Stochasticity,complexity and synchronization in semiconductor lasers
Authors:   , Tiana Alsina Jordi 
Published: October 2023

The purpose of this Thesis is study the dynamical behavior of semiconductor
lasers with optical feedback, as well as analyze the synchronization of this kind of
systems under different coupling arquitectures. This study has been done from an
experimental point of view, but in some cases we have used numerical models in
order to verify and/or extend the experimental results.
A semiconductor laser in absence of any optical feedback emits light at constant
power. If one wants to induce dynamics in the laser, a good strategy is to introduce
an external cavity able to reflect the emitted light back into the laser. Due to this
feedback, the laser can show a large variety of dynamical behaviors. In this Thesis
we will focus mainly in a dynamical regime known as low frequency fluctuations
regime (LFF). The LFF regime takes place when the pump current of the laser is
close to its threshold current and the feedback strength is sufficiently large, and it
consists in sudden intensity dropouts arising at irregular times, followed by a gradual
and stepwise recovery.
During this Thesis, we have characterized in detail the dynamical behavior of
the time between intensity dropouts for a semiconductor laser with feedback, by
using different statistical techniques based on information theory concepts. We
have quantified the probability of appearance of certain patterns within the temporal
series, as well as its degree of complexity. As a result of these studies, we can conclude
that the dynamics of a semiconductor laser with optical feedback is stochastic for
pump current values close to the laser threshold. On the other hand, for larger pump
currents the dynamics is basically deterministic (chaotic). Numerical simulations
have shown a good qualitative and quantitive agreement with the experimental
results.
During this Thesis we have also studied the ability of semiconductor lasers to
synchronize under different coupling architectures. First, we have characterized the
leader-laggard dynamics showed by two semiconductor lasers bidirectionally coupled
operating at the LFF regime, with a method that takes into account the number
of forbidden patterns that appears in the temporal series. We have quantified the
degree of stochasticity of the system as a function of the pump current of both lasers.
A second coupling architecture studied here, consists in two lasers unidirectionally
coupled via two paths. In this case, we have analyzed how the synchronization is
affected under different values of the coupling strength of both paths, as well as
the potential of this system (or rather, the lack thereof) to be used in chaotic
communications.
Finally we have characterized the synchronization at zero lag for two lasers coupled
bidirectionally via a passive relay. In particular, we have studied the desynchronization
events and their statistics for different pump currents.
The experimental results obtained in this Thesis give a global perspective of the
dynamical statistical properties of semiconductor laser dynamics, both isolated or
coupled to other lasers, which contributes to a better understanding of this kind of
dynamical systems.

L’objectiu d’aquesta Tesi ´es l’estudi de la din`amica de l`asers de semiconductor
amb retroalimentaci´o `optica, aix´ý com l’an`alisis de la sincronitzaci´o d’aquest tipus
de sistemes sota diferents arquitectures d’acoblament. Aquest estudi s’ha fet sempre
des d’un punt de vista b`asicament experimental, tot i que en alguns casos hem
utilitzat models num`erics per tal de verificar i/o ampliar els resultats experimentals.
Un l`aser de semiconductor en abs`encia de retroalimentaci´o `optica o altres perturbacions
externes, emet llum a una intensitat pr`acticament constant. Aix´ý doncs, si el
que es vol ´es indu¨ýr din`amica en el l`aser, una bona estrat`egia ´es introdu¨ýr una cavitat
externa capa¸c de reflexar la llum cap al l`aser. Un cop la llum ´es reinjectada, els l`asers
de semiconductor poden mostrar una gran varietat de comportaments din`amics. En
aquesta tesis ens centrarem principalment en un r`egim din`amic anomenat r`egim de
fluctuacions de baixa frequ`encia (LFF en les seves sigles en angl`es). El r`egim d’LFF
es d´ona quan el corrent d’injecci´o del l`aser es troba a prop del seu corrent llindar
i la intensitat de la retroalimentaci´o ´es suficientment gran, i est`a caracteritzat per
sobtades caigudes de la intensitat a temps irregulars, seguides per una recuperaci´o
gradual i escalonada.
Durant aquesta Tesi, hem caracteritzat de forma detallada el comportament din`amic
de la distribuci´o dels temps entre les caigudes d’intensitat d’un l`aser de semiconductor
amb retroalimentaci´o `optica, utilitzant diferents m`etodes estad´ýstics basats
en conceptes de teoria de la informaci´o. En particular, hem quantificat la probabilitat
d’aparici´o de certs patrons dins les s`eries temporals, aix´ý com el grau de
complexitat d’aquestes. Durant aquest estudi hem observat que la din`amica d’un
l`aser de semiconductor amb retroalimentaci´o es estoc`astica per valors del corrent
d’injecci´o propers al corrent llindar del l`aser. D’altra banda, per a valors m´es grans
del corrent d’injecci´o la din`amica ´es m´es determinista (ca`otica). Les simulacions
num`eriques realitzades han mostrat un acord qualitatiu i quantitatiu amb els resultats
experimentals.
Durant aquesta Tesi tamb´e hem estudiat la sincronitzaci´o entre l`asers de semiconductor.
Hem analitzat diferents arquitectures d’acoblament. Primer hem caracteritzat
la din`amica leader-laggard que presenten dos l`asers de semiconductor acoblats
bidireccionalment operant en r`egim de LFFs, amb un m`etode que t´e en compte el
nombre de patrons prohibits que apareixen en la s`erie temporal. Hem quantificat
el grau d’estocasticitat del sistema en funci´o del nivell de bombeig al qual est`an
sotmesos els dos l`asers.
La seg¨uent arquitectura d’acoblament que hem estudiat consisteix en dos l`asers
acoblats unidireccionalment a trav´es de dos camins. En aquest cas hem analitzat
com es veu afectada la sincronitzaci´o sota diferents valors de l’acoblament dels dos
camins, aix´ý com el potencial d’aquest esquema experimental per realitzar comunicacions
ca`otiques.
Per ´ultim hem caracteritzat la sincronitzaci´o a retard zero per dos l`asers acoblats
bidireccionalment, a on els dos l`asers tenen la seva pr`opia realimentaci´o `optica. En
particular, hem estudiat els events de desincronitzaci´o i la seva estad´ýstica per a
diferents corrents d’injecci´o.
Els resultats experimentals obtinguts en aquesta Tesi, ofereixen una prespectiva
global de les propietats estad´ýstiques de la din`amica de l`asers de semiconductor,
tant a¨ýllats com acoblats a altres l`asers, que contribueixen a entendre millor aquests
sistemes din`amics.