definition:
A vector that describes the direction of wave propagation and the phase delay per unit length.
The wave vector of plane waves(kThe vector points in the direction of wave propagation, usually perpendicular to the wavefront. Its size is the wavenumber, defined as:

among whichλIt is the wavelength in the medium (not the vacuum wavelength).
In non isotropic media, the direction of energy flow may differ from the direction of the wave vector, a phenomenon known as random walk.
In absorbing or gain media, wave vectors may have complex components. In the case of decaying fields (see total reflection), the wave vector can even be a pure imaginary number.
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