Dispersion (optics)

In Optics , dispersion is a phenomenon that causes the separation of a Wave into spectral components with different Wavelengths , due to a dependence of the wave's speed on its wavelength. It is most often described in Light waves, though it may happen to any kind of wave that interacts with a medium or can be confined to a waveguide, such as Sound waves.

There are generally two sources of dispersion: material dispersion, which comes from a frequency-dependent response of a material to waves; and '''waveguide dispersion''', which occurs when the speed of a wave in a Waveguide depends on its frequency. The Transverse Mode s for waves confined laterally within a finite Waveguide generally have different speeds (and field patterns) depending upon the frequency (i.e. on the relative size of the wave, the Wavelength , and that of the waveguide).
A related phenomenon is that of modal dispersion, which comes about because a waveguide may have multiple modes at a given frequency, each with different speeds. If a signal consists of a superposition of such modes, dispersion of temporal features (and thus signal degradation) results. A special case of this is Polarization Mode Dispersion (PMD), which comes from a superposition of two modes that normally travel at the same speed due to symmetry (e.g. two orthogonal polarizations in a waveguide of circular or square cross-section), but which travel at different speeds due to random imperfections that break the symmetry.

MATERIAL DISPERSION IN OPTICS

In Optics , the ''phase velocity'' of a wave ''v'' in a given uniform medium is given by:

:

v = rac{c}{n}

where ''c'' is the Speed Of Light in a vacuum and ''n'' is the Refractive Index of the medium.

In general, the refractive index is some function of the frequency ν of the light, thus ''n'' = ''n''(ν), or alternately, with respect to the wave's Wavelength ''n'' = ''n''(λ). The wavelength dependency of a material's refractive index is usually quantified by an empirical formula, the Cauchy or Sellmeier Equation s.

The most commonly seen consequence of dispersion in optics is the separation of white light into a Color Spectrum by a Prism . From Snell's Law it can be seen that the angle of Refraction of light in a prism depends on the refractive index of the prism material. Since that refractive index varies with wavelength, it follows that the angle that the light is refracted will also vary with wavelength, causing an angular separation of the colors known as ''angular dispersion''.

For visible light, most transparent materials (e.g. glasses) have:
:

1 < n(\lambda_{
m red}) < n(\lambda_{
m yellow}) < n(\lambda_{
m blue})\ ,

or alternatively:

Information About

Dispersion (optics)