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

Power Form: Light Propagation in Multi-core Fibers

This Power Form allows one to conveniently simulate the propagation of light in a multi-core fiber. We offer a lot of flexibility for investigating a wide range of aspects.

Basic Features of the Model

• Definition of one core: You first define the refractive index profile of a single fiber core (which must be radially symmetric).
• Pattern of cores: You can define a pattern of cores, which can be square or hexagonal, a combination of rings, or just two cores, or a fully flexible list of core positions.
• Tolerances: You can simulate the effect of offsets of the core positions from the nominal design positions.
• Fiber Properties: You may define arbitrary twisting and/or tapering of the fiber. Also, arbitrary bending in x and/or y direction is possible.
• Optical input: you can input either a specific mode into a specific core, or enter an arbitrary expression for the complex input field amplitude profile, using any mode functions.
• Numerical grid: The grid parameters are set by the user such as to obtain sufficiently high resolution and numerical accuracy.

Definition of One Core

You can define the refractive index profile – for example, with an expression for maximum flexibility:

You may also choose the simpler “single-step” or “multiple steps” option.

The modes of a single core are calculated from these inputs.

Pattern of Cores

Next, you define a pattern of cores. Various grid types are available:

• two cores
• square
• hexagonal
• rings (up to 5 rings, each with a certain radius, some number of cores and a rotation)
• free (for an arbitrary set of core positions, if none of the other options is suitable)

It is possible to further modify the originally defined nominal design by applying arbitrary offsets to the positions of any cores (in ($x$) and ($y$) direction).

Twisting, Tapering, Bending

By default, the defined refractive index profile is assumed to be constant over the length of fiber. However, we can apply various types of modifications (also in combination) in the fiber properties section:

Twisting means applying a ($z$)-dependent rotation of the core pattern. To define a twist, you enter an expression which specifies the rotation (twist) angle (in degrees) as a function of the z (in m) coordinate.

Tapering means applying a ($z$)-dependent expansion or shrinking factor to the refractive index profile.

You can also introduce arbitrary bending in ($x$) and ($y$) direction. For each direction, you specify the bend radius as a function of the ($z$) coordinate.

Absorption

You can choose to include spatially dependent absorption losses in the fiber. There are two ways of defining those: for the whole grid or for one core (then applied to each core individually).

In some cases, it is helpful to add some artificial absorption in a simulation.

Optical Input

The simulation always involves the propagation of a given optical input which is injected into the fiber and propagated through some length of it. This input is always assumed to be monochromatic. Input parameters are:

• the optical wavelength
• an input type, either selecting a mode or defining the shape with an arbitrary expression
• optionally, the total optical power (for rescaling the amplitudes)

Numerical Grid

The simulations are done with numerical beam propagation. This requires a numerical grid, the parameters of which can be defined here: a certain grid range, number of grid points in ($x$) and ($y$) direction, length of fiber, etc.

Diagrams

A number of diagrams can be created:

• radial mode functions and mode intensity profiles (for one core)
• refractive index profile (of the whole grid), e.g. for a sanity check
• field distribution in x/y plane at one or more ($z$) positions
• evolution of optical powers in modes along the ($z$) direction
• mode powers vs. wavelength

Some examples of diagrams:

See also: overview on Power Forms