Using our ad package , you can display your logo, further below your product description, and these will been seen by many photonics professionals.
Find more supplier details at the end of this encyclopedia article , or go to our
The linewidth (or line width) of a laser, e.g. a single-frequency laser, is the width (typically the full width at half-maximum, FWHM) of its optical spectrum. More precisely, it is the width of the power spectral density of the emitted electric field in terms of frequency, wavenumber or wavelength.
Similarly, other spectral lines e.g. from gas discharge lamps have certain linewidths, which can depend on the operation conditions.
The linewidth of a light beam is strongly (but non-trivially) related to the temporal coherence, characterized by the coherence time or coherence length. A finite linewidth arises from phase noise if the optical phase undergoes unbounded drifts, as is the case for free-running laser oscillators, for example. (Phase fluctuations which are restricted to a small interval of phase values lead to a zero linewidth and some noise sidebands.) Drifts of the resonator length can further contribute to the linewidth and can make it dependent on the measurement time. This shows that the linewidth alone, or even the linewidth complemented with a spectral shape (line shape), does by far not provide full information on the spectral purity of laser light. (This is particularly the case for lasers with dominating low-frequency phase noise.) More data are required for full noise specifications.
A simple way to define the linewidth would be to use the root-mean-square (r.m.s.) value of the instantaneous optical frequency:
$$\Delta {\nu _{{\rm{r}}{\rm{.m}}{\rm{.s}}{\rm{.}}}} = \sqrt {\int\limits_{{f_1}}^{{f_2}} {{S_{\Delta \nu }}(f)\;{\rm{d}}f} } $$$$\Delta {\nu _{{\rm{r}}{\rm{.m}}{\rm{.s}}{\rm{.}}}} = \sqrt {\int\limits_{{f_1}}^{{f_2}} {{S_{\Delta \nu }}(f)\;{\rm{d}}f} } $$
where usually some limited integration range for the noise frequencies is chosen. This quantity can be easily calculated from the power spectral density <$S_{\Delta\nu}(f)$> of the instantaneous frequency. Note, however, that the r.m.s. linewidth is not always a sensible measure; one should only use it in cases with strongly increasing <$S_{\Delta \nu}(f)$> for decreasing noise frequency (flicker noise), but not e.g. for white frequency noise. It is more common to define the linewidth as the width of the optical spectrum, but the relation between the r.m.s. linewidth and the width of the optical spectrum (or with the phase noise PSD) is not trivial and depends on the shape of the frequency noise spectrum.
Lasers with very narrow linewidth (high degree of monochromaticity) are required for various applications, e.g. as light sources for various kinds of fiber-optic sensors, for laser spectroscopy (e.g. LIDAR), in coherent optical fiber communications, and for test and measurement purposes. Note that the achieved linewidth can be many orders of magnitude below the linewidth of the used laser transition.
The simplest situation is one where only spontaneous emission (quantum noise) introduces phase noise. In that case, the noise of the instantaneous frequency is white noise, i.e., its power spectral density is constant, and the emission spectrum is of Lorentzian shape. The corresponding linewidth was calculated by Schawlow and Townes [1] even before the first laser was experimentally demonstrated. According to the modified Schawlow–Townes equation (with a correction from M. Lax)
In order to get some feeling for phase noise, you can listen to the following short sound samples of a 440-Hz tone with different linewidths (white phase noise, no amplitude noise):
0 Hz (no noise), 1 Hz, 5 Hz, 10 Hz
You can download these .wav files (each being ≈ 215 KB long) and play them with any sound player software.
For comparison, if you temporally stretch the output of a 1064-nm Nd:YAG laser with a 10-kHz linewidth to 440 Hz, the linewidth will be ≈ 16 nHz – a pretty pure tone indeed!
$$\Delta {\nu _{{\rm{laser}}}} = \frac{{\pi \;h\nu \;{{\left( {\Delta {\nu _{\rm{c}}}} \right)}^2}}}{{{P_{{\rm{out}}}}}}$$$$\Delta {\nu _{{\rm{laser}}}} = \frac{{\pi \;h\nu \;{{\left( {\Delta {\nu _{\rm{c}}}} \right)}^2}}}{{{P_{{\rm{out}}}}}}$$
the linewidth (FWHM) is proportional to the square of the resonator bandwidth divided by the output power (assuming that there are no parasitic resonator losses). The article on the Schawlow–Townes linewidth contains a more practical form of the equation.
The Schawlow–Townes limit is usually difficult to reach in reality, as there are various technical noise sources (e.g. mechanical vibrations, temperature fluctuations, and pump power fluctuations) which are difficult to suppress. There are therefore certain compromises in laser design for narrow linewidth. For example, a long laser resonator leads to a small Schawlow–Townes linewidth, but makes it more difficult to achieve stable single-frequency operation without mode hops, and to get a mechanically stable setup.
