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

Example Case: Pulse Generation in an actively Q-switched Nd:YAG Laser (with Beam Propagation)

Description of the Model

We simulate pulse generation in an actively Q-switched Nd:YAG laser similar to the one from another demo case. However, this time we do not base this on the assumption that the beam radius will be approximately determined by the fundamental mode of the laser resonator. Instead, we do a full numerical beam propagation (wave propagation), so that we can check this aspect. After all, we cannot know for sure how strong gain guiding effects will be. Note that the gain can become rather high in a Q-switched laser.

Basically, the model is set up as follows:


Figure 1 shows how the output power and beam radius evolve in the pulse generation phase. The beam radius, calculated via the second moment of the intensity profile, stays relatively close to the calculated value of the fundamental mode.

pulse shape from Q-switched laser
Figure 1: Evolution of output power and beam radius.

Figure 2 shows the excitation profile after the pulse. One can see that the outer regions of the excitation are not fully depleted, although the pump beam has the same radius as the laser mode.

profile of the excitation after the pulse formation
Figure 2: Profile of Nd excitation after extraction of energy by the generated pulse.

Figure 3 shows the evolution of the beam profiles during the pulse. There is some significant variation, caused by the gain guiding effect of the pump profile. However, that should not have a substantial effect on the performance or on an application.

evolution of the beam profiles
Figure 3: Evolution of the beam profiles during the pulse. For each profile, the color scale is calibrated such that the deep red color applies to the highest intensity. (In that way, we remove the large power variation.)

The resonator mode size in the laser crystal remains close to 100 μm for air path lengths between 20 mm and 30 mm between the crystal and the focusing end mirror. Therefore, it is not surprising that for a spacing of 30 mm, one gets very similar results (not shown here) as for 20 mm (as above). Surely, one would then not expect a significant difference for a spacing of 25 mm. However, we do get something quite different if we try this. The beam radius now varies a lot more, and the power extraction becomes somewhat less efficient:

pulse shape from Q-switched laser
Figure 4: Same as Figure 1, but with a spacing of 25 mm (instead of 20 mm) between crystal and end mirror.

Also see again the evolution of beam profiles:

evolution of the beam profiles
Figure 5: Same as Figure 3, but with a spacing of 25 mm (instead of 20 mm) between crystal and end mirror. Note: the discrete steps are not the result of insufficient numerical resolution, but of significant changes in beam size during a single resonator round-trip.

One can see that now the beam shrinks substantially during the pulse build-up, and later expands a lot. (Despite the clear shrinking, the beam radius based on the second moment increases in that region due to stronger wings of the profile.) In the integrated beam profile (not shown here), one sees a certain deviation from a Gaussian shape. In similar situations, one can also obtain a donut shape at the trailing edge of the pulse, which would of course be difficult to detect experimentally, as that requires a time-resolved measurement.

Apparently, the laser resonator is substantially more sensitive to the gain guiding effect for that particular resonator length – but why is that? The explanation is far from obvious. A resonator design analysis (done with the RP Resonator software) shows that just for 25 mm air gap size, the Gouy phase shift of the resonator per round trip becomes 1.59 rad, which is close to π / 2 (≈ 1.57 rad). A consequence of that is that the TEM40 and TEM22 modes have resonance frequencies which coincide with resonances of the TEM00 fundamental mode. At this point, some resonant mode coupling can occur, which has a strong impact on the beam profiles (see R. Paschotta, “Beam quality deterioration of lasers caused by intracavity beam distortions”, Opt. Express 14 (13), 6069 (2006)). These resonances are usually fairly narrow; in our case, the effects are much weaker if the air gap size deviates by only 2 mm from the point of the resonance.

Some conclusions from this exercise:

And again you see: although developed for fiber devices, RP Fiber Power can easily be applied to bulk devices due to its high flexibility.

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