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Abstract
Traditional optical information recognition (OIR), particle capture and manipulation require many optical devices or mechanical moving system components to achieve a specific function, which is difficult to achieve integration. This paper proposes a new method to realize these functions by using multi-focus metalens combining spectrum and polarization selection. The design incorporates three spectral bands, namely 500 nm, 580 nm, and 660 nm, within the visible light range. Additionally, it utilizes either left-handed or right-handed circularly polarized (LCP/RCP) light, resulting in six distinct focus focusing effects on a single focal plane. By analyzing the normalized light intensity (NLI) at the corresponding focus position, the OIR of any wavelength and polarization detection in the design can be realized, and the particle capture at different focusing positions can be realized. Our work can provide a new idea for the high integration of on-chip light recognition and operation and inspire the design of a highly integrated optical system with a smaller size and more substantial function.
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1. Introduction
Light is an essential medium for humans to observe the objective world and also plays a role in transmitting information and energy. Among them, spectrum and polarization, as two fundamental characteristics of light, carry important information about light propagation. For example, spectral imaging can reveal information on the chemical composition of substances [1,2], while polarization imaging can provide information on the spatial distribution of optical properties [3,4]. The capture, sorting, and targeted transport of particles have been rapidly developed in biomedicine, chemistry, and physics-related fields due to their vast application value [5–9]. In recent years, based on the rapid development of lab-on-a-chip [10,11], a variety of cell or particle sorting methods have been proposed, such as photoelectric tweezer chips [12] and fluorescence-activated cell sorters [13]. However, a large number of instruments are often required to complete a series of precise operations, and electrophoresis damage and fluorescent label contamination may damage the sample. The development of a system that offers higher integration, diversified functions, simpler operation, and enhanced convenience is a compelling challenge in contemporary research. This system should possess the capability to accurately identify optical information, perform multi-dimensional imaging, and enable label-free, non-invasive capture of cells or particles. Addressing this urgent problem is of paramount importance in current scientific endeavors.
Metasurfaces are two-dimensional metamaterials with low transmission loss and easy preparation, thus attracting widespread attention [14,15]. It can control electromagnetic waves arbitrarily in an ultra-compact form and is suitable for integrated design systems [16,17]. However, dispersion engineering and polarization optics are two prominent areas of metasurface development, and the ability to independently spatially manipulate each wavelength and polarization state cannot be achieved in parallel using ordinary optical elements [18]. As a simple application of metasurfaces, metalens can replace traditional objectives to achieve laser focusing [19,20], producing a bright solid spot, thereby playing a role in the process of particle capture and sorting [21–24]. For example, polarization-sensitive metalens can demonstrate the selective capture of metal particles [25,26]. Another example is that spiral phase metalens with different topological charges can carry angular momentum, exert torque on particles, and drive particles to continuously rotate [27–30].
This paper presents a novel approach utilizing a multifunctional metalens that integrates spectral and polarization selection for achieving optical information recognition (OIR) capabilities, as well as particle capture and manipulation. In contrast to conventional techniques, this method offers enhanced convenience and robustness by significantly reducing the required number of optical components, thus enabling convenient experimental operations. Within our designed multifunctional metalens, we demonstrate the ability to measure and analyze the normalized light intensity (NLI) at various focal points on the focal plane when the incident light's spectrum and polarization state are unknown. Theoretically, our design allows for arbitrary wavelength and polarization detection within the specified bandwidth, and enables control over the position and intensity of the focal spot on the focal plane by adjusting the incident light's wavelength and polarization state. Consequently, the capture of particles at different focal positions becomes feasible. Precise control over the capture effect of various particles on the OIR focal plane of the metalens can be achieved by analyzing the disparity in normalized light intensity across different positions. This multifocus metalens approach, which seamlessly integrates spectrum and polarization, broadens the functional capabilities of OIR metalenses, thereby introducing new possibilities in the field of particle capture and sorting. Furthermore, this methodology holds significant potential for widespread applications.
