Fundamental dispersion limit for spectrally bounded On-Off-Keying communication channels and its implications to Quantum Mechanics and the Paraxial Approximation

The fundamental dispersion limit for an optical communication based the On-Off-Keying format is calculated. It is shown both analytically and with numerical simulations that an OOK optical sequence, which passes through a spectrally narrow non-compensated dispersive channel cannot exceed the limit β 2 B²L<π ^{- 1} , where β 2 , L and B are the dispersion coefficient, the fiber's length and the bit rate, respectively. To the best of our knowledge, this is the first time that such a fundamental limit was formulated. In the literature, only approximation evaluations were developed yielding much smaller limiting values. Since this fundamental limit is a manifestation of the Schrödinger equation, a correspondingly similar limit emerges in Quantum Mechanics and in the optical Paraxial Approximation.