The Gouy phase flips sign and becomes complex when a system breaks symmetry.

When focused waves travel, they pick up an extra phase shift called the Gouy phaseGouy phaseA phase shift that waves experience when passing through a focus or specific point.. Researchers studied this effect in relativistic beam wave packets governed by an equation that includes balanced energy gain and loss, known as parity-time symmetry. They found that the Gouy phase detects the exact point where this symmetry breaks, called the exceptional pointexceptional pointA point in parameter space where two eigenvalues and eigenvectors of a non-Hermitian system coalesce.. In the unbroken regime, the phase stays purely real. Once the boundary is crossed into the broken regime, it changes sign and gains an imaginary part. At the transition point, the phase change vanishes for small masses but peaks for large masses. Finally, they propose measuring this phase by tracking how a light beam dims inside a lossy waveguide.

Why it matters

This helps physicists detect critical points in systems with gain and loss. It could improve the design of photonic devices like lasers and sensors.

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