Unfortunately, there are different definitions of the wavenumber of light in the literature. In physics, the definition
is common, where λ is the wavelength in the medium (not the vacuum wavelength). That (angular) wavenumber is the magnitude of the wave vector, and is the phase delay per unit length during propagation of a plane wave.
The other definition
(with units of cm−1) is widely used in the field of spectroscopy and therefore called the spectroscopic wavenumber. 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. Spectroscopic wavenumbers are usually considered in vacuum.
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 imaginary part of the propagation constant γ (called β) is the relevant quantity.
Questions and Comments from Users
Here you can submit questions and comments. As far as they get accepted by the author, they will appear above this paragraph together with the author’s answer. The author will decide on acceptance based on certain criteria. Essentially, the issue must be of sufficiently broad interest.
Please do not enter personal data here; we would otherwise delete it soon. (See also our privacy declaration.) If you wish to receive personal feedback or consultancy from the author, please contact him e.g. via e-mail.
By submitting the information, you give your consent to the potential publication of your inputs on our website according to our rules. (If you later retract your consent, we will delete those inputs.) As your inputs are first reviewed by the author, they may be published with some delay.