Multi-Turing instability spectra and spatial fractals in absorptive systems

Spontaneous optical pattern formation in ring cavities containing saturable absorbers has been increasingly studied over the past two decades, with models often based on the two-level Maxwell-Bloch equations. Linear stability analysis of the weakly-absorptive system tends to be fraught with complexity, and leads ultimately to a threshold instability spectrum for Turing patterns that possesses comparable multiple minima [Patrascu et al., Opt. Commun. 96, 433 (1992)] – a multi-Turing spectrum that we have proposed as a universal signature for predicting a system’s innate capacity to generate spontaneous spatial fractals [Huang and McDonald, Phys. Rev. Lett. 95, 174101 (2005)]. Taking the mean-field limit decreases the overall complexity of the problem [Firth and Scroggie, Europhys. Lett. 26, 521 (1994)] but the multi-Turing spectrum vanishes, leaving only a single instability lobe which provides no obvious mechanism by which fractal patterns can emerge.