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Exponentially tempered Lévy sums in random lasers.

Ravitej Uppu¹, Sushil Mujumdar¹

¹Nano-optics and Mesoscopic Optics Laboratory, Tata Institute of Fundamental Research, 1, Homi Bhabha Road, Mumbai 400 005, India.

Physical Review Letters

|May 23, 2015

Summary

Truncated Lévy flights, a process limiting extreme fluctuations, are perfectly manifested in coherent random lasers. This explains the statistical behavior of nonresonant random lasers, validated by rigorous parameter estimation.

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Area of Science:

Physics
Nonlinear Dynamics
Statistical Mechanics

Background:

Lévy fluctuations present mathematical challenges due to diverging moments.
Truncated Lévy flights address these infinities by restricting fluctuation magnitudes.
Understanding random laser behavior is crucial for developing novel light sources.

Purpose of the Study:

To demonstrate the occurrence of truncated Lévy flights in coherent random lasers.
To establish truncated Lévy flights as the underlying explanation for nonresonant random laser statistics.
To perform rigorous parameter estimation for truncated Lévy flight models in random lasers.

Main Methods:

Modeling random laser intensity using exponentially tempered Lévy sums.
Implementing rigorous parameter estimation for summand variables, truncation, and power-law exponents.
Comparing theoretical models with experimental data on fluctuation behavior.

Main Results:

A perfect manifestation of truncated Lévy flights was observed in coherent random lasers.
The truncated Lévy flight model accurately explains the complete statistical behavior of nonresonant random lasers.
Parameter estimation showed excellent agreement between computed and experimentally observed fluctuation behaviors.

Conclusions:

Truncated Lévy flights provide a unified explanation for random laser statistical properties.
The study validates the application of truncated Lévy flight models in physical systems.
This research bridges theoretical concepts in stochastic processes with experimental observations in random lasers.