Wave Vector

Dr. Rüdiger Paschotta

doi:10.61835/7ok

Wave Vector

Author: the photonics expert Dr. Rüdiger Paschotta (RP)

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

Category: article belongs to category general optics general optics

Page views in 12 months: 2402

DOI: 10.61835/7ok Cite the article: BibTex BibLaTex plain text HTML Link to this page! LinkedIn

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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.

Frequently Asked Questions

This FAQ section was generated with AI based on the article content and has been reviewed by the article’s author (RP).

What is a wave vector?

The wave vector (or k-vector) of a plane wave is a vector that points in the direction of wave propagation and is always perpendicular to the wavefronts.

How is the wave vector's magnitude related to the wavelength?

The magnitude of the wave vector is the wavenumber ($k$), which is given by the formula ($k = 2\pi / \lambda$), where ($\lambda$) is the wavelength in the medium.

Does the wave vector always point in the direction of energy flow?

No, in non-isotropic media, the direction of energy flow, given by the Poynting vector, can deviate from the direction of the wave vector. This phenomenon is called spatial walk-off.

Can a wave vector have complex components?

Yes, in media with optical absorption or gain, the wave vector can have complex components. For an evanescent wave, it may even be purely imaginary.

Questions and Comments from Users

2022-09-11

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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