The topic of searchlight shapes is more complex than I'd originally expected. I'd like to compile a collection of what people are using. I added a "searchlight shapes" label to the relevant posts: clicking that label should bring up all of the entries.
I have contacted some people directly in the hopes of obtaining sufficient details to add their searchlight shapes to the collection. If you have details of a searchlight not included, please send them and I'll add it (or arrange for you to post them). My initial goal is to describe the main (i.e. default) spherical searchlights produced in the most widely used code/programs, but I also plan to include other types of searchlights, like the random ones created by Malin Björnsdotter.