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The wave vector (or k vector) of a plane wave is a vector which points in the direction in which the wave propagates.
It is always perpendicular to the wavefronts.
Its magnitude is the wavenumber as defined by
where λ is the wavelength in the medium (not the vacuum wavelength).
In non-isotropic media, the direction of energy flow can deviate from that of the wave vector.
This phenomenon is called spatial walk-off.
In media with absorption or gain, the wave vector can have complex components.
In case of an evanescent wave (→ total internal reflection), it can even have a purely imaginary component.