6. Conclusion

based on the results shown in Figures 19 and 20, where pulse duration decreases with increasing energy within the limits of absorption saturation. Theoretically, shorter pulse durations can be achieved using an output coupler with less than 10% reflectivity. Practically, the threshold energy and the slope efficiency limit the choice of reflectivity. As Figure 22 shows, higher pump energies are needed to achieve lasing in a low-Q laser resonator. If the reflectivity of the output coupler is 10%, for instance, the lasing threshold for obtaining a 31.5-ps laser pulse is 80 μJ and the slope efficiency is 8%. However, increasing the output coupler reflectivity to

154 Numerical Simulations in Engineering and Science

30% decreases the threshold energy to 40 μJ and increases the slope efficiency to 10%.

Figure 23. Spectro-temporal evolution of the broadband, short-pulse Ce:LiCAF laser emission from an optimized low-Q (R<sup>2</sup> = 30%), short cavity (L = 2 mm) oscillator. A short laser pulse with about 31.5-ps pulse duration, broadband emission centered at 288.5-nm wavelength, and 10 μJ output energy can be obtained practically from a 1-mm long, 1 mol% Ce3+ doped LiCAF crystal when pumped by a 266-nm, 75-ps pump pulse with 140 μJ pump energy. A slope efficiency of about 10% is also feasible with pump energies that are far from the crystal's absorption saturation and damage threshold.

Figure 24. Spectral profile of the broadband, short-pulse Ce:LiCAF laser emission from an optimized low-Q (R<sup>2</sup> = 30%),

short cavity (L = 2 mm) oscillator. Temporal dynamics is shown in Figure 21b.

In summary, the transient cavity method is extended to a solid-state gain medium. Numerical simulations show that the same principles used to generate ultrashort laser pulses in dye lasers using this technique can be applied to solid-state gain media to generate ultrashort broadband pulses in the UV region. The laser gain medium was represented as a system of two homogeneous broadened singlet states and the numerical simulations solved the laser rate equations for broadband emission. The spectral and temporal evolution of the resulting laser emission was investigated in order to find the optimal cavity length and output coupler reflectivity that will give rise to the formation of resonator transients in the laser oscillator cavity. The calculations reveal that a laser oscillator with a short cavity and a low Q is ideal for the formation of resonator transients, which then lead to ultrashort (ps) laser emission. Specifically, a 2-mm cavity length and a 10% output coupler reflectivity can be used to generate a single 31.5 ps pulse using a 1-mm long Ce:LiCAF crystal with 1 mol% Ce3+ ion doping concentration. Although this work used Ce: LiCAF crystal as the laser gain medium, the transient cavity method can also be applied to generate ultrashort laser pulses using other rare earth-doped fluoride crystals.
