But light is a quantum phenomena. It is discrete not continuous. Single photos exist. They are a easily prove to exist using double slit.
So a single photon pulse will have no leading edge.
A Taylor series approximation is a continuous method derived from the constraints the operations of calculus. E.I. calculus requires the inputs to its operations to be continuous. Placing these artificial constrains on a real phenomena will get you absurd results. E.G. needing an infinite series of continues sine waves to make up a discrete event.
Light is also a wave phenomon, or else you couldn't do a defraction experiment, including the two slit one photon experiment.
Even on a quantum level, a photon has frequency associated with it, otherwise all photons would be the same color. Imagine if you will a single round photon, going past a slit. Being round, you'd see at first just a sliver of the photon, then the whole body, then finally just a sliver of the tail end. Leading and trailing edges of a photon. Unless it is your contention that photons are cubes? LOL
All I know is my EE calculus says that you can't generate a perfect sqare wave because you can't generate all of the odd harmonics required. You will always be dealing with a risetime, a falltime, and a certain amount of ringing in the squarewave.