Chaos in optics: field fluctuations for a nonlinear optical fibre loop closed by a coupler

Abstract

Mathematical theories describing chaotic behaviour in physical systems are introduced by developing and reviewing applications to optical fibres. A theory is presented for laser light propagating in a loop formed by an optical fibre and an optical coupler. As the light traverses the fibre it suffers an attenuation and is subjected to a phase shift which will have a component proportional to the light intensity via the nonlinear optics Kerr effect. At each pass through the coupler, an extra fraction of laser light is coupled into the loop. The mathematical formulation leads to a two-dimensional map having a clear physical and geometrical interpretation. The complete solution is given in the linear regime and the onset of nonlinear behaviour is investigated as the laser power is increased. A variety of transitions is obtained including period doubling and iteration onto a strange attractor.