Tailored optical propulsion forces for controlled transport of resonant gold nanoparticles and associated thermal convective fluid flows

The study explores light-induced manipulation of micro- and nanoscale objects using structured optical fields that combine intensity-gradient (trapping) and phase-gradient (propulsion) forces. Building on advances in optical tweezers and phase-tailored beams, the work targets resonant metal nanoparticles (NPs), which, when illuminated near their plasmon resonance, act as efficient nanoscale heat sources. Such optothermal behavior underpins applications in therapy, imaging, and optofluidics. Prior efforts have demonstrated phase-gradient control for particle transport, assembly of optical matter, and rotation/transport in vortex traps, as well as optofluidic flows driven by fixed plasmonic heaters, where mechanisms include natural convection and temperature-induced Marangoni flows associated with nanobubble formation. The research questions here are twofold: (1) Can single and multiple resonant gold nanoparticles (200 nm radius) be transported stably with programmable speed using tailored transverse phase-gradient forces in a 2D optical trap? (2) Can the motion of multiple heated nanoparticles—forming a moving, controllable heat source—induce and control convective fluid flows, and can the size (and temperature) of this moving heater be tuned via nonuniform optical propulsion to split or merge assemblies? The motivation is to create versatile, programmable microscale optofluidic tools by uniting resonant optical heating with robotic-like optical transport.

Classical optical tweezers use intensity-gradient forces for confinement and have broad applications in biology, materials, and light–matter studies. Structured beams enabling phase-gradient forces allow propulsion and complex transport, including optical vortex rings and freestyle traps for 3D programmable routes. Optical matter and electrodynamic binding of particles have been studied under combined intensity/phase gradients. For optofluidics, resonant plasmonic structures generate localized heating that can induce fluid motion via natural convection, with speeds influenced by chamber geometry and substrate properties; periodic plasmonic arrays have produced short-range convection (~1–10 µm/s with absorbing substrates). Large temperature rises (ΔT ~70–250 K) can trigger temperature-induced Marangoni flows at the water/superheated-water interface due to nanobubbles, achieving 15–30 µm/s with single heated gold spheres (~100 nm). Above microbubble thresholds (~580 ± 20 K), strong long-range Marangoni convection enables lithographic NP deposition. Other mechanisms like thermophoresis and Seebeck effects are noted but beyond this study’s scope. Prior work largely used fixed plasmonic substrates; dynamic, controlled moving heat sources have been less explored.

Experimental platform: A freestyle laser trap generated by a circularly polarized polymorphic beam at λ0 = 532 nm is used to create a ring trap of radius R = 4 µm with uniform intensity, positioned ~200 nm above a glass coverslip for axial confinement of resonant gold nanoparticles (spheres, radius 200 nm) in water. The tangential optical propulsion force FI(R,φ) ∝ I(R) · (∂φ/∂φ) with (∂φ/∂φ) = ψ(φ)/(R k0), k0 = 2π/λ0, is tailored via the phase profile along the ring. Phase-gradient designs (three traps): - Uniform ξ-trap: constant phase gradient (∂φ/∂φ) = 0.07 around the ring. - 2-sector ξ1,2-trap: two azimuthal sectors with constant gradients: Φ1 ∈ [0, π), ξ1 = 0.04; Φ2 ∈ [π, 2π), ξ2 = 0.1. - ξ(φ)-trap: a linearly increasing phase gradient ∂φ/∂φ ∝ φ over φ ∈ [0, 0.13], with overall topological charge m = 20 (clockwise motion). Illumination conditions: For the uniform ξ-trap, input power P = 40 mW yields irradiance I = 0.54 mW/µm². For the 2-sector ξ1,2-trap and ξ(φ)-trap, I = 0.73 mW/µm². Trapping stiffness (radial) measured as 1.3 pN/µm. Particle tracking and analysis: NP positions are tracked over time (e.g., 20 s segments) to extract tangential speed vφ = R dφ/dt and its statistics. Speed histograms and temporal profiles are analyzed; Savitzky–Golay filtering is used for smoothed speed curves. Kinetic diagrams in polar coordinates (time as radial coordinate, angular position φ(t) as angle) visualize instantaneous tangential speed vt(t). Numerical simulation: NP dynamics are simulated including Brownian thermal noise to reproduce random position fluctuations and predict mean speed and standard deviation for each phase-gradient configuration. The propulsion scales with I · phase gradient; viscosity reduction due to NP heating is included. Estimated temperature rises for the resonant NP: ΔT ~31 K (uniform ξ-trap) and ΔT ~40 K (2-sector and ξ(φ) traps). Multi-particle and optofluidic observations: Experiments also probe multiple resonant NPs within the same traps, observing self-assembly into quasi-stable groups that act as moving heat sources. Tracer particles are used to confirm induced convective flows toward the assembly. Nonuniform propulsion profiles are applied to demonstrate controllable splitting and merging of NP groups, thereby tuning assembly size and temperature.

