Not all naps will land you into REM...

Let's say you routinely sleep from around 22:00 or 23:00 up to 6:00 or 7:00.

Sleep is relatively dense in REM from after ~4 or 5 hours of sleep (which is 3:00 - 4:00 in this example) up to about 12 hours from when you started sleeping (which would be in this example 11:00 or 12:00). So essentially, depending on individual variation you have 10 - 8 hours of relatively dense REM - which usually means that as long as you sleep from <~4 or 5 hours after the start of sleep> to <4-to-6 hours after your normal waking up time> the chances are very high for you to end up in REM.

Late afternoon naps as well as evening naps and the first few hours of night sleep are usually nearly devoid of REM and are far richer in deep sleep - which is why waking up from them leaves you in a groggy state. Waking up from REM doesn't.

Without completely modifying your own circadian rhythm you can't "artificially evoke" REM... In the normal human circadian rhythm (= 24 hours in a day with 7-8 hours of sleep), to get into REM it depends on which phase you enter sleep.

(As a disclaimer, it's worth noting that most of these numbers vary individually - which is why I wrote them as a range. The range is simply what is true for the majority of people - not necessarily everyone. For example, maybe some people can enter REM in evening naps too - but they are the exception to the rule...)