2. Design principles
The conceptual diagram of the multi-functional metalens optical tweezers system designed in this article for OIR is shown in Fig. 1. The metalens have a multi-focus focusing function with transverse dispersion. When light of a specific wavelength is incident on a matelens, three foci can be created simultaneously. The light intensity of the focus at the designed focal plane is the strongest, while the intensity of the other two crosstalk positions is significantly lower. Ultimately, this device can be equivalent to the linear superposition of three single-wavelength single-focus metalens, focusing 500 nm light to point A, 580 nm light to point B, and 660 nm light to point C. We can adjust the incident light the polarization state and using the idea of shared aperture, the designed multi-functional metalens optical tweezers system for OIR is changed to six spectral bands, six focus points formed by two orthogonal circularly polarized lights, realizing the right of Fig. 1. The YZ trap area shown in the lower corner can achieve three-dimensional (3D) trapping of particles with a wavelength/polarization-controlled multifocal metalens without sacrificing numerical aperture (NA).
First, finite difference time domain (FDTD) software performs parameter scanning of the unit structure. The incident light source selects circularly polarized plane light, takes the wavelength of 580 nm in visible light, and uses periodic boundary conditions along the X and Y directions [31]. A perfect matching layer is used along the Z direction [32], and the incident direction is from the substrate to the positive direction of the Z axis. Figure 2(a) shows the unit structure of the metalens. It is placed on a silicon dioxide layer substrate with a period ${P_x} = {P_y} = 450\; nm$. The height $H = 650\; nm$, the long and short axes L and W vary from 50 nm to 400 nm, and elliptical TiO2 nanopillars have a step size of 5 nm. Figure 2(b) shows the results of the ${\varphi _x}$, ${\varphi _y}$ and transmittance (T) obtained after scanning the unit structure. In order to ensure that the metalens has good focusing effect and polarization conversion efficiency, the required unit structure must satisfy that the difference between the absolute values of the ${\varphi _x}$ and ${\varphi _y}$ is close to $\pi $ and the transmittance is as high as possible. According to these two conditions, we selected the unit structure with $L = 365nm$ and $W = 95nm$ as the unit structure of our multifunctional metalens for OIR, and relevant marks are made in Fig. 2.
Fig. 2. (a) Schematic structural diagram of a multifunctional metalens unit for OIR, with height H, period Px, Py, changing long axis L, short axis W, and rotation angle θ along the x-y plane. (b, c, d) Under the selected wavelength of 580 nm, the transmittance T and phase shift ${\varphi _x}$, ${\varphi _y}$. (L = 365 nm, W = 95 nm) when the long and short axes L and W change conditions with a step length of 5 nm. The yellow pentagram highlights the structural parameters of the multifunctional metalens used in our work for OIR.
The proposed design process of single-layer metasurfaces includes multi-focus intensity-tunable design techniques with wavelength and polarization information. In order to obtain the focus distribution of different focuses at different wavelengths, we first use the hyperbolic phase to obtain the single-wavelength focus phase distribution equation [33]:
Among them, ${\varphi _j}({x,y} )$ is the required phase at the $({x,y} )$ position corresponding to the working wavelength, ${\lambda _j}$ is the corresponding wavelength designed for different focus positions $({{x_j},{y_j}} )$, f is the focal length of the metalens we designed, f is 6 $\mu m$, $\lambda $ designed in this article are 500 nm, 580 nm, and 660 nm, and the six different focus points are ($- 4\mu m, - 4\mu m$), (0$, - 4\mu m$), ($4\mu m, - 4\mu m$), ($- 4\mu m,4\mu m$), ($0,4\mu m$), ($4\mu m,4\mu m$). In order to produce multiple focuses in the same focal plane, we use the combined phase profile equation [34]:
Because the metalens we designed contains three spectral information, we take $N = 3$ here, where ${A_j}$ represents the amplitude corresponding to the jth phase. The amplitude factor ${A_j}$ of each phase profile is set to adjust the weight of different wavelengths. For example, maintaining the same conversion efficiency at different wavelengths to construct high-performance devices, or significantly improving the performance of metalens at specific wavelengths. Because the unit structure in this article is obtained by scanning the unit parameters at a wavelength of 580 nm, this will cause differences in the focusing intensity at different wavelengths, and we can adjust the amplitude factor ${A_j}$ to make the focusing intensity roughly the same, laying the foundation for stable and consistent particle capture and sorting later.
