Analytical signal formalism in the description of optical pulse photodetection

In this paper, we unveil and discuss a theoretical misconception in a classical formalism of Gaussian pulse envelope propagation. With simple analytica la rguments, we explain the mistake and develope a universal result, valid for short and ultra-short optical pulses of arbitrary shape. This general result sheds light on the mathematical separation of a pulse into its envelope (energy) and its coherent characteristics (frequency chirp). With it, a theoretical ground is provided for the use of blind numerical computations to calculate complex photodetected pulse-shapes.