How to create a decal that appears to float without a surface

I have a hi-resolution transparent PNG of a design. I want it to appear as if it is floating by itself instead of on a surface. Initially, I placed it on a plane that had a glass texture applied. However, the glass shows reflections and refractions.

I'd like the decal to cast shadows based on its shape and contours. I just don't want any material of the plane to be visible at all.

Open to suggestions.