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Absolute measurement of the intrinsic helicity in nanophotonics

This paper demonstrates both theoretically and experimentally that the intrinsic helicity of chiral nanophotonic systems can be rigorously defined and measured by exciting them with a focused electron beam and symmetrizing the excitation and detection geometry, thereby overcoming the limitations of traditional circularly polarized light-based methods.

Original authors: Malo Bézard, Simon Garrigou, Jérémie Béal, Andreas Horrer, Yves Auad, Hugo Lourenço-Martins, Davy Gérard, Mathieu Kociak

Published 2026-05-26

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CC BY 4.0

Original authors: Malo Bézard, Simon Garrigou, Jérémie Béal, Andreas Horrer, Yves Auad, Hugo Lourenço-Martins, Davy Gérard, Mathieu Kociak

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, twisted piece of jewelry. In the world of chemistry and biology, we call this "chiral." It's like your left hand and your right hand: they look similar, but you can never stack them perfectly on top of each other. This "handedness" is crucial because it determines how these tiny objects interact with the world, including how they react to light.

For a long time, scientists have had a reliable way to measure this handedness in molecules floating in a liquid. But when they tried to measure it in tiny, engineered metal structures (called nanophotonics), things got confusing. The usual tools gave mixed signals, sometimes saying a straight, non-twisted object was twisted, or failing to detect the twist in a clearly twisted object. It was like trying to weigh a feather with a scale designed for elephants; the tool just wasn't right for the job.

The Problem: The "Twist" was Hiding
The researchers in this paper realized that the problem wasn't the objects; it was how they were looking at them. When you shine a light (or in this case, a beam of electrons) on a tiny metal structure, it glows. If the structure is "twisted" (chiral), the light it glows with should spin in a specific direction (like a corkscrew).

However, because these structures are so small and the measurement tools only catch light from one side (like looking at a sphere through a small window), the "twist" gets scrambled. The researchers found that the "handedness" of the light was being canceled out or hidden by the way the experiment was set up. It's like trying to hear a whisper in a noisy room; the signal is there, but the noise drowns it out.

The Solution: The "Mirror Trick"
The team came up with a clever, universal method to fix this. They realized that if you look at the object from one side, you get a confusing result. But if you look at it from the exact opposite side (or simulate looking from both sides), the confusion disappears.

Think of it like this: Imagine you are trying to figure out if a spinning top is spinning clockwise or counter-clockwise. If you only look at it from the left, it might look like it's spinning one way. If you only look from the right, it might look like it's spinning the other way. But if you take the "spin" you see from the left and add it to the "spin" you see from the right, the true, intrinsic spin of the top reveals itself clearly.

The scientists applied this "Mirror Trick" to their experiments. They took two measurements:

They hit one side of their tiny metal structure with an electron beam and measured the glowing light.
They hit the other side with the beam and measured the light again.

By adding these two measurements together, the "noise" canceled out, and the true "handedness" (or helicity) of the structure popped out.

The Test: The "Dancing Dipole" Toy
To prove this worked, they built a simple model called a "Born-Kuhn system." Imagine two tiny metal antennas (like little sticks) placed near each other but slightly offset, forming a twisted shape.

When they were perfectly aligned (not twisted), the "Mirror Trick" showed zero handedness.
When they were offset (twisted), the "Mirror Trick" showed a clear, strong handedness.

They also showed that this method works for both "left-handed" and "right-handed" versions of the structure, just like your left and right hands.

Why This Matters
This paper doesn't just say, "We found a new way to measure." It says, "We finally found the correct way to define and measure the intrinsic twist of light in these tiny systems."

Before this, scientists were arguing about what "twist" even meant in these tiny structures. This paper provides a clear, mathematical definition (called helicity) and a practical recipe to measure it without getting fooled by the experimental setup. It's like finally agreeing on a standard ruler so that everyone can measure the length of a table correctly, no matter where they stand in the room.

In Summary

The Issue: Measuring the "twist" (chirality) of tiny metal structures was confusing and often wrong because the measurement tools only saw part of the picture.
The Fix: The scientists developed a method where they measure the structure from two opposite angles and add the results together.
The Result: This "Mirror Trick" cancels out the errors and reveals the true, intrinsic twist of the structure.
The Impact: This gives scientists a reliable, universal tool to study and engineer the "handedness" of light in the nanoworld, clearing up years of confusion in the field.

Technical Summary: Absolute Measurement of Intrinsic Helicity in Nanophotonics

Problem Statement
Chirality, the property of an object being non-superimposable on its mirror image, is fundamental to fields ranging from pharmacology to quantum information. While chiroptical spectroscopies (e.g., circular dichroism, CD) provide unambiguous measures of molecular chirality in solution, defining and measuring chirality in nanophotonic systems remains ambiguous. In nanostructures, the observation of circularly polarized dependent optical properties (such as Circular Dichroism in Scattering, CDS) does not necessarily correlate with the intrinsic helicity of the system. Previous studies have shown that CDS can be detected in achiral 2D nanostructures due to "hidden chirality" arising from extrinsic experimental geometries or local field dissymmetries. This lack of a rigorous, universal definition for the helicity of plasmonic excitations has led to substantial confusion in the literature regarding the relationship between local field properties and measurable chiroptical signals.

