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Mathematical Approach Deciphers Orbital Angular Momentum Information

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GUANGZHOU, China, Aug. 14, 2023 — Researchers from Sun Yat-sen University and École Polytechnique Fédérale de Lausanne (EPFL) have made progress in the use of interferometry to decipher orbital angular momentum (OAM) spectrum information. Lightwaves with OAM have become important in technologies including communication, imaging, and quantum information processing. For these to be effective, it’s crucial to know the exact structure of these helical light beams.

So far, this has proven difficult. Interferometry — superimposing a light field with a known reference field to extract information from the interference — can retrieve OAM spectrum information using a camera. As the camera records the intensity of the interference, the measurement technique encounters additional crosstalk known as “signal-signal beat interference” (SSBI), which complicates the retrieval process. It’s like hearing multiple overlapping sounds, making it difficult to distinguish the original notes.
On-axis Kramers-Kronig interferometry retrieves the spectrum of orbital angular momentum in a single-shot. Courtesy of Z. Lin, J. Hu, et al., doi 10.1117/1.AP.5.3.036006.
On-axis Kramers-Kronig interferometry retrieves the spectrum of orbital angular momentum in a single shot. Courtesy of Z. Lin et al., doi 10.1117/1.AP.5.3.036006. 

To overcome these issues, the team used a mathematical tool called the Kramers-Kronig (KK) relation. The approach enabled the readout of both the amplitude and phase relation of an arbitrary OAM state in a single-shot manner without increasing the system complexity. Exploring the duality between the time-frequency and azimuth-OAM domains, the researchers applied the KK approach to investigate various OAM fields, including Talbot self-imaged petals and fractional OAM modes.

The new measurement technique has great potential for advancing technologies that rely on these special light patterns. According to corresponding author Jianqi Hu, now a postdoc at Laboratoire Kastler Brossel, École Normale Supérieure, France, “The proposed method can also be generalized for OAM beams with complex radial structures, making it a powerful technique for real-time measurement of structured light fields, simply by a snapshot with a camera.”

Compared to conventional on-axis interferometry, the KK method demonstrated by the researchers not only accelerates the measurement but also makes it much simpler and cost-effective. The technique enables investigation of structured light with OAM, with the potential to drive advancements in communications, imaging, and quantum information processing in the near future.

The research was published in Advanced Photonics (
Aug 2023
Smallest amount into which the energy of a wave can be divided. The quantum is proportional to the frequency of the wave. See photon.
The study and utilization of interference phenomena, based on the wave properties of light.
1. The additive process whereby the amplitudes of two or more overlapping waves are systematically attenuated and reinforced. 2. The process whereby a given wave is split into two or more waves by, for example, reflection and refraction of beamsplitters, and then possibly brought back together to form a single wave.
structured light
The projection of a plane or grid pattern of light onto an object. It can be used for the determination of three-dimensional characteristics of the object from the observed deflections that result.
Research & Technologyopticscamerasimagingquantumorbital angular momentuminterferometryinterferenceKramers-KronigmathematicsEPFLSun Yat-sen UniversityEuropeAsia-Pacificstructured lightOAM

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