volume | PIER Journals

Abstract

Spatiotemporal optical vortices (STOVs) are electromagnetic wave packets that transport a phase line singularity perpendicular to their propagation direction. We address the problem of the transverse orbital angular momentum (OAM) actually transported by STOVs propagating in free space or non-dispersive media, the most frequent experimental situation. An elliptically symmetric STOV of topological charge l and carrier frequency ω₀ carries an intrinsic transverse OAM per unit energy γl/2ω₀, where γ is the STOV ellipticity. Intrinsic stands for the OAM about a moving transverse axis passing permanently through the STOV center. For circular STOVs (γ = 1) this value is half the intrinsic longitudinal OAM of monochromatic light beams of the same charge and frequency. This result agrees with that in Phys. Rev. Lett. 127, 193901 (2021). The formula (γ+1/γ)l/2ω₀ for the intrinsic transverse OAM in Phys. Rev. A 107, L031501 (2023) yields infinite values and is not conserved on propagation for particular STOVs. When STOVs propagate losing their elliptical symmetry, they preserve the intrinsic transverse OAM γl/2ω₀ despite the phase singularity may split, the split singularities may disappear, or even change the sign of their topological charges. The total transverse OAM of a STOV about a fixed transverse axis crossing its center vanishes because the extrinsic transverse OAM is opposite to the intrinsic OAM, which may preclude applications such as setting particles into rotation, but STOVs could transmit their intrinsic OAM to the photons of other waves, as in nonlinear frequency conversion processes.

1. Shen, Y., X. Wang, Z. Xie, C. Min, X Fu, Q. Liu, M. Gong, and X. Yuan, "Optical vortices 30 years on: OAM manipulation from topological charge to multiple singularities," Light Sci. Appl., Vol. 8, 90, 2019.
doi:10.1038/s41377-019-0194-2 Google Scholar

2. Jhajj, N., I. Larkin, E. W. Rosenthal, S. Zahedpour, J. K. Wahlstrand, and H. M. Milchberg, "Spatiotemporal optical vortices," Phys. Rev. X, Vol. 6, 031037, 2016. Google Scholar

3. Hancock, S. W., S. Zahedpour, A. Goffin, and H. M. Milchberg, "Free-space propagation of spatiotemporal optical vortices," Optica, Vol. 6, 1547, 2019.
doi:10.1364/OPTICA.6.001547 Google Scholar

4. Chong, A., C. Wan, J. Chen, and Q. Zhan, "Generation of spatiotemporal optical vortices with controllable transverse orbital angular momentum," Nat. Photonics, Vol. 14, 350, 2020.
doi:10.1038/s41566-020-0587-z Google Scholar

5. Wang, H., C. Guo, W. Jein, A. Y. Song, and S. Fan, "Engineering arbitrarily oriented spatiotemporal optical vortices using transmission nodal lines," Optica, Vol. 8, 2334-2536, 2021. Google Scholar

6. Chen, J., C. Wan, A. Chong, and Z. Zhan, "Experimental demonstration of cylindrical vector spatiotemporal optical vortex," Nanophotonics, Vol. 10, 4489-4495, 2021.
doi:10.1515/nanoph-2021-0427 Google Scholar

7. Cao, Q., J. Chen, K. Lu, C. Wan, A. Chong, and Q. Zhan, "Non-spreading Bessel spatiotemporal optical vortices," Science Bulletin, Vol. 67, 133-140, 2022.
doi:10.1016/j.scib.2021.07.031 Google Scholar

8. Hancock, S. W., S. Zahedpour, and H. M. Milchberg, "Mode structure and orbital angular momentum of spatiotemporal optical vortex pulses," Phys. Rev. Lett., Vol. 127, 193901, 2021.
doi:10.1103/PhysRevLett.127.193901 Google Scholar

9. Huang, S., P. Wang, X. Shen, and J. Liu, "Properties of the generation and propagation of spatiotemporal optical vortices," Opt. Express, Vol. 29, 26995, 2021.
doi:10.1364/OE.434845 Google Scholar

10. Huang, S., P. Wang, X. Shen, J. Liu, and R. Li, "Diffraction properties of light with transverse orbital angular momentum," Optica, Vol. 9, 469, 2022.
doi:10.1364/OPTICA.449108 Google Scholar

11. Porras, M. A., "Propagation of higher-order spatiotemporal vortices," Opt. Lett., Vol. 48, 367-370, 2023.
doi:10.1364/OL.479566 Google Scholar

12. Bliokh, K. Y. and F. Nori, "Spatiotemporal vortex beams and angular momentum," Phys. Rev. A, Vol. 86, 033824, 2012.
doi:10.1103/PhysRevA.86.033824 Google Scholar

13. Bliokh, K. Y., "Spatiotemporal vortex pulses: Angular momenta and spin orbit interaction," Phys. Rev. Lett., Vol. 126, 243601, 2021.
doi:10.1103/PhysRevLett.126.243601 Google Scholar

