A Red Eye is a coffee drink designed to keep you in some twisted state of consciousness, perfect for studying or reading. It's not advisable to write anything important after drinking one of these as it will almost certainly turn out to be complete and utter garbage when you look at it in the morning. I would also advise against trying to meet new people as you'll soon discover, much to your horror, that you can't stop talking no matter how hard you try.
It's a simple premise, really, and one that was probably dreamt up, pondered over, and finally rejected with a breathy "Naaaaaaah" sometime around The Pyramids' design phase.
Take one cup of strong, black coffee and one (or two, if you're feeling extremely lucky and/or suicidally insane) shots of espresso. Pour the espresso into the coffee. Add raspberry syrup (and milk and whipped cream if you wanna be a wuss about it). Drink very, very carefully. It'll keep you up for hours, the first of which you will be coherent enough to get some work done. After that there's a good shot your eyes will need to be hydrated and taped shut to allow for even the possibility of sleep, hence the name.