Dispersion (optics)
In optics and in wave propagation in general, dispersion is the phenomenon in which the phase velocity of a wave depends on its frequency;[1] sometimes the term chromatic dispersion is used for specificity to optics in particular. A medium having this common property may be termed a dispersive medium (plural dispersive media).
Although the term is used in the field of optics to describe light and other electromagnetic waves, dispersion in the same sense can apply to any sort of wave motion such as acoustic dispersion in the case of sound and seismic waves, and in gravity waves (ocean waves). Within optics, dispersion is a property of telecommunication signals along transmission lines (such as microwaves in coaxial cable) or the pulses of light in optical fiber.
In optics, one important and familiar consequence of dispersion is the change in the angle of refraction of different colors of light,[2] as seen in the spectrum produced by a dispersive prism and in chromatic aberration of lenses. Design of compound achromatic lenses, in which chromatic aberration is largely cancelled, uses a quantification of a glass's dispersion given by its Abbe number V, where lower Abbe numbers correspond to greater dispersion over the visible spectrum. In some applications such as telecommunications, the absolute phase of a wave is often not important but only the propagation of wave packets or "pulses"; in that case one is interested only in variations of group velocity with frequency, so-called group-velocity dispersion.
All common transmission media also vary in attenuation (normalized to transmission length) as a function of frequency, leading to attenuation distortion; this is not dispersion, although sometimes reflections at closely spaced impedance boundaries (e.g. crimped segments in a cable) can produce signal distortion which further aggravates inconsistent transit time as observed across signal bandwidth.
Examples[edit]
The most familiar example of dispersion is probably a rainbow, in which dispersion causes the spatial separation of a white light into components of different wavelengths (different colors). However, dispersion also has an effect in many other circumstances: for example, group-velocity dispersion causes pulses to spread in optical fibers, degrading signals over long distances; also, a cancellation between group-velocity dispersion and nonlinear effects leads to soliton waves.
Material and waveguide dispersion[edit]
Most often, chromatic dispersion refers to bulk material dispersion, that is, the change in refractive index with optical frequency. However, in a waveguide there is also the phenomenon of waveguide dispersion, in which case a wave's phase velocity in a structure depends on its frequency simply due to the structure's geometry. More generally, "waveguide" dispersion can occur for waves propagating through any inhomogeneous structure (e.g., a photonic crystal), whether or not the waves are confined to some region. In a waveguide, both types of dispersion will generally be present, although they are not strictly additive. For example, in fiber optics the material and waveguide dispersion can effectively cancel each other out to produce a zero-dispersion wavelength, important for fast fiber-optic communication.
Higher-order dispersion over broad bandwidths[edit]
When a broad range of frequencies (a broad bandwidth) is present in a single wavepacket, such as in an ultrashort pulse or a chirped pulse or other forms of spread spectrum transmission, it may not be accurate to approximate the dispersion by a constant over the entire bandwidth, and more complex calculations are required to compute effects such as pulse spreading.
In particular, the dispersion parameter D defined above is obtained from only one derivative of the group velocity. Higher derivatives are known as higher-order dispersion.[6][7] These terms are simply a Taylor series expansion of the dispersion relation β(ω) of the medium or waveguide around some particular frequency. Their effects can be computed via numerical evaluation of Fourier transforms of the waveform, via integration of higher-order slowly varying envelope approximations, by a split-step method (which can use the exact dispersion relation rather than a Taylor series), or by direct simulation of the full Maxwell's equations rather than an approximate envelope equation.
In imaging[edit]
In photographic and microscopic lenses, dispersion causes chromatic aberration, which causes the different colors in the image not to overlap properly. Various techniques have been developed to counteract this, such as the use of achromats, multielement lenses with glasses of different dispersion. They are constructed in such a way that the chromatic aberrations of the different parts cancel out.