Important Properties of Fiber Modes

To continue the content of previous page, here we introduce the important properties of fiber nodes.

For a given wavelength, each fiber mode has several important characteristics:

It has a certain complex amplitude profile, from which one obtains the intensity profile. From the intensity profile, one may calculate the effective mode area. This determines how strong nonlinear effects can be.

The phase constant β tells how fast its overall complex phase changes during propagation. For strongly guided modes, it is well above the phase constant of the cladding. In that case, the intensity profile does not substantially extend into the cladding.

From the first and second derivative of the β with respect to the optical frequency, one can calculate the group velocity and the group velocity dispersion (GVD).

Outdoor Optical Cable

For lossy fibers, each mode can have a certain attenuation constant. These values can differ a lot between the modes – sometimes by orders of magnitude. For example, bend losses are often much higher for higher-order modes. They may be calculated with numerical beam propagation or estimated with some analytical techniques. By the way, bending can also shift and distort the mode profile.

The cut-off wavelength is the wavelength above which the mode ceases to exist. (Under some circumstances, a mode can have a higher and lower cut-off.)

Higher-order modes have larger transverse wave vector components than lower-order modes. As a plane-wave component with such a wave vector is tilted against the fiber axis, one may expect that it has an increased path length, so that a higher-order mode will experience a larger phase delay than e.g. the fundamental mode. 

However, the opposite is true! A larger transverse wave vector component implies a smaller longitudinal component, and that implies a reduced phase delay. So in fact the phase constants (β values) of the highest-order modes are the lowest, and are often close to the refractive index of the cladding times the vacuum wavenumber.

By the way, such modes also exhibit a slow decay of intensity in the cladding, i.e., their intensity distributions extend quite far into the cladding. Another property of these modes is the reduced group velocity (see part 10 on chromatic dispersion). That would actually fit to an increased path length, but the probably surprising findings explained above should be a warning: be careful with quick “explanations” of that vague type.

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