Designing Coherent Optical Environment for Dynamic Optical Manipulation with a Simple Control Beam

Abstract

We propose a framework for designing coherent optical environments that enable versatile and dynamic optical manipulation. In contrast to conventional material-based near-field platforms, our approach employs a structured coherent light field -- optimized via a back-propagation-based inverse design algorithm -- as the manipulation environment. This light-based platform allows a simple control beam, such as a single plane wave or a low-numerical-aperture Gaussian beam, to steer micro-objects effectively. By establishing a one-to-one correspondence between control beam parameters (e.g., phase/polarization of a plane wave) and particle trapping positions, our method enables real-time and versatile control of particles. A wide range of two- and three-dimensional trajectories -- including circles, squares, tree-like paths, and epicycle-deferent curves -- can be achieved solely by modulating the phase of the control beam. This design strategy for the structured-light environments offers a dynamically reconfigurable, all-optical, and contact-free platform for advanced optical manipulation in free space, with promising applications in nanorobotics, biological probing, and beyond.

Figures (4)

• Figure 1: (a) The electromagnetic energy density $w_\text{e}$ distribution (color map) and the corresponding in-plane optical force $\boldsymbol{F}_\text{e}$ (overlaid vectors) at $z=0$ plane generated by the optimized coherent optical environment (a designed structured-light) schematically represented by the orange conical-shaped arrow. This environment is designed via back-propagation algorithm to interfere with a single plane wave (control beam) for trapping the particle at arbitrary positions within a square region by phase modulation of the control beam. (b) Total electromagnetic energy density $w_\text{t}$ distribution (color map) and the corresponding in-plane optical force $\boldsymbol{F}_\text{t}$ (overlaid vectors) produced by the interference of the coherent optical environment shown in (a) and a plane-wave control beam (shown schematically by the green arrow) with polarization phase $\varPhi_p = -\varPhi_q = -\pi/3$, see, Eq. \ref{['eq2']}. (c) Three representative cases demonstrating the dynamic "phase-to-position transducer" effect, where the in-plane trapping position $(x, y)$ is determined by the plane-wave control beam. By dynamically adjusting the phase, the particle can be smoothly repositioned along arbitrary trajectories within the region of $8r_{\text{s}}\times 8r_{\text{s}}$ centered at the origin $(x,y)=(0,0)$. The displayed results correspond to $(\varPhi_p, \varPhi_q)=(0.6\pi,0.2\pi), (0.0\pi,-0.5\pi), (-0.3\pi,0.3\pi)$ (top to bottom). Also shown are $w_{\text{t}}$ distribution (color map) and schematic plots of the control beam. (d) Optical potential $U_\text{g}$ and total optical force $\boldsymbol{F}_\text{t}$ exerted on the particle for $\varPhi_p=\varPhi_q=\pi$. The potential minima (red dots) and trapped sites from molecular statics analysis (cyan dots) are shown. The slight discrepancy arises because the optical force consists of both the conservative and non-conservative components Sukhov2017jiang2016decompositionWOS:000486622300012zheng2020decompchiral.
• Figure 2: Two schemes for particle manipulation along a predefined ring-shaped trajectory (white dashed line) using control beams (schematically represented by green arrows) propagating in $\hat{\boldsymbol{z}}$, Case I (a-c), and in $-\hat{\boldsymbol{z}}$, Case II (d-f). In both cases, the coherent structured-light environments (orange conical arrows) consist of plane waves with positive $k_z$ components. (a, d): The energy density profiles $w_\text{e}$ (color map) of the optimized environment for Cases I and II, respectively. Overlaid vectors represent in-plane optical forces $\boldsymbol{F}_\text{e}$ generated by the optical environment, demonstrating particle confinements near the target trajectories. (b, e): The "control-induced" optical forces $\boldsymbol{F}_\text{c} \equiv \boldsymbol{F}_\text{t} - \boldsymbol{F}_\text{e}$, where $\boldsymbol{F}_\text{t}$ is the total force from the combined field of the environment and the control beam. The forces $\boldsymbol{F}_\text{c}$ are decomposed into gradient ($\boldsymbol{F}_\text{c}^{\text{grad}}$) and scattering ($\boldsymbol{F}_\text{c}^{\text{scat}}$) components, normalized by $f = \max\left( \left| \boldsymbol{F}_\text{c}^\text{grad} \right|, \left| \boldsymbol{F}_\text{c}^\text{scat} \right| \right)$. (c, f): The energy density $w_\text{t}$ and in-plane optical force $\boldsymbol{F}_\text{t}$ generated by the total field. Both schemes achieve stable in-plane trapping at $(x,y)=(5 r_{\text{s}},0)$ for $\varPhi=0$, but rely on the gradient (Case I) and scattering (Case II) forces, respectively.
• Figure 3: Phase-controlled optical manipulation along three distinct trajectories using the co-propagating configuration with linear polarization ($E_y=0$) for both control beams and structured-light environments. (a, d): Ring-shaped trajectory: (a) Optimized structured-light environment intensity $w_\text{e}$ distribution; (d) Phase-position mapping. (b, e): Smoothed-corner square trajectory: (b) $w_\text{e}$ profile; (e) Phase-controlled positioning. (c, f): Tree-shaped trajectory: (c) $w_\text{e}$ distribution; (f) Phase-based positioning result. All particle positions are computed via molecular statics analysis. The spheres in (d-f) show trapping sites for $\varPhi=\pi/3$.
• Figure 4: Three-dimensional (3D) phase-to-position control of particle along an epicycle-deferent trajectory. The 3D rendering shows particle positions (color-coded by $\varPhi$) and three orthogonal plane projections, demonstrating full 3D position control by modulating control beam's phase $\varPhi$. All positions are computed via molecular statics analysis of total optical force from combined field.