14. Shen, Y., Q. Zhan, L. G. Wright, D. N. Christodoulides, F. W. Wise, A. E. Willner, Z. Zhao, K. Zou, C. Liao, C. Hernandez-Garcia, M. Murnane, M. A. Porras, A. Chong, C. Wan, K. Y. Bliokh, M. Yessenov, A. F. Abouraddy, L. J. Wong, M. Go, S. Kumar, C. Guo, S. Fan, N. Papasimakis, N. I. Zheludev, L. Chen, W. Zhu, A. Agrawal, S. W. Jolly, C. Dorrer, B. Alonso, I. Lopez-Quintas, M. Lopez-Ripa, I. J. Sola, Y. Fang, Q. Gong, Y. Liu, J. Huang, H. Zhang, Z. Ruan, M. Mounaix, N. K. Fontaine, J. Carpenter, A. H. Dorrah, F. Capasso, and A. Forbes, "Roadmap on spatiotemporal light fields," arXiv.2210.11273, 2022. Google Scholar

15. Hancock, S. W., S. Zahedpour, and H. M. Milchberg, "Second-harmonic generation of spatiotemporal optical vortices and conservation of orbital angular momentum," Optica, Vol. 8, 594-597, 2021.
doi:10.1364/OPTICA.422743 Google Scholar

16. Gui, G., N. J. Brooks, H. C. Kapteyn, M. M. Murnane, and C.-T. Liao, "Second-harmonic generation and the conservation of spatiotemporal orbital angular momentum," Nature Photonics, Vol. 15, 608-613, 2021.
doi:10.1038/s41566-021-00841-8 Google Scholar

17. Fang, Y., S. Lu, and Y. Liu, "Controlling photon transverse orbital angular momentum in high harmonic generation," Phys. Rev. Lett., Vol. 127, 273901, 2021.
doi:10.1103/PhysRevLett.127.273901 Google Scholar

18. Mazanov, M., D. Sugic, M. A. Alonso, F. Nori, and K. Y. Bliokh, "Transverse shifts and time delays of spatiotemporal vortex pulses reflected and refracted at a planar interface," Nanophotonics, Vol. 11, 737-744, 2022.
doi:10.1515/nanoph-2021-0294 Google Scholar

19. Porras, M. A., "Spatiotemporal optical vortex solitons: Dark solitons with transverse and tilted phase line singularities," Phys. Rev. A, Vol. 104, L061502, 2021.
doi:10.1103/PhysRevA.104.L061502 Google Scholar

20. Barnett, S. M., "Optical angular-momentum flux," J. Opt. B: Quantu., Semiclass. Opt., Vol. 4, S7-S16, 2002.
doi:10.1088/1464-4266/4/2/361 Google Scholar

21. Heyman, E., "Pulsed beam propagation in an inhomogeneous medium," IEEE Trans. Antennas Propag., Vol. 42, 311-319, 1994.
doi:10.1109/8.280715 Google Scholar

22. Besieris, I. M. and A. M. Shaarawi, "Paraxial localized waves in free space," Opt. Express, Vol. 12, 3848-3864, 2004.
doi:10.1364/OPEX.12.003848 Google Scholar

23. Lax, M., W. H. Louisell, and W. B. McKnight, "From Maxwell to paraxial wave optics," Phys. Rev. A, Vol. 11, 1365, 1975.
doi:10.1103/PhysRevA.11.1365 Google Scholar

24. Ruiz-Jimenez, C., H. Leblond, M. A. Porras, and B. A. Malomed, "Rotating azimuthons in dissipative Kerr media excited by superpositions of Bessel beams," Phys. Rev. A, Vol. 102, 063502, 2020.
doi:10.1103/PhysRevA.102.063502 Google Scholar

25. Molina-Terriza, G., J. Recolons, J. P. Torres, and L. Torner, "Observation of the dynamical inversion of the topological charge of an optical vortex," Phys. Rev. Lett., Vol. 87, 023902, 2001.
doi:10.1103/PhysRevLett.87.023902 Google Scholar

26. Bliokh, K. Y., "Orbital angular momentum of optical, acoustic, and quantum-mechanical spatiotemporal vortex pulses," Phys. Rev. A, Vol. 107, L031501, 2023.
doi:10.1103/PhysRevA.107.L031501 Google Scholar

27. Bialynicki-Birula, I., "Photon wave function," Progress in Optics, Vol. 36, 245-294, 1996.
doi:10.1016/S0079-6638(08)70316-0 Google Scholar

28. Dror, N. and B. A. Malomed, "Symmetric and asymmetric solitons and vortices in linearly coupled two-dimensional waveguides with the cubic-quintic nonlinearity," Physica D, Vol. 240, 526-541, 2011.
doi:10.1016/j.physd.2010.11.001 Google Scholar

Professor Miguel Angel Porras