Auto completion LookupElement side window Follow

For a custom language I created a CompletionContributor. Everything works fine. But I'm limited to the information I can display (only in the list or the bottom "advertisement" and only 1 line).

When trying to auto-complete on a java class name it will display more information on the selected line in a small side window (looks like javadoc). I would like to exploit that mechanism but I really don't know how it is done.

When looking at the options provided, I can use a custom LookupElementRenderer but there is no method in LookupElementPresentation related to the right window.

How can I use the same mechanism to display custom information?

I'm wondering if this is the DocumentationProvider role to make it work but I'm unable to show something with it on the right window.