Propagation Constant
Definition: a mode- and frequency-dependent quantity describing the propagation of light in a medium or waveguide
German: Propagationskonstante
Category: fiber optics and waveguides
Formula symbol: γ, β
Units: 1/m
How to cite the article; suggest additional literature
Author: Dr. Rüdiger Paschotta
The propagation constant of a mode in a waveguide (e.g. a fiber), often denoted with the symbol γ, determines how the amplitude and phase of that light with a given frequency varies along the propagation direction z:
where A(z) is the complex amplitude of the light field at position z.
In lossless media, γ is purely imaginary; we have γ = i β with the (real) phase constant β, which is the product of the effective refractive index and the vacuum wavenumber. Optical losses (or gain) imply that γ also has a real part.
The propagation constant depends on the optical frequency (or wavelength) of the light. The frequency dependence of its imaginary part determines the group delay and the chromatic dispersion of the waveguide.
Note that different definitions of the propagation constant occur in the literature. For example, the propagation constant is sometimes understood to be only the imaginary part of the quantity defined above, i.e., β. It is then also common to introduce a normalized propagation constant which can only vary between 0 and 1. Here, the value zero corresponds to the wavenumber in the cladding, and 1 to that in the core. Modes which are mostly propagating in the cladding will have a value close to 0.
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.
See also: modes, effective refractive index, waveguides, fibers, group delay, dispersion, propagation losses
and other articles in the category fiber optics and waveguides
 |
If you like this page, please share the link with your friends and colleagues, e.g. via social media:
These sharing buttons are implemented in a privacy-friendly way!