As I understand it REM sleep is at the start and end of each cycle, thus 45 mins would put you squarely in a deep non-REM phase. That said, the cycles get progressively shorter in an overnight sleep, so it's possible a daytime nap sleep cycle would be much shorter than the full 90 mins.

From memory (my 25 year old psychology degree which I clearly misremembered previously), the point of 45 minutes is that it gets you to just before the deep sleep cycle. If you can wake up naturally and alert at around that time mark then you've got the complete light sleep part of the cycle.