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Synthesis of ultrafast wavepackets with tailored spatiotemporal properties


Sculpting light in space and time can provide unprecedented opportunities in many areas of science and technology, ranging from extreme nonlinear optics and quantum networks to new families of ultrafast fibre amplifiers. Although endeavours in accessing the light’s temporal and spatial degrees of freedom have been carried out, controlling the electromagnetic field in its entirety has always been a major challenge. Here we demonstrate a versatile approach to synthesize convoluted ultrafast light structures in which the spatial and temporal dimensions are precisely correlated. By utilizing a two-stage reconfigurable module, we produce separable and non-separable trains of ultrafast wavepackets with time-varying dynamic angular momentum and tailored spectral characteristics. The generated light states are observed using mode- and frequency-resolved tomographic methodologies capable of reconstructing their complex field structure in space and time. Our results could have ramifications in a broad range of applications such as high-resolution microscopy, high-harmonic generation and laser micromachining.

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Fig. 1: Spatiotemporal moulding of light.
Fig. 2: Synthesized spatiotemporal wavepacket with spectral and time-dependent OAM.
Fig. 3: An optical wavepacket with an intricate ST texture.
Fig. 4: On-demand generation of spatiotemporal wavepackets.

Data availability

All data that support the findings of this study are available within the paper and the Supplementary Information and are available from the corresponding author upon request.

Code availability

All the relevant computing codes used in this study are available from the corresponding author upon reasonable request.


  1. Kerse, C. et al. Ablation-cooled material removal with ultrafast burst pulses. Nature 537, 84–88 (2016).

    Article  ADS  Google Scholar 

  2. Malik, M. et al. Multi-photon entanglement in high dimensions. Nat. Photon. 10, 248–252 (2016).

    Article  ADS  Google Scholar 

  3. Mair, A., Vaziri, A., Weihs, G. & Zeilinger, A. Entanglement of the orbital angular momentum states of photons. Nature 412, 313–316 (2001).

    Article  ADS  Google Scholar 

  4. Wang, J. et al. Terabit free-space data transmission employing orbital angular momentum multiplexing. Nat. Photon. 6, 488–496 (2012).

    Article  ADS  Google Scholar 

  5. Li, L. et al. High-capacity free-space optical communications between a ground transmitter and a ground receiver via a UAV using multiplexing of multiple orbital-angular-momentum beams. Sci. Rep. 7, 17427 (2017).

    Article  ADS  Google Scholar 

  6. Teğin, U., Yıldırım, M., Oğuz, İ., Moser, C. & Psaltis, D. Scalable optical learning operator. Nat. Comput. Sci. 1, 542–549 (2021).

    Article  Google Scholar 

  7. Teğin, U., Yıldırım, M., Oğuz, İ, Moser, C. & Psaltis, D. Machine learning with multimode fibers. In 2021 Conference on Lasers and Electro-Optics (CLEO) 1–2 (IEEE, 2021).

  8. Wetzstein, G. et al. Inference in artificial intelligence with deep optics and photonics. Nature 588, 39–47 (2020).

    Article  ADS  Google Scholar 

  9. Lin, D. et al. Reconfigurable structured light generation in a multicore fibre amplifier. Nat. Commun. 11, 3986 (2020).

    Article  ADS  Google Scholar 

  10. Wright, L., Cristodoulides, D. N. & Wise, F. W. Spatiotemporal mode-locking in multimode fiber lasers. Science 358, 94–97 (2017).

    Article  Google Scholar 

  11. Malomed, B. A., Mihalache, D., Wise, F. & Torner, L. Spatiotemporal optical solitons. J. Opt. B: Quantum Semiclass. Opt. 7, R53–R72 (2005).

    Article  ADS  Google Scholar 

  12. Dolev, I., Kaminer, I., Shapira, A., Segev, M. & Arie, A. Experimental observation of self-accelerating beams in quadratic nonlinear media. Phys. Rev. Lett. 108, 113903 (2012).

    Article  ADS  Google Scholar 

  13. Fleischer, A., Kfir, O., Diskin, T., Sidorenko, P. & Cohen, O. Spin angular momentum and tunable polarization in high-harmonic generation. Nat. Photon. 8, 543–549 (2014).

    Article  ADS  Google Scholar 

  14. Gariepy, G. et al. Creating high-harmonic beams with controlled orbital angular momentum. Phys. Rev. Lett. 113, 153901 (2014).

    Article  ADS  Google Scholar 

  15. Rego, L. et al. Generation of extreme-ultraviolet beams with time-varying orbital angular momentum. Science 364, eaaw9486 (2019).

    Article  ADS  Google Scholar 

  16. Dorney, K. M. et al. Controlling the polarization and vortex charge of attosecond high-harmonic beams via simultaneous spin–orbit momentum conservation. Nat. Photon. 13, 123–130 (2019).

    Article  ADS  Google Scholar 

  17. Rego, L. et al.Generation of extreme-ultraviolet beams with time-varying orbital angular momentum. Science 364, eaaw9486 (2019).

    Article  ADS  Google Scholar 

  18. Piccoli, R. et al. Intense few-cycle visible pulses directly generated via nonlinear fibre mode mixing. Nat. Photon. 15, 884–889 (2021).

    Article  ADS  Google Scholar 

  19. Liu, X., Du, D. & Mourou, G. Laser ablation and micromachining with ultrashort laser pulses. IEEE J. Quantum Electron. 33, 1706–1716 (1997) .

    Article  ADS  Google Scholar 

  20. Kraus, M. et al. Microdrilling in steel using ultrashort pulsed laser beams with radial and azimuthal polarization. Opt. Express 18, 22305–22313 (2010).

    Article  ADS  Google Scholar 

  21. Heritage, J. P., Weiner, A. M. & Thurston, R. N. Picosecond pulse shaping by spectral phase and amplitude manipulation. Opt. Lett. 10, 609–611 (1985).

    Article  ADS  Google Scholar 

  22. Thurston, R., Heritage, J., Weiner, A. & Tomlinson, W. Analysis of picosecond pulse synthesis by spectral masking in a grating pulse compressor. IEEE J. Quantum Electron. 22, 682–696 (1986).

    Article  ADS  Google Scholar 

  23. Durnin, J., Miceli, J. J. Jr. & Eberly, J. H. Diffraction-free beams. Phys. Rev. Lett. 58, 1499 (1987).

    Article  ADS  Google Scholar 

  24. Bandres, M. A., Gutierrez-Vega, J. C. & Chavez-Cerda, S. Parabolic nondiffracting optical wave fields. Opt. Lett. 29, 44–46 (2004).

    Article  Google Scholar 

  25. Kaminer, I., Bekenstein, R., Nemirovsky, J. & Segev, M. Nondiffracting accelerating wave packets of Maxwell’s equations. Phys. Rev. Lett. 108, 163901 (2012).

    Article  ADS  Google Scholar 

  26. Siviloglou, G. A., Broky, J., Dogariu, A. & Cristodoulides, D. N. Observation of accelerating Airy beams. Phys. Rev. Lett. 99, 213901 (2007).

    Article  ADS  Google Scholar 

  27. Yao, A. M. & Padgett, M. J. Orbital angular momentum: origins, behavior and applications. Adv. Opt. Photon. 3, 161–204 (2011).

    Article  Google Scholar 

  28. Brittingham, J. N. Focus waves modes in homogeneous Maxwell’s equations: transverse electric mode. J. Appl. Phys. 54, 1179–1189 (1983).

    Article  ADS  Google Scholar 

  29. Chong, A., Renninger, W. H., Christodoulides, D. N. & Wise, F. W. Airy–Bessel wave packets as versatile linear light bullets. Nat. Photon. 4, 103–106 (2010).

    Article  ADS  Google Scholar 

  30. Kondakci, H. E. & Abouraddy, A. F. Diffraction-free space–time light sheets. Nat. Photon. 11, 733–740 (2017).

    Article  ADS  Google Scholar 

  31. Kondakci, H. E. & Abouraddy, A. F. Optical space-time wavepackets having arbitrary group velocities in free space. Nat. Commun. 10, 929 (2019).

