Laguerre–Gauss and Hermite–Gauss soft X-ray states generated using diffractive optics


Light’s capacity to carry angular momentum is integral to our knowledge of physics and ability to probe matter. In addition to spin, photons can occupy free-space orbital angular momentum eigenstates1,2. Visible light orbital angular momentum is used in quantum information experiments, super-resolution microscopy, optical tweezers and angular momentum transfer to atoms in optical lattices3,4. Soft X-ray orbital angular momentum applications, slowed by the lack of suitable optics and the rarity of coherent X-ray sources, could enable the direct alteration of atomic states through orbital angular momentum exchange, and methods to study the electronic properties of quantum materials. We have made soft X-ray diffractive optics that generate single Laguerre–Gauss modes, observed carrying up to 30ħ angular momentum per photon, or their superpositions. We also present Hermite–Gauss diffractive optics and a soft X-ray orbital angular momentum analyser. These tools could enable both the manipulation and finer characterization of topologically complex electronic matter, such as magnetic skyrmions.

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Fig. 1: Coherent soft X-ray diffraction: set-up and fork gratings with b = 1 and b = 10 defect slits.
Fig. 2: OAM analyser transmission function and simulated diffraction pattern.
Fig. 3: OAM analysers and their diffraction outputs.
Fig. 4: Non-OAM carrying TEM modes.

Data availability

The data that support the plots within this paper and other findings of this study are available from J.C.T.L. ( and/or the corresponding author upon reasonable request.


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This research used resources of the Advanced Light Source, a DOE Office of Science User Facility (DE-AC02-05CH11231). Work at the following locations was supported by the DOE Office of Science: University of Oregon (Basic Energy Sciences, DE-SC0010466) and Advanced Light Source (Basic Energy Sciences, Materials Sciences and Engineering Division, DE-AC02-05-CH11231, NEMM program MSMAG).

Author information

B.M., S.R. and S.A. designed the experiment. S.A. fabricated the diffractive optics and performed SEM. J.C.T.L. and S.A. performed the soft X-ray diffraction. J.C.T.L., S.R., S.A., B.M. and S.D.K. wrote the manuscript.

Correspondence to S. Roy.

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Lee, J.C.T., Alexander, S.J., Kevan, S.D. et al. Laguerre–Gauss and Hermite–Gauss soft X-ray states generated using diffractive optics. Nature Photon 13, 205–209 (2019).

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