Achieving inverse shadows? When light hits an object, it of course generally bounces away, leaving a dark area on the opposite side—a shadow.

What I would like to know is, how would I do the opposite? How would I create a material wherein the light both bounce off and be amplified as it shines through, effectively creating an inverse shadow (or "shaglow" I suppose it could be called) of light and illumination?
You can actually input values greater than one to color inputs of any shader. What that would mean is that the shader would reflect or transmit more light than it receives, which is obviously impossible in reality and in normal circumstances should not be used for realistic materials, however it is possible. You can also use Light Paths node to separately control how different kinds of calculated light rays are being rendered. So, it turns out you can chose to display a material as solid only to the camera while to the rest of the scene it can be transparent and have greater than 1 values for the light it transmits producing your desired effect: