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Wave Vector

Definition: a vector indicating the direction of wave propagation and the phase delay per unit length

Category: general opticsgeneral optics


Cite the article using its DOI: https://doi.org/10.61835/7ok

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The wave vector (or <$k$> vector) of a plane wave is a vector which at least in the case of isotropic optical media points in the direction in which the wave propagates. It is always perpendicular to the wavefronts.

The magnitude of the wave vector (with units of m−1) is the wavenumber as defined by

$$k = \frac{{2\pi }}{\lambda }$$

where <$\lambda$> is the wavelength in the medium (not the vacuum wavelength).

In non-isotropic media, the direction of energy flow, which is the direction of the Poynting vector, can somewhat deviate from that of the wave vector, which is always perpendicular to the wavefronts. This phenomenon is called spatial walk-off.

In media with absorption or gain, the wave vector can have complex components. In the case of an evanescent wave, it can even have a purely imaginary component.

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Is the K vector a covariant or contravariant vector?

The author's answer:

It is contravariant: when using smaller distance units, the vector becomes larger.

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