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# Modeling of Pulse Amplification

This is part 5 of a tutorial on pulse amplification modeling from Dr. Paschotta. The tutorial has the following parts:

1:  Models for different pulse duration regimes
2:  Gain saturation
3:  Simulating pumping and pulse amplification
4:  Multimode amplifiers
5:  Amplified spontaneous emission
6:  Bulk amplifiers

## Part 5: Amplified Spontaneous Emission

Fiber amplifiers for pulses often provide a lot of gain – e.g. 40 dB in a single stage or much more than in a multi-stage amplifier system. As a consequence, we also get a substantial amount of amplified spontaneous emission (ASE).

Further, the generated ASE powers may be substantially time-dependent due to the time-dependent amplifier gain. Well, that time dependence is weak in cases with high repetition rate pulse trains, where each pulse causes a negligible amount of gain saturation (as explained in part 2). However, it can be a very strong effect for amplifiers with efficient energy extraction, where ASE may be strong at the beginning of a pulse and negligible afterwards.

In the RP Fiber Power software, we can so far propagate only an ultrashort pulse in one or two optical channels simultaneously, and can thus not simulate the drop of ASE during the pulse, caused by the gain saturation. However, we have the time-dependent ASE powers during all other times (e.g. for pumping). This is usually enough; note that the gain saturation effect by ASE during the short time window for the pulse simulation is normally completely negligible.

We can then easily plot the ASE powers vs. time between any two pulses, or plot the minimum and maximum ASE within such an interval as a function of the pulse number, or show the ASE spectra before and after the pulse. The latter is done in the following diagram:

By the way, to obtain the average ASE powers over many pumping cycle, one often cannot simply take the average between the values before and the pulses, since the time dependence during pumping can be highly nonlinear. So one needs to integrated ASE powers over one pump cycle.

## Conclusions

A few conclusions from this part of the tutorial:

• ASE powers become substantially time-dependent in cases with strong gain saturation by single pulses.
• Due to the quasi-three-level nature of most fiber gain media, surprising details can be observed in the ASE.

Go to Part 6: Bulk amplifiers or back to the start page.

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