The Photonics Spotlight > 2024-09-16

Education With Simulations for Active Engagement of Students: Example With Pump Absorption in an Yb-doped Fiber

Computer simulations are an excellent tool not only for research and development, but also for teaching. In all three areas, of course, the generated deep insight is the core value.

To achieve the optimal benefits in education, it can be helpful to deviate substantially from a traditional approach of teaching. That traditional approach is often along the following lines:

• The teacher first introduces the topic to be treated – for example, saturation effects in the absorption of light.
• Then, the relevant physical entities and their behavior are explained – for example, laser-active ions, properties like transition cross-sections and upper-state lifetimes, and some equations to describe that quantitatively.
• Finally, the stated equations are solved in a few elementary cases, demonstrating the resulting behavior.

Although that seems to make sense, it may not always be easy to get the students sufficiently engaged to actively deal with the presented materials. Various important issues may not become clear enough, and a substantial part of the students may even be lost completely. The following alternative didactic approach can work far better:

• You first present simulated results for some interesting situation, ideally showing some surprising behavior. It may be helpful to first present only quite limited results, which do not give too many clues. (It is good to let people think about what else they would like to know to find the right answers.)
• You then ask what could be the underlying physical effects, and how the observed peculiar behavior can arise. It can be helpful to then present step by step some further simulated results, revealing more about what is going on in the investigated system. The listeners should be put into a situation where they have the chance to find it out themselves, rather than just being told what is the solution.
• Finally, you can wrap it up nicely (in a dialog, not a monolog), making sure that all essential points can be fully understood.

By the way, what I call students here could also be engineers in a training course for developing the competence and efficiency of an R & D team.

Example: Pump Absorption in Yb-doped Fiber

(If you are reading this as someone who is still learning, try to find the answers to the stated questions yourself before reading further!)

To give you an example, we can deal with the absorption of pump light in a fiber amplifier. We assume to have 1 m of an ytterbium-doped single-mode fiber, into which we inject 80 mW of pump light at 975 nm. The pump source is suddenly turned on. First question: what would you qualitatively expect to happen concerning the non-absorbed pump power at the end of the fiber? Will it come immediately, or only after some delay? Any further details?

After collecting some opinions, you show the result of a simulation: pump output power versus time:

During the first 600 microsecond, we get nearly no pump power out; then it rapidly rises to ≈27 mW. What is going on here?

It can hardly be a time delay which is simply caused by the propagation time in the fiber: that is only about 5 ns, and therefore actually neglected in the simulation.

Obviously, the absorption is strongly time-dependent, but why? Probably, the Yb³⁺ ions in the fiber core must play some role here; it appears that a substantial fraction of the ions are excited in this example situation.

Then we can display the simulated pump power vs. position in the fiber at different times – beginning with the moment in which the pump source is turned on:

Now, you can discuss that with the students. We see that here the absorption is so strong that virtually no pump power is left at the fiber end (i.e., after 1 m). But where does the absorbed energy go to? Of course, into the laser-active ions. But it takes a while for some energy to be accumulated, which is associated with some fraction of the ions getting to their excited state. At the moment for which the above diagram holds, the ions are still all in their ground state!

Our simulation can also reveal how the fractional excitation of Yb ions in the fiber evolves – for example, at the input end of the fiber:

That diagram also raises some questions:

• Why does it reach a steady state within only about 0.1 ms, although the upper-state lifetime is closer to about 10 times longer than that?
• Why does it level out at about 50%? What prevents them from reaching an even higher fractional excitation?

Many may expect that such things must evolve on the timescale of the upper-state lifetime. However, the processes can actually be far faster for sufficiently intense pumping – which we do in this case, with a pump power far above the pump saturation power. Only the relaxation of ions back to the ground state after switching off the pump sources would be limited by the upper-state lifetime.

