• Ultrafast lasers emit pulses which can be regular or change over time, but the two behaviours needed different mathematical models
• Aston University’s Dr Sonia Boscolo was part of a team which has shown the two behaviours are two sides of the same coin, with just one model
• By understanding laser behaviours better, scientists will be able to make lasers more reliable and better suited to specific applications.

A team of international researchers, including an Aston University researcher, has cracked the code on how ‘breather’ laser pulses work, creating a single mathematical model that explains two completely different laser behaviours for the first time.

Ultrafast lasers emit extremely short pulses of light, lasting only picoseconds or femtoseconds, making them essential for applications ranging from eye surgery and biomedical imaging to precision materials processing and advanced manufacturing. By understanding laser behaviours better, scientists will be able to control them, making lasers more reliable and better suited to specific applications.

An ultrafast laser produces pulses of light that circulate within the laser cavity, where they can evolve into stable structures called solitons. Solitons tend to maintain their shape as they travel, unlike conventional light pulses which spread out. Usually, these solitons are identical and regular, like a heartbeat, known as steady-state emission. In a ‘breather’ laser, the solitons change over time and successive cavity roundtrips, growing and shrinking before repeating the cycle, like a breathing pattern. This is an example of a non-equilibrium state, where the laser output does not remain constant but keeps evolving over time.

Experiments have shown two distinct forms of behaviour of ‘breathing’ solitons. Above the minimum power needed for the laser to sustain pulse emission, known as the threshold, breathing solitons oscillate in size rapidly, repeating the ‘breathing’ in just a few cycles. Below the threshold, breathing solitons evolve much more slowly, taking hundreds or even thousands of cycles to complete one ‘breath’.

Until now, scientists have required two different mathematical models to explain these two completely different behaviours. The new unified model, developed by a team including Dr Sonia Boscolo from the Aston Institute of Photonic Technologies, explains both types of breathing at once. By combining how the light evolves as it circulates in the cavity with the slower changes in the laser’s energy supply, they proved that these aren't two separate mysteries - they are two sides of the same coin. Their work is described in their paper ‘Unified model for breathing solitons in fiber lasers: Mechanisms across below- and above-threshold regimes’, published in the American Physical Society’s journal Physical Review Letters.

Dr Boscolo said:

“Above- and below-threshold breathing solitons show markedly different behaviours. Above-threshold breathers oscillate rapidly and can lock to the cavity, producing comb-like radiofrequency spectra and higher-order frequency-locked states, with characteristic sidebands in their optical spectrum. Below-threshold breathers evolve much more slowly, producing densely clustered radiofrequency spectra without strict commensurability, and without optical sidebands. Our new simulation accurately predicts both the fast and slow cycles in one go, something that was previously thought to be impossible with a single model.

“Our work introduces a revised discrete model that incorporates the slow dynamics of the laser gain medium while retaining the detailed cavity description. This unified framework accurately reproduces all experimentally observed behaviours in both regimes and reveals their underlying mechanisms: below-threshold breathing arises from Q-switching combined with soliton shaping, while above-threshold breathers are dominated by Kerr nonlinearity and dispersion.

“This discovery closes a long-standing gap in laser science and provides a vital tool for designing the next generation of light-based technologies.”

The researchers believe that as the industry pushes toward more reliable and powerful optical technologies, this unified framework will offer the clarity needed to guide future innovation in ultrafast laser design. They envision that their model will serve as a practical blueprint for engineers, allowing them to predict and explore complex laser behaviours without the need for fragmented simulations.