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

Power Form: Fiber Amplifier for Pulses

This Power Form allows one to set up sophisticated models for fiber amplifiers (multiple input signals, multiple stages, etc.) in pulsed operation. The dynamic behavior is of particular interest – for example, the evolution of pulse energies over multiple cycles in repetitive operation.

This model is limited to not too short pulses, where we can neglect nonlinear and dispersive effects. (Another form is available for ultrashort pulse amplifiers.)

graphic for this Power Form

Basic features of the model

  • Amplifier stages: We simulate a fiber amplifier with up to five different stages. Each stage may be activated or deactivated.
  • Input signals: we start with one or more (up to ten) input signals, each of which being a pulse with a certain temporal shape (e.g. Gaussian, super-Gaussian, rectangular) or a freely user-defined pulse shape in time or frequency domain.
  • Fiber parameters: for each amplifier stage, one can select a fiber parameter set - from a commercially available fiber, for example. One can also override various parameters.
  • Pump sources: each amplifier stage can have up to 5 quasi-monochromatic or broadband forward or backward pump inputs. It is assumed that no pump light can ever get from one amplifier stage to another stage.
  • Single or double pass amplification: normally, the signal light would get from the signal source through some number of amplifier stages, each one passing in just one direction (called forward direction). However, one can have a wavelength-dependent reflector at the end of a stage to realize a double-pass amplifier stage; in that case, the signal is propagating back through the same fiber and then separated from the input with a Faraday circulator before being sent to the next stage.
  • Coupling losses: after each amplifier stage, and after the input signal source, we can introduce coupling losses, which can be wavelength-dependent.
  • Amplified spontaneous emission (ASE) can also be considered. See the encyclopedia article on ASE. ASE may get from one stage to the next one, suffering the above-mentioned wavelength-dependent losses (e.g. from a bandpass filter), but it is assumed that it cannot get to the previous stage (e.g. due to a Faraday isolator preventing that).
  • Simulation cycles: we can simulate either a single pulse amplification or repetitive operation, where we also monitor how various properties evolve over multiple (possible many) pumping/amplification cycles.

Input Signal Details

In the first section of this form, you can define up to 10 different input signals at different wavelengths, which will be sent into the first activated amplifier stage.

definition of input signal pulses

There are tabs for those signals, each of which may have many properties:

  • It can be activated or deactivated so that you can easily switch between cases with different numbers of signals.
  • You specify a pulse energy, which in the case of broadband signals means the total energy of all spectral components.
  • In the time domain, the Temporal shape of the pulse can either be chosen from a list of pre-defined functions (Gaussian, Super-Gaussian or Rectangular) or defined by the user by selecting the user-defined option.
  • In the frequency domain, signals may be defined as either quasi-monochromatic or broadband (i.e., having multiple spectral lines) with a specific shape. For a broadband signal, there are different spectral shapes are available, including freely user-defined shapes.

If there is any coupling loss experienced when coupling the signal power into the first amplifier stage, that can also be specified. This can be a constant value or an expression depending on the wavelength l. The units of this loss can be chosen (transmission percentage %, dB or a zero-to-one scale 0-1).

Amplifier Stages

The Amplifier stages section allows the definition of up to 5 amplifier stages. Each one contains an active fiber as its central piece and some pump source(s).

definition of amplifier stages

These are essentially the same details as for a RP Fiber Power Power Forms cw fiber amplifier and is therefore not explained here once again.

Diagrams

In addition to various numerical outputs in the form and in the output area on the right side, the form offers a large choice of diagrams for displaying various kinds of results:

outputs of the form

Just select those which you need, and configure certain options. For example, most diagrams offer the option of using a dBm scale instead of a linear vertical scale. In some cases, you may show graphs for all individual input signals, or alternatively only a graph for the total signal power.

Each diagram has the option to add some script code, which you may use e.g. to get additional curves, annotations, or output to a file.

The diagrams are grouped into

  • Input diagrams: used mainly for sanity checking your settings for the input signals
  • Output diagrams: display various outputs based on the form settings
  • Variation diagrams: produce diagrams where one of the system parameters is varied in a certain range. For example, you may vary a pump wavelength to see what effect that has on the amplifier performance.

Diagrams for an Example Case: Pulsed Yb Fiber Amplifier

The following screenshots show you a few of the diagrams which can be made with this simulation model. Here, we simulate an amplifier system with the following details:

  • We assume two broadband input signal pulses with 100 nJ, 6 ns, 1050 nm and 500 nJ, 5 ns, 1065 nm, respectively. The latter signal pulses are delayed by 15 ns.
  • We use a single amplifier stage with an Yb-doped single-mode fiber, forward pumped with 200 mW at 940 nm (5 nm bandwidth). As it is a highly doped fiber, we need only 20 cm of it.

We assume the amplifier initially to be in the unpumped state, and then simulate four cycles of pumping and pulse amplification with a repetition rate of 5 kHz. Here you see the evolution of pulse energies and (in gray text) the forward and backward ASE output powers before and after each pulse:

evolution of pulse energy over the cycles

After these 4 cycles, the system has nearly reached its steady state.

Here you see the powers and Yb excitation density vs. position in the fiber of stage 1:

powers and Yb excitation density vs. position in the fiber

The next diagram shows how the peak powers and pulse durations evolve within the active fiber:

evolution of peak powers and pulse durations

We can also examine the spectral evolution, which exhibits a drift of the center wavelengths particularly of the shorter-wavelength signal:

spectral evolution

Finally, we look at the powers and excitation densities before and after the last pulse:

powers and excitation densities before and after the last pulse

You see that the excitation density is most strongly reduced at the right end, where the signal energies are highest. The ASE powers drop to nearly zero after the pulse, as the gain gets quite small.

Clearly, even someone with substantial physics knowledge and experience could not reliably predict at least qualitatively all such performance details – this is why we need simulations! Without that, amplifier design work is fishing in the dark.

Note also that even far more sophisticated models could be set up easily, e.g. with multiple amplifier stages and spectral filters between them.

Case Study

The following case study is available, where we used this Power Form:

See also: overview on Power Forms