Q:

Is there a "scanning" beam sensor? 

As I understand it, photo beam sensors (and perhaps other emission types) work like this...

it occurred to me, it would be great if there was a "scanning" such sensor...

So, it would rotate or swing, at many Hz, over perhaps 90 degrees.   (It could rotate mechanically just like an airport radar or I guess a bar-code scanner, or perhaps "rotate" in some solid state manner.) 
When an object cuts the beam, in fact it could tell you the angular bearing. 
(Of course, if you put two or three of them over an opening, you could calculate a position in 2D nicely.) 
In fact, does this technology exist .. is there such a photoelectric beam sensor -like device, which indeed will give you an "angular bearing"? 
I've spent considerable time searching but not been able to discombobulate. 
(I was astounded to learn there is a lidar-like thing that actually measures distance via time of flight, but that's sort of a further (amazing) complication, not really what I'm wondering about.)   Thx, experts
PS I have no interest at all in model or manufacturer recommendations.  I just want to know if such a thing exists. ( For all I know, it's completely commonplace .. or it may be obviously "ridiculously impossible" to experts.   Cheers)

A:

The main obstacle to this is that a traditional beam break has a point source and a point sensor.  The system as you described would have to have a linear sensor in order to tell you where the break was, which would be more expensive. 
It's certainly not impossible.  Related work includes "structured light" (combining a scanning or otherwise patterned laser with a camera to give a 3D image), or the Flat Frog system for very large touchscreens.  That has a large number of LEDs and photodiodes around the edge and detects fingers by successively illuminating from different angles and looking for the shadow.