Don't overthink it. It's a similar motion to how you would jump off your feet without a snowboard. Bend your knees, then extend upwards and leave the ground with a extra force/thrust from your legs right as you lose contact with the ground(lip of the jump).
It should be a smooth motion, bend the knees during the approach (to generate power), slowly straighten the knees and rise up as you ride up the jump (turn that power into upwards momentum) and then pop. I would recommend skipping the actual popping motion and just ride off the jump at first. If your holding your speed instead of scrubbing during the approach you should get a little bit of air just riding over the jump, which will help you get familiar with the process and get your timing down.
The other part about jumping is you want to be riding relatively straight while engaging a slight edge angle so you are not completely flat based. If you're carving blacks like you say then this shouldn't be too foreign of a concept. This will allow you to jump off both your heel (this will feel a little unnatural at first) and toe edge.