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Case Study: Raman Scattering in a Fiber Amplifier

intro picture

Key questions:

  • What factors determine how strong the impact of stimulated Raman scattering in a fiber amplifier is? Only the input peak power?
  • How important is the input pulse duration?

If a fiber amplifier is used for amplifying ultrashort pulses which develop a substantial peak power in the fiber, it may happen that stimulated Raman scattering (SRS) has strong effects. In some case, these limit the achievable amplifier performance.

In this case study, we explore this in different pulse duration regimes, considering a core-pumped ytterbium-doped fiber amplifier with moderate performance characteristics, with pulse energies of a few hundred nanojoules.

We use the same set of fiber data as in another case study on parabolic pulses in a fiber amplifier: a generic single-mode fiber with 4 μm core radius, Yb-doped with a density of 5 · 10−24 m−3. We pump 10 m of that fiber (in backward direction) with 500 mW at 975 nm.

For the modeling, we use the software RP Fiber Power, which offers a Power Form titled “Fiber amplifier for ultrashort pulses”. We can just fill in all the parameters, including those for configuring some diagrams, and get it calculated. Below you see the initial part of the form with the definition of the input pulse, the settings for the temporal trace (for storing the pulse data):

the form, part 1
Figure 1: The beginning of the Power Form.

We have chosen a relatively high temporal resolution, as required for simulations involving stimulated Raman scattering: only with that, we can cover a sufficiently wide range of optical frequencies. (Still, such a simulation takes only a couple of seconds on an ordinary PC.) The detailed settings, however, will need to be adjusted for each case, as we will be considering very different pulse duration regimes.

You also see that we simulate repetitive operation; we are interested only in the steady state and thus simulate only a single amplification cycle.

In the next part of the form, we define the (single) amplifier stage:

the form, part 2
Figure 2: The next part of the Power Form.

In the form settings for the nonlinearity (in a tab which is not seen above), we select a delayed nonlinear response (as required for Raman scattering) and use detailed Raman data for silica from Ref. [1].

The initial state of the amplifier (concerning the Yb excitation) is calculated based on the average signal input power, which will prepare the amplifier in a state close to the expected steady state in repetitive operation. Note that our pulse energies will stay far below the saturation energy, so that there is no substantial gain saturation caused by a single pulse.

In each case, we use Gaussian-shaped input pulses with 1 nJ pulse energy (but variable durations) at a center wavelength of 1050 nm.

Before considering details of pulses, we inspect the calculated initial state of the amplifier:

initial state of amplifier
Figure 3: The initial state of the amplifier, which is close to the steady state in repetitive operation.

We see that the fiber is actually a bit too long; after 7.5 m of fiber, the pump power is already fully exhausted. However, that does not matter much here.

Case 1: Input Pulses with 1 nJ, 10 ps

Our first case deals with relatively long pulses. Let us first see how the temporal pulse shape evolves in the fiber:

evolution in time domain
Figure 4: Evolution of the temporal pulse shape in the fiber.

You may think that significant temporal broadening sets in after some 3 m, but this is only an effect of the increasing pulse energy in conjunction with the used color scale. At the very end, you see an irregular structure, which we will consider in some detail. But first also see how the pulse spectrum evolves in the fiber:

spectral evolution
Figure 5: Evolution of the pulse spectrum in the amplifier fiber.

For the spectral diagram, we have chosen a logarithmic color scale, covering a 40-dB range of intensities so that we can better see some features coming up at a lower power level. This happens only towards the end of the fiber. Before it happens, we already have a substantial broadening of the pulse spectrum, beginning mainly with self-phase modulation.

For a closer inspection, we don't want to see the output pulse only, but rather want to inspect the pulses at different positions in the fiber. Here, the Power Form gives us two options:

  • We can produce a diagram window where we see the temporal or spectral pulse trace for different positions in a fiber, and can easily move between those with some buttons or a slider.
  • We can call the interactive pulse display window, which can show the pulse in the time and frequency domain for any position in the fiber (limited only by the chosen numerical step size). That is available even without configuring anything in the form - just press Ctrl-D.

Here, we use the latter feature, beginning with the pulse after 8 m of fiber:

pulse after 8 m
Figure 6: The pulse after 8 m of fiber.

We see that the pulse duration is only slightly increased, but the spectrum is substantially widened with an oscillating power spectral density, as is typical for cases with strong self-phase modulation.

After 9 m of fiber, we see some wiggles in the time domain, and still more spectral broadening:

pulse after 9 m
Figure 7: The pulse after 9 m of fiber.

Note that the spectral broadening has accelerated because of the growing pulse energy.

At the fiber end (after 10 m of fiber), this becomes more extreme, and the spectrum now gets quite chaotic:

pulse after 10 m
Figure 8: The pulse after 10 m of fiber.

The origin of these wiggles is that stimulated Raman scattering creates spectral components at substantially longer wavelengths, and those interfere with the original ones in the time domain.