Typical measured linewidths of stable free-running single-frequency solid-state lasers (e.g. for a measurement time of 1 s) are a few kilohertz, which is far above the Schawlow–Townes limit. Various sources of technical noise, e.g. fluctuations of the resonator length, the pump power or the temperature of the laser crystal, can be responsible for the increased linewidth.
The linewidths of monolithic semiconductor lasers are often in the megahertz range and are strongly increased above the Schawlow–Townes limit mainly by amplitude-phase coupling, as described with the linewidth enhancement factor. There can also be excess noise from charge carrier fluctuations with a 1 / f characteristic of the PSD of the frequency fluctuations. In that case, the measurement time influences the measured linewidth value.
Much smaller linewidths, sometimes even below 1 Hz, can be reached by stabilization of lasers, e.g. using ultrastable reference cavities (→ narrow-linewidth lasers, frequency-stabilized lasers). Small linewidths are important, e.g. for spectroscopic measurements and for application in fiber-optic sensors.
A laser linewidth can be measured with a variety of techniques:
Note that an optical frequency measurement always needs some kind of frequency (or timing) reference somewhere in the setup. For lasers with narrow linewidth, only an optical reference can give a sufficiently accurate reference. The self-heterodyne technique is a way to derive the frequency reference from the device under test itself by applying a large enough time delay, ideally avoiding any temporal coherence between the original beam and the delayed version. Therefore, long fibers are often used; however, long fibers tend to introduce additional phase noise due to temperature fluctuations and acoustic influences.
Particularly in cases with <$1 / f$> frequency noise, a linewidth value alone may not be regarded as completely characterizing the phase noise. It may then be better to measure the whole Fourier spectrum of the phase or instantaneous frequency fluctuations and characterize it with a power spectral density; see also the article on noise specifications. Note also that <$1 / f$> frequency noise (or other noise spectra with strong low-frequency noise) can cause problems with some measurement techniques.
The linewidth of a laser depends strongly on the type of laser. It may be further minimized by optimizing the laser design and suppressing external noise influences as far as possible. The first step should be to determine whether quantum noise or classical noise is dominating because the required measures can depend very much on this.
The influence of quantum noise (essentially spontaneous emission noise) is small for a laser with high intracavity power, low resonator losses, and a long resonator round-trip time. Classical noise may be introduced via mechanical fluctuations, which can often be kept weaker for a compact short laser resonator, but note that resonator length fluctuations of a certain magnitude have a stronger effect in a shorter resonator. Proper mechanical construction can minimize the coupling of the laser resonator to external vibrations and also minimize effects of thermal drift. There can also be thermal fluctuations in the gain medium, introduced e.g. by a fluctuating pump power. For superior noise performance, various schemes for active stabilization can be employed, but it is often advisable first to use all practical passive methods.
Single-frequency solid-state bulk and fiber lasers can achieve linewidths of a few kilohertz, or sometimes even below 1 kHz. With serious efforts at active stabilization, sub-hertz linewidths are sometimes achieved. The linewidth of a laser diode is typically in the megahertz region, but it can also be reduced to a few kilohertz, e.g. in external-cavity diode lasers, particularly with optical feedback from a high-finesse reference cavity.
See also the article on narrow-linewidth lasers.
A narrow linewidth from a laser source is not always desirable:
The term linewidth is also used for the width of optical transitions (e.g. a laser transition or some absorption feature). For transitions in single atoms or ions at rest, the linewidth is related to the upper-state lifetime (more precisely, the lifetime of both upper and lower states) (lifetime broadening) and is called natural linewidth. Significant linewidth broadening can be caused by movement of the atoms or ions (→ Doppler broadening) or by interactions, e.g. pressure broadening in gases or interactions with phonons in solid media. If different atoms or ions are subject to different influences, this leads to inhomogeneous broadening.
The linewidth of a transition is often related to a Q factor, which is the frequency divided by the linewidth.
(Suggest additional literature!)
See also: spectral lines, laser lines, linewidth enhancement factor, optical spectrum analyzers, optical phase, coherence time, coherence length, phase noise, optical frequency, frequency noise, noise specifications, laser specifications, laser noise, single-frequency operation, narrow-linewidth lasers, self-heterodyne linewidth measurement, stabilization of lasers, spotlight 2007-06-24, spotlight 2007-10-11, spotlight 2008-07-26
Here you can submit questions and comments. As far as they get accepted by the author, they will appear above this paragraph together with the author’s answer. The author will decide on acceptance based on certain criteria. Essentially, the issue must be of sufficiently broad interest.
Please do not enter personal data here; we would otherwise delete it soon. (See also our privacy declaration.) If you wish to receive personal feedback or consultancy from the author, please contact him, e.g. via e-mail.
Your question or comment:
Spam check:
(Please enter the sum of thirteen and three in the form of digits!)
By submitting the information, you give your consent to the potential publication of your inputs on our website according to our rules. (If you later retract your consent, we will delete those inputs.) As your inputs are first reviewed by the author, they may be published with some delay.
If you have any questions on Line Width Measuring Machine. We will give the professional answers to your questions.