Laser Chaos Generation Utilizing Optical Feedback Technique with Modern Applications
Laser Chaos Generation Utilizing Optical Feedback Technique with Modern Applications
Assistant Professor-Dr- Salam Khalaf Mousa-Department of Physics
Salam.khalaf@uoanbar.edu.iq
chaos theory, is the area as is observed in mathematics and physics used in imitation of describe the behavior regarding dynamical systems which are distinctly sensitive in conformity with preliminary state of the system "i.e. just small perturbation in initial condition leads to significantly varying behavior", also referred to as butterfly effect. This means that long term prediction is impossible even the system is deterministic, also known as "deterministic chaos". Chaos is a native characteristic concerning many nonlinear systems. Minutely, the transition from order to disorder occurs with universality, irrespective of physical properties of the systems. The mathematical foundations of chaos were presented by poincaré in his study on bifurcation theory. The first dynamic system for generating chaos was made by Edward Lorenz and commenced by Haken in 1975 when he proved the mathematical isomorphism between the Maxwell-Bloch equations, "which describes the dynamics of the electric field, the mean polarization of the atoms and the population inversion", and the Lorenz equations for atmospheric convective flow. Since the work of Haken, much attention has been dedicated to the nonlinear dynamics of lasers in general, and laser diodes in particular. An example of a dynamical system (in which time is continuous) is a system of N first- order differential equations:
where x is an N-dimensional vector and t is time. Also, it is usual to refer to a continuous time dynamical system as a flow for a discrete integer-valued. where Χn=(xn(1) ,xn(2),..,xn (N)) given the initial condition xo, The space (x(1),x(2) ,x(3),...) is denoted by the phase space, and the system follows a path in space while it evolves with the time is called the orbit or "trajectory". (x0,x1,x2,.) is the orbit of the discrete time system. A chaotic system represents a special kind of non-linear systems, characterized by its chaotic behavior. There are two indispensable conditions for chaotic motion to take place: (1) the associated phase space of the system must be at least three dimensional, (2) the equation of motion contains a non-linear time period to that amount couples numerous of the variables. The chaotic conduct is determined among realistic functions on deep fields, such namely engineering, biology and economics. In physics, that researches the monitoring over turbulence, government over lasers, power over confusion into plasma, power over the dipole domains. Chaos has been proven in accordance with remain useful into a variety of disciplines, such as information processing, the collapse forbidding of power systems, the circuits and devices of high performance, and mixing of liquids using lower power consumption.