Methodology
The authors propose a universal method to rigorously define and measure the intrinsic helicity ( $H_{pl}$ ) of plasmonic systems. The approach combines theoretical derivation with experimental validation using a model system: the Born-Kuhn System (BKS), consisting of two coupled plasmonic gold nano-antennas (dipoles) with a specific offset and angle.

Theoretical Framework:
- The authors define plasmonic helicity not by the electromagnetic field alone, but by the polarization density field ( $p$ ) of the matter, treating localized surface plasmons (LSPs) as polaritons where the helicity is stored in the matter degree of freedom.
- They utilize the helicity operator $\hat{H}[u] = u \cdot \nabla \times u$ applied to the polarization density $p(r, t)$ .
- For a system of two dipoles, they derive an analytical expression showing that the total helicity is proportional to the scalar triple product of the dipole moments and their separation vector: $H_{pl} \propto (p_1 \times p_2) \cdot (r_1 - r_2)$ .
- They demonstrate that the total integrated CDS signal over a full $4\pi$ sphere ( $g_{4\pi}$ ) is directly proportional to this helicity.
Experimental Strategy:
- Since a full $4\pi$ integration is experimentally impossible (collection mirrors typically cover only one hemisphere), the authors propose a symmetrization technique.
- They utilize Scanning Transmission Electron Microscopy (STEM) coupled with Cathodoluminescence (CL) spectroscopy.
- By exciting the BKS with a focused electron beam at two symmetric positions (the two external tips of the dipoles) and summing the resulting dichroic signals ( $g$ ) from a single hemisphere, they mathematically cancel out the "zeroth-order" extrinsic chirality effects (hidden chirality) and recover the intrinsic helicity.
- The experiments were performed on gold nano-antennas (150 nm length, 50 nm width, 30 nm thickness) separated by a 10 nm silica spacer, with varying angles ( $\alpha$ ) between 0° and 330°.
- A custom drift-noise-free setup allowed for the simultaneous acquisition of left- and right-circularly polarized spectra to calculate the dissymmetry factor $g$ .

Key Contributions

Rigorous Definition: The paper establishes a rigorous definition of plasmonic helicity based on the polarization density of the source rather than the radiated field, resolving the ambiguity between geometric chirality ( $K$ ), optical chirality density ( $C$ ), and the measured CDS signal.
Universal Measurement Protocol: The authors demonstrate that the intrinsic helicity can be experimentally retrieved by symmetrizing the excitation and detection geometry. Specifically, summing the CDS signals acquired from two symmetric excitation points on a chiral nanostructure cancels out extrinsic contributions, yielding a signal directly proportional to the mode's helicity.
Analytical and Experimental Validation: The study provides analytical formulas for the helicity of a two-dipole system and validates them against both first-principles simulations (MNPBEM, pyGDM) and experimental STEM-pCL data.

Results

Symmetry Breaking and Recovery: Simulations and experiments confirm that while a single excitation point on a chiral structure (or even an achiral one) produces a non-zero CDS signal due to local field asymmetries, this signal changes sign when the excitation point is swapped.
Helicity Extraction: The sum of the dichroic signals from the two tips ( $g_{tip1} + g_{tip2}$ $g_{t i p 1} + g_{t i p 2}$ ) yields a signal that:
- Vanishes for achiral structures ( $K=0$ ).
- Changes sign when the handedness of the structure is reversed (e.g., 90° vs. 270°).
- Exhibits opposite signs for bonding and antibonding modes.
- Follows a sinusoidal dependence on the angle $\alpha$ between the dipoles, matching the theoretical prediction $H_{pl} \propto \sin(\alpha)$ .
Hidden Chirality: The results confirm that the strong, localized CDS signals often observed in nanophotonics (even on achiral structures) are dominated by a "zeroth-order" extrinsic effect related to the interference of orthogonal dipoles and dissipation. This effect is successfully filtered out by the proposed symmetrization method, revealing the true intrinsic helicity.

Significance
The paper claims that this methodology provides a foundation for the unambiguous characterization of chiral properties in polaritonic systems. By moving beyond simple intensity-based metrics or single-point measurements, the authors offer a way to rigorously quantify the "handedness" of plasmonic modes. This is significant for:

Resolving the conceptual tension between local field chirality and global scattering observables.
Enabling the engineering of local chirality in nanophotonic devices.
Extending the definition of helicity to quantum plasmonics, where plasmons are treated as quasi-particles with potentially infinite helicity values, distinct from the $\pm 1$ helicity of photons.

The authors note that while the method is demonstrated on plasmonic systems, the underlying principles rely on general dual-symmetry considerations and are expected to be transferable to other polaritonic systems and potentially non-linear techniques, provided the excitation-detection geometry can be appropriately symmetrized.

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