-axis at P1 and P2 can reach up to 718 k_BT and 402 k_BT, respectively. Notably, the proposed metasurface can also control multiple particles, resulting in parallel detection of multiple nanoparticles. We further break the symmetry of the tetramer dielectric metasurface by rotating one of the silicon ellipsoidal cylinders angle to identify and separate enantiomers. Results show that a large optical chirality appears near the R2, leading to the enhancement of chiral optical forces and directly differentiating enantiomers under LCP illumination. Our theoretical research suggests that the all-dielectric quasi-BIC system provides a pathway toward all-optical enantiopure identify. We believe that the proposed quasi-BIC metasurface will provide an efficient way to the optical micromanipulation platform.

2. Symmetric tetramer dielectric metasurface with dual Fano resonances

2.1 Design and theory

The schematic diagram of the symmetric quasi-BIC metasurface based on Si (n = 3.477) resonators on the SiO₂ substrate (n = 1.45) is plotted in Fig. 1(a), which could be fabricated based on electron beam lithography (EBL) followed by atomic layer deposition (ALD) process [11,29]. In order to simulate the suspending capturing target molecules for practical applications, the upper cladding layer is set to the aqueous environment, and the refractive index is 1.33. It can be seen that each unit cell is composed of four elliptical-shaped silicon resonators. Additionally, an elliptical groove is introduced into the center of each elliptical resonator. Figure 1 (b) show the geometrical parameters of the unit cell. The lattice constants Px and Py are both set to P = 700 nm. The values of the long axis a and short axis b of the elliptical nanodisks are set to a = 350 nm and b = 120 nm. The parameter t is the height of the elliptical nanodisks and is set to t = 150 nm. The long axis and short axis of the slot are set to a1 = 150 nm and b1 = 70 nm, respectively. The parameter d is the center distance between adjacent nanodisks and is set to d = 350 nm. In addition, the parameter d’ (d’=P/4-d/2) represents the distance that the metasurface simultaneously moves in the x- and y-direction toward the unit cell center. The structure of each silicon elliptical nanodisk is characterized by a rotation angle $\alpha$ between the long axis and y-axis, with $\alpha$ first set to ${45^\circ }$. In addition, we determine the distributions of electric and magnetic fields via finite element method (FEM) simulations and use the Maxwell stress tensor (MST) method to predict the optical forces exerted on a single nanoparticle by the metasurface [31–33]. The optical forces are calculated on the polymer surface that encloses the nanoparticles.

Fig. 1. Schematic diagram of the proposed quasi-BIC system. (b) Front view and top view of the unit cell, respectively. The geometric parameters are Px = Py = 700 nm, $\alpha$= 45◦, a = 350 nm, b = 120 nm, d = 350 nm, d’=P/4-d/2, t = 150 nm, a1 = 150 nm, b1 = 70 nm.

Download Full Size | PDF

To demonstrate the excitation of BICs, we provide a visual insight of the reflection spectra of the metasurface as a function of wavelength $\lambda$ and parameter d’ (changing from 0 nm to 35 nm). Under normal x-polarized wave illumination, simulations were performed from 900 nm to 1030 nm (which is larger than the period of the metasurface) to allow only 0-order transmission or reflection. For the all-dielectric metasurface based on a symmetric tetramer (|d’|=0 nm), no resonance is observed within the wavelength band, as illustrated in Fig. 2(a). This suggests that the mode does not radiate into free space, demonstrating the existence of the BICs modes. When |d'| is greater than zero, two resonances can be observed in the reflection curve. A symmetry-protected BIC is converted into quasi-BIC, and the resonance peaks are gradually broadened as |d'| increases. To illustrate it in an intuitive and explicit manner, specific reflection curves are plotted in Fig. 2(b). Accompanied by the mirror symmetry of the unit cell, two distinct Fano-type resonances are observed by changing the parameter d’, indicating the presence quasi-BICs. Here, the Fano resonance derives from the interference between discrete bound states supported by silicon ellipsoidal cylinders and the free space continuum. In addition, the relationship between the Q-factor of P1 mode and the parameter d’ is plotted in Fig. 2(c). Here, the Q-factor is defined as $Q = {\omega _0}/2\gamma $, where ${\omega _0}$ is the resonant angular frequency, and $\gamma $ denote the radiation rate [34]. It can be observed that the Q-factor tends to infinity when d’=0 nm, which exhibits the characteristics of the symmetry-protected BICs, even though the unit cell still maintains mirror symmetry and C4v symmetry. Indeed, the change of d’ causes a disturbance in the minimum period in the unit cell. For instance, when d’=0 nm, the minimum period can be regarded as P/4. Changing d’ disrupts this minimum period while also altering the symmetry elements of the material [35,36]. Similarly, Fig. 2(d) shows that the calculated Q-factor diverges at the symmetry point, namely d’=0 nm, for the P2 mode. Since there is no coupling mode with the free space, the resonance cannot be detected in both real systems and simulations. However, once the original symmetry is progressively destroyed, a large Q-factor dramatically arises and gradually decreases as |d’| increases. Notably, in practice, the Q factor of the system will decrease and the field enhancement will be greatly reduced when excited by a tightly focused beam of light that has multiple wavevectors, due to the presence of large spectral dispersion [37].

Fig. 2. (a) Reflection mapping versus wavelength and parameter d’. (b) Specific reflection spectra, there is no resonance when d’=0 nm. The relationship between the Q factor and the parameter d’ of (c) P1 mode, and (d) P2 mode.

