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Longitudinal fields and transverse rotations

Electromagnetic fields in light waves are mainly transverse to propagation direction but actually also have longitudinal components, which may give rise to unexpected optical phenomena involving the angular momentum of light, such as transverse spin and optical torques.

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Fig. 1: Longitudinal and transverse components of optical fields, in free space and in anisotropic media.


  1. Eismann, J. S. et al. Nat. Photon. (2021).

  2. El Ketara, M., Kobayashi, H & Brasselet, E. Nat. Photon. (2021).

  3. Aiello, A., Banzer, P., Neugebauer, M. & Leuchs, G. Nat. Photon. 9, 789–795 (2015).

    Article  ADS  Google Scholar 

  4. Rodríguez-Fortuño, F. J. et al. Science 340, 328–330 (2013).

    Article  ADS  Google Scholar 

  5. Marrucci, L. Nat. Phys. 11, 9–10 (2015).

    Article  Google Scholar 

  6. Zolot’ko, A. S., Kitaeva, V. F., Kroo, N., Sobolev, N. N. & Csillag, L. J. Exp. Theor. Phys. Lett. 32, 158–161 (1980).

    Google Scholar 

  7. O’Neil, A. T., MacVicar, I., Allen, L. & Padgett, M. J. Phys. Rev. Lett. 88, 053601 (2002).

    Article  ADS  Google Scholar 

  8. Bliokh, K. Y., Rodríguez-Fortuño, F. J., Nori, F. & Zayats, A. V. Nat. Photon. 9, 796–808 (2015).

    Article  ADS  Google Scholar 

  9. Cardano, F. & Marrucci, L. Nat. Photon. 9, 776–778 (2015).

    Article  ADS  Google Scholar 

  10. Won, R. Nat. Photon. 11, 619–622 (2017).

    Article  ADS  Google Scholar 

  11. Wang, J., Sciarrino, F., Laing, A. & Thompson, M. G. Nat. Photon. 14, 273–284 (2020).

    Article  ADS  Google Scholar 

  12. Ambrosio, A., Marrucci, L., Borbone, F., Roviello, A. & Maddalena, P. Nat. Commun. 3, 989 (2012).

    Article  ADS  Google Scholar 

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Correspondence to Filippo Cardano or Lorenzo Marrucci.

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Cardano, F., Marrucci, L. Longitudinal fields and transverse rotations. Nat. Photonics 15, 72–74 (2021).

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