The sleep that occurs after your alarm goes off. You must get out of bed for no more then 2 seconds and then return to your slumber knowing that you will be late for something.
This is generally the best kind of slumber due to the fact that you dont give a fuck.
your boss: where were you this morning tom?
tom: I forgot my laptop on my kitchen counter and had to go back across town to get it.
your boss: dont let it happen again
joe: dude you had some after sleep didnt you...
tom: yes it did.