Download Full Size | PDF

Then, we discuss the resonance mechanism of the dual quasi-BICs. We calculate the scattering powers of different multipoles in the Cartesian coordinate system when d’ equals 5 nm, including magnetic dipole (MD), electric quadrupole (EQ), magnetic quadrupole (MQ), electric dipole (ED), and toroidal dipole (TD), as shown in Fig. 3. In the case of harmonic excitation $\exp (iwt)$, the scattering cross-section can be expressed in terms of multipolar modes as [38,39]:

(1)$$I = \frac{{2{w^4}}}{{3{c^3}}}|P{|^2} + \frac{{2{w^4}}}{{3{c^3}}}|M{|^2} + \frac{{2{w^6}}}{{3{c^5}}}|T{|^2} + \frac{{{w^6}}}{{5{c^5}}}{Q_{\alpha \beta }}{Q_{\alpha \beta }} + \frac{{{w^6}}}{{20{c^5}}}{M_{\alpha \beta }}{M_{\alpha \beta }}$$

where P, M, T, ${Q_{\alpha \beta }}$,and ${M_{\alpha \beta }}$ are ED, MD, TD, EQ, and MQ, respectively. In this equation,

Fig. 3. Multipolar decomposition of scattering cross-section in terms of toroidal dipole (TD), electric dipole (ED), magnetic dipole (MD), electric quadrupole (EQ), and magnetic quadrupole (MQ) of (a) P1, and (b) P2.

Download Full Size | PDF

ED:

(2)$$P = \frac{1}{{iw}}\int {j{d^3}r} , $$

MD:

(3)$$M = \frac{1}{{2c}}\int {(r \times j){d^3}r} , $$

TD:

(4)$$T = \frac{1}{{10c}}\int {[(r\cdot j)r - 2{r^2}j]{d^3}r} $$

EQ:

(5)$${Q_{\alpha \beta }} = \frac{1}{{i2w}}\int {\left[ {{r_\alpha }{j_\beta } + {r_\beta }{j_\alpha } - \frac{2}{3}{\delta_{\alpha \beta }}(r \cdot j)} \right]} {d^3}r, $$

MQ:

(6)$${M_{\alpha \beta }} = \frac{1}{{3c}}\int {[{{{(r \times j)}_\alpha }{r_\beta } + {{(r \times j)}_\beta }{r_\alpha }} ]} {d^3}r, $$

where j represents the induced volume current density, c denotes the speed of light, w is the angular frequency, r is the position vector, and $\alpha ,\beta = x,y$. Figure 3(a) illustrates that the contribution of TD dominates the P1 resonance. To further enhance understanding of the P1, we also present the displacement currents distribution in Fig. 4 (a). It can be seen that the displacement currents in the ellipsoidal cylinders nanodisks are twisting in opposite directions and producing four longitudinal magnetic moments oriented along the z-axis. Figure 4(b) shows the distribution of magnetic field vectors in the y-z section of P1. We can see that the direction arrows of the magnetic fields head-to-tail form a loop and circulate counterclockwise between y-direction, which is the characterization of TD [40].

Fig. 4. (a) Displacement currents profile, and (b) Magnetic field vector profile of P1, respectively. (c) Displacement currents profile, and (d) Magnetic field vector profile of P2, respectively.

Download Full Size | PDF

According to Fig. 3(b), it can be concluded that TD also dominates in P2. Figure 4(c) shows that counterclockwise and clockwise closed displacement current loops are obtained in the x-y section, respectively, indicating that an opposite phase of magnetic dipole (MD) is induced in the z-direction. The magnetic field vortexes in the inverse rotation direction between neighboring ellipsoidal cylinders, showing the existence of TD, as plotted in Fig. 4(d).

Next, Fig. 5 analyze the corresponding electric field distributions of P1 and P2 when d’ equals 5 nm, respectively. Figure 5(a) plots the electric field distribution in the x-y plane at the quasi-BIC mode of P1. We can observe from this figure that the electric field distribution is primarily concentrated within the gap of the ellipsoidal cylinder nanodisks. This concentration of the electric field provides a strong gradient force, which is useful for particle trapping. Figure 5(b) illustrates the electric field distribution in the quasi-BIC mode of P2. It is clear that the P2 mode exhibits a similar electric field distribution to that of P1, which makes it a promising candidate for particle trapping applications.

Fig. 5. Electric field profile in the x–y plane of (a) P1, and (b) P2

Download Full Size | PDF

Moreover, to demonstrate the trapping achiral particle ability of this metasurface, we use the comprehensive MST in FEM to calculate the force of trapping the particles [41,42]:

(7)$$F\textrm{ = }\oint {(\langle {T_M}\rangle \textrm{ }\cdot } \textrm{ }n)dS$$

where F denotes the time-averaged force, n represents the unit vector perpendicular to the integration surface and T_M represents the time-averaged MST which can be written as:

(8)$$\langle {T_M}\rangle \textrm{ = }\langle D{E^\ast } + H{B^\ast } - \frac{1}{2}(D \cdot {\textrm{E}^\mathrm{\ast }}\textrm{ + H} \cdot {\textrm{B}^\mathrm{\ast }}\textrm{)I}\rangle $$

where E, D, H, and B represent the electric field, electric displacement, magnetic field, and magnetic flux, respectively. I denote the identity matrix.

2.2 Trapping of achiral particles

At present, the real-time sensing of single microparticles in the environment is important for monitoring air quality and identifying potential health hazards [43]. Aerosols and particulate matter with diameters of several micrometers can penetrate deep into the lungs and cause respiratory problems, cardiovascular disease, and other health issues [44]. Therefore, it is important to monitor and control the levels of these achiral pollutants in the air to protect human health and the environment. To analyze the trapping achiral particle ability of our proposed structure, Fig. 6(a) illustrates the 3D schematic diagram of the quasi-BIC system with a 20 nm polystyrene (PS) sphere trapped above a 30 nm gap. As we can see that a much higher electric field enhancement is obtained near the surface of sphere. This is attributed to the high index contrast between the sphere and the surrounding medium [25]. It is noteworthy that the optical force was calculated at the incident power level of 100 mW. The spectrum of the vertical trapping force (Fz, the optical force component in the z-direction) provided by the structure is plotted in Fig. 6(b). Since the resonance dips are highly concentrated around the P1 and P2, the value of Fz always provides the highest optical force, which is -19 pN/100 mW and -35 pN/100 mW, respectively.