- Demonstration of controlled optical transport of single resonant gold nanoparticles (radius 200 nm) around a 4 µm-radius ring using tailored transverse phase-gradient forces at 532 nm, with stable axial confinement near a coverslip (~200 nm). - Uniform ξ-trap (constant phase gradient 0.07): Experimental mean tangential speed ⟨vφ⟩ = 7 µm/s with standard deviation 3 µm/s at I = 0.54 mW/µm²; simulation predicted ⟨vφ⟩ = 9.4 µm/s with 3 µm/s standard deviation. Brownian thermal noise explains observed speed fluctuations; simulation matches trends. - 2-sector ξ1,2-trap (ξ1 = 0.04 in [0, π), ξ2 = 0.1 in [π, 2π)): Distinct speeds in each sector at I = 0.73 mW/µm²: experimental ⟨vφ1⟩ = 7 µm/s and ⟨vφ2⟩ = 20 µm/s (both ±3 µm/s), giving a 2.86× speed increase; simulation predicted a 2.47× increase (⟨vφ1⟩ = 7.35 µm/s, ⟨vφ2⟩ = 18 µm/s). - ξ(φ)-trap: The NP speed increases approximately linearly with azimuthal angle, vφ(φ) ∝ φ, in agreement with simulations, demonstrating programmable speed profiles via tailored phase gradients. - Thermal effects: Resonant absorption leads to estimated NP temperature rises of ~31 K (uniform) and ~40 K (2-sector and ξ(φ)), reducing local water viscosity and contributing to higher speeds at higher irradiance. - Multiple-NP dynamics: Heated resonant NPs self-organize into quasi-stable assemblies that move under the same propulsion control. These assemblies act as moving nanoscale heat sources that induce convective fluid flows, dragging tracer particles toward them in the trap plane. The flows are consistent with temperature-induced Marangoni effects at the liquid water/superheated water interface. - Assembly control: A nonuniform optical propulsion force enables splitting or merging of NP groups, providing a mechanism to control assembly size and, consequently, local temperature.

The experiments confirm that tailored phase-gradient forces enable precise, programmable control of the motion and speed of resonant gold nanoparticles in a ring trap, addressing the first research goal. The close agreement between measured and simulated speed profiles across uniform, two-level, and linearly varying phase gradients validates the design framework that links propulsion to the product of intensity and phase gradient, while accounting for Brownian fluctuations and viscosity changes due to heating. Extending to multiple particles, the observation that hot nanoparticles form quasi-stable, optically driven assemblies that function as moving heat sources meets the second goal. The induced convective flows, evidenced by tracer migration toward the assemblies, suggest that temperature-induced Marangoni effects at local water/superheated water interfaces are active; thus, optical propulsion indirectly controls microfluidic motion by steering the location and speed of the heat source. The ability to split and merge assemblies via designed nonuniform propulsion adds a further layer of functional control over local temperature fields and associated fluid dynamics, pointing toward programmable micro-optofluidic operations such as targeted mixing, transport, or localized actuation.

This work demonstrates programmable optical transport of single and multiple resonant gold nanoparticles using tailored transverse phase-gradient forces in a ring trap, with experimentally validated control of particle speed and trajectory. Multiple heated nanoparticles self-assemble into movable groups that act as controllable nanoscale heat sources, inducing convective flows that draw in tracer particles. By engineering nonuniform propulsion, the size (and temperature) of these assemblies can be dynamically tuned through splitting or merging. These results establish a pathway to versatile, reconfigurable micro-optofluidic tools that couple resonant optical heating with robotic-like optical manipulation. Future research can refine quantitative control over flow fields, explore broader trap geometries and trajectories, investigate different particle sizes and materials, and elucidate thermal–fluid mechanisms (including thresholds for nanobubble formation and Marangoni transitions) to further enhance performance and functionality.