I think for the most part it's
Lt-deep-REM-lt-deep after 3-4 months. But yeah, babies have strange cycles during infantcy, you really don't see a strong sleep cycle I think until after 6-9 months when day sleep and night sleep are fully developed and appear more adult-like. They spend a large portion of their time in REM sleep, as opposed to adults who spend much much less in REM.
During night sleep, the first half of the night, bedtime to around midnight-1 is spent in deep sleep. The second half becomes mostly REM, hence quite a few of the night wakings happen in the second half of the night (for the most part). This is also part of why it is best to put your lo down for bed in the early evening after 8 or so weeks; they get more deep sleep (which is harder to wake from, but they obviously can, especially if they were overtired for bed to begin with), and are more rested to stay asleep through the second half of the night (unless they need fed, or are in pain, etc.).
*HUGS*
Sonya =P