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

Example Case: Calculating Fiber Modes

Description of the Model

This script demonstrates the calculation of fiber modes with the integrated mode solver. It uses a given refractive index profile of the fiber core, which is defined with tabulated values. (Of course, one could also work with a formula defining the index profile.) With a few lines of script code, these are read into an array, and the index function n_f(r) uses interpolated values from that array:

r_co := 10 um  { core radius }
n_cl := 1.44  { cladding index }
dr := 2 um  { radial resolution of index table }
defarray n_f[0, r_co, dr]
readlist r, n_f[r * um]:
 0, 1.442
 2, 1.444
 4, 1.444
 6, 1.443
 8, 1.441
 10, 1.44
n_f(r) := if r <= r_co then n_f~~[r] else n_cl

That function now simply needs to be associated with the fiber:

calc set_n_profile("n_f", r_co)

Thereafter, a lot of different functions are available, which allow one to access all mode properties, such as the intensity profiles, propagation constants, etc.

Note that for this purpose one could also use a nice Power Form, allowing the user to get such results without any own scripting.


The following figures display properties of the calculated fiber modes. In addition, it would be easily possible to use the mode profiles when defining optical channels for power calculations.

Note that the mode solver is very efficient. Even when a fiber has several hundreds of modes (i.e., many more than in this example case), the whole set of modes is calculated within roughly a second on an ordinary PC.

Figure 1 shows all radial functions for the calculated modes. Different colors are used for different <$l$> values. The refractive index profile and the effective indices of the modes are also shown.

radial fiber mode functions
Figure 1: Radial functions of the calculated fiber modes.

Figure 2 shows the intensity profiles of all modes with animated graphics.

intensity profiles of fiber modes
Figure 2: Intensity profiles of the fiber modes. RP Fiber Power itself has been used to create the animated graphics; no separate graphics software is needed.

Note that we have no wavelength dependence of the defined refractive index profile. Therefore, calculations of wavelength-dependent quantities would not be realistic: we would ignore the material dispersion. However, it is possible to define wavelength-dependent index profiles; for example, see the demo case with a germanosilicate fiber.

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