Period-Doubling Route to Chaos in Photorefractive Two-Wave Mixing

Abstract

This paper investigates the possibilities of complex nonlinear dynamic signal generation using a simple photorefractive two-wave mixing system without any feedback using numerical simulations. The novel idea is to apply a sinusoidal electric field to the system inroder to extract nonlinear dynamic behavior. The mathematical model of the system was constructed using Kogelnick’s coupled wave equations and Kukhtarev’s material equation. The spatio-temporal evolution of the system was simulated in discrete steps numerically. The temporal evolution of the output light intensity exhibits period doubling, behavior which is a characteristic feature of complex nonlinear dynamic systems. A bifurcation diagram and Lyapunov exponentials confirm the presence of the period-doubling route to chaos in the system. The observed complex signal pattern varies uniformly with respect to the amplitude of the applied field, indicating a controllable nonlinear dynamic behavior. Such a system can be very useful in applications such as photonic reservoir computing, in-materio computing, photonic neuromorphic networks, complex signal detection, and time series prediction.

Keywords

• photorefractive two-wave mixing
• lithium niobate
• nonlinear dynamics
• period doubling
• chaos