Universality and scaling in chaotic attractor to chaotic attractor transitions in an optical ring cavity resonator

Abstract

Abstract A new class of second order phase transitions is identified and characterized for a plane wave intracavity field in an optical ring resonator. In this paper we discuss chaotic attractor to chaotic attractor transitions in a ring cavity laser as an external parameter is varied. We show that the transition is sharply defined and may be classed as a second order phase transition. We obtain scaling laws about the critical point ηc, for the average positive Lyapunov exponent, λ+ |η ηc|−β and the average crisis induced mean lifetime, τ ∼ |η ηc|−γ, where η is the parameter that is varied. Here average means averaged over many initial conditions. Futhermore we find that there is an algebraic relationship between the critical exponents and the correlation dimension D c at the critical point ηc, namely, β + γ + D c = constant. We postulate that this is a universal relationship for second order phase transitions in two-dimensional multiparameter non-hyperbolic dynamical systems and we propose that the Ikeda ring cavity resonator be used to test the relationship experimentally.