I need an IR laser whose fall time is as small as possible so it comes as close as possible to an instantaneous stop. What would you recommend?

Almost all lasers' excitation medium are either directly or secondarily electric. Gas lasers are excited via electric current and solid state by optical phenomena that are electrically controlled. This means that most standard lasers have a rise and fall time ultimately limited by electronics if you just consider traditional on and off. Using a low repetition q-switched or mode-locked laser with a pulse duration in the realm of your allowable fall time is best for this application. A femto-second laser might be nice if you can get your hands on one although most common types (Nd:YAG, Ti Sapphire, etc) have such high repetition rates that they might not work for your application. There are some low-repetition mode-locked, femto-second, fiber lasers that generally have fairly low repetition rates that would probably be ideal. Either way, an ultra-short pulse will be as close to instant-off as possible. Currently, we do not offer any lasers that match those criteria.