Open Access
Add to BibSonomy
Abstract
High power continuous-wave (CW) single-frequency 1342 nm lasers are of interest for fundamental research, particularly, for laser cooling of lithium atoms. Using the popular Nd:YVO4 laser crystal requires careful heat management, because strong thermal effects in the gain medium are the most severe limitations of output power. Here, we present a multi-segmented Nd:YVO4 crystal design that consists of three segments with successive doping concentrations, optimized using a theoretical model. In order to quantify the optimization, we measured the thermal lens power of conventional crystal designs and compare them to our multi-segmented design. The optimized design displays a two times lower thermal lens dioptric power for the same amount of absorbed pump power in the non-lasing case. Using the optimized design, we demonstrate a high power all-solid-state laser emitting 10.0 W single-frequency radiation at 1342 nm when operating the laser crystal at room temperature. Further integration of the laser allows us to operate the laser crystal below room temperature for improving output power up to 11.4 W at 8°C. This is explained by the reduction of energy-transfer upconversion and excited-state absorption effects. Stable free-running operation at the low temperature of 8 °C is achieved with the power stability of $\pm$ 0.42 $\%$ by peak-to-peak fluctuation and frequency peak-to-peak fluctuation of $\pm$ 72 MHz in three hours.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
Corrections
28 October 2019: Typographical corrections were made to the article title and abstract.
1. Introduction
CW single-frequency all-solid-state lasers at 1342 nm have important applications in scientific research, such as quantum information [1] and medical treatment [2]. In particular, all-solid-state 1342 nm lasers can produce high output power to generate high power 671 nm lasers after frequency doubling [3], which are of great interest for quantum simulation, in particular for optical cooling and trapping of lithium [4], and other applications such as lithium atom interferometers [5] and lithium isotope separation [6]. In these applications, multi-Watt 671 nm output power is needed for running a system of multiple beams for slowing and trapping the atoms, where each beam typically requires Watt-class input. Even higher requirements come from sub-Doppler cooling schemes [7] and multi-photon Raman schemes in atom interferometry [8]. Therefore, it is of great interest to pursue power scaling 1342 nm single-frequency lasers.
Neodymium-doped yttrium vanadate (Nd:YVO$_4$) is a popular gain medium used for diode-pumped solid state lasers operating at the 1.3 $\mu m$ transition. It has strong emission lines at the desired wavelength of 1342 nm. However, the thermal and mechanical characteristics of Nd:YVO$_4$ are relatively poor compared to Nd:YAG [9]. Moreover, the Nd:YVO$_4$ lasers at 1342 nm suffer from more severe thermal effects than that at 1064 nm because of the large quantum defect and additional non-radiative transitions involved in the energy-transfer upconversion (ETU) and excited-state absorption (ESA) [10–12]. The strong thermal effects represent the most severe limitation for further output power scaling, and careful heat management in the crystal becomes mandatory.
Recently several high-power single-frequency Nd:YVO$_4$ lasers at 1342 nm have been demonstrated. F. A. Camargo et al. reported an 808-nm-pumped Nd:YVO$_4$ laser using an unidirectional ring cavity configuration [13]. The laser provided an optimal single-frequency power of 1.55 W. Y. H. Zheng et al. reported an 880 nm pumped ring laser with the maximum output power of 5.8 W. The cavity was designed for high-power operation with bistability-like phenomenon induced by thermal effects [14]. U. Eismann et al. reported a single-frequency power of 1.3 W at 1342 nm with an 808 nm pump ring laser [15]. Later, the same group demonstrated a 2.5 W 1342 nm laser with an improved 888-nm pump setup [16]. P. Koch et al. demonstrated an 888-nm-pumped, injection-locked Nd:YVO$_4$ amplifier producing 17.2 W of output power [17]. N. Kretzschmar et al. demonstrated an 888-nm-pumped 1342 nm laser that generated output power of 6.6 W. A convex meniscus mirror was used to compensate for thermal lensing [18].
More recently, Y. Y. Ma et al. reported a high-power laser at 1342 nm of 11.3 W [19]. An 880-nm double-end-pumped scheme was implemented with a six-mirror ring cavity. They used a LBO crystal to suppress multimode operation and obtained single longitudinal mode (SLM) output. However, the dual-end-pumped solution for splitting of the thermal load and the six-mirror cavity came at the cost of increased system complexity, and due to the intracavity nonlinear process, predictable wavelength tuning is hard to achieve. This limits the practical applicability of SHG light at 671 nm on the lithium D-line transitions in cold atom experiments.
The reduction of thermal effects remains a challenge, especially for single-frequency operation with a lower gain, larger cavity losses and stronger constraints on the cavity layout. The main thermal problem is the inhomogeneous thermal distribution induced by a conventional single-pass end-pumped crystal. That is the reason why the dual-end-pumped configuration is applied in many designs. Another approach which was reported recently is using multi-segmented crystals with increasing doping concentrations that can homogenize the longitudinal temperature and stress distributions, yielding to lower peak values for both [20–22]. Y. J. Huang et al. realized the concept of the multi-segmented Nd:YVO$_4$ for the first time [23]. Some lasers at 1342 nm with multi-segmented Nd:YVO$_4$ laser were reported in recent years [24,25]. The Nd:YVO$_4$ crystal with increasing doping concentrations could not only mitigate the risk of the thermal fracture inside the laser material, but also maintain a high optical conversion efficiency. Furthermore, this approach can be implemented conveniently into existing designs without modifying the overall configuration, which is important given the complex intracavity setups of single-frequency lasers.
In this work, we demonstrate a multi-segmented Nd:YVO$_4$ design optimized for high power CW single-frequency 1342 nm laser operation. The crystal consists of three parts with varying doping concentrations of 0$\%$ (undoped crystal), 0.4$\%$, and 1.1$\%$. A modified model which is a better approximate to practical conditions of pump light was developed for the multi-segment optimization. In order to quantify the thermal characteristics of the crystal, we perform a measurement to investigate the thermal lens under lasing and non-lasing conditions, comparing with two typical single-doped crystal designs. Then, applying this multi-segmented crystal, we present a high power all-solid-state laser emitting 10.0 W single-frequency radiation at 1342 nm at room temperature of 20 $^{\circ }C$. The laser is single-end-pumped by 888 nm and built up in a four-mirror bow-tie cavity. