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Abstract
Ultrafast deep-UV laser sources have extensive applications across a wide number of fields, whether biomedicine, photolithography, industrial processing, or state-of-the-art scientific research. However, it has been challenging to obtain deep-UV laser sources with high conversion efficiency and output peak power. Here, we simultaneously demonstrated high-peak-power picosecond deep-UV laser sources at two typical wavebands of 263.2 and 210.5 nm via the efficient fourth- and fifth-harmonic generation. The highest peak power of 263.2 and 210.5 nm laser radiations were up to 2.13 GW (6.72 ps) and 1.38 GW (5.08 ps). The overall conversion efficiencies from the fundamental wave to the fourth and fifth harmonic were up to 42.9% and 28.8%, respectively. The demonstrated results represent the highest conversion efficiencies and output peak powers of picosecond deep-UV laser sources at present to our knowledge. Additionally, we also systematically characterized the deep-UV optical properties of typical birefringent and nonlinear borate crystals, including α-BaB2O4, β-BaB2O4, LiB3O5, and CsLiB6O10 crystals. The experiments and obtained numerous new optical data in this work will contribute to the generation of ultrahigh-peak-power deep-UV and vacuum-UV laser sources and crucial applications in both science and industry, such as high-energy-density physics, material science, and laser machining.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Deep-UV laser sources opened great application prospects and exciting possibilities in numerous fields including laser physics [1–3], industrial manufacturing [4,5], spectroscopy [6,7], and biomedicine [8–10], because of their characteristics of short wavelength, high single-photon energy, low filamentation threshold, high electron density in filamentation, and superior temporal-spatial resolution. In the field of nonlinear optics, deep-UV ultrashort pulses can produce rich physical mechanisms such as strong nonlinear broadening, multiphoton ionization, photochemical decomposition, and high-density plasma. In terms of spectroscopy, deep-UV lasers have proved their value in a variety of research fields and become an important tool for environmental monitoring and remote sensing measurements [7,11]. A wealth of information about the Earth’s atmosphere can be obtained via remote sensing technology using UV sources, and measurement of the ozone content by a ground-based UV spectral network or by satellite-borne systems is also the basis for global observations and trend analysis [11,12]. On the other hand, against the backdrop of the ongoing global pandemic of Coronavirus disease 2019 (COVID-19), the control and prevention of COVID-19 has aroused widespread concerns, especially, the highly infectious Omicron variant that has caused large-scale spread, Shanghai, a city with a population of over 25 million, has recently imposed lockdown more than two months for this reason. Deep-UV sources have significant advantages in rapid disinfection or inactivation of bacteria, fungi, and viruses [9,10,13], which can reduce the chance of infection through aerosols and contact spread with a chemical-free approach, and thus their applications in this field are gradually emerging.
Due to the lack of suitable gain medium, it is considerably difficult to directly generate deep-UV laser via stimulated radiation. Presently, one of the most effective approaches to obtaining deep-UV laser sources is nonlinear optical technology [14–17]. In the applications of this technology, nonlinear crystals play an extremely important role. To more efficiently obtain deep-UV lasers with high beam quality, over the years, researchers have never stopped exploring novel and excellent optical materials [18–24]. Although the exploration of materials has involved a variety of material systems, including borate [19,20], phosphate [21], carbonate [22,23], and nitrate [24], so far, borate-family crystals represented by $\alpha$-BaB$_2$O$_4$ ($\alpha$-BBO), $\beta$-BaB$_2$O$_4$ ($\beta$-BBO), LiB$_3$O$_5$ (LBO), and CsLiB$_6$O$_{10}$ (CLBO) are still one of the most typical and widely used birefringent and nonlinear optical materials [15–17,25–28], particularly in deep-UV waveband.
With the development of laser technology, the demand for the peak power of the deep-UV laser is continuously increasing. Although there have been a number of reports on the generation of deep-UV laser sources, currently available ultrafast deep-UV laser sources still exhibit relatively low conversion efficiency and output intensity. Their peak powers are mostly at the level of hundreds of MW or even lower, while there are few reports on the deep-UV laser radiation with peak power exceeding GW level, especially near the wavelength of 200 nm. Here, we collected and presented the output peak powers of repetition-rate deep-UV laser sources at two typical wavebands of $\sim$260 and $\sim$200 nm reported in recent two decades, and the time scales of laser pulses cover from ns [14,16,29–35] to ps [7,8,17,36–44] and fs [45–59], as shown in Fig. 1. It can be seen intuitively that the peak powers of laser pulse around 260 nm band are mostly lower than GW level except at the fs scale, while there are not only fewer reports but also the peak powers are lower (at the level of 100 MW) for the laser near 200 nm band. Since the shorter the wavelength, the higher the photon energy, and both the linear absorption and nonlinear absorption effects are significantly enhanced, it is a great challenge to obtain a high-peak-power laser pulse with an output peak power level of GW in the deep-UV spectral range. On the other hand, understanding the optical properties of materials in the deep-UV region in detail, such as UV transmittance, linear absorption, and nonlinear two-photon absorption (TPA), is very crucial for the high-flux deep-UV laser generation and application. For the commonly used borate materials such as the crystals mentioned above, although their partial UV optical properties were already reported in some literature [60–73], these results are fragmentary, and the full application potential opened by a further expanded parameter coverage has yet to be explored. In this work, based on the fourth- and fifth-harmonic generation (FHG and FiHG) of a Nd:YLF laser, high-peak-power and high-efficiency picosecond deep-UV laser sources at two typical wavelengths of 263.2 and 210.5 nm were simultaneously demonstrated. The maximum peak power of 263.2 and 210.5 nm laser radiations were increased by 2-3 times and an order of magnitude than the previously reported results, reaching 2.13 and 1.38 GW, respectively, as shown in Fig. 1. The total conversion efficiencies from the fundamental wave to the fourth and fifth harmonic were up to 42.9% and 28.8%, respectively, which both are the highest conversion efficiencies of deep-UV laser sources at ps scale. The spot sizes of the focused beams using a lens with a focal length of 100 mm are $\sim$31 and $\sim$23 $\mu$m (2.7 and 2.5 times diffraction limit), respectively, and the corresponding focused peak power densities are 1.22 and 1.43$\times$10$^{15}$ W/cm$^2$, respectively. Meanwhile, aiming at the typical birefringent and nonlinear borate crystals represented by $\alpha$-BBO, $\beta$-BBO, LBO, and CLBO, we comprehensively investigated and compared their optical properties, including transmittances, cut-off edges, band-gap energies, linear absorption, and nonlinear TPA in the deep-UV region. The linear absorption and nonlinear TPA anisotropy of ordinary and extraordinary light (o and e light) in these borate materials were revealed. This work can well help to deeply understand the characteristics of borate materials in the deep-UV waveband, and provide important guidance for the generation and wide applications of high-power deep-UV laser sources.
Fig. 1. Output peak powers of repetition-rate deep-UV laser sources with typical wavebands of (a) $\sim$260 and (b) $\sim$200 nm at ns, ps, and fs time scales reported in recent two decades.
2. Experimental setup and results
The experimental setup is shown in Fig. 2(a). A high-energy Nd:YLF picosecond mode-locked laser (1053 nm) with a $\sim$9 ps pulse duration (FWHM) was used as the fundamental wave. This laser system starts from a fiber master oscillator, which produces a train of the picosecond pulses, and they are amplified by a diode-pumped regenerative amplifier and a flashlamp-pumped power amplifier to up to 45 mJ pulse energy with a repetition rate of 10 Hz, and the output transverse beam profile is a circular spot with a diameter of 4.3 mm. For the deep-UV laser generation, absorption loss is a key factor limiting the increase of the peak power and conversion efficiency. To efficiently generate high-intensity deep-UV laser radiation, we optimized the parameters of output fundamental wave and nonlinear crystals employed in the plan through simulation calculation. Experimentally, an LBO crystal ($\theta = 90^\circ$, $\varphi = 11^\circ$) with a thickness of 4.5 mm was used for the second harmonic generation (SHG) with type-I phase matching, and its temperature was always controlled at 55 $^\circ$C. Subsequently, a 1.2-mm-thick $\beta$-BBO crystal ($\theta = 48.4^\circ$, $\varphi = 0^\circ$, type-I phase matching) was used for the FHG, and another $\beta$-BBO crystal ($\theta = 52.1^\circ$, $\varphi = 0^\circ$, type-I phase matching) with a thickness of 0.8 mm was used to generate the fifth harmonic. The two $\beta$-BBO crystals were always at room temperature. The surfaces of each crystal were coated with anti-reflection films at the corresponding wavelengths.
