Beat Note

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

German: Schwebung

Category: optical metrology

Author: Dr. Rüdiger Paschotta

Cite the article using its DOI: https://doi.org/10.61835/ua7

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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.

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.

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. If one laser has a much larger linewidth than the other one, the beat note will have that linewidth. However, the beat linewidth can even be smaller than that of each laser if the phase noise of both lasers is at least partially correlated. 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.

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

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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 in order to analyze its frequency content. Or use an electronic spectrum analyzer.

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