Self-heterodyne Linewidth Measurement
Author: the photonics expert Dr. Rüdiger Paschotta (RP)
Definition: a technique for laser linewidth measurements, based on a beat note between the beam and a delayed version of itself
Categories:
Related: linewidth coherence length optical heterodyne detection interferometers recirculating fiber loops lasers single-frequency lasers narrow-linewidth lasers
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DOI: 10.61835/ssg Cite the article: BibTex BibLaTex plain text HTML Link to this page! LinkedIn
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Operation Principle of Self-heterodyne Linewidth Measurements
The self-heterodyne method [1] is a heterodyne technique which can be used to measure the linewidth (width of the optical spectrum) of a laser, particularly a single-frequency laser. The basic setup is shown in Figure 1. One portion of the laser beam is sent through a long optical fiber which provides some time delay. Another portion is sent through an acousto-optic modulator (AOM), which is driven with a constant frequency (typically some tens of megahertz) and shifts all the optical frequency components by that frequency. Both beams are finally superimposed on a beam splitter, and the resulting beat note (centered at the AOM frequency) is recorded with a photodetector (typically a photodiode). From this signal, the laser linewidth can then be calculated.
For sufficiently long delays, the superimposed beams are essentially uncorrelated, and the output spectrum becomes a simple self-convolution of the laser output spectrum [1], from which the laser linewidth is easily retrieved. However, what “sufficiently long” means in a specific case, can be a difficult question. The criterion which is usually used is that the delay length must be larger than the coherence length, and the latter is derived from the (measured) linewidth itself. This is correct for white frequency noise, but not in situations with higher (e.g. (1ドル / f$)) low-frequency noise [5], as can occur e.g. for narrow-linewidth fiber lasers. If such issues are not completely understood, the measured linewidth values may be wrong (often too low).
The delay time in the self-heterodyne setup can be interpreted as a finite measurement time, which implies that the impact of noise frequencies below that inverse measurement time is low [2]. A consequence of that is that measurements with shorter delay time yield smaller linewidth values if the instantaneous frequency fluctuations exhibit substantial (1ドル / f$) noise, as is the case for many laser diodes.
For lasers with a very narrow linewidth (long coherence length), it may not be practical to have a long enough time delay to obtain uncorrelated beams. In that case, shorter delays can be used, but the data processing then has to be substantially more sophisticated. Another possibility is to use an extension of this method, based on recirculating fiber loops [3].
Frequently Asked Questions
This FAQ section was generated with AI based on the article content and has been reviewed by the article’s author (RP).
What is the self-heterodyne method for laser linewidth measurement?
It is a heterodyne technique where a laser beam is split into two. One beam is frequency-shifted with an acousto-optic modulator (AOM), while the other is delayed in a long optical fiber. The two beams are then recombined to produce a beat note, from which the laser's linewidth can be determined.
Why is a long optical fiber used in a self-heterodyne setup?
The long fiber introduces a time delay, which should be longer than the laser's coherence length. This ensures that the two recombined laser beams are essentially uncorrelated, which simplifies the analysis of the resulting beat note spectrum.
What is a common problem when measuring laser linewidth with the self-heterodyne method?
If the laser exhibits significant low-frequency noise, such as (1ドル / f$) noise, the standard condition of using a delay longer than the coherence length is not sufficient. This can lead to an underestimation of the true laser linewidth.
What happens if the fiber delay is too short in a self-heterodyne measurement?
A delay time which is too short means that the two interfering beams are not uncorrelated. This often leads to a measured linewidth which is smaller than the true linewidth, especially if significant (1ドル / f$) noise is present. More sophisticated data analysis is then required to obtain a correct result.
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Bibliography
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Questions and Comments from Users
2025年03月05日
Your diagram might be wrong. I think the whole setup has to be fiber-based, including the AOM, because the AOM deflects the beam. Alternatively, a backward pass through the AOM is needed to cancel out the beam deflection, or so I've read.
The author's answer:
No, the beam deflection at the AOM does not matter; it is only a matter of alignment. Note that the figure ignores that beam deflection since it is quite weak.
2025年07月29日
If the delay length is larger than the coherence length, how can the beat signal be generated?
The author's answer:
You then have two statistically independent signals interfering with each other, and [1] explains how you get the information from that.
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