Abstract
Using numerical simulations we show how to realize an optical black hole laser, i.e. an amplifier formed by travelling refractive index perturbations arranged so as to trap light between a white and a black hole horizons. The simulations highlight the main features of these lasers: the growth inside the cavity of positive and negative frequency modes accompanied by a weaker emission of modes that occurs in periodic bursts corresponding to the cavity round trips of the trapped modes. We then highlight a new regime in which the trapped mode spectra broaden until the zero-frequency points on the dispersion curve are reached. Amplification at the horizon is highest for zero-frequencies, therefore leading to a strong modification of the structure of the trapped light. For sufficiently long propagation times, lasing ensues only at the zero-frequency modes.