Chaotic and bifurcating nonlinear systems driven by noise with applications to laser dynamics
Abstract
The objective of this grant is to pursue research in the field of noise driven nonlinear laser dynamical systems by means of both analog and digital simulations. The first, is an electronic circuit modelling of the effects of purely multiplicative noise on the correlated spontaneous emission laser. The second, is a modelling of the general problem of stochastic resonance, and a study of the effects of the modulation and noise as they relate to the recently observed phenomenon in a dye ring laser. Four projects have been completed: The first is a generalization of meanfirstpassage time calculations to problems involving spatiotemporal noise. Specifically considered is a Brownian particle moving in a random spatial potential driven by temporal noise. Second, an experiment and a contemporary theory completed on generalized switching processes in the presence of colored noise. Third, a discovery was made using analog techniques with strongly colored noise: a noise correlation time induced change in the topology of the two dimensional probability density of multistable systems. Fourth, an interesting example problem was given on state dependent diffusion posed by Landauer and Van Kampen.
 Publication:

Annual Report
 Pub Date:
 December 1988
 Bibcode:
 1988umsl.rept.....M
 Keywords:

 Dye Lasers;
 Electromagnetic Noise;
 Modulation;
 Nonlinear Systems;
 Quantum Optics;
 Ring Lasers;
 Analog Simulation;
 Brownian Movements;
 Digital Simulation;
 Particle Diffusion;
 Particle Emission;
 Particle Theory;
 Probability Density Functions;
 Resonance;
 Spatial Distribution;
 Stochastic Processes;
 Lasers and Masers