Coherence time
Encyclopedia
For an electromagnetic wave, the coherence time is the time
over which a propagating wave (especially a laser
or maser
beam) may be considered coherent
. In other words, it is the time interval within which its phase
is, on average, predictable.
In long-distance transmission systems
, the coherence time may be reduced by propagation
factors such as dispersion
, scattering
, and diffraction
.
Coherence time, τ, is calculated by dividing the coherence length
by the phase velocity
of light
in a medium; approximately given by
where λ is the central wavelength
of the source, Δν and Δλ is the spectral width
of the source in units of frequency and wavelength respectively, and c is the speed of light
in vacuum.
A single mode fiber laser
has a linewidth of a few kHz. The Schawlow-Townes limit for some cw lasers can be below 1 Hz. Hydrogen masers have linewidth around 1 Hz; their coherence length
approximately corresponds to the distance from the Earth to the Moon.
Time
Time is a part of the measuring system used to sequence events, to compare the durations of events and the intervals between them, and to quantify rates of change such as the motions of objects....
over which a propagating wave (especially a laser
Laser
A laser is a device that emits light through a process of optical amplification based on the stimulated emission of photons. The term "laser" originated as an acronym for Light Amplification by Stimulated Emission of Radiation...
or maser
Maser
A maser is a device that produces coherent electromagnetic waves through amplification by stimulated emission. Historically, “maser” derives from the original, upper-case acronym MASER, which stands for "Microwave Amplification by Stimulated Emission of Radiation"...
beam) may be considered coherent
Coherence (physics)
In physics, coherence is a property of waves that enables stationary interference. More generally, coherence describes all properties of the correlation between physical quantities of a wave....
. In other words, it is the time interval within which its phase
Phase (waves)
Phase in waves is the fraction of a wave cycle which has elapsed relative to an arbitrary point.-Formula:The phase of an oscillation or wave refers to a sinusoidal function such as the following:...
is, on average, predictable.
In long-distance transmission systems
Telecommunication
Telecommunication is the transmission of information over significant distances to communicate. In earlier times, telecommunications involved the use of visual signals, such as beacons, smoke signals, semaphore telegraphs, signal flags, and optical heliographs, or audio messages via coded...
, the coherence time may be reduced by propagation
Wave propagation
Wave propagation is any of the ways in which waves travel.With respect to the direction of the oscillation relative to the propagation direction, we can distinguish between longitudinal wave and transverse waves....
factors such as dispersion
Dispersion (optics)
In optics, dispersion is the phenomenon in which the phase velocity of a wave depends on its frequency, or alternatively when the group velocity depends on the frequency.Media having such a property are termed dispersive media...
, scattering
Scattering
Scattering is a general physical process where some forms of radiation, such as light, sound, or moving particles, are forced to deviate from a straight trajectory by one or more localized non-uniformities in the medium through which they pass. In conventional use, this also includes deviation of...
, and diffraction
Diffraction
Diffraction refers to various phenomena which occur when a wave encounters an obstacle. Italian scientist Francesco Maria Grimaldi coined the word "diffraction" and was the first to record accurate observations of the phenomenon in 1665...
.
Coherence time, τ, is calculated by dividing the coherence length
Coherence length
In physics, coherence length is the propagation distance from a coherent source to a point where an electromagnetic wave maintains a specified degree of coherence. The significance is that interference will be strong within a coherence length of the source, but not beyond it...
by the phase velocity
Phase velocity
The phase velocity of a wave is the rate at which the phase of the wave propagates in space. This is the speed at which the phase of any one frequency component of the wave travels. For such a component, any given phase of the wave will appear to travel at the phase velocity...
of light
Light
Light or visible light is electromagnetic radiation that is visible to the human eye, and is responsible for the sense of sight. Visible light has wavelength in a range from about 380 nanometres to about 740 nm, with a frequency range of about 405 THz to 790 THz...
in a medium; approximately given by
where λ is the central wavelength
Wavelength
In physics, the wavelength of a sinusoidal wave is the spatial period of the wave—the distance over which the wave's shape repeats.It is usually determined by considering the distance between consecutive corresponding points of the same phase, such as crests, troughs, or zero crossings, and is a...
of the source, Δν and Δλ is the spectral width
Spectral width
In telecommunications, spectral width is the wavelength interval over which the magnitude of all spectral components is equal to or greater than a specified fraction of the magnitude of the component having the maximum value....
of the source in units of frequency and wavelength respectively, and c is the speed of light
Speed of light
The speed of light in vacuum, usually denoted by c, is a physical constant important in many areas of physics. Its value is 299,792,458 metres per second, a figure that is exact since the length of the metre is defined from this constant and the international standard for time...
in vacuum.
A single mode fiber laser
Fiber laser
A fiber laser or fibre laser is a laser in which the active gain medium is an optical fiber doped with rare-earth elements such as erbium, ytterbium, neodymium, dysprosium, praseodymium, and thulium. They are related to doped fiber amplifiers, which provide light amplification without lasing...
has a linewidth of a few kHz. The Schawlow-Townes limit for some cw lasers can be below 1 Hz. Hydrogen masers have linewidth around 1 Hz; their coherence length
Coherence length
In physics, coherence length is the propagation distance from a coherent source to a point where an electromagnetic wave maintains a specified degree of coherence. The significance is that interference will be strong within a coherence length of the source, but not beyond it...
approximately corresponds to the distance from the Earth to the Moon.