Concerning the second question, one might think that the limiting factor is the applied pump input power. However, the simulation would show that for even far higher input powers, the final excitation state would be about the same (except that the excited region extends even further into a long fiber). So it is apparently not spontaneous emission, but some other effect: stimulated emission, shuffling Yb ions from the excited state back to their ground state. The absorption and emission cross-sections of the Yb ions happen to be quite precisely the same at the used wavelength of 975 nm, and that explains the observed excitation level of 50%: that leads to equal rates of ions being excited and deexcited.

Now, let us inspect in more detail what is happening inside the fiber, first concerning the Yb excitation:

When the pump source has just been turned on, the Yb excitation is still zero everywhere (white color). But at later times (higher positions in the diagram), the excitation rises sharply. Interestingly, that rise occurs far later at the right end of the fiber than at the input end. This is because initially there is hardly any pump power in the fiber near the right end; it is still absorbed further to the left! Only once the absorption is saturated on the left side, the pump power can get to the ions on the right side to excite those as well.

Let us also see how the pump power evolves over time inside the fiber:

A more conventional way to show this:

Another question: once the steady state has been reached, where does the absorbed power go?

• The Yb ions are rapidly shuffled between the upper and lower state, but how can that dissipate energy?
• The answer: Fluorescence light is radiated in all directions through spontaneous emission. There is also some heat generation because the average photon energy of the fluorescence is somewhat lower than the pump photon energy.
• In the steady state, the spontaneous emission rate needs to be compensated by pump absorption.

A further question: Why is the decay of pump power in the steady state approximately linear?

• The fiber can dissipate power only due to spontaneous emission.
• That emission rate is constant in the region where the excitation is 50%. That also keeps the dissipated power per unit length constant. Only once the remaining pump power gets below the saturation power, it drops rapidly. This is when the spontaneous emission rate is no longer small compared to the combined rates of absorption and stimulated emission.

So now we get a complete picture of what happens:

• Immediately after turning on the pump source, the ions in the fiber are still all in their ground state, and then cause strong absorption, so that nearly no pump light at all can get through the fiber.
• However, the absorbed energy accumulates in the ions, causing increasing excitation. The excitation cannot grow without limit, but levels off at 50% for the used wavelength because of stimulated emission. (Only for shorter pump wavelengths, it could be more, because the emission cross-section falls off faster than the absorption cross-section.)
• Strong saturation can occur early on near the input end, but only later near the output end, since the pump light can initially not get there.

It can also be useful to discuss the saturation power of the fiber. One finds that this is only 2.4 mW – far less than our pump input power of 80 mW! That explains why we have such strong saturation effects in this example, despite the moderate pump power applied. Note that the saturation power can be so low (a) because of the small effective mode area of a single-mode fiber and (b) because the transition cross-sections at 975 nm are particularly high.

Further surprises may be encountered when trying the same simulation with other pump wavelengths. For example, form 940 nm we get the following output power versus time:

It starts at a higher initial level but levels off at a lower level than before – although the absorption cross-section at 940 nm is substantially lower than at 975 nm! I now leave it to the readers to explain that.

Rich Learning Outcomes

Anyone carefully thinking through all this will arrive at a substantially improved understanding of how things really work in these rare-earth-doped fibers. One develops a more accurate mental representation of these things and have the opportunity to correct various possible misconceptions and get aware of various important details of the involved mechanisms. Important knowledge is created not only for the particular case, but of more general type. For example:

• One understands that excitation means stored energy, and for that to accumulate takes some time.
• The degree of excitation can be limited by the additional effect of stimulated emission.
• The overall behavior of such a system involves both a temporal evolution of excitation influenced by optical intensities and the change of optical intensities by time-dependent absorption. That can lead to peculiar behavior, even in pretty simple situations, for example that the penetration of light into a fiber increases substantially over time, and that the remaining power suddenly rises from extremely low to quite substantial.
• The saturation power is an important parameter for determining whether strong saturation effects will occur. For fibers, it can be surprisingly low.
• Generally, one gets a feeling for the typical orders of magnitude of various quantities. For example, propagation times in fiber amplifiers of a few nanoseconds, upper-state lifetimes of many microseconds or even multiple milliseconds, saturation powers of milliwatts, etc. That kind of important knowledge is often not effectively conveyed by textbooks and lectures.

