adj. of or relating to the state of existence between that of sleep and of wakefulness, characterized by a lingering dreamlike state.
This term is specific to the time leading out of sleep. The corresponding state leading into sleep is a hypnagogic state (from hypno-, sleep + agogos, inducing)
John, in a hypnopompic state, seemed to be dreaming that his car alarm was going off again and again, but upon further waking, he realized it was only his alarm clock.
"Hypnopompic imagery is often incredibly vivid and sometimes even terribly frightening. For instance, people experiencing the phenomenon of awareness during sleep paralysis often have episodes, in which they awake unable to move, while they simultaneously experience nightmarish hypnopompic hallucinations."
I cannot cite this as it was text on a handout for a seminar I took in sleep disorders but I think it was an excerpt from a psychology textbook.