45 minutes is a good period as it gets you to the beginning of your REM cycle. I often aim for 45 minutes as a nap, but for reasons I don't understand, 20 minutes can be disproportionately invigorating.

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.

If I don't set an alarm, my head feels like cement afterwards.

Do you still sleep 8 hours at night?

This is anecdata, but I don't think it affects my overnight sleep if my nap is post lunch, although it definitely does if I sleep later in the day, say from 4pm to 6pm. I think there's enough time and mental exertion in the afternoon and evening that I sleep normally overnight. Possibly it's a slightly shorter sleep overnight, but a net increase per day overall, or, at least no shorter overall.