Chaos synchronization communication using
extremely unsymmetrical bidirectional injections
Wei Li Zhang,* Wei Pan, Bin Luo, Xi Hua Zou, Meng Yao Wang, and Zhi Zhou
School of Information Science and Technology, Southwest Jiaotong University, Cheng’du, 610031, Sichuan, China
* Corresponding author: firstname.lastname@example.org
Received October 19, 2007; revised December 10, 2007; accepted December 15, 2007;
posted December 20, 2007 (Doc. ID 88728); published January 29, 2008
Chaos synchronization and message transmission between two semiconductor lasers with extremely unsym-
metrical bidirectional injections (EUBIs) are discussed. By using EUBIs, synchronization is realized through
injection locking. Numerical results show that if the laser subjected to strong injection serves as the receiver,
chaos pass filtering (CPF) of the system is similar to that of unidirectional coupled systems. Moreover, if the
other laser serves as the receiver, a stronger CPF can be obtained. Finally, we demonstrate that messages
can be extracted successfully from either of the two transmission directions of the system. © 2008 Optical
Society of America
OCIS codes: 140.2020, 140.1540, 060.4510, 190.0190.
Chaos synchronization of semiconductor lasers has
attracted intensive research efforts for its potential
applications to spread spectrum, private, and secure
communications [1–3]. In chaos communication, the
transmitter lasers are often rendered chaotic through
optical or optoelectronic feedback [2–5]. Messages
masked in the chaotic carrier can be extracted from
the receiver, taking advantage of the chaos pass fil-
tering (CPF) effect [6,7]. Most of these studies con-
centrated on unidirectional injection (UI) schemes.
On the other hand, semiconductor lasers with bidi-
rectional injections (BIs) also show complex chaotic
dynamics [8–10]. However, a BI does not guarantee
permanent synchronization; i.e., the leader and lag-
gard roles of the two coupled lasers are time depen-
dent, which assigns asymmetric physical roles to the
lasers even under symmetric operating conditions
[9–11]. Therefore finding ways to enable chaos com-
munication between mutually coupled semiconductor
lasers is of great importance. Recently, some meth-
ods, i.e., adding individual feedback loops [10,11],
have been developed to obtain synchronization that
is suitable for bidirectional message transmission be-
tween two coupled lasers. These studies drive further
effort for research of mutually coupled systems.
This Letter provides a novel method for chaos com-
munication using extremely unsymmetrical bidirec-
tional injections (EUBIs). In this configuration, no
self-feedback loop is needed to realize high-level syn-
chronization, and we can transmit messages bidirec-
tionally, since CPF is shown when either one of the
two lasers serves as the transmitter. Besides, when
one laser, which is locked by the other laser, serves as
the transmitter, the system can exhibit stronger CPF,
which is helpful to message decryption.
We consider two single-mode semiconductor lasers.
strengths in the two directions are very different.
This system can be modeled as [8–10]
= ?1 + i?1?N1E1+ ?1exp?− i?1?E2?s − ?1?, ?1?
= ?1 + i?2?N2E2+ ?2exp?− i?2?E1?s − ?2?
= P1,2− N1,2− ?1 + 2N1,2??E1,2?2.
Subscripts 1 and 2 denote lasers 1 and 2, respec-
tively. E is the normalized slowly varying complex
field, and N is the normalized carrier number. The
normalized time s and injection delay ? are measured
in units of the photon lifetime ?p. Normalized cou-
pling rate ? is the product of the coupling rate and ?p,
and normalized frequency detuning ? is the angular
frequency detuning ?? multiples by ?p. P is the nor-
malized pumping current above the solitary thresh-
old, T is the ratio of the carrier lifetime to ?p, ? is the
linewidth enhancement factor, and ? is the coupling
phase. In the following discussions the default values
of ?, T, P, ?, and ? are 3, 1710, 1.3, 0, 106, and 0.047,
respectively, corresponding to ?p=1.5 ps.
