Could you tell us what kind of laser pulser you are examining? Is it a commercial laser diode pulser? Does it use a transistor operating in avalanche mode? What are you trying to do with your laser pulser? Optical radar (LIDAR) perhaps? Fiber optical communications? Please tell us what you are trying to DO?
Attached is some background information (somewhat dated now, but still a good read) on using a transistor in avalanche mode to obtain fast rising, narrow, optical pulses from a diode laser for use in a laser-ranging application. Bottom line appears to be you have to carefully select from any given lot of transistors the ones that have the proper characteristics for avalanche-mode operation. I would hope that some progress has been made since this paper was published to allow purchase of transistors specifically made for this purpose.