In order to obtain a polarization-sensitive metalens, we adopt a Pancharatnam-Berry phase design and change the handedness $\theta $ of the unit structure to satisfy the linear relationship with the phase $\mathrm{\Phi }({x,y} )={\pm} 2\theta ({x,y} )$, when $\theta $ and $\mathrm{\Phi }$ have the same sign, left-rotating light can be focused, and when $\theta $ and $\mathrm{\Phi }$ have different symptoms, right-rotating light can be focused. We can obtain the phase matrices ${\mathrm{\Phi }_R}$ and ${\mathrm{\Phi }_L}$ that satisfy the incident light of RCP and LCP. It is worth noting that when focusing left-handed light, the focus is actually focused by the converted right-handed light, and the directly passing left-handed light component and the right-handed light component in the incident light are scattered into the background. In order to realize a polarization-dependent metalens with switchable focus, this paper uses a random matrix method to randomly generate a binary matrix A, so that the probability of encountering “0” and “1” in the A matrix is equal. By calculating $\mathrm{\Phi } = {\mathrm{\Phi }_R} \odot A + {\mathrm{\Phi }_L} \odot ({1 - \textrm{A}} )$,where ${\odot} $ represents the Hadamard product, a polarization-dependent metalens design can be obtained, which can avoid potential grating diffraction effects [35]. At this point, by randomly combining two transverse dispersion metalens into a single $20\mu m \times 20\mu m$ metalens, a multifunctional metalens with six focal points for OIR can be obtained.
3. Simulation analysis and discussion
3.1 Wavelength and polarization detection
As shown in Fig. 3(a), we can obtain the normalized light intensities of the focal points at six different positions on the focal plane when controlling the incidence of RCP and LCP light at three discrete wavelengths of 500 nm, 580 nm and 660 nm. It can be found that at the focal plane, when specific spectral information and polarization state are incident, there is basically no crosstalk from other information. As shown in Fig. (b), we can calculate the full width at half maxima (FWHM) at the light focus of different spectral information, and the minimum is $0.31\mu m$, which is related to our choice of size for the particle capture radius later on.
Fig. 3. Metalens FDTD calculation results (a) Focusing diagram at the focal plane when the wavelength is selectively incident with different wavelengths and polarization. (b) Different FWHMs are incident on the RCP when the wavelength is 500 nm, 580 nm, and 660 nm. (c) The 580 nm wavelength is different the electromagnetic field intensity distribution diagram of the yz $x = 4\mu m$ plane when $\delta $ is incident. (d) The electromagnetic field intensity distribution diagram of the xz $y = 4\mu m$ plane when different wavelengths are incident when $\delta $=1. (e) The relationship between the normalized intensity of RCP (or LCP) light ${I_{RCP\textrm{}}}$(or ${I_{LCP}}$) and the polarization parameter $\delta $ in the Jones matrix. (f) The normalized intensity of light of different wavelengths and the A, B, C focus on the focal plane relationship.
The metalens we designed can not only determine the polarization states of two circular polarization states, but also characterize the arbitrary polarization ellipticity on the meridian of the Poincare sphere through NLI at the focus points of the RCP and LCP. We define $\delta = ({{I_{RCP}} - {I_{LCP}}} )/({{I_{RCP}} + {I_{LCP}}} )$. When $\delta ={\pm} 1$, it means RCP or LCP. When $\delta = 0$, it means incident the light is linearly polarized. We select the incident light to be 580 nm wavelength to test the elliptical polarization rate. According to Eq. (1) and (2), we can know that two different focus points can appear simultaneously in the Y-axis direction of the focal plane. When RCP is incident, the corresponding focus point of different wavelengths is one of ABC. When LCP is incident, the corresponding focus point is abc (and corresponds to ABC one-to-one). When we take the incident wavelength of 580 nm, the focus distribution result diagram is shown in Fig. 3(c), corresponds to the polarization state of $\delta ={-} 1\textrm{, }0\textrm{, }1$. The adjustment of the ratio of right circularly polarized and left circularly polarized light, which determines the incident light’s elliptical polarization rate, enables the attainment of varying light field intensities at the focal points. In this study, we propose employing this principle in reverse by detecting the light fields at these two specific points. The elliptical polarization rate of the incident light can be obtained by normalizing the intensity. Of course, this is only for a single wavelength. We select the polarization state of the incident light to gradually change the elliptical polarization rate every 15 degrees from RCP to LCP. The simulation results are shown in Fig. 3(e). It can be seen that the focus normalized intensity at position B increases from 0 to 0.5 up to the maximum value, while the opposite is true at b. In practice, the incident polarization state at a certain wavelength band of a metalens can be obtained by detecting two different focal points with arbitrary relative intensities, and this ellipticity tuning strategy is very convenient, efficient, and versatile in the fields of optical tomography techniques, optical data storage, and so on.
