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Imaginary Poynting momentum driven particle bidirectional rotation along arbitrary trajectory

This paper extends the framework of optical rotational manipulation by demonstrating that tightly focused cylindrically polarized structured light fields with arbitrary intensity trajectories can drive microparticles into bidirectional rotation via imaginary Poynting momentum, offering unprecedented spatial control without relying on net angular momentum.

Original authors: Lifang Zhao, Xue Yun, Yansheng Liang, Ming Lei

Published 2026-06-16

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CC BY 4.0

Original authors: Lifang Zhao, Xue Yun, Yansheng Liang, Ming Lei

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine you have a tiny, invisible hand made of light that can grab a speck of gold and spin it around. Usually, to make something spin with light, scientists rely on the light itself "twisting" like a corkscrew (spin) or swirling like a tornado (orbit). But this paper introduces a completely new trick: a "ghost" force that spins things without the light actually twisting at all.

Here is the story of how the researchers did it, explained simply.

The "Ghost" Force (Imaginary Poynting Momentum)

Think of light as a river. Usually, we care about the water flowing downstream (the real momentum) which pushes boats forward. But this paper focuses on a "ghost" current that exists inside the water's pressure, not the flow itself. The scientists call this the Imaginary Poynting Momentum (IPM).

For a long time, physicists thought this "ghost" force was just a math error with no real power. This paper proves it's real and powerful. It acts like a hidden gear mechanism inside the light beam that can grab a particle and spin it, even though the light beam itself has no overall spin or orbit.

The Magic Shape-Shifter

Most light beams are like simple rings or circles. The researchers in this paper did something cooler: they shaped the light into any path you can imagine.

They made light beams shaped like triangles, squares, pentagons, and even open lines (like a "C" shape).
They focused these shapes very tightly onto a tiny speck of gold.

The Two-Track Dance

Here is the most surprising part. When they shone this shaped light on a gold particle, the particle didn't just spin in one direction. It created a two-way dance:

The Inner Track: If a particle gets trapped on the inside edge of the light shape, it spins one way (like clockwise).
The Outer Track: If a particle gets trapped on the outside edge of the same light shape, it spins the opposite way (counter-clockwise).

It's like a conveyor belt where the inner lane goes forward and the outer lane goes backward, all powered by the same "ghost" force.

The Remote Control

The researchers found a simple "remote control" to switch the direction of this spin. By turning a special crystal (a wave plate) in their setup, they could flip the polarization angle.

Turn it one way: The inner particle spins clockwise, the outer spins counter-clockwise.
Turn it the other way: They instantly swap directions.

This means they can control exactly which way the particles spin just by adjusting the "color" of the light's polarization, without needing the light to carry any actual spinning energy.

The Experiment

To prove this wasn't just a computer simulation, they built a real lab setup using:

A laser (1064 nm wavelength).
A special screen (SLM) that acts like a digital lens to draw the shapes (triangles, squares, etc.) in the air.
A high-powered microscope lens to focus the light.
Tiny gold balls (about the width of a human hair).

They filmed the gold balls moving. The video showed the balls perfectly following the light's shape. When they were on the inside of the shape, they rolled one way; on the outside, they rolled the other. When the researchers flipped the switch, the balls instantly reversed their direction.

The Big Takeaway

This research shows that we don't need "twisting" light to make things spin. We can use this "ghost" force (IPM) to create a custom-made optical track. We can trap particles on the inside or outside of any shape we draw with light and make them spin in opposite directions, all controlled by a simple dial. It's like having a light-based steering wheel that can drive tiny particles along any path you draw, spinning them in perfect sync.

Technical Summary: Imaginary Poynting Momentum Driven Particle Bidirectional Rotation Along Arbitrary Trajectory

Problem Statement
Optical rotational manipulation has traditionally relied on the transfer of Spin Angular Momentum (SAM) or Orbital Angular Momentum (OAM) from light to matter. While structured beams have expanded the scope of optical tweezers, recent theoretical and experimental work has highlighted the mechanical effects of the Imaginary Poynting Momentum (IPM). However, previous investigations into IPM-driven dynamics have been largely confined to cylindrically polarized Gaussian beams, annular beams, or evanescent fields. A significant gap exists in understanding and utilizing IPM forces within tightly focused structured light fields that possess closed or open arbitrary-intensity trajectories. The challenge lies in elucidating whether IPM can drive bidirectional rotational motion along complex, user-defined paths without relying on SAM or OAM, and in experimentally realizing such control.

