Bessel-modulated autofocusing beams for optimal trapping implementation

Abruptly autofocusing beams were proposed and tested for a variety of applications such as optical manipulation, yet their trapping performance associated with the optical forces and trap stiffness remains largely unexplored. In this work, we design and demonstrate specially modulated autofocusing beams. We theoretically and experimentally show improved properties of such beams and their trapping capabilities as compared to their unmodulated counterparts. In particular, an autofocusing beam tailored with a Bessel function exhibits a shorter focal length and a much stronger peak intensity than that of an unmodulated circular Airy beam. Moreover, we perform optical tweezer experiments using both the modulated and unmodulated autofocusing beams to trap microbeads and red blood cells for direct comparison, and find that the Bessel-modulated beam displays an enhanced trapping capability, thanks to a stronger optical trapping force due to its peculiar intensity landscape. Compared with the conventional circular Airy beams, optical tweezers based on our modulated autofocusing beams exhibit a superior performance, which may lead to new photonic tools for optical trapping and manipulation.

Figure 1

Numerical simulations. Direct comparison of propagation dynamics between (a) a CAB and (b) an MAB. (a1), (b1) are side views of 100-mm-long beam propagation. (a2), (a3) and (b2), (b3) are plots of corresponding beam profiles at locations marked by the dashed vertical lines in (a1) and (b1), respectively. (a3) and (b3) also present the transverse power flow. (c) Peak intensity of CAB and MAB along propagation; (d), (e) radial intensity distribution corresponding to (a2), (b2) and (a3), (b3), respectively. White dotted curves in (a1) and (b1) indicate the trajectories of the innermost ring of the beams. Intensities in (a2) and (b2) are enlarged about 2 times for better visualization.

Figure 2

(a) Peak intensity at the focal point and autofocusing length $f_{\mathrm{z}}$ (inset) with different $r_1$ for MAB [red curve from simulation and black-blue circle calculated from Eq. (3)] and for CAB (blue dotted line). (b) Ray description (thin red line) of MAB overlapping with thick red line and blue dotted circles indicating the trajectories of CAB and MAB in Fig. 1, respectively. (c) Trajectories of MAB and its two components. (d) The transversal gradient forces, (e) transversal scattering forces, and (f) total trapping forces of CAB and MAB at the focusing point.

Figure 3

(a) Experimental setup for optical tweezers based on autofocusing beams. L: lens, SLM: spatial light modulator, DM: dichroic mirror, OL: high NA objective lens, CL: condenser lens, WLS: white light source, CCD: camera, QPD: quadrant photodiode. The inset illustrates a trapped bead under the action of the tweezers. (b), (c) experimentally obtained transverse profiles of (b) a CAB and (c) an MAB at two chosen propagation distances. Intensities in (b1) and (c1) are enlarged about 3 times for better visualization and comparison. (d) Beam profiles of CAB and MAB along the dashed lines in (b2) and (c2). Note that the measurement is performed before the beam enters the objective lens.

Figure 4

(a), (b) Measured power spectra from the optical tweezers showing the trap stiffnesses ${\kappa }_{\mathrm{r}}$ of a 2-μm polystyrene bead for (a) an MAB and (b) a CAB that are presented in the insets. Solid lines describe their relative power spectrum fitting and black dashed lines mark the positions of the corner frequency. (c), (d) Trapping stiffnesses ${\kappa }_{\mathrm{r}}$ for two different beams as a function of input power exerting on (c) a 2-μm polystyrene bead and (d) an $\sim 5\text{−}\mu \mathrm{m}$ RBC. The uncertainties are indicated by the shaded regions. (e)–(i) Calculated transverse trapping force and trap stiffness of the CAB and the MAB based on the full-wave generalized Lorenz-Mie theory and Maxwell stress tensor technique [31] for (e), (f) a polystyrene bead and (g), (i) an RBC. Note that the values in (g) and (i) are normalized by using the maximum values associated with the MAB in (e) and (f), respectively.

Figure 5

(a), (b) Direct comparison of the propagation dynamics of (a) Bessel beams $[\psi \left(r,z=0\right)=A_0{J}_0\left(\frac{r_1-r}{w}\right)$, $r_1=300\mu \mathrm{m}$] and (b) CAB ($r_0=120\mu \mathrm{m}$, $\alpha =0.13$, and $v=-2$, $r_1=r$) with same incident conditions as MAB (1W, $w=24\mu \mathrm{m}$, $\lambda =960\mathrm{nm}$), respectively. (a1) and (b1) are the 100-mm side-view propagation of the beams. (a2), (b2) and (a3), (b3) plot corresponding beam profiles at locations marked by the dashed vertical lines in (a1) and (b1), respectively. (c) Trajectories of CAB and MAB with same radial scale factor, i.e., $w=24\mu \mathrm{m}$. (d), (e) radial intensity distribution and radial gradient forces of Bessel beam, CAB and MAB at the focusing point. Intensities in (a2) and (b2) are enlarged about 2 times for better visualization.