3.1.1 Results

The results of the high-power CW single-wavelength 348.7-nm laser are presented in Figure 3. As seen in Figure 3(a), the total maximum output power of 1.033 W was achieved for the CW single-wavelength UV laser at 348.7 nm. The output power was corrected by the transmittance of the M2 mirror. The optical-to-optical conversion efficiency with respect to the absorbed power could be calculated to be approximately 9.4%. The threshold of the laser was 0.58 W (absorbed pump power). The M ² factors were measured to be 2.0 and 2.8 in the x and y directions, respectively. Since our LD array could not work for a long enough time under the maximum output power to finish the measurement of the M ² factors, we measured the M ² factors under a relatively low pump power with a UV laser power of approximately 0.6 W. The M ² factors at the maximum output power should be a little higher. The highly elliptical UV laser beam profile should be mainly introduced by the relatively large work-off angle of the $\unicode{x3b2}$ -BBO crystal and the relatively strong thermal lensing effects in the π direction of the YLF crystal.

Figure 3 Output powers, laser spectrum and M ² factors of the high-power CW single-wavelength UV laser at 348.7 nm. (a) Output powers with respect to absorbed pump powers and the laser spectrum. (b) M ² factors of the 348.7-nm laser beam in the x and y directions.

3.1.2 Analyses

Compared with the previous work on 698-nm laser freque ncy doubling^[ Reference Liu, Cai, Xu, Zeng, Huang, Wang, Yan and Xu^37], the output power was greatly improved (~31 times). However, the optical-to-optical conversion efficiency was little improved, despite the much higher pump power. To explain the reason, we did some simulations based on the intracavity frequency doubling theory under plane wave approximation proposed by Smith^[ Reference Smith^40] and Agnesi et al. ^[ Reference Agnesi, Guandalini and Reali^41]:

(1) \begin{align}{P}_{2\omega}=\frac{\pi {\omega}_1^2}{8k}{I}_{\mathrm{s}}^2{\left\{-\left(k+\frac{L_{\mathrm{i}}}{I_{\mathrm{s}}}\right)+{\left[{\left(k+\frac{L_{\mathrm{i}}}{I_{\mathrm{s}}}\right)}^2+4\frac{k}{I_{\mathrm{s}}}\left(2{K}_{\mathrm{c}}{P}_{\mathrm{a}}-{L}_{\mathrm{i}}\right)\right]}^{1/2}\right\}}^2,\end{align}

(2) \begin{align}k=\frac{4{\pi}^2}{\lambda_{\omega}^2}{Z}_0\frac{d_{\mathrm{eff}}^2{\ell}^2}{n^2}\frac{\omega_1^2}{\omega_2^2}\beta,\end{align}

where ${\omega}_1$ and ${\omega}_2$ are the laser beam sizes in the gain medium and nonlinear crystal, ${I}_{\mathrm{s}}$ is the saturation intensity of the 698-nm transition, ${K}_{\mathrm{c}}$ is the coupling efficiency, ${L}_{\mathrm{i}}$ is the intracavity loss, ${P}_{\mathrm{a}}$ is the absorbed pump power, ${P}_{2\omega }$ is the power of the frequency-doubled laser, ${\lambda}_{\omega }$ is the wavelength of the fundamental laser, ${Z}_0$ = 337 Ω is the vacuum impedance, ${d}_{\mathrm{eff}}$ is the nonlinear coefficient of the nonlinear crystal (which also depends on the type of phase matching), $\ell$ is the length of the nonlinear crystal (7 mm), $n$ is the refractive index of the nonlinear crystal at ${\lambda}_{2\omega }$ (1.7 in the simulation) and $\beta$ is the phase mismatching factor (~2 in the simulation). Here, ${\omega}_1$ and ${\omega}_2$ were calculated through the well-known ABCD matrix theory by using different effective thermal focal lengths of the gain medium; ${I}_{\mathrm{s}}$ was calculated to be 5.3 × 10⁸ W/m²; ${K}_{\mathrm{c}}$ was evaluated to be approximately 0.043 W^–1; ${L}_{\mathrm{i}}$ was evaluated to be approximately 0.05 according to the transmission of the $\unicode{x3b2}$ -BBO crystal at 698 nm (~98%); ${d}_{\mathrm{eff}}$ of the $\unicode{x3b2}$ -BBO crystal under type-I phase matching could be obtained through the parameters in Ref. [Reference Nikogosyan39]. The simulation results are presented in Figure 4. As seen, the UV laser performances are sensitive to the thermal lensing effects, and the output powers are lower when the thermal lensing effects become stronger. Thus, we can see that the optical-to-optical conversion efficiency was not significantly improved due to the much stronger thermal lensing effects introduced by the higher pump power compared with the previous work^[ Reference Liu, Cai, Xu, Zeng, Huang, Wang, Yan and Xu^37].

