Theory of photon statistics and optical coherence in a multiple-scattering random-laser medium
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Bibliographic record
Abstract
We derive the photon-number probability distribution and the resulting degree of second-order optical coherence for light emission from a uniformly distributed active species within a multiple-light-scattering medium. This is obtained from a master equation describing the probability distribution for photons in the vicinity of position r, traveling with a wave vector k, related, in turn, to a coarse-grained average of the optical Wigner coherence function. Using a simple model for isotropic, spatially uncorrelated scatterers, this reduces to a generalization of the master equation of a conventional laser in which the medium behaves like a random collection of low-quality factor cavities that are coupled by photon diffusion between a given cavity and its neighbors. Laserlike coherence, on average, is obtained in the random laser above a specific pumping threshold. Photon-number statistics above and below the lasing threshold are computed by first assuming that the atomic response to the local electromagnetic fields is nearly instantaneous. Corrections to this simple model, arising from nonadiabatic atomic dynamics, are then estimated. The dependence of the photon statistics on scatterer density, gain concentration, and position within a sample reveal that, on average, increase of the scattering strength (decrease of the photon transport mean free path) in the medium leads to a sharper peak in the local photon-number distribution, characteristic of increased local coherence in the optical field. We also evaluate the coherence of the output field at points outside the random-laser medium. This is a weighted average of radiation emitted at different positions in the sample, exhibiting varying degrees of coherence due to variations in the local pumping intensity.
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it