  Using numerical simulations we show how to realise 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 horizon. 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.
