One-dimensional photonic crystal enhancing spin-to-orbital angular momentum conversion for single-particle tracking

Abstract

Single-particle tracking (SPT) is an immensely valuable technique for studying a variety of processes in the life sciences and physics. It can help researchers better understand the positions, paths, and interactions of single objects in systems that are highly dynamic or require imaging over an extended time. Here, we propose an all-dielectric one-dimensional photonic crystal (1D PC) that enhances spin-to-orbital angular momentum conversion for three-dimensional (3D) SPTs. This well-designed 1D PC can work as a substrate for optical microscopy. We introduce this effect into the interferometric scattering (iSCAT) technique, resulting in a double-helix point spread function (DH-PSF). DH-PSF provides more uniform Fisher information for 3D position estimation than the PSFs of conventional microscopy, such as encoding the axial position of a single particle in the angular orientation of DH-PSF lobes, thus providing a means for 3D SPT. This approach can address the challenge of iSCAT in 3D SPT because DH-PSF iSCAT will not experience multiple contrast inversions when a single particle travels along the axial direction. DH-PSF iSCAT microscopy was used to record the 3D trajectory of a single microbead attached to the flagellum, facilitating precise analysis of fluctuations in motor dynamics. Its ability to track single nanoparticles, such as 3D diffusion trajectories of 20 nm gold nanoparticles in glycerol solution, was also demonstrated. The DH-PSF iSCAT technique enabled by a 1D PC holds potential promise for future applications in physical, biological, and chemical science.

Fig. 1

The 1D PC enhances the spin-to-orbital angular momentum conversion of the scattered light from a single particle. a Schematic of the spin-to-orbit angular momentum conversion for scattered light from a single particle under illumination by a circularly polarized beam. This particle can be placed on a glass or 1D PC substrate. The inset shows the structure of the 1D PC. Calculated far-field angular-dependent intensity distributions (BFP image) of the total scattered light (E_scat-Total) from a single particle when the particle was placed on a glass (b) or 1D PC substrate (d), and the wavelength of the incident light was 635 nm. Calculated far-field angular-dependent intensity distributions (BFP image) of the RCP-scattered light (E_scat-RCP) for the particle on the glass (c) or 1D PC substrate (e). f Calculated angular-dependent transmittance through the glass and 1D PC substrate, where θ is the incidence angle with respect to the direction normal to the substrate. NA = n*sin θ, where n is the refractive index

Fig. 2

Single-particle imaging via DH-PSF iSCAT microscopy. DH-PSF iSCAT images for a particle on the glass substrate when the incident light and the detected light are of identical circular polarization (a) or nearly orthogonal polarization (b), (c, d) for a particle on the 1D PC substrate. e, f Simulated intensity (I_scat) and spatial phase (ϕ_scat) distributions of the forward-scattered light from a single particle. g, h Simulated intensity (I_inter) and phase (ϕ_inter) distributions of the interference field between the scattered light from the particle and the nonscattered transmitted light, which corresponds to the iSCAT image in (d). Scale bars in (a), 1 µm

Fig. 3

Axial tracking of single particles via DH-PSF iSCAT microscopy. a–c iSCAT images of the same particle at three different axial positions (Z-axis), (d) typical calibration curve of the angle between two lobes on (a–c) with respect to the axial position measured with a piezo-controlled stage. e–h Simulated DH-PSF iSCAT images and the corresponding calibration curve. Scale bars on (a, e), 1 µm

Fig. 4

3D motion tracking of the particle attached to the filament stub of a living bacterium. a Schematic view of the sample. A living bacterium was adhered to the 1D PC substrate with a particle (500 nm in diameter) attached to the filament stub that rotated on an approximately circular trajectory. b 3D trajectories of the particle observed by DH-PSF iSCAT microscopy. c, d The projected trajectories on the X-Y and X-Z planes. e Graph of the 3D spatial position (X, Y, Z) of a particle changing over time

Fig. 5

3D single nanoparticle tracking with DH-PSF iSCAT microscopy. a The simulated image shows the ratio of the angular-dependent electric field intensity between the RCP radiation light and the total radiation light from an electric dipole that is placed on a 1D PC. b Raw DH-PSF iSCAT image of a single 20 nm Au nanoparticle. c Resulting ratiometric image of a 20 nm Au particle obtained by subtracting the background without particles. d The calibration curve of the angular orientation vs. axial position of the Au nanoparticle. e Representative trajectory of a single 20 nm Au nanoparticle in glycerol solution with a duration of 1.8 s and an exposure time of 1 ms. f Plots of the mean-square displacement (MSD) in r and z versus diffusion time (blue for r, pink for z) for a nanoparticle’s trajectory over 1 s. The thin lines show the MSD extracted from each individual trajectory. The thick circles and lines show the weighted average and a linear fit to the MSD for displacements r and z, respectively

Fig. 6

Simulated PSF images of standard iSCAT microscopy and DH-PSF iSCAT microscopy. a1–a6 Standard PSF image of iSCAT working in reflection mode; (b1–b6) standard PSF image of iSCAT working in transmission mode (also named COBRI); (c1–c6) DH-PSF iSCAT image. The imaged object is a single polystyrene particle with a diameter of 100 nm. The three rows of images are recorded when this single nanoparticle moves axially within a range of 1 μm near the DOF of the imaging objective lens (100 X, NA 1.49). The axial distance traveled by the nanoparticle on adjacent images is 200 nm. Scale bar, 1 µm. The right color bars denote the imaging contrast, whose definitions are given in the Materials and methods section