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Modeling of Pulse Amplification

This is part 6 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 6: Bulk amplifiers

Instead of an active fiber, one may use a laser crystal or glass as the laser gain medium of an optical amplifier. Such a bulk amplifier can be used to amplify pulses to far higher energies, essentially because nonlinear effects are weaker by many orders of magnitude.

The modeling of most bulk amplifiers can be done with largely the same methods as applied for fiber amplifiers, although various parameters are very different – for example, we have a far shorter gain medium, larger mode areas and lower gain. Besides, we usually have no waveguiding in the gain medium, but as long as the effective mode area does not vary much within the light path in the crystal, this has no impact on the model; otherwise, one may need to extend the model accordingly.

In case that substantial beam distortions occur in the amplifier – for example, due to thermal lensing –, one may need to include those as well - which is not common for fiber amplifier models. Numerical beam propagation can be used in a relatively straight-forward way, and we also offer that in our RP Fiber Power software, except in combination with ultrashort pulses, which would introduce various serious challenges.

Due to the low single-pass gain of a bulk amplifier, one often implements extensions such that multiple passes of the signal pulses through the amplifier crystal (or glass) are realized. One possibility is a multipass amplifier with a set of mirrors for getting multiple passes under different angles (unfortunately with variable spatial overlap with the pumped region, asymmetric thermal lensing effects etc.). This can also be simulated with numerical beam propagation. It is a bit more tricky (but highly convenient) to implement it with an automatic calculation of all beam angles for given mirror positions.

Regenerative Amplifiers

A regenerative amplifier is another possibility to realize multiple passes – possibly even dozens or hundreds, all with the same propagation direction. That way, one can achieve a very high amplifier gain despite a modest gain per pass through the gain element. The basic idea is

  • to use a kind of laser resonator where the pulse can circulate,
  • to inject an input signal pulse at a certain time, and
  • to extract the pulse after a given number of resonator round-trips.

The injection and extraction can be done with electro-optic components, for example. See the article on regenerative amplifiers for more details.

The simulation of the operation is not particularly challenging, given that we have a software with great flexibility, where we can easily program the multiple passes of the signal pulse and in addition possible additional interactions with the resonator – for example, chromatic dispersion from the electro-optic switch and the resonator mirrors, and the (often substantial) nonlinear effects in the switch.

The RP Fiber Power software also comes with a demo file for regenerative amplifier simulations:

regenerative amplifier simulation form

The following diagram shows an example for the calculated evolution of pulse parameters:

Figure 1: Evolution of pulse parameters in a regenerative amplifier.

The pulse energy grows exponentially, except in the last round trips where the amplifier gain is already saturated significantly. The pulse bandwidth can be reduced due to gain narrowing, but in the given case it is increased due to self-phase modulation. The interplay of normal chromatic dispersion with the Kerr nonlinearity actually leads to the formation of a parabolic pulse with quite linear chirp:

regen output pulse


A few conclusions from this part of the tutorial:

  • Bulk amplifiers can largely be simulated with similar methods as used for fiber amplifiers.
  • However, various details may require adapted models, for example
  • beam distortions, to be treated with numerical beam propagation
  • multipass operation with different beam angles, also a case for numerical beam propagation
  • regenerative amplifier operation with multiple passes and additional interactions

Some conclusions from the tutorial as a whole:

  • Depending on the situations, different physical aspects need to be taken into account, and adapted simulation methods are required.
  • The right choice of simulation method can often cut down the required computational load enormously. In most practical cases, computation times are actually not a significant issue, even when using an ordinary office PC.
  • In order to efficiently model and optimize device operation, a highly flexible commercial software such as our product RP Fiber Power is a vital tool. Developing a home-made tool with comparable power and flexibility would be a daunting task, probably also leading to higher cost and project delays.

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