Chaos Modulation by Mach-Zehnder Interferometer
Abstract
We report an experimental evidence of the generation of spiking in semiconductor laser (SL) with optoelectronic feedback (OEFD) using Mach-Zehnder modulator (MZM). The chaotic optical output of SL has been modulated by an external periodic perturbation with different frequencies (0 -110) MHz range. Two white noise-induced phenomena, the coherence resonance (CR) and the stochastic resonance (SR) have been studied at chaotic laser output. The noise intensity range -36 dBm to12 dBm has been utilized,. In SR, periodic signal with constant frequency 500 KHz and different noise level from (-36 dBm to12 dBm) have been applied as a control parameter in this condition.
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Introduction
The term Chaos is a paradigmatic name used to describe deterministic dynamical systems whose behavior is complex, unpredictable and extremely sensitive to initial conditions [1,2].Sensitive dependence on initial conditions means that if two chaotic temporal sequences start from very close but slightly different initial conditions, the two sequences behave similarly at the beginning, however, they start to diverge exponentially in time and never show the same behavior again [3].
Irregular spiking sequences in biological, chemical, and electronic systems have been frequently observed to be the result of multiple time scale dynamics. Indeed, a variety of natural systems showing this behavior (neural cells , cardiac tissues , chemical reactions , to name just a few) can be mathematically described by means of slow and fast variables coupled together (slow-fast systems). The chaotic spiking regime can be understood in terms of excitability of a chaotic attractor, where the small chaotic background spontaneously triggers excitable spikes in an erratic but deterministic sequence [4].When a semiconductor (SL) is subjected to one or more perturbations such as Optical feedback (OFB), Optical injection (OI), Optoelectronic feedback (OEFB) and optical modulation, it can display rich nonlinear dynamics including chaos [5]. A Mach-Zehnder interferometer (MZI) is the source of nonlinearity while the semiconductor laser that provides the optical power acts as a linear current-to-optical frequency converter. The nonlinearity of the interferometer coupled with the delay in the feedback loop combine to produce a range of steady state, periodic, and chaotic behavior [6].white noise is a random signal with a constant power spectral density [7].The response of dynamical system to noise has attracted large attention recently. There are many examples demonstrated that noise can lead to more order in the dynamics. To be mentioned are the effects of noise induced order in chaotic dynamics [8]. Coherence resonance (CR) refers to coherent motion stimulated by noise on the intrinsic dynamics of the system without the presence of an external periodic forcing [9], (i.e.) noise can induce and optimize the temporal regularity of the system dynamics, regardless of the presence of any external signal.
Stochastic resonance (SR) is probably the most famous and established effect among noise-induced phenomena. SR can be defined as an enhancement of the regularity of a system output for certain range of noise amplitudes when the system is driven by a weak periodic signal. In fact, the system is helped by noise to follow the frequency of the periodic signal in a resonance-like behavior [10]. SR describes the improved synchronization of the system output with the input due to an intermediate and optimal noise intensity.SR refers to a generic physical phenomenon typical for nonlinear systems in which one of the characteristic time scales is controlled by noise [11,12].
The work aims to study the CR and the SR in chaotic laser output. The SL has been coupled to the MZM as in a feedback arm. Studying the external periodic perturbation effect on the system chaotic output. This method could be invested in a secure communication.
Conclusion
To conclude, the bias voltage of MZM acts a good control parameter ingenerating regular and irregular spiking. When the voltage increases, this does not always give chaotic behavior. The different frequencies have been applied as a control parameters, when the chaotic output signal under the effect of the external perturbation, so, the appearance and hidden of these frequencies is achieved for the security of optical communication. From results we noticed that we can't use frequencies (28,30,40 and 50) MHz for security communication because we can't hide these frequencies in both states high and low amplitude.