Fig. 6. (a) 3D schematic diagram of the quasi-BIC system. and (b) The spectra of Fz experienced by a 20 nm PS.

Download Full Size | PDF

Besides, the optical trapping force acting on particles varies at different positions. Therefore, we conducted a study on the optical trapping force and potential wells by altering the positions of the particles. Since the symmetry of the structure, only certain force components were needed to visualize the trapping incident. Figure 7 calculate the F_x, F_y, and F_z for a 20 nm PS nanoparticle moving along the x, y, and z axis. When the particle was moved along the x and y axis, it was set to maintain a distance of 30 nm from the top surface of the dielectric metasurface along the z-axis. The corresponding potentials (U_x, U_y, U_z) were normalized in the k_BT unit, where k_B represents the Boltzmann constant and T represents the ambient temperature (300 K). Here, a standard requirement for stable trapping nanoparticles is the potential depth of more than 10 k_BT for suppressing Brownian motion [45]. The potential can be written as:

(9)$$U(x) ={-} \int_{ - \infty }^x {{F_x}\textrm{ }\cdot \textrm{ }{d_x}} $$

The red curve in Fig. 7(a) and 7(d) plot the evolution of optical force in the x-component of P1 and P2, respectively. Since the electric field highly concentrates around the gap of the quasi-BIC system, the direction of F_x always points towards the center, and the equilibrium of F_x occurs at the position x = 0. Then, we present the optical potential by integrating the produced force for the PS spheres along the x-path, as shown by the blue lines in Fig. 7(a) and 7(d). It can be seen that the potential of 718 k_BT and 402 k_BT were obtained at x = 0 for these cases. Figure 7 (b) and 7(e) show the trapping characteristics when the PS moves along the path in the y-direction of P1 and P2, respectively. It is also evident that the direction of optical force also always points to the center of the quasi-BIC system. However, the equilibrium of F_y occurs at the dip of ellipsoidal cylinders nanodisks due to the higher electric field of the ellipsoidal cylinders nanodisks than the center of the quasi-BIC system. For the potential distribution of U_y, the deepest U_y of 1132 k_BT and 940 k_BT of P1 and P2 occur at the dip of ellipsoidal cylinders nanodisks, respectively. Figure 7(c) and 7(f) illustrate the trapping characteristics in the z-direction of P1 and P2 by moving the PS along the path in the z-direction with x = y = 0. It can be seen that the optical force of F_z first increases as the PS nanoparticle gets closer and overlaps more with the intense field, and then decreases as the particle moves away from the structure.

Fig. 7. Trapping force and potential for the slotted quasi-BIC system with 20 nm PS sphere moving along the (a) x-axis (F_x, U_x), (b) y-axis (F_y, U_y), and (c) z-axis (F_z, U_z) of P1. Trapping force and potential for the quasi-BIC system with 20 nm PS nanoparticle moving along (d) x-axis (F_x, U_x), (e) y-axis (F_y, U_y), and (f) z-axis (F_z, U_z) of P2.

Download Full Size | PDF

The trapping performance of the proposed quasi-BIC system is compared to that of previous theoretical studies using MST method that trapped PS nanoparticles, as illustrated in Table 1. Here, a strict performance comparison between these different structures is not possible due to the differences in input intensity and particle size in each system. In general, the smaller the nanoparticle is, the smaller the optical force is. However, the higher the input intensity is, the larger the optical force is. When the equal size nanoparticles were investigated, we can see that the optical force in the proposed structure increased by one order of magnitude compared with the plasmonic tweezers [46]. Compared to the dielectric nano-tweezer with larger nanoparticles, the proposed design employs smaller particles but generates an optical force 316.67 times (P1) greater than that reported in Ref. [47]. As a result, the performance improvement of the proposed work compared to other systems.

Table 1. Performance comparison with reported structures

View Table

Notably, the proposed quasi-BIC tweezer can also control multiple particles at multiple positions, resulting in parallel detection of multiple nanoparticles. As the diameter of the particles increases (e.g., 30 nm), the electric field gradient they experience also increases, allowing for the capture of a greater number of particles. Here, we analyze the effects of different numbers of randomly distributed nanoparticles on the reflection spectra. As illustrated in Fig. 8(a) and 8(c), the resonant wavelength has a redshift when the number of nanoparticles varies from 0 to 4 with a step of 1. This is because the interaction between the nanoparticles and the quasi-BIC metasurface becomes stronger as the number of nanoparticles increases, resulting in a larger redshift in the resonant wavelength. Figure 8(b) and 8(d) show the linear change of the resonant wavelength with the number of nanoparticles. When the number of nanoparticles increases by 1, the resonant wavelength will shift about 0.0093 nm and 0.0181 nm, respectively. The number of trapped nanoparticles can therefore be monitored in real time by recording the resonance frequency. This technique can be useful in various applications, such as sensing and detection, where the presence of certain particles can be detected by monitoring the shift in the resonant wavelength of the metasurface.

Fig. 8. Simulated reflection spectra when the number of particles changes from 0 to 4 with a step of 1 of (a) P1, and (c) P2, respectively. Fitted results of resonant wavelength shift varying n of (b) P1, and (d) P2, respectively.

