By Allen H. Cherin

This booklet is especially necessary for an advent to makes use of and functions of fiber optics

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Phase Plane Analysis Nonlinear system frequently has more than one equilibrium point. It can also oscillate at fixed amplitude and fixed period without external excitation. This oscillation is called limit cycle. However, limit cycles in nonlinear systems are different from linear oscillations. First, the amplitude of self-sustained excitation is independent of the initial condition, while the oscillation of a marginally stable linear system has its amplitude determined by the initial Nonlinear Photonic Fibre Ring Lasers 27 conditions.

A phase modulator driven in the region of 1 GHz modulation frequency assumes the role as a mode locker and controls the states of locking in the fiber ring. At input of the phase modulator, a polarization controller (PC) consisting of two quarter-wave plates and one half-wave plate is used to control the polarization of light which relates to the nonlinear polarization evolution and influences to multi-pulse operation in formation of bound soliton states. A 50 m Corning SMF-28 fiber is inserted after the phase modulator to ensure that the average dispersion in the loop is anomalous.

The shape of the phase graph exposes the phase between the displacement and its derivative. As the multiplication factor increases, the system trajectories are moving away from the origin. As for the 4-times and 8-times multiplications, there is neither stable limit cycle nor stable node on the phase planes even with the ideal multiplication parameters. Here we see the system trajectories spiral out to an outer radius and back to inner radius again. The change in the radius of the spiral is the transient response of the system.

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