Good luck with that. A perfect square wave of frequency x consists of the fundamental sine wave x plus the sum of all odd harmonic sine waves of frequency x.
Infinity is a mighty big number to shoot for, and the infinitely high odd harmonic of a frequency of light is also a tad above a dog's hearing range.
Well, sure, everybody knows that. But what if you send it through the Stargate two or three times first? ;-)
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.