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

Power Form: Continuous-wave Fiber Amplifier

This Power Form allows one to set up sophisticated models for fiber amplifiers (with multiple input signals, multiple stages, etc.) in continuous-wave operation. Only the steady state is considered. (Other forms are available for pulsed signals, also considering dynamic behavior.)

Basic Features of the Model

• Amplifier stages: We simulate a fiber amplifier with up to five different stages.
• We assume continuous-wave operation, i.e., with constant pump and signal powers. We investigate only the steady-state operation, not e.g. the turn-on behavior.
• Input signals: we start with one or several input signals, each of which can be either quasi-monochromatic or broadband (e.g. with Gaussian, super-Gaussian or rectangular or user-defined spectral shape).
• 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 five 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, passing each one in just one 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 (e.g. for simulating a filter).
• 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).

Input Signal Details

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

There are tabs for those signals, each of which may be activated or deactivated.

Signals may be defined as either quasi-monochromatic or broadband with a specific shape. The following diagram shows an example with two broadband signals centered at 1040 nm and 1060 nm, respectively:

For a broadband signal, different spectral shapes are available: Gaussian, super-Gaussian or rectangular. Alternatively, a user-defined shape may be chosen, where you can enter a wavelength-dependent expression containing the wavelength variable l. It can also depend on the center wavelength l_s_c and the bandwidth FWHM_signal, referencing the values in those input fields.

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. (Example: if l > 1080 nm then 30 else 0.5) The units of this loss can be chosen (transmission percentage %, a zero-to-one scale 0-1) or dB.

Amplifier Stages

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

Each amplifier stage can be activated or not. For example, one may enable only stage 3 and 4, which means that the input signals are sent into stage 3 and from there into stage 4, which generates the final output. This is convenient, for example, if you want to focus your attention to a specific part of an amplifier system.

You can select a fiber data set (typically for a commercially available fiber), which usually contains spectroscopic data (wavelength-dependent transition cross-sections, upper-state lifetime) and data on the waveguide (pump and signal mode sizes, losses, etc.). The form also offers overriding of various parameters; for example, you may modify the doping concentration of laser ions or the propagation losses for a sensitivity analysis.

Most fiber amplifiers work with a single pass of the signals, but you can also configure a double-pass amplifier by specifying an expression for the wavelength-dependent reflectance at the end. The reflected signal is then sent back through the stage, realizing a double pass (with signal output extraction, e.g. with a Faraday circulator).

There can also be wavelength-dependent losses at the output of the stage, affecting both signals and ASE.

A Brillouin gain coefficient can be entered; it is used to estimate the Brillouin gain caused by the signal light.

Each amplifier stage can have up to five pump sources, which may be quasi-monochromatic or broadband (then represented by a combination of spectral lines).

For each stage, amplified spontaneous emission (ASE) can be taken into account. Further, you can determine whether ASE from one stage can propagate to the next stage. It may then experience wavelength-dependent output losses, as explained above. The number of guided modes can also be specified (e.g. 2 for a single-mode fiber with two polarization directions). The wavelength range for ASE is specified outside the amplifier stage tabs, as that range is common to all active stages with ASE considered.

Within each amplifier stage tab, there is a stage outputs box where outputs specific to the selected stage are shown:

• residual pump powers for forward and backward direction (due to incomplete absorption of pump light)
• signal gain and noise figure in dB (separate for each signal)
• total ASE powers leaving the fiber in both directions
• fractional excitation (in percent) of the upper level of the laser-active ions, averaged over all positions in the fiber
• Brillouin gain (the highest such gain value of all signals), if all the signals are quasi-monochromatic

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:

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 the form, 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.

Each diagram has the option to add some script code, which will then be executed directly after other code for generating that diagram. This allows the user to add any plots, lines or annotations, for example, without modifying the script code of the form. One may also use such code to display additional numerical items in the output area. Another possibility would be code to write certain data to a file. In case that you need help, call our technical support.

Diagrams for an Example Case: Dual-stage 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 signals at 1040 nm and 1080 nm as shown above.
• The first stage is a Yb-doped single-mode fiber amplifier, forward pumped with 200 mW at 940 nm (4 nm bandwidth). As it is a highly doped fiber, we need only 15 cm of it.
• The second stage is a double-clad Yb-doped fiber amplifier, backward pumped with 1.8 W at 975 nm (3 nm bandwidth). Here, the fiber is 2.5 m long to obtain sufficient pump absorption despite the double-clad design.
• We assume no filtering between the two stages.

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

This diagrams contains various interesting details – for example, substantially less gain for the longer-wavelength signal, and ASE build-up in both directions, but with rather different power evolution due to the asymmetry of the Yb excitation profile.

The same diagram for stage 2 looks quite different:

Here, the longer-wavelength signal experiences a higher gain. This is because the double-clad stage is operated with substantially lower Yb excitation, which shifts the gain maximum to longer wavelengths. Further, forward ASE is now seeded by ASE from the first stage. We could add a spectral filter between the stages in order to much reduce that.

We can also inspect the spectral evolution of the signals within both stages:

In the first stage, particularly the shorter-wavelength signal drifts substantially towards shorter wavelengths, where the amplifier gain is higher. However, the opposite happens in the second stage, where the gain maximum is at a longer wavelength.

Further, we can see the evolution of ASE inside the amplifier fiber, first in stage 1:

We used a logarithmic color scale to cover a large dynamic range. You see that forward ASE is dominantly around 975 nm, but does not fully make it to the right end, as it is strongly reabsorbed in the last section. The strong asymmetry between forward and backward ASE results from the asymmetric profile of Yb excitation in the fiber.

Let's also inspect ASE in stage 2:

Here, the asymmetry between forward and backward ASE results mainly from the fact that forward ASE is seeded with the output ASE of the first stage. Note also that the input ASE around 975 nm is quickly absorbed; with the low level of Yb excitation in that stage, we get strong absorption in that spectral region.

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, design work is fishing in the dark.

Case Studies

The following case studies are available, where we used this Power Form:

See also: overview on Power Forms