Fig. 2. (a) Schematic diagram of the experimental setup for the generation of high-peak-power picosecond deep-UV laser radiation. $\lambda / 2$, half-wave plate; PBS, polarization beam splitter; HR, high reflector; DM, dichroic mirrors; L1 ($f$ = 300 mm), L2 ($f$ = 400 mm), L3 ($f$ = 400 mm), and L4 ($f$ = 300 mm), lens (deep-UV fused silica); VSF, vacuum spatial filter; BS1 and BS2, beam sampling (2-mm-thick CaF$_2$ crystal). (b) Measured spectrums of the fundamental wave, second harmonic, fourth harmonic, and fifth harmonic. Results of the (c) fourth- and (d) fifth-harmonic pulse durations measured by TPA pump-probe experiments, where a 5-mm-thick deep-UV fused silica was used for TPA material, a Gaussian temporal profile is assumed for the fit, and a deconvolution factor of 1.414 is used to extract the FWHM pulse duration.
Figure 3(a) shows the second harmonic energies ($E_2$) and SHG efficiencies ($\eta _2 = E_2 / E_1$) as a function of the fundamental wave energy ($E_1$). $E_1$ gradually increases from zero to $\sim$40 mJ with a step size of $\sim$2.5 mJ. When the incident energy is 32.6 mJ, the SHG efficiency reaches a maximum value of 78%. At the incident energy of 39.7 mJ, a 526.5 nm laser with an energy of 30.4 mJ was obtained, and the corresponding efficiency was 76.7%. For the FHG, the conversion efficiencies ($\eta _4 = E_4 / E_1$) from the fundamental wave to the fourth harmonic and the generated fourth harmonic energies ($E_4$) vary with $E_1$ are shown in Fig. 3(b). Similarly, $E_1$ gradually increases from zero to $\sim$40 mJ with a step size of $\sim$2.5 mJ. At the incident energy of 19.7 mJ, the maximum efficiency of FHG was up to 42.9%, and the corresponding fourth harmonic energy was 8.43 mJ. A maximum $E_4$ of 14.3 mJ was obtained with a conversion efficiency of 35.9% at an incident second harmonic energy of 39.8 mJ. In the FiHG stage, Fig. 3(c) plots the energies ($E_5$) and efficiencies ($\eta _5 = E_5 / E_1$) of the generated fifth harmonic as a function of $E_1$. As we can see, $\eta _5$ reaches a maximum value of 28.8% when $E_1$ is 14.6 mJ. At the fundamental wave energy of 40 mJ, the maximum fifth harmonic energy was up to 7.02 mJ, and the corresponding efficiency was 17.6%.
Fig. 3. Efficiencies and energies of generated (a) second harmonic, (b) fourth harmonic, and (c) fifth harmonic as a function of input pulse energy. In (a), (b), and (c), the solid and dashed lines denote the calculated results of efficiency and energy, respectively; the squares and circles denote the experimental results of efficiency and energy, respectively. The measured transverse near-field distribution of the (d) fundamental wave, (e) second harmonic, (f) fourth harmonic, and (h) fifth harmonic. The far-field beam spots of the focused (g) fourth and (i) fifth harmonic using a lens with a focal length of 100 mm.
