Discovery of the exact 3D one-way wave equation.
basic_science · Level V
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- Record sourced from PubMed, PMID 40593648.
- Also identified by DOI 10.1038/s41467-025-61220-3 and PMC identifier 12215765.
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Abstract
The standard wave equation describing symmetrical wave propagation in all directions in three dimensions, was discovered by the French scientist d'Alembert, more than 250 years ago. In the 20<sup>th</sup> century it became important to search for 'one-way' versions of this equation in three dimensions - i.e., an equation describing wave propagation in one direction for all angles, and forbiting it in the opposite direction - for a variety of applications in computational and topological physics. Here, by borrowing techniques from relativistic quantum field theory - in particular, from the Dirac equation -, and starting from Engquist and Majda's seminal, approximative one-way wave equations, we report the discovery of the exact one-way wave equation in three dimensions. Surprisingly, we find that this equation necessarily - similarly to the innate emergence of spin in the Dirac equation - has a topological nature, giving rise to strong, spin-orbit coupling and locking, and non-vanishing (integer) Chern numbers.