Limitations to bit rate and spatial capacity of an optical data transmission channel

The maximum bit rate of a slab waveguide is ultimately determined by the waveguide dispersion. We show that while the maximum bit rate in a waveguide is inversely proportional to the waveguide's width, the bit rate per unit width (i.e., spatial capacity (SC)) decreases, and in the limit of a zero-width waveguide it converges to ∼ω/ √(λL) (where L is the length and ω and λ are the beam frequency and wavelength respectively). This result, which is independent of the waveguide's refractive indices, is qualitatively equivalent to the transmission rate per unit of width in free space. We also show that in a three-dimensional waveguide (e.g., fibres), unlike free space, the SC vanishes in the same limit.