You may have noticed that the temporal features are starting not right at the peak, but somewhat left of it. This is because the Raman-scattered light propagates somewhat faster than the original pulse. (The fiber has normal chromatic dispersion.) Therefore, that light drifts towards the left side in the time domain.

Note also that if we run the simulation repeatedly, this diagram will look somewhat different in detail each time. This is because we have added some fluctuations to the input, simulating quantum fluctuations. What physically happens: there is a large Raman gain in spectral regions where the pulse has no significant power. In that situation, the Raman gain will amplify the tiny quantum fluctuations (which are changing all the time) up to a substantial power level. In detail, the pulse will have somewhat different features each time – which also means that the pulse will not be mutually coherent, at least not fully coherent. So our simulations resemble that well.

An optical spectrum analyzer will usually show a spectrum which is averaged over many pulses. Some of the spectral structures will then be washed out. Similarly, temporal measurements with an autocorrelator, for example, will be partially washed out. It is good to know that in reality each pulse is somewhat different. That is typical for the regime of relatively long and narrow-band pulses. If we wanted, we could create a diagram which runs multiple simulations and shows averaged temporal and spectral traces.

One would normally not want to operate an ultrafast amplifier in this regime, delivering strongly distorted and fluctuating pulses. However, the purpose of this case study is not to design a good amplifier, but to study what effects we have to expect in such devices.

Case 2: Input Pulses with 1 nJ, 1 ps

We now reduce the input pulse duration from 10 ps to 1 ps. Considering that the peak power of the input pulses is now 10 times higher, you might think that we now get far stronger effects of Raman scattering. However, we find that the difference is not that strong. We again first look at the color plots for the evolution in the temporal and spectral domain:

temporal evolution
Figure 9: The temporal evolution for 1-ps input pulses.
spectral evolution
Figure 10: The spectral evolution for 1-ps input pulses (again with a log scale).

The pulse broadening is now far stronger, so that the output peak power does not rise as much as one might have expected. Strong Raman effects are again observed only on the last meter.

We again inspect the pulses at a few positions in the fiber – first after 5 m:

pulse after 5 m
Figure 11: The pulse after 5 m of fiber.

In the time domain, we now also display the deviation of the instantaneous optical frequency from the original center frequency; we nicely see the steady up-chirp, created by the interplay of normal dispersion and nonlinearity. The pulse trace (power vs. time) has some characteristics of parabolic pulses, although it is quite asymmetric; this is because the higher frequency components, coming in the second half, experience higher gain. (The ytterbium gain peaks around 1030 nm in our case.)

In the spectrum, we now see much less pronounced wiggles; this is because of the stronger impact of chromatic dispersion.

After 8 m, we see in the time domain starting wiggles, resulting from Raman scattering:

pulse after 8 m
Figure 12: The pulse after 8 m of fiber.

The spectrum becomes quite asymmetric. It is formed by a complex interplay of wavelength-dependent amplifier gain and the nonlinear effects – hard to interpret in detail.

At the end (after 10 m) it again gets quite chaotic:

pulse after 10 m
Figure 13: The pulse after 10 m of fiber.

Case 3: Input Pulses with 1 nJ, 0.1 ps

With again 10 times shorter input pulses, the situation again changes quite substantially. In the time domain, we get strong broadening, and a drift towards positive times:

temporal evolution
Figure 14: The temporal evolution for 0.1-ps input pulses.

Note that positive times mean that the pulse has been delayed more than the input pulse would have been delayed without all the processes in the fiber. This is because the mean wavelength has become significantly longer due to Raman scattering.

The spectral evolution diagram shows a rapid spectral broadening at the beginning, and again strong effects of stimulated Raman scattering only on the last meter or so.

spectral evolution
Figure 15: The spectral evolution for 0.1-ps input pulses.

The output pulse is temporally spread even more than before:

pulse after 10 m
Figure 16: The pulse after 10 m of fiber.

Of course, a lot of details could change if we change parameters such as the pump power and wavelength, the input pulse wavelength, or the fiber's chromatic dispersion.


RP Fiber Power

The RP Fiber Power software is an invaluable tool for such work – very powerful and at the same time pretty easy to use!

You can learn various things from this study:

  • One might expect that the input pulse duration is crucial for the strength of stimulated Raman scattering effects. However, this is often not the case, because dispersive pulse broadening is particularly rapid for short input pulses.
  • The detailed evolution of the pulses in the fiber can be rather complicated. Numerical simulations are the only way to find out how things really work, i.e., to reliably predict and optimize the performance.

By trying out different parameter sets with suitable simulation software , you can develop a much deeper understanding. Any wrong expectations can be corrected by checking them against simulations.

More to Learn

Encyclopedia articles:


[1]D. Hollenbeck and C. D. Cantrell, “Multiple-vibrational-mode model for fiber-optic Raman gain spectrum and response function”, J. Opt. Soc. Am. B 19 (12), 2886 (2002); https://doi.org/10.1364/JOSAB.19.002886

(Suggest additional literature!)

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