In the whole experiment, the involved spectrums of the fundamental wave, second harmonic, fourth harmonic, and fifth harmonic are shown in Fig. 2(b). The pulse durations of the generated fourth and fifth harmonic were measured using the TPA autocorrelation technique, where 5-mm-thick deep-UV fused silica was used for the TPA pump-probe material. The measured results were 6.72 and 5.08 ps, respectively, and the intensity autocorrelations were shown in Figs. 2(c) and (d). Figures 3(d)-(g) show the measured transverse near-field distribution of the fundamental wave, second, fourth, and fifth harmonic beam, respectively, and Figs. 3(h) and (i) are the far-field beam spot of the focused fourth and fifth harmonic, respectively, using a lens with a focal length of 100 mm. The diameters of the near-field and far-field beam sizes of the fourth harmonic are 5.66 mm and $\sim$31 $\mu$m, respectively, and the corresponding diffraction limit, peak power, and maximum intensity are 2.7 times, 2.13 GW, and 1.22$\times$10$^{15}$ W/cm$^2$, respectively. Similarly, for the fifth harmonic, the diameters of the near-field and far-field beam sizes are 5.61 mm and $\sim$23 $\mu$m, respectively, and the corresponding diffraction limit, peak power, and maximum intensity are 2.5 times, 1.38 GW, and 1.43$\times$10$^{15}$ W/cm$^2$, respectively. The maximum peak powers of the fourth and fifth harmonics generated here were 2-3 times and an order of magnitude higher than ever reported results to our knowledge.
Here, the thicknesses of employed nonlinear crystals are thin because the used Nd:YLF picosecond laser has peak intensity (>10 GW/cm$^2$) and the nonlinear crystals have large effective nonlinear coefficients. Furthermore, for the lasers with short pulses (ps or fs time scale), the temporal walk-off effect (i.e., group velocity mismatch) is a crucial factor that affects the conversion efficiency. Usually, the temporal separation occurs when the interacting waves propagate only several millimeters in the crystal, especially in the deep-UV spectral region with more serious dispersion, and the conversion efficiency cannot be effectively improved by simply increasing the crystal thickness but will increase the energy loss. Consequently, the crystal used for frequency conversion of short pulse laser should not be too thick generally. For the beam output from this Nd:YLF laser, the parameters of the LBO and two $\beta$-BBO crystals employed here are near the optimal thicknesses.
Based on nonlinear coupled wave equations [74–81] and experimental parameters, we simulated the SHG, FHG, and FiHG, and the results were shown by solid and dashed lines in Figs. 3(a)-(c), which show a good agreement between the calculated results and experimental results. Since the fundamental wave has a large spatial profile and the thicknesses of the employed nonlinear crystals are also thin, the influence of the temporal effects (e.g., group velocity mismatch and group velocity dispersion) and the absorption losses on the nonlinear interaction processes of picosecond pulses are significantly greater than the spatial effects (e.g., diffraction and walk off) [75–77,80]. Therefore, the diffraction and walk-off effects were ignored in the simulation. The SHG in LBO crystal can be described as:
For the fourth and fifth harmonics, there is not only linear absorption, but also significant nonlinear TPA occurs in $\beta$-BBO crystal, which is a key factor limiting the conversion efficiency and output peak power. The FHG in the $\beta$-BBO crystal can be written as:
Similarly, for the FiHG process, its nonlinear coupled-wave equations are:
In Eqs. (1–3), $i$ is the imaginary unit; the subscripts 1, 2, 4, and 5 represent the fundamental wave, second harmonic, fourth harmonic, and fifth harmonic, respectively; the superscript $^*$ denotes complex conjugate; $A$ and $I$ are the complex amplitude and intensity of the optical field, respectively; $z$ represents the propagation distance; $k$, $n$, and $\lambda$ are the wave vector, refractive index, and laser wavelength in vacuum, respectively; $v_f$ and $v_g$ are the reference frame velocity and group velocity, respectively; GVD represents group velocity dispersion; $\kappa$ represent the coefficient of the nonlinear term; $\alpha$ and $\beta$ are the coefficients of linear absorption and nonlinear TPA, respectively. The relation between complex amplitude and pulse energy ($E$) can be described as [80]:
Table 1. Numerical values of parameters used in the simulation.
