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Wavelength or Optical Frequency

Posted on 2021-04-30 as part of the Photonics Spotlight (available as e-mail newsletter!)

Permanent link: https://www.rp-photonics.com/spotlight_2021_04_30.html

Author: Dr. Rüdiger Paschotta, RP Photonics AG, RP Photonics AG

Abstract: For various reasons, it would actually be more natural and convenient to specify optical frequencies rather than optical wavelengths, e.g. of lasers. However, it is understandable why in the past it became common to specify wavelengths. It is probably too late to change this convention. At least, one should be aware of the difference between vacuum wavelengths and wavelength in air.

Dr. Rüdiger Paschotta

It is very common to specify the wavelength rather than the optical frequency of light, e.g. of the light emitted by a laser source. But wouldn't it actually be better to specify the frequency? I think it would, although it is quite understandable how the convention to specify wavelengths was created.

Historical Aspects

It is actually not surprising that wavelength specifications have become so common because in the early times of optics people learned to measure wavelengths with interferometers, while optical frequency measurements were basically impossible. One could only calculate that frequency based on the measured wavelength and the also measured velocity of light.

In the meantime, things have changed. We now have instruments for measuring optical frequencies with extremely high precision – in fact much higher than the precision with which we can measure wavelengths. Note that wavelength measurements are plagued by certain technical details (e.g. unavoidable deviations of light beams from plane waves), which do not occur in frequency measurements.

Well, these frequency measurement instruments are very sophisticated and expensive devices, involving highly stabilized mode-locked lasers, frequency combs and the like. So for everyday use it is still much simpler to measure a wavelength directly. In practice, however, people often use an optical spectrum analyzer, and here it is technically just as easy to display the resulting optical spectra with wavelength or frequency units. Wavelengths are just much more common.

Uncertainties Concerning the Refractive Index

A nasty problem with the wavelength is that it depends on the refractive index of the medium in which light propagates. You may think this doesn't matter very much, since usually we have laser beams and the like in air, where the refractive index is quite close to 1. But exactly this proximity makes it nasty: it is often not clear whether a specified wavelength is actually meant to be a vacuum wavelength or the wavelength in air, and in the latter case under which conditions exactly concerning temperature, pressure and humidity. The differences are small, but not so small that they would be relevant only in exceptional situations. For example, a common red helium–neon laser has a vacuum wavelength of 632.991 nm, while the wavelength in air under standard conditions (1013.25 mbar, 15 °C, zero humidity) is 632.816 nm. So you are off by nearly 0.2 nm if you take the wrong version.

It is most common to specify the wavelength in air at standard conditions, since this is closest to the usual conditions when measuring a wavelength with an interferometer. (Interferometers are usually not evacuated, but filled with air.) However, it is often not explicitly stated that this is what is meant, and if it is, it is often not clear whether the standard conditions have been carefully observed, or possibly the measurement result was corrected for deviations from the standard conditions.

All that trouble would of course not occur if we would work with optical frequencies. For example, the standard HeNe laser would then be specified with 473.61 THz instead of 632.816 nm or 632.991 nm. No matter through what kind of medium a HeNe laser beam propagates, its frequency is everywhere the same.

Other Advantages of Using the Optical Frequency

In many situations, the wavelength in air does not have any relevance, for example because light propagation in air is not even involved, or at least the spatial aspects do not matter. For example, an atom or ion exposed to light cannot “see” the wavelength since its size is only a very small fraction of it. It would then actually be more natural to operate with optical frequencies. For sound waves, by the way, it is absolutely common to specify frequencies rather than wavelengths.

In spectroscopy, it is common to work with wavenumbers, which are essentially inverse wavelengths and are proportional to optical frequencies. This is quite natural, since the optical frequencies correspond to transition energies, which are related to energy differences between involved electronic levels.

In various other circumstances, it would also be somewhat more convenient to work with frequencies:

  • For example, differences of optical frequencies determine the frequencies of beat notes.
  • Also, the resonance frequencies of an optical resonator are equidistant if there is no chromatic dispersion within the resonator, while the resonance wavelengths are not equidistant. That frequency difference, called the free spectral range of the resonator, is also the round-trip frequency, i.e., the inverse round-trip time.
  • If the bandwidth of a mode-locked laser is specified as a frequency value rather than in the wavelength domain, it is easier to calculate the lower limit for the pulse generation.

Conventions are Hard to Change

Unfortunately, long used conventions are pretty hard to change: it is not only habits, but also there are numerous scientific papers, textbooks etc. containing wavelength instead of frequency specifications. Realistically, I am afraid we are stuck to the old convention, even though I think there would be good reasons to go for frequencies in the future – as it is also common in acoustics, for example.

This article is a posting of the Photonics Spotlight, authored by Dr. Rüdiger Paschotta. You may link to this page and cite it, because its location is permanent. See also the RP Photonics Encyclopedia.

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