Similarly, we perform the related crosstalk analysis and spectral information identification for the wavelength modulation part. As can be seen in Fig. 3(d), crosstalk occurs when different wavelengths are incident because of transverse dispersion, but the focusing intensity at the target focal point is basically higher than that at the other two wavelength crosstalk, and the focusing position is unchanged when wavelength modulation is performed at the set focal plane, so this crosstalk basically does not affect the multifocal selective capture of particles in the later text. Therefore, we can detect different wavelength states of the incident light according to the normalized light field intensity at three points designed in the x direction of the focal plane, we change the wavelength of the incident light from 500 nm to 660 nm at an interval of 20 nm in the RCP state, and detect NLI of the three points of the ABC at the focal plane $Y = 4$, and get the simulation results as shown in Fig. 3(f), we can see that NLI at the three ABC points satisfies the overall trend. Taking B as an example, when the incident wavelength is gradually close to the design wavelength at B, NLI at B gradually decreases and reaches the maximum value at the design wavelength, and vice versa. Because we only have three wavelengths corresponding to 500 nm, 580 nm, and 660 nm as the focal points on the plane $Y = 4$, it is not very effective in detecting the wavelengths in the broadband, the resolution is low, and there is no detecting ability for wavelengths far away from the pre-designed wavelengths. Of course, we can design more working wavelengths in the $Y = 4$ axis of the focus to solve the problem of low resolution spectral detection, we only need to rewrite Eq. (1) and (2), the working band is designed for the desired broadband band, so that N tends to infinity, that is, $Y = 4$ axis can produce N foci, and the spectral information of the incident light can be obtained by analyzing NLI of the N foci. However, this paper does not do this design because it is limited by the wavelength of light, polarization design, and multi-focal metalens particle capture efficiency.
3.2 Multifocal metalens particle capture
When traditional mechanical tweezers are used to clamp objects, the tip of the tweezers must contact the object and apply a certain amount of pressure before the object is clamped and a series of operations are performed. Compared with mechanical tweezers, optical tweezers are a gentle, non-mechanical contact method for gripping and manipulating objects. Particles are affected by two forces in optical tweezers: scattering force and gradient force; scattering force is caused by the impact of photons on cells along the propagation direction of the beam; and gradient force is caused by uneven light field intensity. Along the vertical direction of light propagation, point to the point where the light intensity is maximum.
The numerical calculation of optical force is through the Maxwell stress tensor (MST):
In the system we designed, the stability of particle capture is also one of the things that needs to be discussed. The optical trap stiffness $k\; $ is mainly used to evaluate the stability of particle capture and can be calculated by the following equation:
Among them, F is the optical force, here the maximum $F\; $ is used for calculation, $r\; $ is the position of the particle when F is the maximum value, and ${r_0}$ is the equilibrium point position. The integral displacement of light force along its capture direction can be represented by the potential well U, which can also be used to evaluate the stability of particle capture:
For the focal area of any focused beam, the optical potential well is a 3D physical quantity, and $U(r )$ represents the energy required for particles to move from infinity to position r. In order to obtain a stable optical trap, a trapping potential depth greater than 10${k_B}T$ is usually required to overcome the interference of thermal effects [36,37], where ${k_B}$ is Boltzmann’s constant, T is the temperature of the surrounding environment, here we take $T = \; 300\; K$. The curve shape of the optical potential well U is similar to a trap. It is found that the stable capture point of the particle is located at the minimum of the optical potential well. This also means that the closer the particle is to the minimum of the optical potential well, the more stable the trapped particle will be. Well, that is, it is more difficult for particles to be bound by the light trap force.