Download Full Size | PDF

3. Asymmetric tetramer dielectric metasurface with multi-Fano resonances

3.1 Design and theory

The above analysis focused on the achiral nanoparticles. However, many biologically active molecules are chiral, including proteins, amino acids, enzymes, and hormones, which play a critical role in biochemistry and the evolution of life itself [48]. Chirality refers to the geometric symmetry property of an object without any mirror symmetry or inversion symmetry [49]. When a protein loses its original chirality, it can become toxic to cells [50]. To study the optical chirality of the proposed dielectric metasurface, one of the silicon ellipsoidal cylinders is rotated by angle $\theta = {25^ \circ }$ to break the mirror symmetry of the structure as plotted in Fig. 9(a). Here, the distance of the ellipsoidal cylinders nanodisks is d = 350 nm, which means the d’ is 0 nm. Notably, the quasi-BIC can induce resonant interference between a collective subradiant dark mode and the superradiant collective bright mode, and hence, the asymmetric dielectric tetramer metasurface can also support multi-Fano resonances under the left-circularly polarized (LCP) excitation along the z-axis, as shown in Fig. 9(b). In order to determine the chiral properties of an electromagnetic field, we first calculate the electromagnetic density of chirality, C, which can be written as [51]:

(10)$$C ={-} \frac{w}{{2{c^2}}}{\mathop{\rm Im}\nolimits} ({E^ \ast }\cdot H) ={-} \frac{w}{{2{c^2}}}|E||H|\cos ({\beta _{iE,H}})$$

where E is the complex electric field, H represents the complex magnetic file, $w$ is the angular frequency of light, ${\varepsilon _0}$ denotes the permittivity of free space and ${u_0}$ is the permeability of free space. The ellipticity of the electromagnetic fields is captured by ${\beta _{iE,H}}$, which shows the phase angle between $iE$ and H. For circularly polarized light (CPL), the parallel components of E and H have a $\pi /2$ phase difference, giving $\cos ({\beta _{iE,H}}) ={\pm} 1$; for CPL in a vacuum, ${C_{CPL}} ={\pm} \frac{{{\varepsilon _0}w}}{{2c}}E_0^2$, where E₀ is the magnitude of the incident electric field. And $C/{C_{CPL}}$ will represent enhancements in the optical chirality due to the metasurface. Hence, designing platforms that concentrate electromagnetic fields while creating or maintaining circular polarized states provides a means to increase the chiroptical response of molecules. Here, we denote enhancements in the optical chirality under the LCP excitation as $C/{C_0}$. Figure 9(c) calculates the corresponding enhancement of optical chirality across the volume of metasurface. It is observed that the enhancement of optical chirality can be up to 362 with R2, which is larger than most of the previous results [52,53]. Moreover, Fig. 9(d) shows the case with $\theta = {45^ \circ }$ and d’=5 nm, which corresponding to Fig. 1(b). Comparing the enhancement factors of optical chirality between Fig. 9(c) and Fig. 9(d), it also can be seen that the enhancement factor of the asymmetric tetramer dielectric metasurface is much larger than that symmetric tetramer dielectric metasurface.

Fig. 9. Schematic structure and multi-Fano resonances of the proposed asymmetric metasurface. (a) 3D schematic diagram of the asymmetric metasurface. (b) The corresponding variation of reflection spectra with wavelength. (c) The optical chirality enhancement with the case of silicon ellipsoidal cylinders rotation with $\theta = {25^ \circ }$ under the LCP excitation. (d) The optical chirality enhancement with the case of sustaining silicon ellipsoidal cylinders symmetry with d’=5 nm under the LCP excitation.

Download Full Size | PDF

Then, we added a chiral particle with a radius of 10 nm to the system, as synthetic chiral nanoparticles typically have a size of around 10 nm. Notably, the chiral particle can be modeled as a pair of interacting electric and magnetic dipoles. When an electromagnetic wave acts on the nanoparticle, the induced dipole moments can be written as [54]:

(11)$$ \left[\begin{array}{l} p \\ m \end{array}\right]=\left[\begin{array}{cc} \alpha_{e e} & \mathrm{i} \alpha_{\mathrm{em}} \\ -\mathrm{i} \alpha_{\mathrm{em}} & \alpha_{\mathrm{mm}} \end{array}\right]\left[\begin{array}{l} E \\ H \end{array}\right] $$

here p and m are the electric and magnetic dipole moments, respectively. ${\alpha _{ee}}$, ${\alpha _{mm}}$,and ${\alpha _{em}}$ denote the electric, magnetic, and electromagnetic polarizabilities of the chiral particle, respectively. The electromagnetic polarizability ${\alpha _{em}}$ is strongly with the chirality parameter $k$ of the chiral nanoparticle [5,50]:

(12)$${\alpha _{em}} ={-} 12\pi r_p^3\frac{{k\sqrt {{u_0}{\varepsilon _0}} }}{{({\varepsilon _r} + 2{\varepsilon _{rm}})({u_r} + 2) - {k^2}}}$$

where ${\varepsilon _0}$ and ${u_0}$ represent the permittivity and permeability of vacuum, ${r_p}$ denote the radius of the chiral nanoparticle, ${\varepsilon _r}$ and ${u_r}$ are the relative permittivity and permeability of the chiral nanoparticle, ${\varepsilon _{rm}}$ represent the relative permittivity of the medium where the particle is embedded. It can be seen that the sign ${\alpha _{em}}$ depends on the parameter k. When ${\alpha _{em}} = 0$, it corresponds to an achiral nanoparticle. In addition, the electric and magnetic polarizabilities can be written as:

(13)$${\alpha _{ee}} = 4{\varepsilon _0}\pi r_p^3\frac{{({\varepsilon _r} - {\varepsilon _{rm}})({u_r} + 2) - {k^2}}}{{({\varepsilon _r} + 2{\varepsilon _{rm}})({u_r} + 2) - {k^2}}}$$

(14)$${\alpha _{mm}} ={-} 4{u_0}\pi r_p^3\frac{{{k^2}}}{{({\varepsilon _r} + 2{\varepsilon _{rm}})({u_r} + 2) - {k^2}}}$$

From the above equations, we can know that the sign of electric polarizability ${\alpha _{em}}$ or magnetic polarizability ${\alpha _{mm}}$ is independent k. Typically, the optical force acting on the chiral nanoparticle can be expressed as [5,50]:

(15)$$F = \frac{1}{2}\textrm{Re} [(\nabla {E^ \ast })\cdot p + ({\nabla {H^ \ast }} )\cdot m - \frac{{c{k^4}}}{{6\pi \sqrt {{\varepsilon _{rm}}} }}(p \times {m^ \ast })]$$

where E and H are the fields acting on the nanoparticle. When substitute Eq.(11) into Eq.(15), the force expression then can be written as:

(16)$$\begin{array}{l} F = \nabla U + \sigma \frac{{\left\langle S \right\rangle }}{c} - {\mathop{\rm Im}\nolimits} [{\alpha _{em}}]\nabla \times \left\langle S \right\rangle + c{\sigma _e}\nabla \times \left\langle {{L_e}} \right\rangle + c{\sigma _m}\nabla \times \left\langle {{L_m}} \right\rangle \\ \textrm{ + w}{\gamma _e}\left\langle {{L_e}} \right\rangle + w{\gamma _m}\left\langle {{L_m}} \right\rangle + \frac{{ck_0^4}}{{12\pi }}{\mathop{\rm Im}\nolimits} [{{\alpha_{ee}}\alpha_{mm}^ \ast } ]{\mathop{\rm Im}\nolimits} [E \times {H^ \ast }] \end{array}$$

here $U = 1/4(\textrm{Re} [{\alpha _{ee}}]|E{|^2} + \textrm{Re} [{\alpha _{mm}}]|H{|^2} - 2\textrm{Re} [{\alpha _{em}}]{\mathop{\rm Im}\nolimits} [H\cdot {E^ \ast }])$ is the term due to the particle-field interaction. $\left\langle S \right\rangle = \frac{1}{2}\textrm{Re} [E \times {H^ \ast }]$ denote the time-averaged Poynting vector, $\left\langle {{L_e}} \right\rangle = \frac{{{\varepsilon _0}{\varepsilon _{rm}}}}{{4wi}}E \times {E^ \ast }$ and $\left\langle {{L_m}} \right\rangle = \frac{{{u_0}}}{{4wi}}H \times {H^ \ast }$ are the time-averaged spin densities, ${\sigma _e} = \frac{{{k_0}}}{{{\varepsilon _0}}}{\mathop{\rm Im}\nolimits} [{\alpha _{ee}}]$, ${\sigma _m} = \frac{{{k_0}}}{{{u_0}}}{\mathop{\rm Im}\nolimits} [{\alpha _{mm}}]$, $\sigma = {\sigma _\textrm{e}} + {\sigma _m},\,{\gamma _e} = - 2w{\mathop{\rm Im}\nolimits} [{\alpha _{em}}] + \frac{{c{k^4}}}{{3\pi {\varepsilon _0}{\varepsilon _{rm}}\sqrt {{\varepsilon _{rm}}} }}\textrm{Re} [{\alpha _{em}}\alpha _{em}^ *$, and ${\gamma _m} ={-} 2w{\mathop{\rm Im}\nolimits} [{\alpha _{em}}] + \frac{{c{k^4}}}{{3\pi {u_0}\sqrt {{\varepsilon _{rm}}} }}\textrm{Re} [{\alpha _{mm}}\alpha _{em}^ \ast ]$ are the coefficients with the dimension of a cross-section.

The first section in Eq.(15) is the gradient force ${F_g}$, which can be written as [50]:

(17)$${F_g} = \frac{1}{4}(\textrm{Re} [{\alpha _{ee}}]\nabla |E{|^2} + \textrm{Re} [{\alpha _{mm}}]\nabla |H{|^2} - 2\textrm{Re} [{\alpha _{em}}]\nabla {\mathop{\rm Im}\nolimits} [H\cdot {E^\ast }])$$

which also can be subdivided into dielectric gradient force ${F_d}$ and chiral gradient force ${F_k}$, the expressions can be written as:

(18)$${F_d} = \frac{1}{4}\textrm{Re} [{\alpha _{ee}}]\nabla |E{|^2} + \frac{1}{4}\textrm{Re} [{\alpha _{mm}}]\nabla |H{|^2}$$

(19)$${F_k} ={-} \frac{1}{2}\textrm{Re} [{\alpha _{em}}]\nabla {\mathop{\rm Im}\nolimits} [H\cdot {E^\ast }]$$

As seen from Eq. (17) and (18), the dielectric gradient force ${F_d}$ is associated to the gradients of the electric field and magnetic field, and chiral gradient force ${F_k}$ is associated to the gradient of optical chirality.

As we know, asymmetric tetramer dielectric metasurface based on silicon ellipsoidal cylinder rotation can generate strong optical chirality under the excitation of LCP light. To further illustrate the difference between the configurations with and without cylinder rotation, Fig. 10 calculates the magnitudes of F_d (red solid) and F_k (blue solid line), respectively. Here, we only consider the positive values of F_d and F_k. As shown in Fig. 10(a), the magnitude of F_k is larger than that F_d at the resonance wavelength of R2 due to the significant optical chirality gradient resulting from the rotation of the silicon ellipsoidal cylinders. However, it should be noted that in the symmetric tetramer dielectric metasurface, the magnitude of F_d at the resonance wavelength of P1 is larger than the amplitude of F_k, as illustrated in Fig. 10(b). Therefore, the asymmetric tetramer dielectric metasurface can induce strong chiral optical responses, making it a better candidate for realizing chiral separation and detection applications compared to the symmetric tetramer dielectric metasurface.

Fig. 10. Numerically analyzed the dielectric gradient force F_d and chiral gradient force F_k with the (a) silicon ellipsoidal cylinders rotation of $\theta = {25^ \circ }$, and (b) sustaining silicon ellipsoidal cylinders symmetry structure.