The implementation of efficient FHG and FiHG in this work is closely related to multiple factors, including high-beam-quality laser source, nonlinear materials with excellent optical quality, achievement and maintenance of phase matching, analysis of deep-UV laser energy loss, and selection of appropriate crystal parameters. The laser source with high beam quality is conducive to energy utilization and achievement and maintenance of phase matching among the interacting waves, thereby improving the conversion efficiency. For deep-UV laser generation, absorption loss is also a key factor limiting efficient frequency conversion. The transmittance of crystal in the deep-UV waveband is greatly affected by the growth quality. Therefore, nonlinear crystal with excellent optical quality is essential to obtain high optical conversion efficiency. Additionally, since the FHG and FiHG of picosecond laser not only involve the cascade of $\chi ^{(2)}$ nonlinear effects, but also need to comprehensively consider multiple physical processes (including group velocity, GVD, linear absorption, nonlinear TPA, and energy balance), it is necessary to accurately simulate the evolution of nonlinear optical interaction among waves in the crystal through the systematic numerical calculation to optimize the parameters of materials in each nonlinear process and guide the experiment. In short, achieving high-efficiency deep-UV laser generation requires a combination of high-beam-quality laser, optical material with excellent performance, comprehensive numerical simulation, systematic optimization of crystal parameters, and necessary experimental skills.
3. UV optical properties of borate crystals
3.1 Deep-UV and vacuum-UV transmittances
As one of the most widely used deep-UV optical materials in both scientific and industrial fields, the UV optical properties of borate crystals have been lacking systematic data, especially the polarization-dependent optical absorption properties at the typical wavebands of the fourth and fifth harmonic of the $\sim$1 $\mu$m laser. Here, by using a vacuum-ultraviolet (VUV) spectrophotometer (Metrolux ML6500, Germany, operation pressure: <3$\times$10$^{-3}$ Pa, wavelength ranges with double lamps: 115 to 230 nm and 160 to 320 nm) and the above high-intensity deep-UV laser sources, we systematically characterized the UV optical properties of common borate materials. Four uncoated crystal samples of $\alpha$-BBO, $\beta$-BBO, LBO, and CLBO were prepared, as shown in Fig. 4(a), and their specific parameters, including length and orientation used in the subsequent calculation of UV properties, were shown in Table 2. The $\alpha$-BBO, $\beta$-BBO, and LBO crystal samples were grown by flux method, and the CLBO crystal sample was obtained by top-seeded solution growth. Since these crystal samples have hygroscopicity, especially CLBO crystal, air dehumidifiers were used to ensure that the crystal samples were always in a dry environment during the polishing process, and then they were sealed in a nitrogen environment. The sealed crystal samples were stored in a drying cabinet before the experimental measurement, and the temperature and relative humidity of the drying cabinet were controlled at 25 $^\circ$C and <30%.
Fig. 4. (a) Prepared $\alpha$-BBO, $\beta$-BBO, LBO, and CLBO crystal samples. (b) Experimentally measured absolute transmittance spectrums of the $\alpha$-BBO, $\beta$-BBO, LBO, and CLBO crystal samples in the UV spectral region of 160-290 nm. (c) Band-gap energies of the $\alpha$-BBO, $\beta$-BBO, LBO, and CLBO crystals were determined from the Tauc plot. The fitted linear parts are used to evaluate the band-gap energy at the $x$-axis intercept.
Table 2. Parameters of the crystal samples.
Firstly, the deep-UV and vacuum-UV absolute transmittances of the crystal samples were measured in the range of 160-290 nm, as shown in Fig. 4(b). Their UV cut-off edges, which are defined by transmittance at the “0” level, are shown in Table 3. It can be seen that $\alpha$-BBO and $\beta$-BBO have similar transmittance characteristics and UV cut-off wavelengths. Compared with $\alpha$-BBO, $\beta$-BBO, and CLBO crystals, the LBO crystal has a shorter UV cut-off edge, which means that it has larger band-gap energy $\left ( E_g \right )$.
Table 3. Experimentally measured UV cut-off edges and calculated band-gap energies of the crystal samples.
