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

• Published in: Journal of modern optics 2001-05, Vol.48 (6), p.1043-1058
• Main Authors: Stynes, D., Heffernan, D. M.
• Format: Article
• Language: English
• Subjects: Dynamical laser instabilities; noisy laser behavior; Dynamics of nonlinear optical systems; optical instabilities, optical chaos and complexity, and optical spatio-temporal dynamics; Exact sciences and technology; Fundamental areas of phenomenology (including applications); Laser optical systems: design and operation; Nonlinear dynamics and nonlinear dynamical systems; Nonlinear optics; Optics; Physics; Statistical physics, thermodynamics, and nonlinear dynamical systems
• ISSN: 0950-0340; 1362-3044
• DOI: 10.1080/09500340108230974

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 η c , for the average positive Lyapunov exponent, λ + |η η c | −β and the average crisis induced mean lifetime, τ ∼ |η η c | −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 η c , 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.