Physics Letters A 376 (2012) 1295–1299
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Physics Letters A
Experimental observation of chaotic phase synchronization of a periodically
pump-modulated multimode microchip Nd:YVO
, Chie-Tong Kuo
, Hengtai Jan
, Shiang-Yi Han
, Ming-Chung Ho
Department of Physics, National Sun Yat-Sen University, Kaohsiung 804, Taiwan, ROC
Department of Applied Physics, National Pingtung University of Education, Pingtung 900, Taiwan, ROC
Department of Physics, National Kaohsiung Normal University, No. 62, Shenjhong Rd., Yanchao District, Kaohsiung City 824, Taiwan, ROC
article info abstract
Received 27 October 2011
Received in revised form 3 February 2012
Accepted 15 February 2012
Available online 21 February 2012
Communicated by A.R. Bishop
Microchip solid-state laser
Correlation probability of recurrence
In this Letter we demonstrate the experimental observation of chaotic phase synchronization (CPS) in
a periodically pump-modulated multimode microchip Nd:YVO
laser. PS transition is displayed via the
stroboscopic technique. We apply the recurrence probability and correlation probability of recurrence to
estimate the degree of PS. The degree of PS is studied taking into account the modulation amplitude
and modulation frequency. We also propose an experimental compatible numerical simulation to reﬂect
the fact that the Arnold tongues are experimentally and numerically exhibited in the periodically pump-
modulated multimode microchip Nd:YVO
2012 Elsevier B.V. All rights reserved.
Phase synchronization (PS) of chaotic systems was systemati-
cally studied  after the ﬁrst demonstration proposed in 1996 .
It is deﬁned by the concept of phase locking that is when the os-
cillatory amplitudes of the coupled systems are different, and may
chaotically ﬂuctuating and uncorrelated, the value of n
is still bounded for all times, i.e.,
are two instantaneous phases of two coupled sys-
tems, and n and m are integers. PS is a type of synchronization
reﬂecting mutual adjustment of rhythms of self-sustained oscilla-
tory systems, which has been widely applied to nonlinear systems,
such as plasma [3,4],ﬂuid, chemical reaction [6,7],electronic
circuits [8–10],biology,brain, and secure communica-
tions , and so on.
PS has also been extensively studied because of the practical
importance in the ﬁeld of lasers [14–20]. Gaussian ﬁlter is used to
compute phase variables for detecting PS happening in three par-
allel and lateral coupled chaotic lasers . The intracavity electro-
optic modulator is applied to investigate the transition route of PS
laser via modulating the loss of chaotic laser
output . McAllister et al. investigated a driving signal with two
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distinct frequencies to drive an intracavity acousto-optic modulator
to phase synchronize the intensity dynamics of a chaotic Nd:YAG
laser . Furthermore, PS also can be observed in optically cou-
pled Nd:YAG lasers , electronically coupled Nd:YAG lasers 
and optically coupled diode lasers .
Recently, chaotic phase synchronization (CPS) is experimentally
demonstrated in a chaotic frequency-doubled Nd:YAG laser .
However, the experimental demonstration of CPS for a chaotic
“multimode microchip” solid-state laser has not yet been reported.
Since the microchip solid-state laser is easy to be set up, and we
can operate it with less cost, it is important to discuss its phase dy-
namics for academic researches and practical applications. There-
fore, in this Letter we attempt to propose experimental demon-
stration of CPS for a periodically pump-modulated multimode mi-
laser. Firstly, we investigate PS transition in terms
of the phase space via the stroboscopic technique. It shows that
by increasing the modulation amplitude voltage, we can observe
the formation of CPS through a PS transition process. To verify the
observation of PS, we apply recurrence quantiﬁcation analysis to
our experimental results. Both methods, the analysis of recurrence
probability and correlation probability of recurrence (CPR), indicate
that PS does occur in our laser system. In addition, an aﬃrmative
veriﬁcation of PS is further given by a numerical simulation with
using the N-mode Tang–Statz–deMars model.
This Letter is organized as follows: the experimental setup and
the dynamical behavior of the laser system are introduced in Sec-
tion 2. The experimental results of CPS are presented in Section 3.
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2012 Elsevier B.V. All rights reserved.