Download Full Size | PDF

3.2 Separation of chiral particles

To ensure the stable trapping of chiral particles, the trapping potential of the asymmetric metasurface for both enantiomers ($k ={\pm} 0.5$) under the excitation of LCP light is plotted in Fig. 11(a). Here, we analyze the one-dimensional trapping potential of the chiral particle along the z-axis. Similarly to achiral particles, in order to stably trap the chiral particles, the trapping potential must be greater than 10 k_BT. This is necessary to counteract the Brownian motion of nanoparticles suspended in solution [5,50]. It can be observed that the proposed structure produces a positive trapping potential of 16 k_BT for the chiral nanoparticle when its chirality is 0.5. However, the chiral particle with a chirality of -0.5 exhibits a negative trapping potential of -33 k_BT at the same location. The structure stably captures only chiral nanoparticles with a chirality of -0.5, while repelling chiral particles with a chirality of 0.5. Figure 11(b) shows the trapping potential for both enantiomers when using the symmetric tetramer dielectric metasurface with a distance of 5 nm (d’=5 nm). Without rotating the silicon ellipsoidal cylinders, the metasurface generates negative trapping potentials for chiral particles of both enantiomers. It has been demonstrated that the all-dielectric metasurface based on a symmetric tetramer is unable to distinguish and separate chiral particles.

Fig. 11. The trapping potential along the z-axis for both enantiomers when using the (a) asymmetric metasurface and (b) symmetric metasurface under the excitation of LCP light.

Download Full Size | PDF

The above analysis only discusses the fixed value for the chirality of nanoparticles. Therefore, we will analyze the effect of the magnitude of the nanoparticle chirality k on the separation of enantiomers. As shown in Fig. 12(a) and 12(b), we have plotted the total optical force F (red solid lines), the dielectic gradient component F_d (red dash lines), and the chiral gradient component F_k (orange dash lines) of the asymmetric and symmetric metasurface as functions of chirality k under the excitation of LCP light. Here, the positive (negative) sign indicates the direction of the optical force along the z-axis (-z-axis). It can be observed from Fig. 12(a) that the magnitude of F_d is greater than F_k when k varies from 0 to ${\pm} 0.2$ for the asymmetric metasurface. This implies that the chiral particles cannot be trapped by such a configuration within this range. Furthermore, for the symmetric metasurface, the magnitude of F_d is consistently greater than that of F_k within the range of k = [-0.8, 0.8], as illustrated in Fig. 12(b). In such a situation, the symmetric metasurface is unable to distinguish between chiral particles.

Fig. 12. Optical force F and its components F_d and F_k acting on the chiral particle are shown as a function of chirality k, under the excitation of LCP light at 919.18 nm, for both the (a) asymmetric metasurface and (b) symmetric metasurface.

Download Full Size | PDF

4. Conclusion

In conclusion, our study demonstrates the potential of silicon elliptical tetramer dielectric metasurfaces for both achiral nanoparticle trapping and chiral nanoparticle separation. Under excitation of x-polarized light, the symmetric tetramer dielectric metasurface provides dual resonances with high electromagnetic field enhancement and high Q-factor, making it an exceptional optical tweezer platform for trapping achiral nanoparticles. Additionally, the proposed symmetric tetramer metasurface can control multiple particles, enabling parallel detection of multiple nanoparticles. However, under excitation of LCP, the asymmetric tetramer dielectric metasurface enables identification and separation of chiral nanoparticles using chiral optical forces. The proposed metasurface provides multiple Fano resonances and high trap potential wells, making it a promising approach for manipulating light-matter interactions. Overall, the proposed quasi-BIC based all-dielectric metasurface exhibits high performance in nanoparticle detection and provides novel ideas and methods for research in bio-chemistry, on-chip optics, and various optical manipulation devices.

Funding

National Natural Science Foundation of China (61771419).

Disclosures

The authors declare that there are no conflicts of interest related to this article.

Data availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

References

1. A. Ashkin, J. M. Dziedzic, J. E Bjorkholm, and S. Chu, “Observation of a single-beam gradient force optical trap for dielectric particles,” Opt. Lett. 11(5), 288 (1986). [CrossRef]

2. A. Ashkin, “Inaugural Article:Optical trapping and manipulation of neutral particles usinglasers,” Proc. Natl. Acad. Sci. U. S. A. 94(10), 4853–4860 (1997). [CrossRef]

3. K. C. Neuman and S. M. Block, “Optical trapping,” Rev. Sci. Instrum. 75(9), 2787–2809 (2004). [CrossRef]

4. R.-C. Jin, J.-Q. Li, L. Li, Z.-G. Dong, and Y. Liu, “Dual-mode subwavelength trapping by plasmonic tweezers based on V-type nanoantennas,” Opt. Lett. 44(2), 319 (2019). [CrossRef]

5. Y. Zhao, A. A. E. Saleh, and J. A. Dionne, “Enantioselective Optical Trapping of Chiral Nanoparticles with Plasmonic Tweezers,” ACS Photonics 3(3), 304–309 (2016). [CrossRef]

6. D. V. Verschueren, S. Pud, X. Shi, L. De Angelis, L. Kuipers, and C. Dekker, “Label-Free Optical Detection of DNA Translocations through Plasmonic Nanopores,” ACS Nano 13(1), 61–70 (2019). [CrossRef]

7. J. Berthelot, S. S. Acimovic, 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]

8. K. Wang and K. B. Crozier, “Plasmonic trapping with a gold nanopillar,” ChemPhysChem 13(11), 2639–2648 (2012). [CrossRef]

9. W. Zhang, L. Huang, C. Santschi, and O. J. Martin, “Trapping and sensing 10 nm metal nanoparticles using plasmonic dipole antennas,” Nano Lett. 10(3), 1006–1011 (2010). [CrossRef]

10. V. Garcés-Chávez, R. Quidant, P. J. Reece, G. Badenes, L. Torner, and K. Dholakia, “Extended organization of colloidal microparticles by surface plasmon polariton excitation,” Phys. Rev. B 73(8), 085417 (2006). [CrossRef]

11. S. Yang, M. He, C. Hong, J. D. Caldwell, and J. C. Ndukaife, “Engineering Electromagnetic Field Distribution and Resonance Quality Factor Using Slotted Quasi-BIC Metasurfaces,” Nano Lett. 22(20), 8060–8067 (2022). [CrossRef]

