🔬 optics

Sorting light's radial momentum and orbital angular momentum with a parabola-like lens

The authors propose and experimentally demonstrate a parabola-like lens capable of efficiently sorting and distinguishing a light field's orbital angular momentum and radial momentum into distinct spatial positions, enabling full transverse momentum characterization for applications in optical information processing and quantum states.

Original authors: Yuan Li, Ye Xing, Wuhong Zhang, Lixiang Chen

Published 2026-05-22

📖 4 min read☕ Coffee break read

CC BY 4.0

Original authors: Yuan Li, Ye Xing, Wuhong Zhang, Lixiang Chen

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 a beam of light not just as a simple flashlight beam, but as a complex, swirling dance of invisible particles. In the world of physics, this light carries two specific types of "movement" sideways (transverse momentum) that are crucial for sending information:

The Spin (Orbital Angular Momentum - OAM): Think of this like a corkscrew or a spiral staircase. The light twists around its center as it travels.
The Pulse (Radial Momentum - RM): Think of this as the light either expanding outward like a blooming flower or shrinking inward like a closing iris as it moves forward.

For a long time, scientists have been very good at sorting the "spins" (OAM) to send different messages. However, sorting the "pulses" (RM) at the same time has been like trying to catch two different types of fish in the same net without them getting tangled.

The New Solution: The "Parabola-Like" Lens

The researchers in this paper (from Xiamen University) have invented a special optical tool they call a parabola-like lens. You can think of this lens as a magical sorting machine or a traffic director for light.

Here is how it works, using a simple analogy:

The Problem: Imagine you have a crowd of people (light beams) entering a room. Some are spinning (OAM), and some are walking at different speeds toward the door (RM). If you just let them walk, they all mix up in a big jumble.
The Old Way: Previous tools could separate the spinners from the non-spinners, but they couldn't easily tell who was walking fast versus slow at the same time.
The New Lens: The authors' new lens acts like a clever floor plan. When the mixed-up light hits this lens, it doesn't just scatter randomly. Instead, it organizes the light into a very specific pattern: parabolas (the U-shaped curves you see in satellite dishes or the path of a thrown ball).

The Sorting Magic

The lens sorts the light based on two rules:

The Spin Rule: Light with different amounts of spin (OAM) lands on the same U-shaped curve (parabola) but at different spots along that curve.
The Pulse Rule: Light with different expansion speeds (RM) lands on different U-shaped curves entirely.

So, if you look at the output, you don't see a messy pile. You see a neat grid of U-shapes. Each specific combination of "spin" and "pulse" lands in its own unique, non-overlapping spot.

What They Actually Did

The team didn't just do math on a computer; they built a real machine to prove it works.

The Setup: They used a laser, mirrors, and a special screen (called a Spatial Light Modulator) to create light beams with specific spins and pulses.
The Test: They sent these beams through their new lens.
The Result: The lens successfully separated the beams. They tested it with single beams and even with complex mixtures of many beams at once.
The "Single Photon" Test: They even turned the light down so low that only one particle of light (a photon) was present at a time. The lens still worked, sorting these individual particles correctly. This is important because it means the tool works for the most delicate levels of light, which is essential for future quantum technologies.

Why This Matters (According to the Paper)

The paper claims this device is a major step forward because:

It can identify both types of sideways movement (spin and pulse) at the same time using just one simple piece of equipment.
It can handle many different signals at once (multiplexing), which could help pack more information into a single beam of light.
It works with high efficiency, meaning very little light is wasted.

In short, they built a "parabola-shaped" traffic cop for light that can instantly sort complex, twisting, expanding beams into neat, organized lines, paving the way for faster and more complex ways to send information using light.

