Theoretical and experimental analysis of phase noise in semiconductor lasers biased below threshold

We report a theoretical and experimental study of phase noise in semiconductor lasers when the bias current is below the threshold value. The theoretical study is performed by using two types of rate equations, with additive and multiplicative noise terms. We find the conditions for which the evolut...

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Main Authors: Iker Pascual de Zulueta, Angel Valle
Format: Article
Language:English
Published: IOP Publishing 2025-01-01
Series:JPhys Photonics
Subjects:
Online Access:https://doi.org/10.1088/2515-7647/adaa42
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author Iker Pascual de Zulueta
Angel Valle
author_facet Iker Pascual de Zulueta
Angel Valle
author_sort Iker Pascual de Zulueta
collection DOAJ
description We report a theoretical and experimental study of phase noise in semiconductor lasers when the bias current is below the threshold value. The theoretical study is performed by using two types of rate equations, with additive and multiplicative noise terms. We find the conditions for which the evolution in those rate equations can be described by 1-dimensional and two dimensional Brownian motions, respectively. The main statistical differences between the additive and multiplicative noise models are then illustrated by using the simplified Brownian motion models. Additive and multiplicative noise models predictions are compared with measurements of the phase noise with a coherent receiver using a 90 ^∘ optical hybrid. We develop a novel method to extract the phase noise directly from our measurements, that in contrast to the usual direct method is not based on the analysis of the phase noise difference. The method permits a direct visualization of the phase noise trajectories and a calculation of the averages and the distribution that is valid in the short-time limit. Our results are in very good agreement with the results obtained with the method based on the phase noise difference. Our experimental results show that the variance of the phase noise grows linearly in time and has Gaussian statistics, supporting the modelization of the phase noise statistics with the additive noise model.
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spelling doaj-art-b73b98e9834f4da0ac0a3fe019f4f7f02025-01-24T13:00:19ZengIOP PublishingJPhys Photonics2515-76472025-01-017101501310.1088/2515-7647/adaa42Theoretical and experimental analysis of phase noise in semiconductor lasers biased below thresholdIker Pascual de Zulueta0Angel Valle1https://orcid.org/0000-0002-3307-5485Instituto de Física de Cantabria, Universidad de Cantabria-CSIC , Santander, SpainInstituto de Física de Cantabria, Universidad de Cantabria-CSIC , Santander, SpainWe report a theoretical and experimental study of phase noise in semiconductor lasers when the bias current is below the threshold value. The theoretical study is performed by using two types of rate equations, with additive and multiplicative noise terms. We find the conditions for which the evolution in those rate equations can be described by 1-dimensional and two dimensional Brownian motions, respectively. The main statistical differences between the additive and multiplicative noise models are then illustrated by using the simplified Brownian motion models. Additive and multiplicative noise models predictions are compared with measurements of the phase noise with a coherent receiver using a 90 ^∘ optical hybrid. We develop a novel method to extract the phase noise directly from our measurements, that in contrast to the usual direct method is not based on the analysis of the phase noise difference. The method permits a direct visualization of the phase noise trajectories and a calculation of the averages and the distribution that is valid in the short-time limit. Our results are in very good agreement with the results obtained with the method based on the phase noise difference. Our experimental results show that the variance of the phase noise grows linearly in time and has Gaussian statistics, supporting the modelization of the phase noise statistics with the additive noise model.https://doi.org/10.1088/2515-7647/adaa42semiconductor laseroptical phasegain-switchingspontaneous emission noisequantum random number generationquantum key distribution
spellingShingle Iker Pascual de Zulueta
Angel Valle
Theoretical and experimental analysis of phase noise in semiconductor lasers biased below threshold
JPhys Photonics
semiconductor laser
optical phase
gain-switching
spontaneous emission noise
quantum random number generation
quantum key distribution
title Theoretical and experimental analysis of phase noise in semiconductor lasers biased below threshold
title_full Theoretical and experimental analysis of phase noise in semiconductor lasers biased below threshold
title_fullStr Theoretical and experimental analysis of phase noise in semiconductor lasers biased below threshold
title_full_unstemmed Theoretical and experimental analysis of phase noise in semiconductor lasers biased below threshold
title_short Theoretical and experimental analysis of phase noise in semiconductor lasers biased below threshold
title_sort theoretical and experimental analysis of phase noise in semiconductor lasers biased below threshold
topic semiconductor laser
optical phase
gain-switching
spontaneous emission noise
quantum random number generation
quantum key distribution
url https://doi.org/10.1088/2515-7647/adaa42
work_keys_str_mv AT ikerpascualdezulueta theoreticalandexperimentalanalysisofphasenoiseinsemiconductorlasersbiasedbelowthreshold
AT angelvalle theoreticalandexperimentalanalysisofphasenoiseinsemiconductorlasersbiasedbelowthreshold