Dynamics of polaritons in semiconductor microcavities near instability thresholds

A theoretical study is presented on the dynamics of polaritons in semiconductor microcavities near parametric instability thresholds. With upward or downward ramp of optical pump, different instability modes emerge in parameter space defined by damping and detuning. According to these modes, stationary short-wave, stationary periodic, oscillatory periodic, and oscillatory uniform parametric instabilities are distinguished. By multiple scale expansion, the dynamics near threshold can be described by a critical mode with a slowly varying amplitude for the last three instabilities. Furthermore, it is found that the evolutions of their amplitudes are governed by real or complex Ginzburg–Landau equations. -- Highlights: ► Phase diagrams for different instability in extended parameter space. ► Different instability modes near thresholds. ► Different envelop equations near thresholds obtained by multi-scale expansion.