What can a driver do with another driver's license plate number?

I almost got into a car accident today. As I was trying to cross a median, I didn't see another car coming and I cut them off. I saw the driver writing down my license plate number (presumably, as he was scribbling something down and kept looking up). As we came to a stop at the nearest traffic light, he came to the right side of my car and motioned me to roll the window down. I apologized, he didn't yell but he was angry (understandably) and said he had three children in the back of the car. He then went in front of me and then switched lanes again. I'm guessing he either took a picture of me or at least let his children take a good look at the reckless person who nearly killed them. I don't know what to do. Can he report my license plate number to the authorities? I'm a little paranoid that he might spot me on the road again.