SU(2) symmetry of spatiotemporal Gaussian modes propagating in isotropic dispersive media
Phys. Rev. A 112, 033521 – Published 16 September, 2025
DOI: https://doi.org/10.1103/2jxt-d8pg
Abstract
The far-field intensity distribution of spatiotemporal Laguerre-Gaussian (STLG) modes propagating in free space exhibits a multipetal pattern analogous to that observed in tilted Hermite-Gaussian modes. Here, we show that this phenomenon can be explained by the SU(2) symmetry of spatiotemporal Gaussian modes, which can support the irreducible representation of the SU(2) group and enable the construction of the spatiotemporal model Poincaré sphere. We have also derived analytical expressions for the STLG mode with an arbitrary radial and angular indices propagating in the isotropic media. The propagation dynamics can be understood as a unitary transformation generated by a conserved quantity, where the rotation angle is exactly the intermodal Gouy phase of the spatiotemporal modes in the same order subspace. This spatiotemporal Gouy phase depends on the ellipticity of the wave packets and the group velocity dispersion of the media. The phase, as a function of propagation distance, is categorized into three distinct regimes: normal dispersion, anomalous dispersion, and zero dispersion. Interestingly, in the regime of anomalous dispersion, the nonmonotonic behavior induces both distortion and revival of the intensity distribution, thereby establishing a phase-locked mechanism that is analogous to the Talbot effect.