Figure 4 Simulation results of the 348.7-nm laser output powers under different effective thermal focal lengths. Here, f is the value of the effective thermal focal length and ${\omega}_1$ and ${\omega}_2$ are the laser beam sizes in the gain medium and nonlinear crystal, respectively.

Figure 5 Measured results for the CW discrete tunable UV lasers. (a) Laser output powers at different wavelengths. (b) Laser spectra corresponding to (a). (c) Output powers with respect to the absorbed pump powers of the two lasers with relatively high output powers. (d) M ² factors of the 347.9-nm laser beam in the x and y directions. (e) The transmittance of the $\unicode{x3b2}$ -BBO crystal (normal incidence) in the deep red region.

Figure 6 Simulation results to further understand the wavelength tuning. (a) Round trip TM mode transmittances comparison of using only the 1-mm thick quartz plate and both the plate and the $\unicode{x3b2}$ -BBO crystal at the same time. (b) Relative phase-matching angles at different wavelengths of the $\unicode{x3b2}$ -BBO crystal.

3.2.1 Results

The measured results of the CW discrete tunable UV lasers are presented in Figure 5. The wavelength tunability was realized by rotating the intracavity Lyot filter and tilting the $\unicode{x3b2}$ -BBO crystal. As seen in Figure 5(a), lasers at different wavelengths were obtained by wavelength tuning. Most of the output powers achieved were at the level of tens of milliwatts, except for the lasers at 347.8 and 360.3 nm (~500 mW). The fundamental lasers in the σ and π polarization directions were both realized to generate the UV lasers. As seen from Figure 5(b), lasers from 334.7 to 364.6 nm were achieved, including both the σ and π polarization directions. Continuous tunability was only realized in some narrow ranges (from 360.0 to 360.6 nm, and from 347.8 to 349.1 nm). The input–output characteristics of the lasers with relatively high output powers are presented in Figure 5(c). The maximum output powers of the lasers at 348.7 and 360.3 nm were 0.518 and 0.505 W, respectively. The thresholds of the two lasers at 348.7 and 360.3 nm were 0.58 and 0.4 W, respectively. The 347.9-nm laser generated through the σ-polarized fundamental laser had a maximum output power of 128 mW with a threshold of 2.30 W. As seen from Figure 5(d), although the YLF crystal in the scheme for σ-polarized fundamental laser tuning suffered higher waste heat, the M ² factors of the generated UV laser beam (2.2 and 1.8 in the x and y directions, respectively) were smaller than the aforementioned one generated through the π-polarized fundamental laser. The reason could be that the thermal lensing effects in the π direction of the YLF crystal are stronger than those in the σ direction. The stronger thermal lensing effects could introduce detrimental influences to the beam quality. Due to the slightly stronger thermal lensing effects in this scheme (compared with the single-wavelength scheme) and the higher intracavity losses introduced by the extra Lyot filter due to the laser divergence angle, the output power obtained at 348.7 nm was much lower than that of the laser achieved by the single-wavelength scheme. The 360.3-nm laser output power was expected to be higher than that of the laser at 348.7 nm due to the larger emission cross-section at approximately 721 nm (compared with the emission cross-section at ~698 nm). However, as seen from Figure 5(e), the quality of the AR coating on the $\unicode{x3b2}$ -BBO crystal was not so ideal. When the $\unicode{x3b2}$ -BBO crystal was tilted to the correct phase-matching angle, the transmittance of the crystal at approximately 721 nm might be lower than the normally incident transmittance at approximately 698 nm. The other reason was that when the fundamental laser was normally incident, a part of the laser reflected by the $\unicode{x3b2}$ -BBO crystal could re-enter the laser cavity; however, when it was not normally incident, all the reflected fundamental lasers would go out of the cavity.

