high chaotic spiking rate using mach-zehnder modulator...al-khafaji and al-naimee iraqi journal of...

Al-Khafaji and Al-Naimee Iraqi Journal of Science, 2016, Special Issue, Part B, pp: 362-369

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High Chaotic Spiking Rate Using Mach-Zehnder Modulator

Rabab K. Al Khafaji*1

and Kais A. Al Naimee1,2

1 Department of Physics, College of Science , University of Baghdad, Al Jadiriah , Baghdad , Iraq

2 CNR-Istituto Nazionale di Ottica Applicata, Largo E Fermi 6, 50125 Firenze, Italy

Abstract We report experimentally the generation of spiking in semiconductor laser (SL)

with an ac-coupled optoelectronic feedback by using nonlinear device Mach-

Zehnder modulator (MZM) . This study is considered in conditional parameter when

the DC bias voltage of Mach-Zehnder Modulator is varied . By changing the control

parameter , time series , the corresponding Fast Fourier Transform FFT and attractor

have been measured . To investigate chaotic evolutions ( history of chaos ) for the

change of control parameter , the bifurcation diagram is extracted .

Keywords: Chaos, laser, feedback, Mach-Zehnder Modulator (MZM)

معدل عالي التكرارية للنبضات الفوضوية باستخدام مضمن الماخ زنيدر

قيس النعيمي رباب الخفاجي ,

العراق, بغداد, كلية العلوم ,جاهعة بغداد ,قسن الفيزياء

الخالصة ة الكيرو ذو التغذية العكسي ACمع مقترن ) Mach-Zehnder Modulatorالديناميكية الالخطية لـ)

.بصرية قد ُدرست عمميًا Mach-Zehnderواخذ بنظر االعتبار في ىذه الدراسة عامل مشروط عندما الفولتية االساسية لـ)

Modulator ) ُغيرت . بتغيير ىذا العامل المسيطر , التسمسل الزمني(time series ) ويل وتح ُقيست . (attractor)المطابق وفضاء الطور FFTفورير السريع

تم ( Bifurcation diagram )لمعامل المسيطر , المخطط المتشعب (chaos)الختبار تطور الشواش استخراجو .

Introduction

The qualitative study of unstable aperiodic behavior in deterministic non-linear

dynamical systems can be defined as Chaos theory [1]. The field of study in mathematics

and physics used to describe the behavior of dynamical system which is called the chaos

theory, that is highly sensitive to initial state i.e. small perturbation in initial condition yields

ISSN: 0067-2904


252

significantly varying behavior [2]. A high-dimensional phase space is needed in a nonlinear

system to produce the high-dimensional chaos required for these applications, Time delayed

feedback is used to achieve this effect [3]. The principle of chaotic carrier communications

scheme is that the chaotic carrier is used to conceal and transmit the message between the

transmitter and the receiver and thus a broadband spectrum of frequencies is used as a

carrier for the message [4]. Chaotic systems are characterized by sensitive dependence on

initial conditions, similarity to random behavior , and conditions broad –band power

spectrum [5].

A nonlinear device Mach–Zehnder Modulator (MZM) could be utilized to transform in a nonlinear

way the phase variations into intensity variations, which are finally detected by photodetector . One of

the possibilities of external modulation is to use a Mach-Zehnder structure in a material showing

strong electro-optic effect. Mach-Zehnder modulators provide both the required bandwidth and

equally important means for minimizing the effects of dispersion . MZM is a device used to determine

relative phase shift between two collimated beams from a coherent light source either by changing

length of one of the arms or by placing a sample in path of one of the beams. MZM has two input

ports and two output ports. A basic MZM as shown in Figure 1 is constructed using two couplers, one

at the input acts as splitter and another at the output acts as combiner. The light is split in two arms of

the interferometer by the input coupler and recombined at the output by the output coupler. The optical

path length of two arms is unequal making the phase shift corresponding to delay to be a function of

wavelength of the input signal [6].

In chaos theory, an attractor is a pattern that forms when behavior of the system is plotted

in phase space , Attractors have four types ) Point attractor , Periodic attractor ,Torus

attractor and Strange attractor ) [7] .

Bifurcation diagram could be described as a record of change in the behavior of a dynamical

system as parameter changes. Bifurcation diagram is a useful tool in viewing more globally the

dynamics of chaotic system over a range of parameter values, thereby allowing simultaneous

comparison of both periodic and chaotic behaviors i.e. the way in which chaos is reached when a

parameter value is varied continuously [8] . A system transitions from one type of behavior to another

depending on the value of a set of important parameters. The parameters responsible for these regime

changes are called bifurcation parameters [9] . The plot of bifurcation diagram is used to investigate

chaotic evolutions for the change of a certain parameter. A bifurcation diagram is obtained from a time

series by sampling and plotting local peaks and valleys of the waveforms for the parameter changes

[10].

The Experiment

The chaotic behavior of the opto-electronic feedback loop OEFB is investigated under the effects

of the Bias Voltage as control parameter. A Schematic of the experimental setup for investigation of

chaotic behavior in nonlinear device Mach-Zehnder Modulator with OEFB is shown in Figure-2.

Figure 1- Mach-Zehnder modulator [7]


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This section includes the measurements and results of the chaotic behavior by using nonlinear

device which is a Mach-Zehnder modulator (MZM). In our system the Mach-Zehnder Modulator is

the source of nonlinearity while semiconductor laser that provides the optical power acts as a linear

current-to-optical-frequency converter . A semiconductor laser supplies continuous-wave (1310 nm)

optical power to the MZM . The optical power inside the MZM is modulated .The output of the MZM

connect into photodetector (PD) and the signal is driven to the amplifier than into RF electrode of

MZM . The feedback input to the RF electrode of MZM will modify the optical power input inside the

modulator which will produce a new signal with rich dynamics [11] .

