Rational responses to potential home invasion threat?

About three hours ago—in the very early morning, pre-dawn—someone knocked on my window to get my attention and made a lewd proposition. Less than two weeks ago, someone—probably the same person; definitely someone with a similar voice and build—woke me up by whispering ‘open the door’ until I looked out the window. I am, needless to say, not amused.

Since the first incident, I’ve been leaving my porch light on, and I’ve had a webcam sitting prominently in the window. The webcam has been commented on by both of the people who know me and would have an opportunity to do so, so I expected that it would be a reasonable deterrent, but apparently this guy is very stupid, very desperate, or both.

I called the police both times, and they responded promptly, but didn’t see anyone walking around near my apartment. This leads me to believe that I’m being harassed by a nearby neighbor.

The webcam was not on during the second incident, but it will be on nightly from now on. I also intend to add a light in the window near my bed—I didn’t get a good look at the guy, even though he was right there and not making any apparent attempt to hide, because he was between me and the porch light.

I’d appreciate any other practical suggestions that anyone might have, bearing in mind that I’m in an apartment and can’t make many changes to the building itself. Also, I was already working on buying a house before the first incident even happened, so suggestions that I move aren’t useful—I’m already working on that, thank goodness.

(The chances of me having trouble with this individual in any situation other than a home invasion seem pretty small—I don’t leave the house often, and not on a regular schedule at all, plus I don’t drive so I generally have a friend in a car watching me to and from the door, so the usually more risky situation of getting in and out of the house isn’t an issue for the most part. I will be extra-careful about getting my mail and thoughtful about when I leave to do my laundry.)