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RP Fiber Power – Simulation and Design Software for Fiber Optics, Amplifiers and Fiber Lasers

Power Form: Mode Properties of a Fiber

This Power Form allows to conveniently calculate properties of guided modes of an optical fiber with a given refractive index profile.

graphic for this Power Form

Defining the Refractive Index Profiles

You have three options:

Simple Step-index Profile

When you choose the profile type single step, you can simply enter core diameter, cladding index and numerical aperture:

defining a single-step profile

Multi-step Profile

When you choose the profile type multiple steps, you can enter up to eight radial segments with different refractive indices:

defining a multi-step profile

Refractive Index Expression

For still more flexibility, you can define the refractive index vs. radial position r in the fiber core with an expression:

enter expression for refractive index

In this example, we have a parabolic index profile, as it may be used for a typical graded-index fiber.

Display of Mode Properties

Below the index definition area, the form displays a table with calculated mode properties for a given wavelength:

table with mode properties

For each mode, you get the following:

Besides, the M2 factor of the fundamental mode is displayed. It is often close to 1, but in some cases with deformed mode profile it may also be substantially higher.

Note that chromatic dispersion properties cannot be calculated, since for that we would need wavelength-dependent refractive indices as inputs. That, however, is possible in our form for germanosilicate fibers.


The form offers several diagrams for displaying mode properties:

diagrams for mode properties

Just select those which you need, and (in the right column) select certain options.

The following screenshots show you for our last example case (parabolic index profile) what you can get from this form:

example diagram
example diagram
example diagram
example diagram
example diagram
effective indices

Case Studies

The following case studies are available, where we used this Power Form:

Case Studies

case study multimode fibers

Case Study: Mode Structure of a Multimode Fiber

We explore various properties of guided modes of multimode fibers. We also test how the mode structure of such a fiber reacts to certain changes of the index profile, e.g. to smoothening of the index step.


Case Studies

case study number of modes

Case Study: Number of Modes of a Highly Multimode Fiber

We seek a simple equation for estimating for the number of modes of a highly multimode fiber, which can be applied to fiber designs with arbitrary shapes of the refractive index profile. Instead of applying complicated mathematics, we build a hypothesis and subject that to multiple numerical tests.


Case Studies

case study numerical aperture

Case Study: The Numerical Aperture of a Fiber

The requirement of total internal reflection would seem to set a strict limit for the angular distributions of fiber modes. However, some modes are found to exceed that limit significantly. We investigate that in detail for single-mode, few-mode and multimode fibers.


Case Studies

case study fiber dispersion engineering

Case Study: Dispersion Engineering for Telecom Fibers

We explore different ways of optimizing refractive index profile for specific chromatic dispersion properties of telecom fibers, resulting in dispersion-shifted or dispersion-flattened fibers. This also involves automatic optimizations.


See also: overview on Power Forms