I like the effect you have managed with your solution.
You can use a shader in Eevee with the node setup shown.
The inputs on the left control intensity, scan (vertical offset) and focus (sorry I forgot to rename this one). Thhis can be modded for different scan orientations using the mapping node.
Thought I would offer some explanation on this, it was 0400 hrs when I posted this so I was quite tired.
The magic happens in the mapping node (purple), basically I use the scale vector to squash the texture in the Z direction and scan it using the location vector. I use a math node to scale the input controls and make them more friendly.
Then pipe this into a a gradient texture and onto the emmision shader.
I've added some white noise to give that laser effect (although this should probably get its vector from texture-node->object rather than the mapped as white noise shouldn't be squashed.
The rest should be pretty much obvious.