3.2 Band-gap energy
Based on the measured UV transmittances, the band-gap energies of $\alpha$-BBO, $\beta$-BBO, LBO, and CLBO crystals can be calculated via the Tauc method [82], which is a typical approach to estimating the $E_g$ by using the optical absorption spectrums. The relationship between the energy-dependent absorption coefficient $\alpha$ and $E_g$ can be described by the following equation:
where $h$ is the Planck constant, $\nu$ is the photon frequency, $A$ is the proportionality constant, and the factor $n$ depends on the nature of the electron transition and is equal to 1/2 or 2 for the direct and indirect transition, respectively. The calculated results are shown in Fig. 4(c) and Table 3. As one can see, the obtained UV cut-off edges and band-gap energies revealed an almost perfect agreement with the reported data. One of the reasons there are slightly different from the results reported in the literature is that the crystal transmittance is related to its thickness, and the thicknesses of the crystal samples employed here are different from those in the literature. Secondly, since the purity of raw materials (e.g., BaCO$_3$, Li$_2$CO$_3$, Cs$_2$CO$_3$, and H$_3$BO$_3$), growth process (e.g., dry atmosphere and temperature and rotation rate control), and water impurity have a significant impact on the optical quality of borate-family crystals [83–87], the transmittances of crystal samples with different growth processes in the literature also have a discrepancy. In addition, the measured transmittances of vacuum spectrophotometers produced by different manufacturers may be slightly different. Accordingly, the band-gap energies of materials calculated by the Tauc method based on measured transmittances were slightly different from the results of the literature.3.3 Linear absorption
To accurately obtain the linear absorption coefficients of the aforementioned crystals in the deep-UV spectral region, it needs to employ the laser with low intensity to avoid the influence of nonlinear absorption, since the significant nonlinear absorption effect generally occurs in these optical materials in a high-intensity regime [68]. For this part measurement, the peak intensity of the probe laser is always controlled below 100 MW/cm$^2$. The schematic of the measurement setup is shown in Fig. 5(a), where L1 ($f$ = 400 mm) and L2 ($f$ = 300 mm) are lenses (deep-UV fused silica); VSF is a vacuum spatial filter; BS is a 2-mm-thick CaF$_2$ crystal used for beam sampling; WBS (wedged beam splitter) is a 3-mm-thick MgF$_2$ crystal.
Fig. 5. (a) Schematic for the measurement of optical absorption coefficients. Low-intensity transmittances of $\alpha$-BBO, $\beta$-BBO, LBO, and CLBO crystal samples at (b)-(e) 263.2 and (f)-(i) 210.5 nm.
The deep-UV beam normally incident into the crystal sample, and the surface reflection $R$ and linear transmittance $T_{\mathrm {L}}$ of the crystal sample can be described as [69]:
where $n$ is the refractive index of o light or e light in the crystal sample, $\alpha$ is the linear absorption coefficient, and $L$ is the crystal sample length.Figures 5(b)-(i) show the measured low-intensity transmittances of o light and e light in $\alpha$-BBO, $\beta$-BBO, LBO, and CLBO crystal samples. It can be seen that the measured results have good consistency, which indicates that the nonlinear absorption effect is very weak here. According to the crystal parameters, measured transmittances, and Eq. (6) and (7), the anisotropic linear absorption coefficients of the crystal samples were obtained from the numerical calculation, and the results were shown in Table 4. For the $\beta$-BBO crystal, it can be seen that the measured results are consistent with the reported. Since we did not find the linear absorption coefficients of $\alpha$-BBO, LBO, and CLBO crystals, the comparison results cannot be given here. The linear absorption coefficient error mainly originates from the pulse energy measurement, and the errors of the energy calibration are 2-5% in the experiment. Therefore, there is little impact on the measurement results.
Table 4. Experimentally measured linear absorption coefficients of the crystal samples at 263.2 and 210.5 nm.
3.4 Nonlinear TPA
For the measurement of the nonlinear TPA coefficient, there are two critical steps: accurately measuring the intensity-dependent energy transmittance and reconstructing the distribution of laser intensity. In our experiment, two energy meters with the same model calibrated each other were used to measure the intensity-dependent transmittance of the deep-UV laser pulses, and the intensity distribution was reconstructed according to the measured pulse widths and near-field distributions of the fourth and fifth harmonic. Meanwhile, MgF$_2$ was chosen for the material of WBS, because it has high transmittance and a very weak TPA effect in the deep-UV waveband [81]. And to ensure that the sampling rate of the WBS is not affected by the laser intensity as far as possible, the reflection scheme of the back surface was adopted to characterize the incident laser energy before the sample, while the laser energy output from the sample was measured by the reflection scheme of the front surface, as shown in Fig. 5(a).