    Article  ADS  Google Scholar 

  32. Yessenov, M. et al. Space-time wave packets localized in all dimensions. Preprint at (2021).

  33. Chong, A., Wan, C., Chen, J. & Zhan, Q. Generation of spatiotemporal optical vortices with controllable transverse orbital angular momentum. Nat. Photon. 14, 350–354 (2020).

    Article  ADS  Google Scholar 

  34. Cao, Q. et al. Sculpturing spatiotemporal wavepackets with chirped pulses. Photon. Res. 9, 2261–2264 (2021).

    Article  Google Scholar 

  35. Wan, C., Chen, J., Chong, A. & Zhan, Q. Photonic orbital angular momentum with controllable orientation. Natl Sci. Rev. nwab149 (2021).

  36. Chen, J., Wan, C., Chong, A. & Zhan, Q. Experimental demonstration of cylindrical vector spatiotemporal optical vortex. Nanophotonics 10, 4489–4495 (2021).

    Article  Google Scholar 

  37. Wan, C., Chen, J., Chong, A. & Zhan, Q. Generation of ultrafast spatiotemporal wave packet embedded with time-varying orbital angular momentum. Sci. Bull. 65, 1334–1336 (2020).

    Article  Google Scholar 

  38. Wan, C., Cao, Q., Chen, J., Chong, A. & Zhan, Q. Photonics toroidal vortex. Preprint at (2021).

  39. Zdagkas, A. et al. Observation of toroidal pulses of light. Preprint at (2021).

  40. Mounaix, M. et al. Time reversed optical waves by arbitrary vector spatiotemporal field generation. Nat. Commun. 11, 5813 (2020).

    Article  ADS  Google Scholar 

  41. Baxter, G. et al. Highly programmable wavelength selective switch based on liquid crystal on silicon switching elements. In 2006 Optical Fiber Communication Conference and the National Fiber Optic Engineers Conference 1–3 (IEEE, 2006).

  42. Morizur, J. F. et al. Programable unitary spatial mode manipulation. J. Opt. Soc. Am. A 27, 2524–2531 (2010).

    Article  ADS  Google Scholar 

  43. Fontaine, N. K. et al. Laguerre-Gaussian mode sorter. Nat. Commun. 10, 1865 (2019).

    Article  ADS  Google Scholar 

  44. Gabolde, P. & Trebino, R. Self-referenced measurement of the complete electric field of ultrashort pulses. Opt. Express 12, 4423–4429 (2004).

    Article  ADS  Google Scholar 

  45. Gabolde, P. & Trebino, R. Single-frame measurement of the complete spatiotemporal intensity and phase of ultrashort laser pulses using a wavelength-multiplexed digital holography. J. Opt. Soc. Am. B 25, A25–A33 (2008).

    Article  ADS  Google Scholar 

  46. Kimel, I. & Elias, L. R. Relations between Hermite and Laguerre Gaussian modes. IEEE J. Quantum Electron. 29, 2562–2567 (1993).

    Article  ADS  Google Scholar 

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This effort was sponsored, in part, by the Department of the Navy, Office of Naval Research, (N00014-20-1-2789); the National Science Foundation (EECS-1711230); the Simons Foundation (733682); the US-Israel Binational Science Foundation (BSF; 2016381); the Army Research Office of Scientific Research (W911NF1710553 and W911NF1910426); and NASA (80NSSC21K0624).

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All authors contributed to all aspects of this work. D.C.D. performed the experiments in consultation with all the team members.

Corresponding authors

Correspondence to Rodrigo Amezcua-Correa or Miguel A. Bandres.

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Nature Photonics thanks Jose Azana, Pierre Bejot and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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Supplementary Figs. 1–19 and Sections I–IX.

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Cruz-Delgado, D., Yerolatsitis, S., Fontaine, N.K. et al. Synthesis of ultrafast wavepackets with tailored spatiotemporal properties. Nat. Photon. 16, 686–691 (2022).

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