Using EUBIs means that, first, laser 1 is injection
locked by a strong injection from laser 2; second, to
obtain chaotic output, laser 1 also provides a very
weak injection to laser 2. This weak injection serves
as external disturbance to cause chaotic oscillations
in the system, and it should be weak enough so as not
to affect the permanent injection-locking synchroni-
zation. Through simulation we find that when ?2is
between 3% and 16% of ?1, the above conditions are
satisfied. In the following discussions, we set ?1=0.2
and ?2=0.05?1(where lasers 1 and 2 show the larg-
Figure 1(a) gives the output waveforms of the two
lasers with the time delay ?=1500 ns compensated.
The two lasers show almost similar chaotic wave-
forms, and the corresponding correlation index (CI)
in Fig. 1(b) shows a maximum nearly to 1 at ?t=
−1500 ns. Here, ?t denotes the time shift of output of
laser 2. It is negative, indicating that laser 1 is injec-
February 1, 2008 / Vol. 33, No. 3 / OPTICS LETTERS
0146-9592/08/030237-3/$15.00© 2008 Optical Society of America
tion locked by laser 2. Figure 1(c) presents the value
of CI at ?t=−1500 ns as functions of parameter mis-
matches. We can see the synchronization is robust
against the mismatch of laser parameters; i.e. the
max-CI stays above 0.9 when the mismatch of P or ?
is smaller than 20%. Thus we can conclude that the
weak injection is to some extent neglectable com-
pared with the strong injection, and the physical
mechanism of synchronization in our system is simi-
lar to injection-locking synchronization of the UI sys-
tem [1,4]. However, when ? is mismatched, CI at ?t
=−1500 ns decreases markedly, because the max-CI
will appear at a different value ?t.
In Fig. 2, CPF of the given system is evaluated.
Figures 2(a) and 2(b) show the power spectra of the
two lasers, taking lasers 1 and 2 as the transmitter,
respectively. The black (gray) jagged curve corre-
sponds to laser 1 (laser 2). A sine signal is added to
the transmitter through external modulation. That
is, the output of the transmitter multiples a term 1
+0.05 sin?2?fmt? before being injected to the receiver,
where 0.05 is the modulation index and fmis the
modulation frequency. In both Figs. 2(a) and 2(b), the
message amplitude ?fm=1 GHz? is damped by the re-
ceiver. Furthermore, the message experiences stron-
ger damping in Fig. 2(a) than in Fig. 2(b). To study
CPF in a wider range of message frequency, Fig. 2(c)
presents the amplitudes of message in the power
spectra of the two lasers versus fm. The solid (dotted)
curves denote laser 1 (laser 2) as the transmitter, and
the difference between the two curves with the same
marks indicates the strength of CPF. When laser 2 is
the transmitter, the case is similar to injection-
locking synchronization in UI systems; i.e., CPF is
strong at small fm, and CPF becomes weaker and
weaker as fmincreases to the relaxation-oscillation
frequency. When laser 2 is the transmitter, CPF is
stronger, because laser 2 almost does not reproduce
messages transmitted from laser 1.
For message transmission, there exist three cases:
(1) only laser 1 is the transmitter, (2) only laser 2 is
the transmitter, and (3) lasers 1 and 2 are transmit-
ters and receivers at the same time. Obviously, case 3
is a generic instance for cases 1 and 2, so it is studied
as an example in the following discussion. Chaos
modulation (CM), chaos masking (CMS), and chaos
shift keying (CSK) are the three basic encoding/
decoding methods . In case 3, if messages are
added through direct current modulation (CSK or in-
ternal CM), both the outputs of the two lasers include
messages, and messages may not be decoded success-
fully by taking the difference between the input and
output of one laser. Therefore external CM or CMS
should be considered. For example, when external
CM is used, the chaotic carrier of one laser (without
messages) can be obtained before external modula-
tion is adopted, and when the difference is taken be-
tween this chaotic carrier and the injection (with
messages) from the other laser, messages transmit-
ted from the other laser can be extracted.
Figure 3(a) presents the decoding results corre-
sponding to case 3. Messages (binary pseudorandom
sequences) are encoded to the two lasers by external
CM. The modulation index is 0.05, and the bit rate is
1 Gbit/s. The decoded messages are filtered by a
three-order low-pass Butterworth filter with the cut-
off frequency at 1.2 times of the message frequency.