In order to obtain a stable trapping potential, the gradient force of a tightly focused beam must balance the scattering force exerted on the particle, and the efficiency of the metalens diffraction is critical for optical tweezers applications. Any light whose polarization is not converted (polarized in the same state as the incident polarization) carries no phase information from the metalens and contributes nothing to the focusing, but only increases the radiation pressure on the particles and reduces the trapping efficiency. The average FWHM of the metalens designed in this paper is 363 nm, and the minimum FWHM of 310nm, so the radius of the particles is set to 150 nm. The numerical aperture is defined as $NA = {n_s} \cdot \textrm{si}{\textrm{n}^{ - 1}}({D/2f} )]$, where D is the size of the metalens we designed, ${n_s}$ is the refractive index of the medium surrounding the metalens. In this paper, the medium environment is air, i.e., ${n_s} = 1$, and the incident optical power is kept at 100 mW, and $NA = 0.86$ is calculated to satisfy the 3D capture operation of particles.
As shown in Fig. 4(a), we first analyze the X-direction light-trapping force on the SiO2 spheres at the corresponding focal points of the RCP incidence at different wavelengths, with the X-axis center coordinates of the focal point design coordinates -4, 0, 4, and carry out the calculation of the light-trapping force in the vicinity of the center coordinates of 1$\mu m$. The light-trapping force change curves in the X-direction on the spheres in different locations are obtained, and it is found that for particles in different locations, all three curves are negative in the $({\textrm{X},\textrm{}0} )$, the light trap force are all 0, indicating that the stable capture point of the particle in the transverse direction happens to be in the middle of the optical axis, when $x > X,$ the values of the transverse light trap force are all negative, proving that when the particle is located above the optical axis, the direction of the transverse light trap force points to the center of the optical axis, and particles in the optical potential trap are attracted to the optical axis of the light beam. Because the transverse light trap force has $x = 0$ as the axis of symmetry, the size of the transverse light trap force on the left and right sides is equal, and the direction is opposite, so when $x < X$, the value of the transverse light trap force is positive, which proves that when the particles are located below the optical axis, the direction of the transverse light trap force is directed to the center of the optical axis, and the particles in the optical potential well are attracted to the optical axis of the light beam. As shown in Fig. 4(b), the corresponding optical potential well plot obtained by calculation, at $x\; = \; X$, the depth of the potential well under the corresponding three wavelengths is 50, 64, and 66 ${k_B}T$, respectively, which indicates that there is a strong transverse gradient force at the focusing place, and that the sphere can be completely captured under the highest light intensity, and we can also see that we have roughly the same effect of trapping the particles under the three discrete wavelengths, which meets the design of Eq. (2) conditions. In Fig. 4 (c, d) we demonstrate the relationship between the magnitude of the optical force ${F_z}$, the depth of the potential well ${k_B}T$ and the displacement in the z-direction for the SiO2 sphere when the RCP enters at different wavelengths, and we can see that the distribution of ${F_z}$ in the z-direction is asymmetric, which is caused by the uneven distribution of the focal intensity in the z-direction, and the intensity of the focal intensity in the direction of the near-superlens will be slightly greater than that in the direction of the focal intensity in the direction of the away from the superlens, but all of them are in the vicinity of $Z = 5.8\mu m$ at three discrete wavelengths, and the potential well depth ${k_B}T$ is larger than 10, so stable 3D trapping of SiO2 spheres at different focal points at different b-wavelength incidence can be realized.
Fig. 4. (a, b) Optical trapping force and potential energy depth distributions of 150 nm SiO2 particles trapped in the X-axis at different wavelengths at their respective focusing positions. (c, d) Optical trapping force and potential energy depth distributions of 150 nm SiO2 particles captured in Z-axis at different wavelengths at their respective focusing positions.
