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, bit rate per unit width (i.e., spatial capacity) decreases, and in the limit of a zero-width waveguide it converges to a value, which is independent of the waveguide's refractive indices. This value is qualitatively equivalent to the transmission rate per unit of width in free space. We also show that in a 3D waveguide (e.g., fibers), unlike free space, the spatial capacity vanishes in the same limit.