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

Example Case: Tapered Fiber

Here we investigate how light propagates in tapered fibers, i.e., fibers which have been heated and stretched such that the core dimension is reduced in some taper region.

Description of the Model

The reduction in fiber diameter is described with a simple function:

t_min := 0.5
t(z) := t_min + (1 - t_min) * 0.5 * (1 + cos(1 * 2pi * z / z_max))

When we later define the refractive index profile, we can easily use that function to modify a predefined two-dimensional function:

  bp_set_n_z('n_f(sqrt(x^2 + y^2) / t(z))', 'z'); { index profile }

The numerical resolution needs to be chosen such that cladding modes are realistically modeled, because we must expect that some light is lost from the core in the tapered region.

Results

Initially, we assume a single-mode step-index fiber. The incident light is assumed to be fully in the guided mode (the LP01 mode) of the fiber. Figure 1 shows the amplitude distribution along the fiber. The gray curves illustrate the taper, reducing the fiber diameter in the middle by 50%. The red curve shows about 13% of the optical power are lost. This is because the LP01 becomes quite weakly guided in the taper region, and the taper is a bit too fast for an adiabatic transition.

amplitude distribution along the fiber
Figure 1: Amplitude distribution along the fiber.

Figure 2 shows how various parameters evolve. Three different measures are used for the beam size:

amplitude distribution along the fiber
Figure 2: Evolution of beam parameters along the fiber.

In a second simulation, we assume a fiber with doubled numerical aperture (0.2 instead of 0.1). That more strongly guiding fiber also supports LP11 modes – but not in the tapered region. If we launch the initial beam into the LP01 mode (as above), it can “survive” the tapered region without substantial losses, as it is guided quite strongly – see Figure 3. The beam size (not shown here) undergoes only quite moderate changes.

amplitude distribution along the fiber
Figure 3: Amplitude distribution along the fiber with higher numerical aperture.

If we launch into the LP11 mode, the light is entirely lost in the taper region, as seen in Figure 4:

amplitude distribution along the fiber
Figure 4: Amplitude distribution along the fiber for launching into the LP11 mode.

One sees in Figure 4 that reflections from the edges of the grid – a numerical artifact – are not completely suppressed. This, however, is no problem for the purpose of this investigation; only the detailed curve for the power drop and the calculated 0.1% transmission for the LP11 mode are not accurate – the latter should be essentially zero.

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