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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.
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.
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