3.2.2 Analyses

To further understand the wavelength tuning, we did some simulations about the transmittances of the Lyot filter used in the experiment at different angles (the angle between the optical axis of the quartz plate and the incident plane) and wavelengths, and the relative phase-matching angles (0° corresponds to the normal incidence) of the $\unicode{x3b2}$ -BBO crystal corresponding to different wavelengths. The transmittances of the Lyot filter could be obtained through the Jones matrix^[ Reference Zhu^42]:

(3) \begin{align}{M}_{\mathrm{b}}=\left(\begin{array}{@{}cc@{}}{\cos}^2\alpha +{\sin}^2\alpha \exp \left(-i2\delta \right)& q\sin \alpha \cos \alpha \left[1-\exp \left(-i2\delta \right)\right]\\ {}q\sin \alpha \cos \alpha \left[1-\exp \left(-i2\delta \right)\right]& {q}^2\left[{\sin}^2\alpha +{\cos}^2\alpha \exp \left(-i2\delta \right)\right]\end{array}\right),\end{align}

where $n$ is the refractive index (1.54 in the simulation) of the quartz, $q=2n/\left(1+{n}^2\right)$ , $\alpha$ is the angle between the incident plane and the plane defined by the optical axis of the quartz crystal and the refractive ray and $-2\delta$ is the phase retardation. By setting the transmission peak at 698 nm, a round trip transverse magnetic (TM) mode transmission curve is presented as a dashed line in Figure 6(a). By taking the influence of the $\unicode{x3b2}$ -BBO crystal on the tuning into consideration (the $\unicode{x3b2}$ -BBO crystal could be treated as a phase retarder because it is a uniaxial crystal with an AR coating around 698 nm), another simulation result is presented as a red line in Figure 6(a). As seen, the $\unicode{x3b2}$ -BBO crystal under the type-I phase-matching condition in our experiment could broaden the transmission peak and reduce the capability of wavelength selection. It could be one of the reasons why we could not obtain continuous tuning and could be improved by multiplying the quartz plates in the future. The phase-matching angle (type-I phase matching) could be calculated through the following equation^[43]:

(4) \begin{align}{\sin}^2{\theta}_{\mathrm{m}}=\frac{{\left({n}_{\omega}^{\mathrm{o}}\right)}^{-2}-{\left({n}_{2\omega}^{\mathrm{o}}\right)}^{-2}}{{\left({n}_{2\omega}^{\mathrm{e}}\right)}^{-2}-{\left({n}_{2\omega}^{\mathrm{o}}\right)}^{-2}},\end{align}

where the refractive indexes ( $n$ ) at different frequencies and polarization directions can be intuitively read by the superscripts and subscripts and ${\theta}_{\mathrm{m}}$ is the phase-matching angle. The refractive indexes could be calculated through the Sellmeier equations from the following^[ Reference Kato^44]:

(5) \begin{align}{n}_{\mathrm{o}}^2&=2.7359+\frac{0.01878}{\lambda^2-0.01822}-0.01354{\lambda}^2, \nonumber\\{n}_{\mathrm{e}}^2&=2.3753+\frac{0.01224}{\lambda^2-0.01667}-0.01516{\lambda}^2,\end{align}

where $\lambda$ is the laser wavelength. The simulation results are shown in Figure 6(b). As seen, the relative phase-matching angles required in the experiment were not very large (in ±2°). Thus, only slight tilting of the $\unicode{x3b2}$ -BBO crystal was needed in the experiment to achieve the wavelength tuning.