Viscoelastic dynamics of nanoparticles optically trapped in moving fringe pattern in air-filled hollow-core fiber

We report optical trapping and transport of nanoparticles in a moving interference pattern in hollow-core photonic crystal fiber at atmospheric pressure, when competition between trapping and drag forces causes the particle velocity to oscillate as it is momentarily captured and accelerated by each passing fringe, followed by release and deceleration by viscous forces. As a result the average particle velocity is lower than the fringe velocity. We refer to this phenomenon as drag-trapping. An analytical model of the resulting motion shows excellent agreement with experiment. Additional control is possible by introducing an imbalance in the backward and forward powers. The high precision of this new technique makes it of interest for example in characterizing nanoparticles, exploring viscous drag forces in different gases and liquids, and temperature sensing.

💡 Research Summary

In this work the authors demonstrate a novel method for trapping and transporting silica nanoparticles inside a hollow‑core photonic crystal fiber (HC‑PCF) filled with air at atmospheric pressure. By launching two counter‑propagating 1064 nm continuous‑wave laser beams into the fiber and imposing a controllable frequency detuning via a Pockels phase modulator, a moving interference pattern (fringe) is created along the fiber axis. The fringe spacing is set by the vacuum wavelength and the effective modal index of the core mode, while the fringe velocity is directly proportional to the applied frequency offset.

Nanoparticles of nominal diameter ≈195 nm are introduced into the fiber core using an ultrasonic nebulizer; individual particles are captured at the fiber entrance with an external tweezer and then launched into the hollow core. Inside the fiber the particles experience three main forces: (i) a gradient force arising from the intensity gradient of the standing‑wave fringe, which pulls the particle toward the intensity maximum; (ii) a radiation‑pressure force that appears when the forward and backward beam powers are unbalanced, pushing the particle away from the fringe centre; and (iii) a viscous drag force due to the surrounding air, which is modeled using Sutherland’s temperature‑dependent viscosity together with a Cunningham correction to account for finite Knudsen numbers.

When the fringe moves, the particle is periodically captured by a fringe, accelerated by the gradient force, and then dragged toward the fringe edge by the viscous drag. If the drag exceeds the restoring gradient force, the particle slips out of the current fringe and is captured by the next one. This “drag‑trapping” cycle repeats, leading to an average particle velocity that is systematically lower than the imposed fringe velocity. The authors develop a nonlinear damped harmonic‑oscillator model for the axial motion in the frame moving with the fringe. In the high‑damping regime (at atmospheric pressure) the inertial term can be neglected, yielding an analytical solution that predicts the particle’s position as a function of time, the critical fringe velocity at which stable trapping breaks down, and the dependence on the power‑imbalance parameter.

Experimental validation is performed by monitoring side‑scattered light with a fast video camera and an InGaAs photodiode. For a fringe velocity of 4.79 mm s⁻¹ the measured particle velocity is 2.2 mm s⁻¹, in excellent agreement (within 5 %) with the analytical model. By deliberately introducing a forward‑backward power imbalance (up to a few percent) the authors demonstrate controlled displacement of the particle within a fringe, confirming the role of the radiation‑pressure term. Low‑pressure measurements (≈12 mbar) reveal thermally driven axial resonances at ~39 kHz, matching the theoretical axial trap frequency derived from the gradient‑force model.

The paper thus provides a comprehensive quantitative description of the interplay between optical gradient forces, radiation pressure, and viscous drag in a moving interference pattern inside a HC‑PCF. It establishes that, even at atmospheric pressure, stable optical trapping and controlled transport of sub‑200 nm particles over centimeter distances are feasible. The technique opens new avenues for long‑range manipulation of nanoparticles in gases or liquids, precise viscosity and temperature sensing via the particle’s dynamical response, and the study of nonlinear optomechanical phenomena in a low‑loss, diffraction‑free waveguide environment.