  The Hamiltonian of optical fields in a nonlinear dispersive fiber is studied.
Quantum field fluctuations are spontaneously created close to an optical event
horizon through the analog Hawking effect. The simplest model is considered for
an optical black-hole laser, where the Hawking radiation is produced and
amplified inside a cavity formed by two horizons: a black hole and a white
hole. It is found that resonant Hawking radiation originates from a discrete
set of instabilities and tunnels out of the horizons. Finally, the numerical
results are compared with the resonance and instability conditions and a
phenomenological model is developed to give a clear physical picture.