Technical Summary: Sorting Light's Radial Momentum and Orbital Angular Momentum with a Parabola-like Lens

Problem Statement
The spatial modes of light offer an unbounded state space for high-dimensional information encoding, a capability central to mode-division multiplexing (MDM) in optical communications. While Orbital Angular Momentum (OAM) has been extensively utilized for this purpose, Radial Momentum (RM) represents the other component of a light field's transverse momentum and has recently shown promise in fundamental quantum tests (e.g., Einstein–Podolsky–Rosen paradox relations) and potential communication applications. However, a critical bottleneck remains: existing technologies can efficiently sort OAM states using interferometric, diffraction, or coordinate transformation methods, but there is a lack of effective techniques to simultaneously discriminate and sort both OAM and RM. Previous radial mode sorters designed for Bessel-Gauss or Laguerre-Gaussian (LG) modes are insufficient because they rely on beam propagation characteristics that differ from the definition of RM (where $p_r \neq 0$ implies a changing spot size during propagation). Consequently, a method to efficiently separate these two distinct transverse momentum components within a single optical field is required to fully characterize the field and unlock higher information capacities.

Methodology
The authors propose a novel optical device: a parabola-like lens. This pure phase element is designed to transform the input OAM ( $\ell$ ) and RM ( $p_r$ ) into distinct spatial positions in the output plane.

Theoretical Framework: The input light field is defined as a beam with annular intensity, carrying both OAM and RM. The phase distribution of the proposed lens, $T(\rho, \phi)$ , is derived to modulate the input field such that different momentum states focus at specific coordinates.
Mapping Principle: Using Photonic Momentum Transformation (PMT) analysis, the authors derive analytical expressions for the focal positions $(x, y)$ in the observation plane. The results indicate that modes with the same RM but different OAM values align along a parabola, while modes with different RM values are distributed along different, parallel parabolas. The position along the parabola is determined by the OAM, while the specific parabola is determined by the RM.
Experimental Setup: The device was implemented using a Spatial Light Modulator (SLM) to generate the required phase mask. The setup involved a 532 nm laser, a 4F filtering system to create the input field (containing specific $\ell$ and $p_r$ values), and a second SLM acting as the parabola-like lens. The output was captured by a CMOS camera for intensity measurements and an Intensified Charge-Coupled Device (ICCD) camera for single-photon level verification.

Key Contributions and Results

Simultaneous Sorting: The study demonstrates the successful separation of individual OAM and RM states, as well as complex superposition states, into non-overlapping spatial positions.
Parabolic Mapping: Experimental results confirm the theoretical prediction that different momentum states map onto a grid of parabolas. Specifically, 21 distinct modes (combinations of 3 RM values and 7 OAM values) were successfully sorted with high concentration and minimal overlap.
Superposition Handling: The lens effectively separated a superposition of 15 modes (3 RM values $\times$ 5 OAM values). While diffraction effects caused some scattered light, the primary modes were correctly positioned. The authors noted that reducing the number of input modes improved the separation quality by minimizing adjacent mode interference.
Single-Photon Capability: The system was tested at the single-photon level. By accumulating 15,470 single-photon images, the predicted mode distributions were reconstructed, proving the device's viability for quantum state applications.
Resolution Analysis: The resolution for single-mode inputs was found to be superior to superposition inputs due to reduced interference. The OAM resolution ranged from $4\hbar$ to $15\hbar$ (single mode) and $10\hbar$ to $20\hbar$ (superposition), while RM resolution ranged from $10,000\hbar m^{-1}$ to $20,000\hbar m^{-1}$ . The authors observed that OAM resolution decreases as RM increases, but can be improved by optimizing the lens radius ( $R_0$ ) and focal length ( $f$ ).

Significance and Claims
The paper claims that the proposed parabola-like lens provides a practical solution for the "fundamental and priority problem" of discriminating OAM and RM simultaneously. By achieving two-dimensional transverse momentum identification with a single optical element, the device offers a pathway to:

Complete Characterization: It enables the full characterization of the transverse momentum of an optical field.
Multiplexing/Demultiplexing: The device can serve as a demultiplexer for optical information, potentially achieving unit efficiency.
Quantum Applications: Its ability to function at the single-photon level makes it suitable for applications involving quantum states of light.
Integration: The authors suggest that the lens could be manufactured using a single metasurface, facilitating further optical integration.

The work positions the parabola-like lens as a significant step toward boosting the information capacity of single photons by utilizing both radial and orbital degrees of freedom.

Technical Summary: Sorting Light's Radial Momentum and Orbital Angular Momentum with a Parabola-like Lens

More like this