REM sleep is high frequency low amplitude waves of about 60 to 70 Hz. This is in the gamma frequency of consciousness.
REM sleep decreases as a person gets older.
REM sleep frequency is higher than lucid dreaming g frequency of 30 you 40 Hz.
A little off-topic from REM sleep but I’ve had good results (therapeutic) using tDCS with the square-wave frequency set at around 12 Hz (alpha). That is, if you can stand the internal light show (I like it).