Dispersion

A medium is called dispersive when its wave speed depends on the wavelength (or equivalently, on the wavenumber k). Formally: whenever ω(k) is not a straight line through the origin, the medium disperses. Vacuum, to high precision, does not. Glass, water, plasma, optical fibre, and the ocean all do.

The practical consequence is that any real pulse — which is always a superposition of many frequencies — cannot keep its shape. The red part arrives at a different time from the blue part, and the envelope broadens. The broadening rate is set by the second derivative d²ω/dk², called the group velocity dispersion parameter β. Fibre engineers compensate β by cascading segments of opposite-sign dispersion so that the accumulated smear cancels over a link.

Newton showed in 1666 that glass disperses white light into a spectrum. The word 'dispersion' itself, in its modern wave-physics sense, came into general use in the nineteenth century with the work of Fresnel, Cauchy, and Rayleigh.