Definition: phase change per unit length for light propagating in a medium or waveguide

German: Propagationskonstante

The propagation constant of a mode in a waveguide (e.g. a fiber), often denoted with the symbol β, determines how the phase and amplitude of that light with a given frequency varies along the propagation direction z:

where A(x,y,z) is the complex amplitude of the light field. β may actually be complex; its real part is then the phase delay per unit propagation distance, whereas the imaginary part describes optical gain (if negative) or loss (if positive). The propagation constant can be expressed as the product of the effective refractive index and the vacuum wavenumber.

The propagation constant depends on the optical frequency (or wavelength) of the light. This frequency dependence 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 real part of the quantity defined above, or real and imaginary part are exchanged.

It is 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.

See also: modes, effective refractive index, waveguides, fibers, group delay, dispersion

Category: fibers and other waveguides

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