Dispersiedispersion

Dispersiedispersion is a neologism that appears in some discussions to refer to the frequency dependence of a medium’s dispersion itself. In other words, it describes how the parameters that govern dispersion change with wavelength or frequency, rather than describing dispersion in isolation. Because the term is not widely standardized, its exact meaning can vary by author, but it is often used to highlight higher-order effects that arise when dispersion varies across a spectrum.

Mathematically, dispersion in a medium is commonly described by the wave number k as a function of angular frequency ω, with group-velocity dispersion (GVD) given by D(ω) = d^2k/dω^2. Dispersiedispersion then corresponds to the rate at which this dispersion changes with frequency, D′(ω) = dD/dω = d^3k/dω^3. In practice, D′(ω) is closely related to higher-order dispersion phenomena, such as third-order dispersion, and it becomes significant in ultrashort-pulse propagation and in broadband or engineered media.

Context and applications include ultrafast optics, fiber-optic communications, and metamaterials, where controlling not only the amount of dispersion but also its spectral variation is important for pulse shaping and distortion management. Techniques for characterization and measurement include spectral phase retrieval methods such as FROG or SPIDER, as well as interferometric approaches that resolve phase as a function of wavelength.

Terminology note: because dispersiedispersion is not universally defined, some authors treat the idea as part of existing concepts like higher-order dispersion or TOD rather than a separate category. Readers should consult specific sources for the precise definition used in a given context.