Dispersion (optics)
Dispersion (from the Latin dispergere, " spread, scatter " ) is understood in physics, the dependence of a value of the frequency. In the optical system, this is especially the abhängende of the frequency of the light propagation speed of light in the media. As a result, the sunlight is refracted to different degrees on the surfaces of a prism. On the other side of the prism shows a colored spectrum.
The relationship between the angular frequency (or the energy ) of a shaft and the shaft is called the dispersion relation vector, in particular the particle waves is at exactly the energy-momentum relation of the particle.
Normal and anomalous dispersion
For most transparent materials in the visible region increases the refractive index with frequency, glass breaks blue light more than red light. This is called normal dispersion. A positive derivative of the refractive index according to the frequency of the shaft ( ) is equivalent to a negative derivative with respect to the wavelength ().
If, however, the refractive index with increasing frequency, then there is an anomalous dispersion. She was discovered in an alcoholic solution of fuchsin by Christian Christiansen in 1870., The effect is not a special property of this dye, but always in wavelength ranges it occurs near a strong absorption. More generally linked the Kramers -Kronig relation to the profile of the refractive index with the absorption.
Quantitative description
A simple measure of the dispersion of an isotropic transparent medium is the Abbe number. The sell - Meier equation, however, tries to accurately reproduce the empirically determined profile of the refractive index on the wavelength. In addition there exists a simpler description by the Cauchy equation. In addition, there are numerous other dispersion formulas, eg:
- Helmholtz - Ketteler- Drude dispersion formula,
- Schottsche dispersion formulas
- Geffckensche dispersion formula,
- Buchdahlsche dispersion formula,
- Kettlersche dispersion formula,
- Kramers- Heisenberg dispersion formula,
- Breit- Wigner dispersion formula,
- Hartmannsche dispersion formula,
- Herzbergsche dispersion formula ( for the visual field ) or
- As Polynomformel:
Effects
The dispersion of the phase velocity of the determined group velocity dispersion.
Dispersion of the phase velocity
- A prism separates light into its color spectrum.
- Pictures by lenses exhibit undesirable color fringes, which can be corrected by a combination of lenses from optical glasses of different dispersion ( see Achromat and Apochromat ).
- Also, magnetic lenses of an electron microscope show dispersion as a function of the velocity of the electrons. Countermeasures have a narrow energy distribution of the electrons of the field instead of thermionic emission, a high acceleration voltage and a small aperture.
Group velocity dispersion
- Light pulses in optical fibers, which are used for example in optical data transmission, learn due to the group velocity dispersion broadening during transmission. The lower the duration of a light pulse, the wider is its frequency spectrum and the more pronounced is the change in pulse shape, especially on long transmission lines (see dispersion in optical fibers ).
- Electrical cables have depending on the frequency due to their insulating different propagation speeds, as reflected for example in the time domain reflectometry to broadened reflected pulses. The effect leads to delay distortion in broadband signals (for example in the form of flatter pulse edges ), and may be avoided by suitable insulating materials.
Examples
The dispersion of water waves is described in Dispersion ( water waves); the dispersion relation of phonons in the local section dispersion.