The upper and the lower waveforms correspond to
the recovered messages by lasers 2 and 1, respec-
tively. We can see therefore that messages transmit-
ted in both directions are recovered successfully, and
their Q factors are as large as 5.6.
Besides the above aspects, the security of the sys-
tem still deserves to be discussed. As it was reported
, outputs of lasers 1 and 2 (?1and ?2) are both ac-
cessible from the transmission links, so cases 1 and 2
should not be considered for secure use. For case 3,
?1−?2=1 means the message transmitted by laser 1
(laser 2) is 1 ?−1?; ?1−?2=−1 means a reverse result.
When ?1−?2=0, the eavesdropper could not judge the
states of the two lasers’ output . From this point
of view, case 3 can be considered secure. However,
like UI systems, an eavesdropper can get the trans-
mission from laser 1 or 2 ??1,2? and use the amplified
sers, taking lasers 1 and 2 as the transmitters, respectively.
(c) Message amplitudes of the two lasers versus modulation
(Color online) (a), (b) Power spectra of the two la-
tion index of outputs of lasers 1 and 2; (c) correlation index
at ?t=−1500 ns as functions of P, ?, and ?.
(a) Output powers in the time domain; (b) correla-
OPTICS LETTERS / Vol. 33, No. 3 / February 1, 2008
?1,2to lock a similar laser (laser 3). Then laser 3 could Download full-text
regenerate a chaotic carrier ?1,2
sages by using ?1,2−?1,2
? . Fortunately, laser 3 must re-
generate the chaotic carrier through injection lock-
ing; namely, laser 3 must show CPF similar to that of
laser 1 and show weaker CPF than laser 2. We can
increase the bit rate and decrease the modulation in-
dex moderately, so messages included in ?1,2cannot
be filtered by laser 3 and ?1,2−?1,2
messages. On the other hand, since laser 2 shows
stronger CPF, it can recover the messages from laser
1. That is, in case 3, message transmission in the di-
rection of strong injection shows similar CPF and se-
curity to UI systems, while messages can be deliv-
ered more securely in the direction of weak injection.
If laser 2 wants to transmit more secure messages to
laser 1, the strong and the weak injections should ex-
change their directions. An example is given in Fig.
3(b), wherein the bit rate is 2.5 Gbit/s and the modu-
lation index is 0.025. We can see laser 2 recovers the
messages successfully, while the messages recovered
by laser 3 (eavesdropper) show large distortions.
In fact, we can also use another method to ensure
communication safely in both directions. As shown in
and recover mes-
does not expose the
Fig. 1(c), the location of the max-CI is very sensitive
to ?, so we can monitor the CI at the end of the two
coupled lasers; a breaking of the link by an eaves-
dropper will change the location of the max-CI (injec-
tion delay), and when this is detected, the two lasers
should stop communication immediately.
In conclusion, chaos synchronization communica-
tion between two semiconductor lasers with EUBIs is
discussed. The characteristic of EUBI system is to
some extent similar to UI systems. Furthermore, it
can provide some inherent advantages. Chaos syn-
chronization is obtained without adding self-feedback
loops, and the two lasers can communicate bidirec-
tionally. This is especially the case when communica-
tion in the weak injection direction shows higher
CPF and security, which is superior to UIs. By using
injection delay as the key, communications in both di-
rections can be considered secure. These results ex-
tend the investigation of mutually coupled systems
and provide us with simple and reliable ways for
W. L. Zhang thanks K. A. Shore for his helpful
guidance and stimulating discussions. This work was
supported by the Specialized Research Fund for the
Doctoral Program of Higher Education of China
(20070613058) and by the Doctoral Innovation Fund
of Southwest Jiaotong University (2007).
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case 3. In (a), the upper and the lower waveforms corre-
spond to decoding at the end of lasers 2 and 1, respectively.
In (b), the upper and the lower waveforms correspond to
decoding at the end of lasers 2 and 3, respectively. Values of
the parameters of laser 3 are set the same as those of
Decoded and original messages corresponding to
February 1, 2008 / Vol. 33, No. 3 / OPTICS LETTERS