# Optical Frequency

Author: the photonics expert Dr. Rüdiger Paschotta

Definition: the oscillation frequency of the electric field of light

Categories: general optics, optical resonators, optical metrology, physical foundations

Formula symbol: <$\nu$>

The optical frequency (for example of a quasi-monochromatic laser beam) is the oscillation frequency of the corresponding electromagnetic wave. For visible light, optical frequencies are roughly between 400 THz (1 terahertz = 10^{12} Hz = 1 trillion hertz) and 700 THz, corresponding to vacuum wavelengths between 700 nm and 400 nm. Infrared light has correspondingly lower optical frequencies, while ultraviolet light has higher frequencies.

Many equations in optics involve *angular optical frequencies*, which are <$2 \pi$> times the optical frequency: <$\omega = 2\pi \nu$>.

Usually, light does not have one particular optical frequency; its optical power is distributed over some frequency range, which sometimes spends a whole octave (i.e., a factor of two in terms of frequency) or even substantially more. The optical spectrum tells one how the power is distributed over the frequencies, i.e., it specifies the power spectral density as a function of frequency or vacuum wavelength.

There are technical light sources (highly frequency-stabilized lasers) which can produce light with a very small optical bandwidth – sometimes even well below 1 Hz, which is an extremely small fraction of the mean optical frequency of hundreds of terahertz – and a very high stability of that frequency. Such light sources are called optical frequency standards and are required for optical clocks, for example.

The optical frequency can be calculated as the vacuum velocity of light divided by the vacuum wavelength:

$$\nu = c / \lambda$$For calculating the frequency difference of two quite similar wavelength, one can use the following approximate equation:

$$\Delta \nu = \frac{c}{\lambda^2} \Delta \lambda$$where the denominator contains the mean wavelength.

Optical frequencies can be measured far more precisely than wavelengths; see the article on optical frequency metrology. Optical frequencies cannot be directly detected like microwave frequencies; there is simply no counter which can register so fast oscillations. Nevertheless, with indirect methods, nowadays usually involving stabilized frequency combs, it has become possible to exactly relate optical frequencies (from some optical frequency standards, for example) to microwave frequencies (e.g., from cesium clocks), or to other optical frequencies. As optical frequency standards can be more precise than microwave frequency standards and also allow for much more rapid frequency comparisons, it is expected that the definition of the second is the fundamental unit for the time in the international system of units (SI system) will soon be redefined based on an optical frequency standard.

If two optical frequencies are relatively close, there difference can be measured relatively easily: a beat note is obtained by superimposing the two beams on a fast photodetector, and the photodetector's output signal can be processed with an electronic frequency counter, for example.

The optical frequency of light is in a sense more fundamental than the optical wavelength. 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 essentially just registers a fast oscillation, i.e., the optical frequency. If that frequency coincides with certain internal resins frequencies, resonant excitation processes can occur. The internal resonant frequencies are not related to some distance equal to the optical wavelength. Nevertheless, for historical reasons it is more common to specify wavelengths rather than optical frequencies of light. (For example, Nd:YAG lasers operating on their standard laser transition are commonly said to emit light with 1064 nm vacuum wavelength, rather than with a frequency of 282 THz.) This is essentially because optical wavelengths could soon be determined by using various kinds of interferometers, whereas it was difficult in the early times to measure or even to estimate optical frequencies.

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