Methodology
The authors employed a combined theoretical and experimental approach to investigate IPM-mediated particle rotation:

Theoretical Framework: The study utilizes the Richards-Wolf vectorial diffraction integral theory to model the tightly focused electric and magnetic fields of cylindrically polarized vector beams with arbitrary intensity trajectories (including ring, ellipse, triangle, square, and pentagon shapes, as well as non-closed paths). The complex Poynting vector is decomposed into its real and imaginary parts to analyze momentum density. The optical forces acting on 4 μm diameter gold microparticles were calculated using the T-matrix method, considering a wavelength of 1064 nm and a high numerical aperture (NA = 1.33).
Experimental Setup: The experimental configuration utilizes a free-space lens modulation system. A linearly polarized laser (1064 nm) is converted into a cylindrically polarized vector beam using a vortex half-wave retarder (VHW) and a spatial light modulator (SLM) that generates a digital lens hologram. The beam is tightly focused by a high-NA oil-immersion objective (NA 1.45) onto a sample containing gold nanoparticles. Particle motion is recorded via a CMOS camera. The polarization angle ( $\alpha$ ) is controlled to modulate the IPM flow direction.

Key Contributions

Extension of IPM Framework: The work extends the application of IPM-driven manipulation from standard Gaussian/annular beams to tightly focused arbitrary-trajectory structured light fields.
Mechanism Elucidation: The study systematically characterizes the rotational dynamics induced by IPM in generic cylindrically polarized vector fields, demonstrating that azimuthal forces arise solely from the imaginary part of the Poynting vector, independent of SAM and OAM.
Bidirectional Control: The research establishes a method to drive microparticles into bidirectional rotation along predefined trajectories. By adjusting the polarization angle ( $\alpha$ ), the direction of the azimuthal force can be reversed, allowing for control over the rotation direction of particles trapped on opposite sides of the trajectory.

Results

Theoretical Simulations:
- Simulations of tightly focused beams with ring, triangle, square, and pentagon shapes reveal that the real part of the Poynting vector is primarily longitudinal, while the IPM is confined to the transverse plane.
- The IPM flow exhibits opposite directions on the inner and outer sides of the intensity trajectory. For a polarization angle of $\alpha = -45^\circ$ , the azimuthal IPM component is maximized.
- Force calculations show stable trapping positions on both the inner and outer sides of the trajectory where the radial force is zero and the gradient is negative. At these equilibrium points, the azimuthal forces are equal in magnitude but opposite in direction. For example, in a ring trajectory at $\alpha = -45^\circ$ , the inner azimuthal force is approximately 0.966 pN, while the outer is -0.759 pN.
- Similar bidirectional driving capabilities were observed for non-closed (open) arbitrary trajectories, although the force magnitudes on the two sides were found to be unequal due to trajectory curvature and endpoint effects.
Experimental Verification:
- Experiments using gold nanoparticles (3–5.5 μm) confirmed the theoretical predictions.
- In closed arbitrary trajectories (ring, triangle, square, pentagon), particles trapped on the inner and outer sides of the beam rotated in opposite directions. Reversing the polarization angle from $+45^\circ$ to $-45^\circ$ reversed the rotation direction of both particles.
- In non-closed trajectories, particles were successfully trapped and transported along the sidewalls of the trajectory. The direction of transport was controlled by the polarization angle, with particles on opposite sides moving in opposite directions.
- The experimental observations of bidirectional rotation and polarization-controlled directionality aligned closely with the theoretical force maps.

Significance
The paper claims that this work advances the fundamental understanding of momentum transfer mechanisms in complex structured light fields. By demonstrating that IPM can drive robust, bidirectional orbital rotation along arbitrarily tailored paths without the need for SAM or OAM, the study establishes IPM as a novel degree of freedom in optical micromanipulation. The authors posit that this IPM-mediated optical spanner offers unprecedented spatial degrees of freedom, paving the way for high-precision rotational manipulation along user-defined trajectories. This capability provides a robust pathway for realizing reconfigurable bidirectional optical tools, expanding the functional scope of optical tweezers beyond conventional intensity-gradient-based trapping.