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.