FIRST OBSERVATION OF DETERMINISTIC CHAOS IN PASSIVE Q-SWITCHING PULSATION

HAL Id: jpa-00227715

https://hal.archives-ouvertes.fr/jpa-00227715

Submitted on 1 Jan 1988

HAL

is a multi-disciplinary open access archive for the deposit and dissemination of sci- entific research documents, whether they are pub- lished or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.

L’archive ouverte pluridisciplinaire

destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

FIRST OBSERVATION OF DETERMINISTIC CHAOS IN PASSIVE Q-SWITCHING PULSATION

M. Tachikawa, K. Tanii, F.-L. Hong, T. Tohei, M. Kajita, T. Shimizu

To cite this version:

M. Tachikawa, K. Tanii, F.-L. Hong, T. Tohei, M. Kajita, et al.. FIRST OBSERVATION OF DE-

TERMINISTIC CHAOS IN PASSIVE Q-SWITCHING PULSATION. Journal de Physique Colloques,

1988, 49 (C2), pp.C2-413-C2-416. �10.1051/jphyscol:1988298�. �jpa-00227715�

JOURNAL DE PHYSIQUE

Colloque C2, Supplement au n06, Tome 49, juin 1988

FIRST OBSERVATION OF DETERMINISTIC CHAOS IN PASSIVE Q-SWITCHING PULSATION

M. TACHIKAWA, K. TANII, F.-L. HONG, T. TOHEI, M. KAJITA' and T. SHIMIZU

Department of Physics, Faculty of Science, University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113, Japan

'~nstitute for Molecular Science, Myodaiji, Okazaki 444, Japan

R B S U ~ ~ : Nous proposons un modSle qui dscrit des diffsrents types de l'instabilite' pe'riodique du laser C 0 2 avec un absorbant saturable.

~ ' a n a l y s e par des Bquations d'Evolutions basses sur ce modsle prsdit l'existence d'un chaos dsterministique dans la pulsation du Q switch passif. La pulsation chaotique a BtS observse pour la premizre fois dans un laser de mode unique qui contient un absorbant saturable.

Abstract: A model which well describes various types of periodic instability in a C 0 2 laser containing a saturable absorber is proposed.

The rate-equation analysis based on the model predicts the existence of deterrnimistic chaos in the passive Q-switching pulsation. The chaotic pulsation has been observed for the first time in a single-mode laser system with saturable absorber.

A single-mode laser containing a saturable absorber inside the cavity shows a periodic self-pulsation well known as passive Q-switching (PQS). Dynamical properties of the gain (laser) and loss (absorber) media critically influence the transient PQS pulse structures. In a C 0 2 laser with a gaseous absorber, various types of PQS are observed depending on the lasing conditions and characteristics of the absorbing molecules. Typical examples of the PQS pulses are shown in Figures l(a)-(dl. We call them single spikes [(a)], sinusoidal modulation C(b) 1, and PQS with undulation [(c) and (d)]. Thus far there has been no model that systematically reproduces these transient features of periodic PQS. Especially the mechanism of the undamped undulation superposed on the quasi-cw pulse tail was not understood at all.

Recently we have proposed a novel rate-equation model which describes the laser medium as a three-level system /I /. All the PQS pulse shapes observed thus far in a CO laser are reproduced with detailed fidelity in computer simulations as 2shown in Figures I (a8)-(d'). The model includes a fast vibrational relaxation of the lower laser level as an important process to produce the complicated structures of the PQS pulse with undulation. The undulation on the pulse tail can be interpreted to be a relaxation oscillation caused in the balance between the induced emission and the relaxation of the lower laser level.

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1988298

JOURNAL DE PHYSIQUE

200 psec 200 psec

HCOOH

1

500 psec

psec

Fig.1 Observed [ (a)-(d) 1 and calculated I (a1)-(d') I ^periodic PQS pulsations under different conditions of the laser and absorber.

It has been found out through numerical analysis based on the model that not only regular but chaotic passive Q-switching exists in the limited ranges of the absorber parameters such as an absorption coefficient and a population relaxation rate. Figure 2 shows numerically calculated PQS pulse trains [(a)-(e) 1 and their power spectra [ (a1)-(el)l as functions of the pumping parameter in the laser medium. With an increase in the pumping rate P the period-doubling bifurcation successively occurs and then chaotic pulsation appears. The power spectrum at the pumping rate of 60.0 Hz has a frequency component f and its harmonics. The f/2 and f/4 components and their overtones clearly appear in the power spectra of period-2 and -4 time series. The chaotic pulsation has a broadband spectrum as is shown in Fig.2(d1). A periodic window that has the f/6 and f / 3 components is obtained at a larger pumping rate.

The critical conditions for the chaotic PQS are fulfilled by finely adjusting the controllable parameters of a CO laser with a formic acid absorber, and chaos has been observed for the girst time in a single-mode

laser-with-saturable-absorber system. The absorption is controlled by changing the pressure of formic acid and the laser frequency. A favorable value of the relaxation rate of the absorptive levels is achieved by adding a buffer gas (SF6) to the absorber.

Figure 3 shows the period-doubling route to chaos and the periodic window observed as a function of the discharge current i together with the power spectra. Good agreement is achieved between the observed features and the theoretical results. According to the procedure developed by Grassberger and Procaccia /2/ the fractal dimension of the chaotic orbit has been measured to be approximately 2.3.

Fig.2 PQS-pulse trains [ (a)- (e) I and their power spectra [ (a')-(e') I as functions of the pumping rate P obtained from the numerical calculations based on the rate-equation model. The power spectra are plotted in logarithmic units.

The lasers which exhibit chaos in the single-mode oscillation have been limited to high gain lasers such as a N H 3 FIR laser / 3 / and a Xe laser / 4 / since the bad-cavity condition is generally needed. However the present experiment demonstrates that chaotic instability can be provoked even id a small-gain laser far from the bad-cavity condition by introducing a saturable absorber, namely another degree of freedom, into the laser cavity.

C2-416 JOURNAL DE PHYSIQUE

The single-mode chaotic instabilities observed thus far in intrinsic (without any electric devices) laser systems /3,4/ are qualitatively interpreted to be caused by the mode-splitting effect due to strong dispersion. These instabilities can not be analyzed without considering the molecular polal-ization and the phase of the electromagnetic field /5,6/. On the other hand the present chaos is well described by the rate equations.

This means the transient variations of populations of the relevant energy levels in the amplifier and absorber play a dominant role to produce the chaotic dynamics in the PQS pulsation.

(dl (d' )

( e 4

0 ^kHz

Fig.3 Observed PQS pulse trains [(a)-(e)] and their power spectra [(a')-(el)]

as functions of the discharge current i. The power spectra are plotted in logarithmic units. The laser line is 9 pm R(20).

ferences

M.Tachikawa, K.Tanii, M.Kaj ita, and T.Shimizu, App1.Phys.B 2 (1 986) P.Grassberger and I.Procaccia, Physica (1983) 189-208.

C.O.Weiss, W-Klische, P.S.Ering, and M.Cooper, 0pt.Commun. 52 (1 985 R.S.Gioggia and N.Abraham, Phys.Rev.Lett.

a

H-Zeghache and P.Mande1, J.0pt.Soc.Am.B 2 ( 1 985) 18.

M.Shih, P.Milonni, and J-Ackerhalt, J.0pt.Soc.Am.B 2 (1 985) 1 30.

After writing this paper we were informed by Prof.Arimondo that his group had observed the chaotic PQS in advance of our work (D.Hennequin et al.,