# Controlling the polarization and vortex charge of attosecond high-harmonic beams via simultaneous spin–orbit momentum conservation

## Abstract

Optical interactions are governed by both spin and angular momentum conservation laws, which serve as a tool for controlling light–matter interactions or elucidating electron dynamics and structure of complex systems. Here, we uncover a form of simultaneous spin and orbital angular momentum conservation and show, theoretically and experimentally, that this phenomenon allows for unprecedented control over the divergence and polarization of extreme-ultraviolet vortex beams. High harmonics with spin and orbital angular momenta are produced, opening a novel regime of angular momentum conservation that allows for manipulation of the polarization of attosecond pulses—from linear to circular—and for the generation of circularly polarized vortices with tailored orbital angular momentum, including harmonic vortices with the same topological charge as the driving laser beam. Our work paves the way to ultrafast studies of chiral systems using high-harmonic beams with designer spin and orbital angular momentum.

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## Data availability

The datasets and analysis routines utilized to prepare the data presented in this manuscript are available, free of charge, from the corresponding authors under reasonable request.

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## Acknowledgements

The authors are thankful for useful and productive conversations with E. Pisanty, C. Durfee, D. Hickstein, S. Alperin and M. Siemens. H.C.K. and M.M.M. graciously acknowledge support from the Department of Energy BES Award No. DE-FG02–99ER14982 for the experimental implementation, as well as a MURI grant from the Air Force Office of Scientific Research under Award No. FA9550–16–1–0121 for the theory. J.L.E., N.J.B. and Q.L.N. acknowledge support from National Science Foundation Graduate Research Fellowships (Grant No. DGE-1144083). C.H.-G., J.S.R. and L.P. acknowledge support from Junta de Castilla y León (SA046U16) and Ministerio de Economía y Competitividad (FIS2013–44174-P, FIS2016–75652-P). C.H.-G. acknowledges support from a 2017 Leonardo Grant for Researchers and Cultural Creators, BBVA Foundation. L.R. acknowledges support from Ministerio de Educación, Cultura y Deporte (FPU16/02591). A.P. acknowledges support from the Marie Sklodowska-Curie Grant, Agreement No. 702565. We thankfully acknowledge the computer resources at MareNostrum and the technical support provided by Barcelona Supercomputing Center (RES-AECT-2014–2–0085). This research made use of the high-performance computingresources of the Castilla y León Supercomputing Center (SCAYLE, www.scayle.es),financed by the European Regional Development Fund (ERDF). Certain commercial instruments are identified to specify the experimental study adequately. This does not imply endorsement by the National Institute of Standards and Technology (NIST) or that the instruments are the best available for the purpose.

## Author information

Authors

### Contributions

C.H.-G., K.M.D., M.M.M., H.C.K., L.R. and L.P. conceived and designed the SAM–OAM HHG experiment. K.M.D., N.J.B., C.-T.L., J.L.E. and Q.L.N. conducted the experiment. K.M.D. analysed the experimental data. C.H.-G., L.R., J.S.R., A.P. and L.P. performed the theoretical simulations and analysed the resulting data. J.M.S. prepared the EUV MCD sample. C.H.-G., L.P., M.M.M. and H.C.K. supervised the theoretical simulations and experimental work and developed the required facilities and measurement capabilities. C.H.-G., K.M.D., L.R., J.S.R., M.M.M. and L.P. wrote and prepared the manuscript, to which all authors provided constructive improvements and feedback.

### Corresponding authors

Correspondence to Kevin M. Dorney or Carlos Hernández-García.

## Ethics declarations

### Competing interests

M.M.M. and H.C.K. have a interest in KMLabs. The other authors declare no competing interests.

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## Supplementary information

### Supplementary Information

This file contains Supplementary Figures 1–4 and additional information about the work.

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Dorney, K.M., Rego, L., Brooks, N.J. et al. Controlling the polarization and vortex charge of attosecond high-harmonic beams via simultaneous spin–orbit momentum conservation. Nature Photon 13, 123–130 (2019). https://doi.org/10.1038/s41566-018-0304-3

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