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Definition: optical fibers with a step-index refractive index profile
Optical fibers can have different refractive index profiles. Apart from such fibers where light is guided at the air-glass interface, the simplest index profile is a rectangular one, where the refractive index is constant within the fiber core, and is somewhat higher than in the cladding. Fibers of that kind are called step-index fibers.
The assumption of a step-index profile is often used for calculations in fiber optics, even though standard fabrication techniques often lead to significant deviations from this simple situation. In particular, preferential evaporation of the dopant during the collapse of the preform (assuming that the preform is made with chemical vapor deposition) often leads to a pronounced dip of the refractive index profile at the center. For profiles deviating from a step-index profile, an effective step-index profile may be defined which leads to rather similar mode properties as the actual profile.
The propagation modes of step-index fibers can be described with functions belonging to the family of Bessel functions, multiplied by an exponential phase factor exp(i β z) (with the propagation constant β) for the azimuthal phase variation. Concerning the radial dependence, the field strength in the core is proportional to the zero-order Bessel function of first kind, and the cladding part is given by a modified Bessel function of the second kind. The mode function and its first derivative are always continuous at the core-cladding interface.
Figure 1: Mode functions of a step-index fiber. This fiber supports 4 modes, disregarding different polarization states.
Various fiber parameters, in particular the numerical aperture and the V number, are originally defined only for step-index fibers, even though effective values are sometimes used for other fiber types. For large V values, the number of modes is proportional to V2.
Deviations from a step-index profile can result from certain techniques of fiber fabrication. In some cases, such features are intentionally used in order to achieve certain guiding properties. For example, a region with depressed refractive index between core and cladding can introduce an additional cut-off wavelength, above which the propagation losses become very high.
See also: fibers, numerical aperture, V number
Category: fibers and other waveguides
This encyclopedia is authored by Dr. Rüdiger Paschotta, the founder and executive of RP Photonics Consulting GmbH. Contact this distinguished expert in laser technology, nonlinear optics and fiber optics, and find out how his technical consulting services (e.g. product designs, problem solving, independent evaluations, or staff training) could become very valuable for your business!