12. B. Wang, W. Liu, M. Zhao, J. Wang, Y. Zhang, A. Chen, F. Guan, X. Liu, L. Shi, and J. Zi, “Generating optical vortex beams by momentum-space polarization vortices centred at bound states in the continuum,” Nat. Photonics 14(10), 623–628 (2020). [CrossRef]

13. C. W. Hsu, B. Zhen, A. D. Stone, J. D. Joannopoulos, and M. Soljačić, “Bound states in the continuum,” Nat. Rev. Mater. 1(9), 16048 (2016). [CrossRef]

14. S. I. Azzam and A. V. Kildishev, “Photonic Bound States in the Continuum: From Basics to Applications,” Adv. Opt. Mater. 9(1), 2001469 (2021). [CrossRef]

15. K. Koshelev, S. Lepeshov, M. Liu, A. Bogdanov, and Y. Kivshar, “Asymmetric Metasurfaces with High-Q Resonances Governed by Bound States in the Continuum,” Phys. Rev. Lett. 121(19), 193903 (2018). [CrossRef]

16. S. Li, C. Zhou, T. Liu, and S. Xiao, “Symmetry-protected bound states in the continuum supported by all-dielectric metasurfaces,” Phys. Rev. A 100(6), 063803 (2019). [CrossRef]

17. C. Zhou, L. Huang, R. Jin, L. Xu, G. Li, M. Rahmani, X. Chen, W. Lu, and A. E. Miroshnichenko, “Bound States in the Continuum in Asymmetric Dielectric Metasurfaces,” Laser Photonics Rev. 17(3), 2200564 (2023). [CrossRef]

18. Y. Yu, A. Sakanas, A. R. Zali, E. Semenova, K. Yvind, and J. Mørk, “Ultra-coherent Fano laser based on a bound state in the continuum,” Nat. Photonics 15(10), 758–764 (2021). [CrossRef]

19. Q. Shi, J. Zhao, and L. Liang, “Two dimensional photonic crystal slab biosensors using label free refractometric sensing schemes: A review,” Prog. Quantum Electron. 77, 100298 (2021). [CrossRef]

20. B. Zhen, C. W. Hsu, L. Lu, A. D. Stone, and M. Soljacic, “Topological nature of optical bound states in the continuum,” Phys. Rev. Lett. 113(25), 257401 (2014). [CrossRef]

21. D. Andren, D. G. Baranov, S. Jones, G. Volpe, R. Verre, and M. Kall, “Microscopic metavehicles powered and steered by embedded optical metasurfaces,” Nat. Nanotechnol. 16(9), 970–974 (2021). [CrossRef]

22. H. A. Atwater, A. R. Davoyan, O. Ilic, D. Jariwala, M. C. Sherrott, C. M. Went, W. S. Whitney, and J. Wong, “Materials challenges for the Starshot lightsail,” Nat. Mater. 17(10), 861–867 (2018). [CrossRef]

23. O. Ilic and H. A. Atwater, “Self-stabilizing photonic levitation and propulsion of nanostructured macroscopic objects,” Nat. Photonics 13(4), 289–295 (2019). [CrossRef]

24. J. Wang, Z. Han, C. Wang, and H. Tian, “Parallel trapping of multiple nanoparticles using a quasi-bound state in the continuum mode,” J. Opt. Soc. Am. B 39(9), 2356 (2022). [CrossRef]

25. S. Yang, C. Hong, Y. Jiang, and J. C. Ndukaife, “Nanoparticle Trapping in a Quasi-BIC System,” ACS Photonics 8(7), 1961–1971 (2021). [CrossRef]

26. H. Qin, W. Redjem, and B. Kante, “Tunable and enhanced optical force with bound state in the continuum,” Opt. Lett. 47(7), 1774–1777 (2022). [CrossRef]

27. G. Wang and Z. Han, “Investigations on the optical forces from three mainstream optical resonances in all-dielectric nanostructure arrays,” Beilstein J. Nanotechnol. 14, 674–682 (2023). [CrossRef]

28. X. Chen, Y. Zhang, G. Cai, J. Zhuo, K. Lai, and L. Ye, “All-dielectric metasurfaces with high Q-factor Fano resonances enabling multi-scenario sensing,” Nanophotonics 11(20), 4537–4549 (2022). [CrossRef]

29. Y. Chen, C. Zhao, Y. Zhang, and C. W. Qiu, “Integrated Molar Chiral Sensing Based on High-Q Metasurface,” Nano Lett. 20(12), 8696–8703 (2020). [CrossRef]

30. N. Levanon, S. R. K. C. Indukuri, C. Frydendahl, J. Bar-David, Z. Han, N. Mazurski, and U. Levy, “Angular Transmission Response of In-Plane Symmetry-Breaking Quasi-BIC All-Dielectric Metasurfaces,” ACS Photonics 9(11), 3642–3648 (2022). [CrossRef]

31. Z. Xu, W. Song, and K. B. Crozier, “Direct Particle Tracking Observation and Brownian Dynamics Simulations of a Single Nanoparticle Optically Trapped by a Plasmonic Nanoaperture,” ACS Photonics 5(7), 2850–2859 (2018). [CrossRef]

32. Z. Xu and K. B. Crozier, “All-dielectric nanotweezers for trapping and observation of a single quantum dot,” Opt. Express 27(4), 4034–4045 (2019). [CrossRef]

33. Z. Xu, W. Song, and K. B. Crozier, “Optical Trapping of Nanoparticles Using All-Silicon Nanoantennas,” ACS Photonics 5(12), 4993–5001 (2018). [CrossRef]

34. L. Cong and R. Singh, “Symmetry-Protected Dual Bound States in the Continuum in Metamaterials,” Advanced Optical Materials (2019).

