←

**Laser linewidth** is the

spectral linewidthThe spectral linewidth characterizes the width of a spectral line, such as in the electromagnetic emission spectrum of an atom, or the frequency spectrum of an acoustic or electronic system...

of a

laserA 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...

beam.

Two of the most distinctive characteristics of laser emission are

spatial coherenceIn 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....

and

spectral coherenceIn 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....

. While spatial coherence is related to the

beam divergenceThe beam divergence of an electromagnetic beam is an angular measure of the increase in beam diameter or radius with distance from the optical aperture or antenna aperture from which the electromagnetic beam emerges. The term is relevant only in the "far field", away from any focus of the beam...

of the laser, spectral coherence is evaluated by measuring the laser linewidth of the radiation. Although the concept of laser linewidth can have varied theoretical descriptions here this article provides a simple experimental description. One of the first methods used to measure the coherence of a laser was

interferometryOptical interferometry combines two or more light waves in an opticalinstrument in such a way that interference occurs between them.Early interferometers used white light sources and also monochromatic light from atomic sources...

. An alternative approach is the use of spectrometry.

## CW lasers

Laser linewidth in a typical single-

transverse-modeA transverse mode of a beam of electromagnetic radiation is a particular electromagnetic field pattern of radiation measured in a plane perpendicular to the propagation direction of the beam...

He-Ne laser (at a

wavelengthIn 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 632.8 nm), in the absence of intracavity line narrowing optics, can be of the order of 1 GHz. On the other hand, the laser linewidth from stabilized low-power continuous-wave lasers can be very narrow and reach down to less than 1 kHz. Often this type of linewidth is limited by fundamental quantum processes. This limit is known as the Schawlow–Townes linewidth which can be lower than Hz for some kind of CW lasers. Nevertheless observed linewidths are larger due to a technical noise (from noise in current, vibrations etc.).

## Pulsed lasers

Laser linewidth from high-power high-gain pulsed lasers, in the absence of intracavity line narrowing optics, can be quite broad and in the case of powerful broadband

dye laserA dye laser is a laser which uses an organic dye as the lasing medium, usually as a liquid solution. Compared to gases and most solid state lasing media, a dye can usually be used for a much wider range of wavelengths. The wide bandwidth makes them particularly suitable for tunable lasers and...

s it can range from a few nm wide to as broad as 10 nm.

Laser linewidth from high-power high-gain pulsed laser oscillators, comprising line narrowing optics, is a function of the geometrical and dispersive features of the laser cavity. To a first approximation the laser linewidth, in an optimized cavity, is directly proportional to the

beam divergenceThe beam divergence of an electromagnetic beam is an angular measure of the increase in beam diameter or radius with distance from the optical aperture or antenna aperture from which the electromagnetic beam emerges. The term is relevant only in the "far field", away from any focus of the beam...

of the emission multiplied by the inverse of the overall

intracavity dispersionThe first description of multiple-prism arrays, and multiple-prism dispersion, was given by Newton in his book Opticks. Prism pair expanders were introduced by Brewster in 1813. A modern mathematical description of the single-prism dispersion was given by Born and Wolf in 1959...

. That is,

This is known as the

*cavity linewidth equation* where

is the

beam divergenceThe beam divergence of an electromagnetic beam is an angular measure of the increase in beam diameter or radius with distance from the optical aperture or antenna aperture from which the electromagnetic beam emerges. The term is relevant only in the "far field", away from any focus of the beam...

and the term in parenthesis (elevated to –1) is the overall intracavity dispersion. This equation was originally derived from classical optics. However, in 1992

DuarteF. J. Duarte is a laser physicist and author/editor of several well-known books on tunable lasers. He introduced the generalized multiple-prism dispersion theory and has discovered various multiple-prism grating oscillator laser configurations...

derived this equation from

quantum interferometricQuantum mechanics was first applied to optics, and interference in particular, by Paul Dirac. Feynman, in his lectures, uses Dirac’s notation to describe thought experiments on double-slit interference of electrons...

principles, thus linking a quantum expression with the overall intracavity angular dispersion.

An optimized

multiple-prism grating laser oscillatorMultiple-prism grating laser oscillators, or MPG laser oscillators, use multiple-prism beam expansion to illuminate a diffraction grating mounted either in Littrow configuration or grazing-incidence configuration...

can deliver pulse emission in the kW regime at single-longitudinal-mode linewidths of

≈ 350 MHz (equivalent to

≈ 0.0004 nm at a laser wavelength of 590 nm).

## Linewidth equivalence

In the frequency domain the laser linewidth is denoted as

and is given in units of GHz, MHz, or kHz. In the spectral domain the laser linewidth is denoted as

and is often given in units of nm. In the field of

spectroscopySpectroscopy is the study of the interaction between matter and radiated energy. Historically, spectroscopy originated through the study of visible light dispersed according to its wavelength, e.g., by a prism. Later the concept was expanded greatly to comprise any interaction with radiative...

the use of the reciprocal cm, or cm

^{-1}, is widespread.

In more detail, the laser linewidth in frequency units can be written as

where

*c* is the speed of light (in units of meters per second) and

is the

*coherence length* (in meters) so that the linewidth

is in units of Hz. The equivalent definition in the wavelength domain is

Thus the quantity

is the common factor between the equivalent linewidths in Hz and meter units. With these definitions it can shown, for example, that

≈ 350 MHz is equivalent to

≈ 0.0004 nm at a laser wavelength of 590 nm.

## See also

- Multiple-prism dispersion theory
The first description of multiple-prism arrays, and multiple-prism dispersion, was given by Newton in his book Opticks. Prism pair expanders were introduced by Brewster in 1813. A modern mathematical description of the single-prism dispersion was given by Born and Wolf in 1959...

- Multiple-prism grating laser oscillator
Multiple-prism grating laser oscillators, or MPG laser oscillators, use multiple-prism beam expansion to illuminate a diffraction grating mounted either in Littrow configuration or grazing-incidence configuration...

- N-slit interferometric equation
Quantum mechanics was first applied to optics, and interference in particular, by Paul Dirac. Feynman, in his lectures, uses Dirac’s notation to describe thought experiments on double-slit interference of electrons...

- Oscillator linewidth
The concept of a linewidth is borrowed from laser spectroscopy. The linewidth of a laser is a measure of its phase noise. The spectrogram of a laser is produced by passing its light through a prism. The spectrogram of the output of a pure noise-free laser will consist of a single infinitely thin...

- Solid state dye lasers
Solid state dye lasers were introduced in 1967 by Soffer and McFarland. In these solid state lasers, the gain medium is a laser dye-doped organic matrix such as poly , rather than a liquid solution of the dye...