Results and Discussions

The behavior of the dynamical optoelectronic feedback system will be discussed. We

will present experimentally measured time series showing the wide variety of dynamical

behavior that can be exhibited by the system. The dynamics of the physical system under

investigation depend on changing the magnitude of the bias voltage while all other

parameters are constant. The constant control parameters are the amplifier gain and the

photodetecor gain .

A wide range of behaviors (change of nonlinear dynamics behavior) is noticed as the bias

Voltage is varied . As bias Voltage varies, the feedback gain will also vary i.e the value of

the feedback loop will vary which will effect on the dynamics behavior of the Mach-

Zehnder modulator .

By incrementally increasing the bias voltage, the time series transition from a line at (0V)

of bias voltage to periodic oscillations that steadily increase in amplitude to types of other

periodic oscillations to more complex waveforms and finally to a chaos .Some of these

transition evolve gradually and others are abrupt.

Figure-3, plot a selection of these waveforms within this sequence when the bias voltage

of (6 volt) the detected optical power is stable and has a periodic oscillations as shown in

Figure-3a. Phase space reconstruction is extracted by taking the only amplitude of the output

of the oscillator which is recorded within the time series, and a shift is made in the initial

condition to observe the behavior of the system as shown in Figure-3b which is represent

corresponding attractor by using an embedding technique with appropriate delays.Figure-3c

represents the corresponding Fast Fourier spectrum FFT.

As the bias voltage of the MZM increases, the dynamics of the system turns into period

doubling than into a chaotic behavior.

Figure-4 shows the dynamics behavior (period doubling) of the system when the bias

voltage at (9 V) where Figure-4a shows time series of this behavior, Figure-4b represents

corresponding attractor for the same value and Figure-4c will represent corresponding Fast

Fourier spectrum FFT.In Figure-5.The system will become more chaotic when the bias

voltage of MZM at (18 V) as seen from the attractor plotting. So Figure-5a will show time

series of this value, Figure-5b will represent corresponding attractor for the same value and

Figure-5c will represent corresponding Fast Fourier spectrum FFT.

Figure 2-Illustration the experimental configuration


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b

C

Figure 3- periodic behavior when bias voltage at (6V) : a- time series , b- corresponding attractor

, c- corresponding FFT.


255

a

b

c

Figure 4- periodic behavior when bias voltage at (9V) : a- time series , b- corresponding attractor

, c- corresponding FFT.


256

Figure 5- periodic behavior when bias voltage at (18V) : a- time series , b- corresponding attractor ,

c- corresponding FFT.

To study the dynamical behavior of the chaotic oscillator of the transmitter under certain

conditions, the bifurcation diagram should be plotted.

From these time series, the bifurcation diagram will be presented in Figure-6. Time series

are recorded for bias voltages ranging from 0 V up to 140 V, with (0.1V) increments.

a

b

c


257

The rout of chaos is summarized with a bifurcation diagram as shown in Figure-6 . At the

bias voltage (6V) , the oscillation begins as shown in the Figure-3. These oscillations are

periodic. At the bias voltage ((7-9) V) , a fast scale dynamics behave like a period doubling .

Finally a large number of points corresponds to chaos behavior at the bias voltage (9-14) V.

Conclusions

In conclusions, the chaotic spiking in semiconductor laser with an OEFB using MZM is

experimentally demonstrated. The control parameter is based on the change of the bias voltage. The

effect of DC bias voltage on chaotic behavior are studied experimentally, with the increasing of this

parameter the system turn from steady state to unstable periodic state and then to chaotic state as have

been noticed. The chaotic behavior could be studied in terms of attractor, FFT corresponding to time

series; we show different attractor and FFT for different state (stable, periodic, double periodic, quasi-

periodic and chaotic). The bifurcation diagram is drawn as a function for each parameter show that the

system could be controlled by this parameter.

References

1. Kamran Rauf and Muhammad Yasir. 2013 .Chaos Based Optical Communication), International

Journal of Computer and Communication Engineering, Vol. 2, No. 2, March.

2. Neil McBride. 2005. Chaos Theory as a Model for Interpreting Information Systems in

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3. Kathy Ludge. 2012.Nonlinear Laser Dynamics: from Quantum Dots to Cryptography, Wiley-

VCH Verlag & Co.,

4. Tilmann Heil, Josep Mulet, Ingo Fischer, Claudio R. Mirasso, Michael Peil, Pere Colet, and

Wolfgang Elsäßer. 2002. ON/OFF Phase Shift Keying for Chaos-Encrypted Communication

Using External-Cavity Semiconductor Lasers, IEEE Journal of Quantum Electronics, Vol. 38, No.

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5. Ljupco Kocareva , Marjan Sterjevb , Attila Feketec and Gabor Vattayd .2004. Public-key

encryption with chaos , American Institute of Physics , Vol. 14, No. 4, Nov.

Figure 6-A bifurcation diagram , the output power versus the bias voltage as control parameter.


258

6. Rekha Mehra , Heena Shahani and Aslam Khan. 2014. Mach Zehnder Interferometer and its

Applications, International Journal of Computer Applications (IJCA), (0975 – 8887),

7. Lorenz, E. .1993. The Essence of Chaos. Seattle , University of Washington Press,

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International Journal of Science and Technology Vol. 1, No. 3, Sep.

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Electro-Optical Chaos Cryptography, PhD Thesis Georgia Institute of Technology Dec..

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