CW operation of amplifiers and lasers

We assume constant input power for all channels. We will now consider dynamic simulations, where all input powers may be time-dependent. After all, fiber amplifiers and lasers typically operate with optical pulses and/or pulsed pump sources.

As long as we do not enter the realm of ultrashort pulses, as we discuss in the next section, a simple generalization of the equations and numerical methods used can often be made:

• Any input power (eg of pump and signal beams) may be time dependent. RP Fiber Power is a flexible software that can handle tabulated values of input power over time for any given function or for all channels.
• Calculation of gain or loss value gj(z) cannot be based on intensity alone but needs to consider dynamic saturation effects. In other words, gain values depend not only on current light intensities, but also on their values in the near past. Essentially, the software needs to introduce additional kinetic variables for the excitation of laser-active ions. Their time evolution is calculated by numerically integrating the rate equation, which we have discussed in Section 4. This is not difficult in principle, even for rate equations involving nonlinear terms.

For example, fiber amplifiers can first be pumped for a while and then injected with short signal pulses (e.g. Gaussian or super-Gaussian temporal shape). During the pumping phase, the (not yet correlated) signal gain rises steadily. When a signal pulse is injected, it initially benefits from high gain, but then quickly saturates that gain. As a result, other parts of the pulse will experience reduced gain and correspondingly lower output power. This can lead to significant distortion of the temporal pulse shape. Figure 1 shows a numerical example, taken from the detailed case study.

Figure 1: Output power and ytterbium excitation versus time for an ytterbium-doped fiber amplifier with pulsed pump and signal.

In pulse amplifier systems, propagation time is usually negligible.

Note that in this case we can safely ignore the propagation time, the time delay caused by the light traveling through the amplifier fiber. Even if the pulse duration is shorter than the propagation time, it usually doesn’t matter that different parts of the fiber “see” the pulse at slightly different times. After all, the usual level has a much longer lifetime. The time step used in the numerical algorithm can be larger or smaller than the propagation time; it only needs to be small enough to properly sample all temporal features, including saturation effects. Note that if the amplifier gain is saturated by very high signal strengths, it will drop rapidly. Therefore, the numerical step size may have to be much lower than the lifetime of the metastable energy level.

See also Part VII of our fiber amplifier tutorial, which discusses the behavior of fiber amplifiers in amplifying nanosecond pulses.

Q-switched laser

When simulating Q-switched fiber lasers, something new comes into play. We now need to consider the propagation time, since the round-trip time of the laser resonator now plays a crucial role. Therefore, we need to substantially expand the algorithm:

For modeling Q-switched lasers, the propagation time of light in the resonator must be considered.

• We need to use a time step that is a fraction of the round trip time of the resonator. In one time step, the entire power distribution in a laser device is spatially shifted by a small fraction of the device length while being affected by gain or loss.
• There may also be a time delay outside the active fiber because the laser resonator may contain additional components such as a free-space region containing the modulator (Q-switch). So, at least for lasers, some kind of numerical buffer is needed to store the optical power values corresponding to the locations outside the fiber.

​In principle, neither the required equations nor the algorithms are very complex. However, the implementation is a bit cumbersome due to various “bookkeeping” requirements.

As an example, we can use the case study of a Q-switched fiber laser made with the software RP Fiber Power.

Figure 2: Output Power and Ytterbium Excitation vs. Time.

Figure 2 shows the evolution of the output power and excitation level during the first two pulse periods after switching on the laser. The resulting pulse shape may look very surprising. There are large variations in power within a single round-trip time, which typically do not occur in Q-switched bulk lasers. An important factor behind this phenomenon is the high gain of active optical fibers. ASE results in a very non-uniform distribution of optical power (at fairly low levels) within the active fiber until the Q-switch is turned on (transparent). If the Q-switch is turned on very quickly, then an uneven power distribution starts to propagate around the resonator, creating a spiked structure at the output. Think about it and the details will become apparent, but it’s definitely more complicated at these high gains – certainly more work on this number is needed. One can also study aspects such as the finite switching time of Q-switches.