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Beat Note

Author: the photonics expert (RP)

Definition: an oscillation of the optical intensity arising from the superposition of light with different optical frequencies

Category: article belongs to category optical metrology optical metrology

Related: frequency metrologyoptical frequencyphotodetectorsoptical heterodyne detectionBeat Signals with Zero LinewidthNo Beat Note for Orthogonal Modes

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DOI: 10.61835/ua7   Cite the article: BibTex BibLaTex plain textHTML   Link to this page!   LinkedIn

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What is a Beat Note?

If two laser beams with different optical frequencies are superimposed on a photodetector measuring the optical intensity, a beat note — i.e., a signal with the difference of the optical frequencies — can usually be observed, if some conditions are met:

  • The spatial distributions of the two light fields must overlap and must not be orthogonal. (For example, there may be no beat note if a laser beam with TEM00 and TEM01 modes excited hits a detector.) Somewhat clipping the beams, or even just some non-uniformity of the detector surface, can solve that problem.
  • The polarization states also must not be orthogonal.
  • The optical frequency difference must be within the bandwidth of the photodetector.
  • Obviously, the wavelengths must be within the range where the photodetector is sensitive.
beat note
Figure 1: Superposition of two optical oscillations with a frequency difference of 25 THz. The bottom two curves show the electric field strengths of the isolated oscillations, and the top curve the additive superposition. A sufficiently fast intensity detector would record an oscillation of the power with the difference frequency. (In practice, beat note frequencies need to be much smaller for beating to be detected.)

As a fast photodetector can have a bandwidth of tens of gigahertz (or even higher), optical frequency differences of that order of magnitude can be measured e.g. by analyzing the photodetector output with an electronic frequency counter or an electronic spectrum analyzer. An important application of this is in frequency metrology. For example, the frequency of some laser can be measured by recording a beat note between that laser and a close-by optical signal with known optical frequency. Such measurements are greatly facilitated by an optical frequency comb which can cover a wide range of well-defined optical frequencies, so that a sufficiently nearby reference frequency for a beat measurement can be found for any optical frequency in that large range.

Optical beat notes are essential for the technique of optical heterodyne detection.

Linewidth of Beat Notes

The linewidth of a beat note of two free-running lasers with uncorrelated laser noise (which is the usual situation) is larger than the linewidth of each laser separately. For Lorentzian line shapes, the linewidth of the beat note is the sum of the individual laser linewidths. For Gaussian lines, there is a different rule:

($\Delta \nu = \sqrt{(\Delta\nu_1)^2 + (\Delta\nu_2)^2}$)

If the phase noise of both lasers is at least partially correlated, the beat linewidth can even be smaller than that of each laser. In an extreme case, one of the lasers may be phase-stabilized so as to obtain a constant beat frequency, as defined e.g. by some electronic oscillator. The linewidth of the beat note, measured against a clock in synchronism with the electronic oscillator, can then be exactly zero, if the phase difference exhibits only small stationary fluctuations.

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 an optical beat note?

It is an electronic signal generated by a photodetector when two light beams with different optical frequencies are superimposed on it. The frequency of this signal equals the difference between the two optical frequencies.

What conditions are necessary to observe a beat note?

The two light beams must have overlapping spatial distributions and non-orthogonal polarization states. Also, their frequency difference must be within the photodetector's bandwidth, and their wavelengths must be in its sensitivity range.

What is the linewidth of a beat note?

For two lasers with uncorrelated noise, the beat note's linewidth is the sum of the individual laser linewidths. However, if the phase noise of the lasers is strongly correlated, the beat note linewidth can be much smaller.

What are beat notes used for?

A primary application is in optical frequency metrology for measuring a laser's frequency by beating it with a reference laser of known frequency. Beat notes are also essential for optical heterodyne detection.

Questions and Comments from Users

2023-05-18

Could you please explain why two beams with orthogonal polarization states cannot beat in photodiodes?

The author's answer:

In that case, the detected optical power is simply the sum of the optical powers of the two beams — without any beat note. It is easy to see that, for example, you cannot have destructive interference between such beams: Their electric fields cannot cancel each other.

2023-06-18

Can the beat frequency of light beat signals be calculated by analyzing them with Fourier transform?

The author's answer:

Sure. You can, for example, take a beat signal from a fast photodetector, digitally sample it and apply a Fourier transform to analyze its frequency content. Or use an electronic spectrum analyzer.

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