I've seen a photographer using a dark background (plastic made or something similar) that, once lit from behind, produced a really nice glow. I'm looking for something similar to generate a translucent backdrop. I've really searched the internet a lot, but can't find a name to it, nor something similar to buy. Can you suggest what should I look for?
The most popular material for such uses is Savage Translum (in the US). In Europe, Translum is sold under the Tetenal brand name. (Canadians will have to import it themselves in any case; neither Savage nor Tetenal distribute it here. It is equally difficult to find in some other regions, and while the stuff is cheap enough, shipping can add up.) It's a thin, semi-rigid PVC sheet (200-300 microns) usually sold in rolls as both a background and diffuser (thus the 54" width).
Translum still requires separation from the subject in order to be lit separately, but because it is backlit and a good diffuser, it produces very clean, smooth gradients with no visible texture. It's a little trickier to handle than seamless paper as is, but you can take the curl out of it effectively with a hair dryer and a bit of patience if you don't have a weight bar for the bottom.
You can also use styrene sheeting meant for backlit signage. It generally is too stiff and fragile to roll, though, and difficult to store if it's not framed. The upside is that it's available just about everywhere once you know what you're looking for - if there is no jobber you can visit locally, there's always a signmaker handy who can get it for you.
Achieving the effect is deceptively hard as you have to control reflections and stray light to make it work. Looking at the sample image that you have something like this...
A plain white background.
Black plastic / PVC / Vinyl under the object on a table with a gap between that and the background. Put down roughly in this case to give an uneven surface.
A gridded softbox to the left & another to the right of and behind the object. The grids help to stop light from radiating too much.
To get the background / glow it's a light with a conical snoot. Probably hung above the table somewhere shining on the background with an overspill falling into the gap between the table and the background.
And here's a (terrible) diagram so you can visualise it.