A Paradox about the Analytic Signal of Laser Beams

In the signal theory framework the "analytic signal" is a particular polar representation of a signal . It defines an envelope (a modulus) and a phase (an argument) and these parameters are basic in communications. In this paper, we show that amplitude demodulations generally change envelopes and reduced phases. Consequently we show that recent results in laser communications about these parameters are erroneous.