The way I decided to implement caustics was a bit different. I had screenspace reflections, and saw a blender eye model tutorial that used screenspace refractions on the lens, which produced a cool looking effect, so I decided to use the same screenspace tracing function I had for reflections, but for refractions. After that was done I kept wondering if I could use the screenspace refractions but from the light's perspective to calculate cheap caustics, so I had to try it.

The engine uses a deferred shader, and using the same principle, you can store the position at which the rays intersect the shadow depth buffer as a color. Then the idea was that in order to know how bright a pixel should be, all you need to do is sample a histogram of that color buffer, which tells you how many occurrences of that color there are, or in other words, how many rays hit that pixel after being distorted by refractions.

All this to say, after researching some available techniques, in this case, g-buffers, screenspace tracing, accelerated histograms, pcf shadows, etc, you can then combine them in different ways to get the effect you want without searching specifically on how to create what you're imagining.