Hawking radiation1—the emission of quantum particles at the event horizon of a black hole2—connects gravity with quantum mechanics and thermodynamics3–5. But Hawking radiation has never been observed in astronomy, only in laboratory analogues6–9, and the chances of ever observing it in space are astronomically small9. The energy of Hawking radiation must come from the gravitational field around the black hole2, but how field quanta generate Hawking quanta has been unknown. Here we report on experimental and theoretical evidence for the process that generates Hawking radiation in a fibre-optical analogue of the event horizon10,11. There, as in gravity2, it has been believed that Hawking radiation comes from a complicated, cascaded process12; here we have identified theoretically a simple, direct process and observed experimentally how this process reacts back onto the field. Our findings suggest an equally direct process for other laboratory analogues6–8,13–17 and perhaps also for gravitational fields, shedding light on how black holes might radiate.