35. R. Chai, W. Liu, Z. Li, H. Cheng, J. Tian, and S. Chen, “Multiband quasibound states in the continuum engineered by space-group-invariant metasurfaces,” Phys. Rev. B 104(7), 075149 (2021). [CrossRef]

36. Y. Cai, Y. Huang, K. Zhu, and H. Wu, “Symmetric metasurface with dual band polarization-independent high-Q resonances governed by symmetry-protected BIC,” Opt. Lett. 46(16), 4049–4052 (2021). [CrossRef]

37. A. Ndao, L. Hsu, W. Cai, J. Ha, J. Park, R. Contractor, Y. Lo, and B. Kanté, “Differentiating and quantifying exosome secretion from a single cell using quasi-bound states in the continuum,” Nanophotonics 9(5), 1081–1086 (2020). [CrossRef]

38. X. Chen, W. Fan, and H. Yan, “Toroidal dipole bound states in the continuum metasurfaces for terahertz nanofilm sensing,” Opt. Express 28(11), 17102–17112 (2020). [CrossRef]

39. L. Guo, Z. Zhang, Q. Xie, W. Li, F. Xia, M. Wang, H. Feng, C. You, and M. Yun, “Toroidal dipole bound states in the continuum in all-dielectric metasurface for high-performance refractive index and temperature sensing,” Appl. Surf. Sci. 615, 156408 (2023). [CrossRef]

40. D. Zhang, Y. Wang, Y. Zhu, Z. Cui, G. Sun, X. Zhang, Z. Yao, X. Zhang, and K. Zhang, “Ultra-high Q resonances governed by quasi-bound states in the continuum in all-dielectric THz metamaterials,” Opt. Commun. 520, 128555 (2022). [CrossRef]

41. A. H. Yang and D. Erickson, “Stability analysis of optofluidic transport on solid-core waveguiding structures,” Nanotechnology 19(4), 045704 (2008). [CrossRef]

42. Z.-S. Li, T.-W. Lu, P.-R. Huang, and P.-T. Lee, “Efficient nano-tweezers via a silver plasmonic bowtie notch with curved grooves,” Photonics Res. 9(3), 281 (2021). [CrossRef]

43. J. Wang, C. Aegerter, X. Xu, and J. J. Szykman, “Potential application of VIIRS Day/Night Band for monitoring nighttime surface PM 2.5 air quality from space,” Atmos. Environ. 124, 55–63 (2016). [CrossRef]

44. S. Weichenthal, E. Lavigne, G. Evans, K. Pollitt, and R. T. Burnett, “Ambient PM2.5 and risk of emergency room visits for myocardial infarction: impact of regional PM2.5 oxidative potential: a case-crossover study,” Environmental Health 15 (2016).

45. L. Wang, Y. Cao, T. Zhu, R. Feng, F. Sun, and W. Ding, “Optical trapping of nanoparticles with tunable inter-distance using a multimode slot cavity,” Opt. Express 25(24), 29761–29768 (2017). [CrossRef]

46. Q. Zhao, C. Guclu, Y. Huang, F. Capolino, R. Ragan, and O. Boyraz, “Plasmon optical trapping using silicon nitride trench waveguides,” J. Opt. Soc. Am. B 33(6), 1182 (2016). [CrossRef]

47. D. Conteduca, G. Brunetti, G. Pitruzzello, F. Tragni, K. Dholakia, T. F. Krauss, and C. Ciminelli, “Exploring the Limit of Multiplexed Near-Field Optical Trapping,” ACS Photonics 8(7), 2060–2066 (2021). [CrossRef]

48. M. L. Solomon, J. Hu, M. Lawrence, A. García-Etxarri, and J. A. Dionne, “Enantiospecific Optical Enhancement of Chiral Sensing and Separation with Dielectric Metasurfaces,” ACS Photonics 6(1), 43–49 (2019). [CrossRef]

49. G. Rui, S. Zou, B. Gu, and Y. Cui, “Surface-Enhanced Circular Dichroism by Localized Superchiral Hotspots in a Dielectric Dimer Array Metasurface,” J. Phys. Chem. C 126(4), 2199–2206 (2022). [CrossRef]

50. S. S. Hou, Y. Liu, W. X. Zhang, and X. D. Zhang, “Separating and trapping of chiral nanoparticles with dielectric photonic crystal slabs,” Opt. Express 29(10), 15177–15189 (2021). [CrossRef]

51. A. García-Etxarri and J. A. Dionne, “Surface-enhanced circular dichroism spectroscopy mediated by nonchiral nanoantennas,” Phys. Rev. B 87(23), 235409 (2013). [CrossRef]

52. K. Yao and Y. Liu, “Enhancing circular dichroism by chiral hotspots in silicon nanocube dimers,” Nanoscale 10(18), 8779–8786 (2018). [CrossRef]

53. E. Mohammadi, A. Tavakoli, P. Dehkhoda, Y. Jahani, K. L. Tsakmakidis, A. Tittl, and H. Altug, “Accessible Superchiral Near-Fields Driven by Tailored Electric and Magnetic Resonances in All-Dielectric Nanostructures,” ACS Photonics 6(8), 1939–1946 (2019). [CrossRef]

54. S. B. Wang and C. T. Chan, “Lateral optical force on chiral particles near a surface,” Nat. Commun. 5(1), 3307 (2014). [CrossRef]

Trapping systems	Input power	Particles diameter (nm)	Trapping force (pN)	Trapping potential (K_BT)	Ref.
Plasmonic tweezer	10 [mW]	20	0.14		[46]
Dielectric tweezer	26 [mW]	100	0.06		[47]
P1 of this work	100[mW]	20	19	718	-
P2 of this work	100[mW]	20	35	402	-

Achiral nanoparticle trapping and chiral nanoparticle separating with quasi-BIC metasurface

Abstract

1. Introduction

2. Symmetric tetramer dielectric metasurface with dual Fano resonances

2.1 Design and theory

2.2 Trapping of achiral particles

3. Asymmetric tetramer dielectric metasurface with multi-Fano resonances

3.1 Design and theory

3.2 Separation of chiral particles

4. Conclusion

Funding

Disclosures

Data availability

References

Data availability

Cited By

Figures (12)

Tables (1)

Equations (19)

Optics Express