Unravelling 3D Dynamics and Hydrodynamics during Incorporation of Dielectric Particles to an Optical Trapping Site

Abstract

Mapping of the spatial and temporal motion of particles inside an optical field is critical for understanding and further improvement of the 3D spatio-temporal control over their optical trapping dynamics. However, it is not trivial to capture the 3D motion, and most imaging systems only capture a 2D projection of the 3D motion, in which the information about the axial movement is not directly available. In this work, we resolve the 3D incorporation trajectories of 200 nm fluorescent polystyrene particles in an optical trapping site under different optical experimental conditions using a recently developed widefield multiplane microscope (imaging volume of 50 × 50 × 4 μm³). The particles are gathered at the focus following some preferential 3D channels that show a shallow cone distribution. We demonstrate that the radial and the axial flow speed components depend on the axial distance from the focus, which is directly related to the scattering/gradient optical forces. While particle velocities and trajectories are mainly determined by the trapping laser profile, they cannot be completely explained without considering collective effects resulting from hydrodynamic forces.

Keywords: 3D imaging; hydrodynamics; multiplane widefield microscopy; optical field; optical trapping; particle tracking.

Figure 1

Schematic of the multiplane widefield microscope with an optical tweezer unit. The trapping laser and the proprietary prism are the two main components that differ from conventional widefield microscopes. The main axis of the prism acts as a beam splitter and splits the light 3 times, which results in 2³ (8) imaging planes, thereby yielding a total volume of 50 × 50 × 4 μm³ acquired simultaneously. The position of the planes was determined by calibration using a sample of 200 nm beads spin-casted on a coverslip (see Materials and Methods for a full description of the home-built multiplane widefield microscope).

Figure 2

Incorporation of individual fluorescent nanoparticles in the trapping site. (a) 3D traces of all the trapping events acquired from 150 independent videos. The focal spot (i.e., trapping site) was localized approximately at z = 0 μm. (b) Representative incorporation trajectories going through the inner and outer cones (red and blue lines, respectively). (c) Distribution of 3D flow speed vectors for incorporation of the particles. The length of the arrow and its color denotes the magnitude of the speed/optical force vector.

Figure 3

(a) A representative incorporation trace flowing through the external cone. As a visual aid (gold line), the trajectory is smoothed using a third-order Savitzky–Golay filter. The color scale denotes the time scale. (b) Relative distance between the previous trace and the smoothed trace in the x and y directions (red and blue lines, respectively).

Figure 4

Images of the average concentration field c(x,y), 1064 nm laser reflection intensity, radial flow speed v_r(x,y), axial flow speed v_z(x,y), and optical force F(x,y) for six different depth sections. The length of the scale bar is 2 μm. The optical conditions are the following: laser power after the objective, 36 mW; NA, 1.20 (60× water immersion objective); circularly polarized laser.

Figure 5

Average concentration field c(x,y) for three different laser polarizations (linear horizontal, lineal vertical, and circular) for different depth sections. The length of the scale bar is 2 μm. As a visual aid, we have saturated the color scale to show only high-concentration regions and included dashed lines at the regions where the c(x,y) field is larger (see Figure S5 for unsaturated color scale from 0 to 0.01 NP/μm³).

Figure 6

Average concentration field c(r,z) for different effective NA conditions. The effective NA is modified by changing the trapping laser beam size through an iris diaphragm. The length of the scale bar is 2 μm.

Figure 7

NP flux analysis for different trapping laser powers (36, 60, 120, and 240 mW). (a) NP flux map J(r,z). (b) NP flux variation along the radial coordinate for two different depth sections: top (z = −1.0 μm), bottom (z = −3.5 μm). Both internal (blue) and external (red) NP channels are fitted using a Gaussian function. (c,d) Maximum flux dependence with the trapping laser power for both internal (red) and external (blue) NPs channels at a depths of −1.0 and −3.5 μm (c and d, respectively). Numbers beside the dashed lines indicate the exponents of the best fit to power laws for the inner channel (red) and outer channel (blue). The length of the scale bar is 1 μm.