Considering both linear absorption and nonlinear TPA absorption, for the laser pulse propagating along the $z$-direction, the change of intensity $I$ with propagation can be expressed as Eq. (8) [81]. For a beam with a temporal Gaussian intensity profile, its three-dimensional intensity distribution $I_{\mathrm {in}}$ and the intensity-dependent transmittance $T_{\mathrm {NL}}$ through the crystal sample can be described as [69,81]:
The measured intensity-dependent transmittances of o light and e light in $\alpha$-BBO, $\beta$-BBO, LBO, and CLBO crystal samples are shown in Fig. 6. Combined with the intensity distribution of the laser beam, crystal sample parameters, measured linear absorption coefficients, and Eqs. (8)–(10), the transmittance data were numerically fitted by varying the value of the TPA coefficients, and finally, the optimal results are listed in Table 5. It can be seen that measured results of TPA coefficients at 263.2 and 210.5 nm are almost consistent with the reported results. The errors in the pulse duration determination ($\sim$350-500 fs) and energy calibration (2-5%) are the main factors that contributed to the error (<$15\%$) in the TPA coefficient determination.
Fig. 6. Intensity-dependent transmittances of $\alpha$-BBO, $\beta$-BBO, LBO, and CLBO crystal samples at (a)-(d) 263.2 and (e)-(h) 210.5 nm. The symbols denote the experimental results, and the solid and dashed lines denote the best-fitted results by varying the value of the TPA coefficients.
Table 5. Experimentally measured nonlinear TPA coefficients of the crystal samples at 263.2 and 210.5 nm.
As important members of borate-family materials, $\beta$-BBO, LBO, and CLBO crystals are the key nonlinear optical materials to obtain deep-UV laser radiation, and the aforementioned results can offer practical guidance for their application. Although $\alpha$-BBO is a centrosymmetric crystal and does not have even order nonlinear optical effects [80], it has odd order nonlinear optical effects, such as two-photon absorption (TPA). Hence, $\alpha$-BBO crystal not only can be used as a birefringent optical material (e.g., Glan prism, Rochon prism, and Wollaston prism, especially in the deep-UV waveband) but also is a key material for measuring deep-UV laser pulse based on TPA pump-probe experiment [28,88,89]. Since linear absorption and nonlinear TPA are both important loss mechanisms during the propagation of deep-UV laser radiation in these crystals, especially in a high-intensity regime, the investigation of absorption in the deep-UV spectral region presented here has important practical significance for understanding the generation, propagation, loss, and application of deep-UV beam in borate-family materials.
4. Conclusion
In summary, we have demonstrated high-intensity 263.2 and 210.5 nm picosecond deep-UV laser sources with peak powers of up to 2.13 GW and 1.38 GW, respectively, obtained by the high-efficiency FHG and FiHG of a Nd:YLF laser, which are 2-3 times and an order of magnitude higher than the previously reported results, respectively. The peak intensities of both the focused fourth and fifth harmonic beams exceed $10^{15}$ W/cm$^2$. The highest conversion efficiencies of 42.9% and 28.8% were achieved from the infrared laser to the fourth harmonic and fifth harmonic, respectively. To the best of our knowledge, these results represent the highest conversion efficiencies from infrared picosecond laser to two typical deep-UV wavebands of 263.2 and 210.5 nm and the highest peak powers of picosecond deep-UV laser radiations. Based on the generated deep-UV laser sources, we further completely characterized the deep-UV optical properties (including absolute transmittance, UV cut-off edge, band-gap energy, linear absorption, and nonlinear TPA) of $\alpha$-BBO, $\beta$-BBO, LBO, and CLBO crystals, which are the most comprehensive characterization and comparison of UV optical parameters of borate materials to date. Since the borate crystals and deep-UV lasers are widely used in both academic and technological fields, this work can provide crucial technical references for the generation of ultrahigh-intensity deep-UV and vacuum-UV laser radiations and extensive applications.
Funding
National Natural Science Foundation of China (12004404, 61975218); Shanghai Rising-Star Program (18YF1425900); Strategic Priority Research Program of Chinese Academy of Sciences (XDA25020202); Youth Innovation Promotion Association of the Chinese Academy of Sciences (2018282).
Acknowledgment
The authors wish to thank Prof. Weili Zhang and Dr. Hu Wang from Shanghai Institute of Optics and Fine Mechanics, CAS for the helpful discussion.
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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