Multiplicative Noise in Nanolaser Amplification: From Discrete Emission Events to the Additive-Noise Limit
Abstract
Laser amplification kicks off with just a few photons in the cavity, a regime where standard additive Langevin noise cannot capture the real fluctuations. To understand how this amplification begins, we map out a single-mode photon-carrier model that links macroscopic lasers directly into nanolasers. Stationary rate equations reveal that stimulated emission takes over across a tight pump window. In nanolasers, however, spontaneous processes coexist across a much broader range. Because steady-state averages miss the individual events that lead to the macroscopic photon number, we frame the stochastic dynamics around the actual discrete transitions, deriving a state-dependent diffusion approximation. The destruction of an excited carrier concurrent with the generation of a photon creates a negative photon-carrier cross-correlation. This unavoidably leads to a correlated, multiplicative Gaussian-noise framework. We track the resulting discrete dynamics with an established, event-based Laser Markov Chain (LMC) which stochastically samples pump, relaxation, emission, and cavity-loss events keeping all physical quantities as non-negative integers. Comparing its predictions to those of our multiplicative model proves that the latter reproduces excellently well the statistical behavior of photons and carrier, as long as a continuous diffusion description holds. Once the emission drops into the few-photon regime, however, the discrete model becomes indispensable. On the other hand, at large photon counts relative fluctuations shrink to a level where the state-dependence of the diffusion matrix can be ignored, to leading order, thus returning to the classic Langevin description of the system's stochastic dynamics.
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BibTeX
@misc{sonnino2026multiplicative,
title = {{Multiplicative Noise in Nanolaser Amplification: From Discrete Emission Events to the Additive-Noise Limit}},
author = {G. Sonnino and Ph. Peeters and P. Nardone and G. L. Lippi},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.25520},
eprint = {2610.25520},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.25520},
note = {CC BY-NC-SA 4.0},
}
RIS
TY - UNPB
TI - Multiplicative Noise in Nanolaser Amplification: From Discrete Emission Events to the Additive-Noise Limit
AU - G. Sonnino
AU - Ph. Peeters
AU - P. Nardone
AU - G. L. Lippi
PY - 2026
DA - 2026/10/18
PB - arXiv
DO - 10.48550/arxiv.2610.25520
UR - https://arxiv.org/abs/2610.25520
AB - Laser amplification kicks off with just a few photons in the cavity, a regime where standard additive Langevin noise cannot capture the real fluctuations. To understand how this amplification begins, we map out a single-mode photon-carrier model that links macroscopic lasers directly into nanolasers. Stationary rate equations reveal that stimulated emission takes over across a tight pump window. In nanolasers, however, spontaneous processes coexist across a much broader range. Because steady-state averages miss the individual events that lead to the macroscopic photon number, we frame the stochastic dynamics around the actual discrete transitions, deriving a state-dependent diffusion approximation. The destruction of an excited carrier concurrent with the generation of a photon creates a negative photon-carrier cross-correlation. This unavoidably leads to a correlated, multiplicative Gaussian-noise framework. We track the resulting discrete dynamics with an established, event-based Laser Markov Chain (LMC) which stochastically samples pump, relaxation, emission, and cavity-loss events keeping all physical quantities as non-negative integers. Comparing its predictions to those of our multiplicative model proves that the latter reproduces excellently well the statistical behavior of photons and carrier, as long as a continuous diffusion description holds. Once the emission drops into the few-photon regime, however, the discrete model becomes indispensable. On the other hand, at large photon counts relative fluctuations shrink to a level where the state-dependence of the diffusion matrix can be ignored, to leading order, thus returning to the classic Langevin description of the system's stochastic dynamics.
ER -