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RP Fiber Calculator is a convenient tool for calculations on optical fibers.
RP Fiber Power is an extremely flexible tool for designing and optimizing fiber devices.
RP Resonator is a particularly flexible tool for laser resonator design.
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RP Fiber Power – Simulation and Design Software
for Fiber Optics, Amplifiers and Fiber Lasers

Example Case: Mode-locked Fiber Laser

Description of the Model

Here, we numerically simulate the pulse formation in an all-normal-dispersion mode-locked fiber laser (also called a dissipative soliton laser). Comparing with a typical mode-locked bulk laser or a soliton fiber laser, the details of pulse formation in such a laser are rather sophisticated, because there is a complicated interplay of nonlinear effects, spectral filtering and a saturable absorber. The pulse evolution in such fiber lasers has been discussed in W. H. Renninger et al., “Pulse shaping and evolution in normal-dispersion mode-locked fiber lasers”, IEEE J. Sel. Top. Quantum Electron. 18 (1), 389 (2012).

In each resonator round trip, the circulating pulse is transmitted through the following optical components:

This means that we need to define three different fibers in this model.

An interesting detail is the treatment of gain saturation. Normally, it would take millions of resonator round trip for the system to settle at its steady state. However, as the actual gain dynamics (with slow relaxation oscillations) are not of interest here, a solution is implemented which lets us find the steady state much faster – within only 100 round trips. In each round trip, the gain in the active fiber is calculated for the steady state which would be reached (after many round trips) for the given average signal power. The great flexibility of RP Fiber Power makes it easy to implement such tricks.

Results

Figure 1 shows the time-dependent optical powers during the first 100 resonator round trips. It also displays the instantaneous frequency, showing a pronounced up-chirp of the generated pulses.

pulses in time domain

Figure 1: Pulses for the first 100 round trips in the time domain.

Figure 2 shows the same pulses in the frequency domain. One sees that the optical spectrum obtains a roughly rectangular shape, whereas the spectral shape is approximately parabolic, at least in the range with substantial power spectral density.

pulses in frequency domain

Figure 2: Pulses for the first 100 round trips in the frequency domain.

Figure 3 shows how the generated output pulse can be dispersively compressed. The amount of second-order dispersion required for optimum compression is calculated automatically. The small side pulses arise from the approximately rectangular spectral shape, not from imperfect dispersion compensation.

dispersive compression of output pulse from a mode-locked fiber laser

Figure 3: Output pulse in the time domain before and after dispersive compression.

Figure 4 shows how the intracavity pulse parameter evolve during the 100 round trips. One sees that after 100 round trips the system is close to the steady state.

evolution of pulse parameters

Figure 4: Evolution of the pulse parameters during the first 100 round trips.

Figure 5 shows how the pulse parameters vary within the three fibers. The curves are shown in blue within the passive fibers and in red within the active fiber.

pulse parameters in the fibers

Figure 5: Pulse parameters within the passive and active fibers. The active part is shown in red.

(back to the list of example cases)

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