Note that a traditional approach as outlined above would very likely be far less effective in generating that kind of comprehensive understanding. Part of the reason is that an active engagement with the situation is more likely reached when confronting students with quite surprising behavior, which stimulates intense reasoning.

Further, the perhaps unusual way of presenting information – not like in an encyclopedia article, but closer to how things may be investigated in real life –, also supports more active engagement of students.

Another Learning Approach: Students Playing with Simulation Models

We have seen that even listening to a lecture (a tentatively passive thing) can induce active mental engagement when the lecture is properly structured. Of course, they are even more active approaches: in particular, letting students play themselves with a simulation model. That is quite likely to result in even deeper learning results, since they need to think about every step – what exactly to enter into the model, what results to look at, etc. Here, the role of the teacher is quite different: essentially, arranging the whole situation, also giving some directions on what to explore. Here are some thoughts on how that can work:

• First, students need to get the opportunity to directly interact with computers which are equipped with suitable simulation software. This might be one computer per student, or perhaps one for a group of two or three, who will then intensely work together. (Their internal discussions may substantially support the learning process.)
• We support that kind of software use by offering pretty cheap classroom licenses. These are usable only for that kind of purpose, that is for teaching students, not for scientific research or even for business purposes, and don't include additional support time. Only the course instructor requires a regular (not only non-commercial) user license.
• Further, the students need some basic knowledge to understand sufficiently much to start their active engagement. That may be achieved in a more classical type of lecture, explaining the essential properties of laser-active ions and light.
• Next, a problem needs to be formulated, and some instructions given, leading students to a suitable path of exploration. In our example case:
  • Simulate the absorption of pump light in the fiber, when the pump source is suddenly turned on.
  • Try to explain the obtained results.
  • Create more simulation results, including what happens inside the fiber, to get a more complete picture.
  • Try to predict what qualitatively would happen for a shorter pump wavelength (e.g. 940 nm), try it out and fully explain the outcome.
• Note that one will generally not have full control over which path the students will take. That is not necessarily a bad thing! For example, based on certain misconceptions, they may take a path which you did not anticipate, but that may be a very effective way of clarifying this – for themselves, and for you as a teacher.
• Finally, there needs to be a proper discussion of not only what results they arrived at, but what they experienced. Although it would normally be the quickest way that the teacher just summarizes the expected learning outcomes, it will usually be more effective if that list of learning outcomes is created in a lively discussion.

Some people may be concerned that this type of learning requires more time than if you just explain things in the classical way – teachers speaking, students listening. However, that in itself is a misconception: one should not overlook that the learning outcome will be far better with active engagement, so that any further learning will then be more effective. Therefore, I would rather somewhat reduce the number of details to be treated but then reach a really profound and long-lasting understanding.

Why not Play with Real Fibers?

You may now ask whether it would be even better to let students play with real fibers. Isn't it always better to be as close to reality as possible?

Well, that experimental approach has some serious disadvantages:

• The main issue is that while some quantities can be measured relatively easily – for example, the pump output powers vs. time –, others are very challenging to get hold of. How would you ever measure the pump power versus time and position in the fiber? Only for the Yb excitation, there would be an opportunity to measure that at least partially: by monitoring the fluorescence light; the power of that is proportional to the fractional excitation. But you would not be able to calibrate the scale, finding out that you get only 50% excitation.
• A second issue is the time required to set this up. There are various additional technical issues which may distract from the interesting physics. Looking into the relevant quantities is far quicker with a simulation model.
• Third, you can hardly provide the equipment for letting 20 students simultaneously do such measurements. A lot of expensive hardware and space would be required.
• Note also that additional learning topics will generally require additional expensive hardware, while a simulation model allows for many further investigations without any additional investment.

For these reasons, a simulation model will often be by far the most practical tool for active learning.

This article is a posting of the Photonics Spotlight, authored by Dr. Rüdiger Paschotta. You may link to this page and cite it, because its location is permanent. See also the RP Photonics Encyclopedia.

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