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The laser source of the LASER4DIY project is a diode pumped solid state laser with a Neodymium-doped yttrium orthovanadate (Nd:YVO4) crystal. This widely-used laser is especially suitable for this usecase, since the Nd:YVO4 cristal is cheap, easy to obtain and also, based on the use of the so called bounce geometry, very powerful. In figure 1 you can see the setup of the laser system, which is very similar to the puplication by Thomas and Damzen, 2011 [1]

figure Figure 1: Schematic representation of the Nd:YVO4 laser with a passive Q-switch

and a Cr4+:YAG saturable absorber crystal and a additional KTP crystal for frequency doubling [1]

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Simulation was done using the program LASCAD. A finite element analysis (FEA) for the thermal effects of the Nd:YVO4 crystal is possible with it, allowing to determine the exact geometry of the resonator. Especially the distances of mirror 1 and the uncoupling mirror to the crystal (see diagram figure 1) are important for the construction later on. Additionally the simulation program can calculate the average power in CW mode (continuous wave mode), as well as the peak power of the laser source when using the Q switch. The simulation was done without frequency doubler, as it is less important for the laser geometry.

In order to do the simulation with the used program, we had to simplify the laser setup. Firstly, the simulation was done with a rectangular crystal instead of a trapedzoid one. Secondly, the program assumed a 100% anti reflection in the crystal, being about 99,9% in reality. Additionally, it was not possible to simulate a bounce geometry in the crystal. Therefore the laser beam was set to the lower end of the crystal, as the temperature gradient in this area is comparable best with the real bounce geometry (see diagram figure 2). The thermal lens is quite large with the bounce geometry and extends through the whole beam path. As the thermal strain stress is uniform in every point in the beam path, the thermal lens is compensated well and a high radiated power can be achived. With a side pumped laser the thermal lens is quite strong and the thermal strain stress varies along the beam path, leading to a high power reduction of the generated laser beam. The efficiency then lies at about 10% only, whereas bounce geometry reaches an efficiency of 50%. Because of this we needed to do a better adaption for the simulation in order simulate the bounce geometry more precise. As the laser reaches the crystal with an inclined angle using the bounce geometry and is reflected with the same angle there, the laser geometry at that spot can be considered as done in diagram figure 3. Is the geometry mirrored at the crystal surface then, you get a laser running in a straight line with uniform distribution of thermal strain stress in the crystal. This can be simulated in the used program by pumping the crystal from the side at the lower end (see diagram figure 2). In this pumping area a smaller thermal lens is created, leading to thermal strains similar stress similar to the bounce geometry. Diagram figure 4 and 5 show the temperature distribution in a side pumped crystal and one based on the bounce geometry, respectively.

Diagram Figure 2: Real (a) and simulated (b) path of the laser beam

Diagram Figure 3: Scematic view of the beam path with bounce geometry (left)

and beam path adapted for simulation (right)

Diagram Figure 4: Temperature distribution for side pumped crystal

Diagram Figure 5: Temperature distribution for simulated crystal

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The following simulatino results were calculated with distances L1 = L2 = 25 mm between the reflection mirrors and the crystal. As only an approximation of the bounce geometry could be simulated, a deviation of up to 50% with the resulting output pwoer figures must be considered.

In diagram figure 5 the average output power of the laser beam in CW mode is shown as a function of the absorbed pumping power. The reflecivity of the uncoupling mirror was set to R=0.9. The beam power approximately increases linearly to the absorbed pumping power up to 35W and then turn into an exponential function up to a pumping power of 51W, where the maximum output power of 24W is reached. Thus, a effiency of about 50% is achieved. *Thomas and Damzen, 2011* reached an output power of 13.8W (with R=0.7) and efficiency of only 30%.

Diagram Figure 6: Simulated average output power of the laser beam as a function

of the absorbed pumping power; CW mode with R=0.9

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Additionally, a simulation with Q switch was performed (diagram figure 7). Here, too, a linear dependency of average output power and absorbed pumping power can be observed, as in CW mode. This simulation resulted in an output power of 17W at a maximum pumping power of 51W. Compared to *Thomas and Damzen, 2011*, where an output power of 11W at R=0.7 was measured, this computed value is much higher. The cause of this is the lack of a real bounce geometry in the simulation. A lower output power needs to be expected in reality, therefore, as in CW mode.

Diagram Figure 7: Simulated average output power of the laser beam as a function

of the absorbed pumping power; with Q switch and R=0.9

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The simulation was also used to calculate the average output power as a function of the reflecitity ouf the output mirror. Diagram Figure 8 shows a power reduction with increasing reflectifity. Taking the results of *Thomas and Damzen, 2011* in consideration, here we can expect a less intense reduction of the power in experimental test runs, too.

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Abbildung 8: Simulated average output power of the laser beam as a function

of the output mirror reflectivity with a pumping power of 51W

Diagram Figure 9 shows a peak power of 16kW with a pulse length of 9.39ns. Taking account the appoximate factor for the bounce geometry, in this simulation also results in a significantly higher peak power of Ps ≈ 24kW compared to *Thomas und *Damzen*, 2011,* where a peak power of 1.9kW was measured in experiments.

Diagram Figure 9: Simulated peak power as a function of pulse length with a output mirrow

reflectivity of 0.9 and a pumping power of 51W

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