Lasers have not only fascinated scientists for decades, but they have also become an integral part of many electronic devices. To create scientific-grade lasers, physicists try to control the temporal, spatial, phase, and polarization properties of the laser beam’s pulse to be able to manipulate it. One of these properties is called the orbital angular momentum (OAM), and its phase, or shape, swirls as the doughnut-shaped laser beam travels through space. There are two types of OAM, spatial (S-OAM) and spatial-temporal (ST-OAM). S-OAM describes the angular momentum of the laser beam that is parallel to the light source's propagation direction. In contrast, ST-OAM has angular momentum that moves in a motion perpendicular to the light source’s propagation direction, which creates a time component to the momentum [1, 2]. Because of these differences, ST-OAM is more difficult to study due to this time component. According to senior scientist Dr. Chen-Ting Liao: “The problem is that ST-OAM is very difficult to see or measure. And if we can't see or measure this easily, there's no way we can fully understand and optimize it, let alone use it for potential future applications.” To try to overcome this difficulty, a collaboration led by Dr. Liao and other researchers, including JILA Fellows Margaret Murnane and Henry Kapteyn, worked out a method to image and better analyze ST-OAM beams. Their work was subsequently published in ACS Photonics and featured on the cover .
A Two-Step System
“Our overarching goal was: How do we get a very simple, straightforward way to characterize and measure these kinds of light pulses?” Liao said. To develop their imaging method, the team of researchers first looked at how S-OAM beams were imaged. “People measure S-OAMs by using a cylindrical lens [a concave shaped lens which enlarges light at a single point], which can form special patterns to reveal the S-OAM's shape,” explained graduate student and the paper’s first author, Guan Gui. “So, our idea was initially inspired by the traditional method in spatial OAMs and we adapted that to the spatial-temporal OAM.”
As ST-OAMs have both a spatial and a temporal (time) component to the laser beam's angular momentum, the process to image the beam's structures was more complicated than just using a cylindrical lens, due to the constraints of the time component. To solve this problem, Gui, Liao, and their team had an idea. “The idea is that we only need two optical elements in this very simple yet powerful method,” added Liao. “The first one is a grating, and the second one is a cylindrical mirror.” Like the two-step dance that uses two steps to move the dancers, this method used two different components to resolve the ST-OAM into images that could be analyzed in space and in time.
The first component the beam interacts with is a grating, or a time equivalent analyzer, which converts the time component of the ST-OAM into other quantitative for calculation and analysis. “We use a grating which maps the time domain information into the spectral domain [this changes the time component into a spatial one with different laser beams],” Liao elaborated, “That's why we get this rainbow-like light.” From there, the beam's rainbow spectra move into a cylindrical (non-spherical) mirror, a space-equivalent analyzer. This analyzer helps to break up the shape of the laser. “After we disperse the light into different colors using the grating,” said Liao, “we use a cylindrical mirror that breaks the symmetry of the structured laser pulse. So, in this case, we can map out both the spatial-temporal information.” The researchers did this by converting the time component into a spectral component, and then breaking up the spectral structure to analyze the laser pulse. The raw images created by this process could reveal the presence or absence of the ST-OAM. According to Liao, the striped patterns in the raw images can indicate the sign (positive or negative) and the space-time topological charge numbers (quantitative descriptors of the shape of the ST-OAM) as well. The positive or negative charge told the researchers which direction the ST-OAM was rotating. This new imaging system not only gave the researchers a better understanding of the structures of the ST-OAM but created a method giving immediate initial results.
Using 3D Structured Light
Excited by this new technique, the researchers realized it would help in multiple applications. “Thanks to our method, we can easily find the imperfections in the ST-OAM and better characterize it,” added Gui. “Measuring imperfections is important in research—it not only provides practical approaches toward perfections, but sometimes, these imperfections can also carry extra information that researchers are interested in. For example, these imperfections might reveal how ST-OAM light interacts with materials.” Liao and collaborators also saw potential opportunities for their new method in microscopy and imaging. “When people do microscopy and imaging, they use 2D structured light to enhance their images, such as structured illumination and super-resolution microscopy,” he said. “In our case, we are exploring the potential of ST-OAM in terms of better 3D imaging.” The researchers are hopeful others will utilize their methods to discover more information about ST-OAM.
After publishing in ACS Photonics, the researchers were notified that their paper was chosen for an ACS Editor's Choice award and was also selected to be featured on the journal cover. Papers are chosen for this award based on nominations. The team was delighted by the news. As Gui said: “I am very excited that our research got recognized by the community—it can be very helpful to this field. I'm also grateful for the people who worked together on this project. Our team always starts a project by discussing what is important and beneficial to the community, and these discussions help cultivate ideas than can solve a problem.”
References  Kenna Castleberry. "From Plane Propellers to Helicopter Rotors." JILA Light & Matter Winter 2022. https://jila.colorado.edu/news-events/articles/plane-propellers-helicop…
 G. Gui, N. J. Brooks, H. Kapteyn, M. Murnane, and C.-T. Liao. "Second harmonic generation and the conservation of spatiotemporal orbital angular momentum of light.” Nature Photonics 15(1): 608–613 (2021). DOI: https://doi.org/10.1038/s41566-021-00841-8
 Guan Gui, Nathan J. Brooks, Bin Wang, Henry C. Kapteyn, Margaret M. Murnane, and Chen-Ting Liao. "Single-Frame Characterization of Ultrafast Pulses with Spatiotemporal Orbital Angular Momentum." ACS Photonics 2022 9 (8), 2802-2808. DOI: 10.1021/acsphotonics.2c00626
Written by Kenna Castleberry, JILA Science Communicator