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Definition: the phase delay per unit length, or that quantity divided by 2π
Unfortunately, there are different definitions of the wavenumber of light in the literature. In physics, the definition
is common, which is the phase delay per unit length during propagation of a plane wave, whereas the definition
(with units of cm−1) is widely used in the field of spectroscopy. The former quantity can be called angular wavenumber (in analogy with angular frequency) to avoid confusion, but that term is not very common.
For light in a medium, the wavenumber is the vacuum wavenumber times the refractive index.
The wavenumber is related to the phase change per unit length of a plane wave in a homogeneous medium. For focused beams, the phase change per unit length is modified with respect to that for a plane wave. For Gaussian beams, for example, this modification is the Gouy phase shift. For propagation of guided waves in waveguides, the propagation constant β is the relevant quantity.
See also: propagation constant, refractive index
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