Creating a visual effect- transparent in middle and spreading outwards

Hello,

I've been working at this for too long and I can't seem to get the effect quite right. I want to create a scene with a dark room but a circle in the middle that can be seen through, as if there's a light source the viewer cant see (a laptop facing away). Then I want the transparent circle to expand, gradually revealing the room, as if I've turned on a light. I feel like I'm very close, but I'm not super happy with the whiteout in the center obscuring the background, I'd rather have a sharper contrast or something. Any ideas?