Spontaneous one-dimensional optical-bandgap formation in suspensions of dielectric particles

It is shown that under certain conditions a collection of dielectric Rayleigh particles suspended in a viscous medium and enclosed in a high-Q bidirectional ring cavity pumped by a strong laser field can spontaneously self-organise to produce a one-dimensional optical bandgap. Using a linear stability analysis, a dispersion relation is derived which determines the region of parameter space in which the region of spontaneous bandgap formation occurs. A numerical analysis is carried out to observe the dynamics of the interaction in the nonlinear regime. In the nonlinear regime, depletion of the pump field due to the formation of the bandgap is almost 100%. An important feature of the optical bandgap described here is its inherent tunability.