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Propagation of Waves

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Updated: Jan 8, 2026

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids

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Published on: December 4, 2017

Higher-order spatiotemporal wave packets with Gouy phase dynamics.

Wangke Yu¹, Yijie Shen^1,2

¹Centre for Disruptive Photonic Technologies, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore 637371, Singapore.

Nanophotonics (Berlin, Germany)

|December 17, 2025

Summary

Researchers introduce a new family of higher-order spatiotemporal (ST) wave packets. These optical pulses exhibit unique properties like self-healing and tunable sub/superluminal propagation, advancing ultrafast optics.

Keywords:

Gouy phase phase and group velocity spatiotemporal revivals (self-healing)spatiotemporal wave packets structured light ultrashort pulse

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Area of Science:

* Physics
* Optics
* Wave Phenomena

Background:

* Spatiotemporal (ST) wave packets exhibit non-separable spatial and temporal characteristics.
* This non-separability leads to exotic effects like non-diffraction and tunable propagation speeds (sub/superluminal).

Purpose of the Study:

* To present a higher-order generalized family of ST modes.
* To explore the structural complexity and anomalous dynamics of these modes, analogous to higher-order Gaussian modes.
* To introduce a stretch parameter for decoupling pulse duration from modal order.

Main Methods:

* Development of a theoretical framework for higher-order ST modes.
* Incorporation of spatial eigenmodes and existing ST pulses (e.g., toroidal light pulses).
* Introduction of a stretch parameter for temporal envelope manipulation while preserving Gouy-phase dynamics.
* Proposal of a method to analyze phase and group velocities for characterizing sub/superluminal effects.

Main Results:

* Demonstration of anomalous ST Gouy-phase dynamics, including ultrafast cycle-switching and ST self-healing.
* Exhibition of sub/superluminal propagation effects.
* Achieved stretch invariance, decoupling pulse duration from modal order without affecting phase/group velocity laws.
* Universal applicability of the analysis method to complex structured pulses.

Conclusions:

* The proposed higher-order ST modes enrich the complexity of space-time structured light.
* The findings enable precise control over pulse duration and propagation characteristics.
* This work provides a foundation for fundamental physics research and advanced applications in ultrafast optics and structured light.