NoLineal 2016. Book o abs ac s. Pos e s. 91
Simula ion o An iphase Dynamics in Lase s wi h Cellula Au oma a. A
Wo k in P og ess
F. Jiménez-Mo ales*, J.L. Guisado**
(*)Dp o. Física de la Ma e ia Condensada. (**) Dp o. A qui ec u a y Tecnología de Compu ado es.
Uni e sidad de Se illa, A da. Reina Me cedes s/n, 41012 Se illa, (Spain)
emails: [email p o ec ed], [email p o ec ed]
Cellula au oma a(CA) a e aclass o spa ially and
empo allydisc e e ma hema icalsys ems cha ac e -
ized by local in e ac ions and synch onous dynami-
cal e olu ion. They ha e he abili y o gene a e com-
plex beha io om se s o componen s ha ollow
simple ules. xAwide a ie y o physicalsys ems such
as magne iza ion in solids, eac ion di usion p o-
cesses, luid dynamics, g ow h phenomena,... ha e
beenmodeled by CA.In[1]a CAwas p oposed o sim-
ula e lase dynamics which was able o cap u e he
essen ial ea u es and phenomenology encoun e ed
in lase s such as elaxa ion oscilla ions, spiking be-
ha io and pa e n o ma ion. The model can also
simula e he physics o pulsed pumped lase s [2].
0
2000
4000
6000
0 2000 4000 6000
I1
0
2000
4000
6000
8000
0 2000 4000 6000
I1+I2
0
2000
4000
0 2000 4000 6000
I2
-4000
-2000
0
2000
4000
0 2000 4000 6000
I1-I2
FIGURE 1. To model an iphase dynamics in lase s
wi h a CA wo lase subsys ems a e conside ed. Time
se ies o he in ensi y o bo h popula ions, he o al
in ensi yand he di e enceo in ensi ies. The pump-
ing p obabili y is p=0.01 and he coupling pa ame-
e β=0.8.
In his wo k we ex end he o iginal CA o s udy
an iphase oscilla ions in lase s ha was expe imen-
ally obse ed in a class B Nd:YAG lase [3]. The CA
ule o e olu ion is composed o ou di e en p o-
cesses ep esen ing he pumping o elec ons, he
s imula ed emission, and he decaying o elec ons
and pho ons. We also conside he lase o be com-
posed o wo subsys ems associa ed wi h wo o hog-
onal pola iza ion eigens a es. The e o e, each one is
desc ibed by i s in ensi y I1,2 and popula ion in e -
sion D1,2. The wo subsys ems a e coupled by c oss-
sa u a ion phenomena: he in ensi y o one pola iza-
ion is ampli ied by he popula ion in e sion associa-
ed o he o he popula ion and he s imula ed emi-
ssion in one pola iza ion sa u a es he popula ion in-
e sion o he o he pola iza ion. Theo e ically i has
been shown ha he o al in ensi y I1+I2and he o-
al popula ion in e sion D1+D2p esen elaxa ion
oscilla ions wi h a equency Rwhile he di e ence
I1−I2and D1−D2exhibi slow elaxa ion oscilla ions
whose equency is L=1−β
1+β R. P elimina y esul s
o he CA simula ions a e shown in Figu e 1. The
classical poin o iew o s udy he lase dynamics a e
heMaxwell-Blochequa ions howe e heCA models
a ecomplemen a y ools ha ep esen anad an age
in cases in which he sys em o di e en ial equa ions
ha e con e gence p oblems.
Keywo ds: cellula au oma a, lase s, an iphasedyna-
mics.
Bibliog aphy
[1]J.L. Guisado and F. Jiménez-Mo ales and J.M. Gue a. Cellula
au oma on model o he simula ion o lase dynamics. Phys.
Re . E, 67:066708, 2003.
[2]J.L. Guisado and F. Jiménez-Mo ales and J.M. Gue a. Simula-
ion o he Dynamics o Pulsed Pumped Lase s Based on Cel-
lula Au oma a. Lec u e No es in Compu e Science, 3305, 278-
285,2004.
[3]Edua do Cab e a and Osca G. Calde ón and J.M. Gue a.
Expe imen al e idence o an iphase popula ion dynamics in
lase s. Phys. Re . A, 72:043824, 2005.