The nonlinear fabry-pérot cavity: Complexity in a simple optical feedback system

The nonlinear Fabry-Perot (FP) cavity [see Fig. 1(a)] is a generalization of the classic diffusive Kerr slice with a single feedback mirror [1,2]. Such apparent simplicity is deceptive. Historically, analysis of the FP geometry has proved to be a non-trivial problem [3]: it is the epitome of a complex system capturing the interplay between diffraction (in the free-space path), counter-propagating fields, transverse diffusion of carriers (driven by local incoherent light intensity) and a host of cavity effects (periodic pumping, mirror losses, and interferomic mistuning). In addition, phenomena can be present on several distinct time-scales. We have considered an instantaneous medium response in the plane-wave limit (where transverse effects such as diffraction and diffusion have been neglected). Even with these simplifications the FP cavity routinely exhibits remarkably complicated dynamics. The behaviour has been investigated as functions of system parameters (such as slice reflectivity and mistuning) using time series to visualize phase-space attractor geometries. Careful inspection of bifurcation diagrams [see Fig. 1(b)] has also shown that Ikeda-type instabilities [4] can dominate the system response. These plane-wave results are expected to play a key role in the subsequent analysis of spontaneous spatial pattern-forming instabilities. References [1] G. D’Alessandro and W. J. Firth, Phys. Rev. Lett. 66, 2597 (1991). [2] J. G. Huang and G. S. McDonald, Phys. Rev. Lett. 95, 174101 (2005). [3] G. S. McDonald et al., Proceedings on Nonlinear Dynamics in Optical Systems 7, OSA, Oklahoma, June 48 (1990). [4] K. Ikeda, H. Daido, and O. Akimoto, Phys. Rev. Lett. 45, 709 (1980).