Shakespeare the Tempest help?

When Prospero says 'this thing of darkness I acknowledge mine' I thought he ment that caliban is his as in Caliban is his slave. When prospero first came upon the island, he was nice to Caliban and treated him well as Caliban showed him around the island. but then Caliban tried to rape his daughter, Miranda i think her name was?, and that is when Prospero turned against him and forced him to become a slave.