## 2 Crystals and Lasers  
### Characteristics of Ho: GdVO4 Crystal  
As a common vanadate crystal, Ho: GdVO4 has a large birefringence, good mechanical properties, and stable chemical properties. An a-cut Ho: GdVO4 crystal (Company: Shanghai Institute of Ceramics, Chinese Academy of Sciences, Shanghai, China) with dopant concentration of 1.0 at.% was used in our experiment, which has a dimension of 4 mm (width) \(\times\) 4 mm (height) \(\times\) 20 mm (length).  
The upper-level fluorescence lifetime is an important indicator for evaluating the energy storage performance of laser gain media. The longer the upper-level lifetime, the easier it is to form population inversion. The gain medium is also easier to store energy. The experimental set up for measuring the fluorescence lifetime of the upper-level is shown in Figure 1. The pump source is a 2 \(\upmu\)m pulsed Ho:YLF laser (pulse repetition frequency: 500 Hz, pulse width: 25 ns). After the excited fluorescence of the crystal passes through the WDM1-3 grating monochromator, the fast response InGaAs detector (the shortest response time can reach 100 ns) is used to detect the fluorescence attenuation signal. Finally, the wavejet 332 digital oscilloscope (bandwidth: 350 MHz) produced by Lecroy Company records the fluorescence decay curve. Figure 2 shows the measured fluorescence decay curve of the Ho: GdVO4 crystal energy band. According to the exponential decay of e, the fluorescence lifetime of the crystal can be obtained by fitting Figure 2 to 2.012 ms.  
The absorption spectrum of the crystal is an important basis for determining the pump wavelength and polarization mode. It can be seen from Figure 3 that the strongest absorption peak of Ho: GdVO4 crystal in \(\sigma\) polarization direction is near 1942 nm, the position with weaker absorption intensity is near 1958 nm, and the corresponding absorption cross sections are 2.76 \(\times\) 10\({}^{-20}\) and 2.50 \(\times\) 10\({}^{-20}\) cm\({}^{2}\), respectively. In \(\pi\) polarization direction, the strongest absorption peak is located near 1940 nm, and the corresponding absorption cross section is 2.44 \(\times\) 10\({}^{-20}\) cm\({}^{2}\). In order to obtain better laser performance, a laser with a wavelength of 1.94 \(\upmu\)m will be selected as the pump source of the Ho: GdVO4 crystal.  
Figure 1: Experimental setup for measuring the upper state fluorescence lifetime.  
Figure 2: Decay curve of \({}^{5}\)I\({}_{7}\)\(\rightarrow\)\({}^{5}\)I\({}_{8}\) fluorescence in Ho: GdVO4.  
In order to obtain the emission cross section of the laser gain medium, we used the fluorescence spectrum measurement system shown in Figure 4 to record the fluorescence spectrum of Ho: GdVO4 crystal at room temperature. After processing by the simulation software, the polarization-stimulated emission cross section of the Ho: GdVO4 crystal is shown in Figure 5. There are two obvious emission peaks in \(\pi\) polarization direction of Ho: GdVO4 crystal, which are located near 2038 nm and 2048 nm, and the corresponding emission cross sections are 3.64 \(\times\) 10\({}^{-20}\) cm\({}^{2}\) and 3.61 \(\times\) 10\({}^{-20}\) cm\({}^{2}\), respectively. In \(\sigma\) polarization direction, the largest emission peak is located near 2005 nm, and the corresponding emission cross-section is 1.90 \(\times\) 10\({}^{-20}\) cm\({}^{2}\). In addition, there are four emission peaks with relatively weak intensity, respectively near 2025 nm, 2045 nm, 2059 nm, and 2096 nm. In summary, it can be seen that the stimulated emission cross section of the strongest emission peak of Ho: GdVO4 crystal in the 2 \(\mu\)m waveband is on the order of 10\({}^{-20}\) cm\({}^{2}\), and the fluorescence branching ratio and the upper-level fluorescence lifetime (ms-level) are also relatively large. It is sufficient to prove that Ho: GdVO4 crystal can provide excellent mid-infrared laser performance.  
Figure 4: Setup for measuring the fluorescence spectrum of Ho: GdVO4 crystal.  
Figure 3: Polarized absorption cross section of Ho: GdVO4 crystal.