Measuring maximal eigenvalue distribution of Wishart random matrices with coupled lasers

Area of Science:

• Physics
• Optics
• Statistical Mechanics

Background:

• Coupled fiber lasers exhibit complex output power fluctuations.
• Understanding these fluctuations is crucial for laser applications and fundamental physics.
• Random matrix theory provides models for complex systems.

Purpose of the Study:

• To determine the probability distribution of combined output power from multiple coupled fiber lasers.
• To compare experimental results with established theoretical distributions from random matrix theory.
• To validate the applicability of Tracy-Widom and Majumdar-Vergassola distributions in this context.

Main Methods:

• Acquired 500,000 measurements of combined output power from 25 coupled fiber lasers.
• Analyzed the probability distribution of the power measurements.
• Compared the experimental distribution with theoretical predictions without using fitting parameters.

Main Results:

• The combined output power distribution closely matched the Tracy-Widom distribution for small power deviations.
• The distribution aligned with the Majumdar-Vergassola distribution for large power deviations.
• Excellent agreement was observed between experimental data and theoretical models.

Conclusions:

• The study experimentally validates the use of Tracy-Widom and Majumdar-Vergassola distributions for describing coupled fiber laser output power.
• This finding offers a parameter-free method for predicting laser power statistics.
• The results contribute to the understanding of complex systems and random matrix theory applications in optics.