In Fig. 5 (a, b) we demonstrate the graphs of the optical trapping force in the X-direction for SiO2 spheres with different refractive indices versus its corresponding optical potential well at the focusing point at 580 nm RCP incidence, and it can be seen that when the trapped particle is a SiO2 sphere, the ${F_x}$ can be up to 0.48 $pN/W$, while at the refractive index of the particle of 1.1, the ${F_x}$ is only 0.08 $pN/W$. However, both of their capture potentials are all greater than 10${k_B}T$, which can form a stable 3D capture, and can also indicate that the greater the difference in refractive index between the captured particle and its surroundings, the stronger the optical force. Based on the polarization control selective trapping, as shown in Fig. 5(c, d) we simply demonstrate the optical trapping force versus potential trap depth curves at point B in the case of light incident at 580 nm wavelengths with different polarization states, we can find that in $\delta $ is linearly related to ${F_x}$, and we find that at $\delta ={-} 0.5$, the potential trap depth is only 9 ${k_B}T$, which is not able to form a stable 3D trapping. So we can control the different polarization states of the incident light to determine the stable trapping effect of the particles.
Fig. 5. (a, b) Optical trapping force and potential energy depth distributions of particles with different refractive indices trapped in the X-axis at point B for RCP incidence at 580 nm wavelength. (c, d) Optical trapping force and potential energy depth distributions of 150 nm SiO2 spheres captured in X-axis by different $\delta $ incidence at point B at 580 nm wavelength.
In the multifunctional metalens optical tweezer system designed in this paper for optical information recognition, we can not only realize the stable 3D capture of particles and the selective capture of wavelength and polarization information derived from the above analysis, but we can also realize the multi-focused capture of different incident wavelengths and polarization information, Fig. 6 demonstrates the intensity distributions of the metalens in the xz-plane in the focusing state of different wavelengths of the incident light as well as polarization information. We can achieve controllable 3D trapping of particles similar to the multi-trap optical tweezers, which can realize simultaneous manipulation and trapping of multiple SiO2 particles and arrange them into desired patterns. Compared with the metalens optical tweezers array, or the popular phase change material tunable multiwell optical tweezers, our design is more simple and feasible, and we can achieve the controllable multiwell optical tweezers effect by only adjusting the spectral and polarization state of the incident light; this is for the current single-wavelength and single-focus metalens optical tweezers system, and we only need to convert a single-wavelength laser into a continuously tunable laser, which makes the experiments simple and easy to operate, and can further improve the efficiency and practicality of optical tweezers, and provide a new design idea of metalens optical tweezers.
Fig. 6. Focusing state of metalens with different wavelengths of polarized light incident on xy-plane electromagnetic field strength distribution to realize multi-focal point trapping
4. Conclusion
In this study, we discuss the design process of a multifocal metalens that incorporates polarization and wavelength modulation. We propose a design for a multifunctional metalens optical tweezer system aimed at optical information recognition. For optical information detection, we find that the polarization information of a certain wavelength band of the incident light can be accurately obtained by detecting the normalized light intensity at the two focal points, denoted as Aa/Bb/Cc. However, detecting the optical wavelength information of a particular polarization state presents challenges, as our designed wavelength range only has three focal points, limiting the detection capability and accuracy. To address this issue, we propose increasing the number of focal points. Our designed metalens has a high numerical aperture, making it capable of capturing particles in three dimensions. Furthermore, by controlling the incident light's wavelength and polarization information, we demonstrate that different capture effects on particles can be achieved, allowing for selective capture with multiple focal points. While this paper does not include experimental studies due to equipment limitations, the feasibility of our design scheme is assessed through numerical simulation. We believe our research provides a novel approach for realizing multi-dimensional, multi-method, and multi-path lab-on-a-chip particle manipulation.
Funding
The Postgraduate Scientific Research Innovation Project of Hunan Province (CX20230007); National Natural Science Foundation of China (60907003, 61805278, 61875168, 62275269); National Key Research and Development Program of China (2022YFF0706005).
Acknowledgments
The authors would like to thank the support of the laboratory and university.
Disclosures
The authors declare no conflicts of interest.
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.
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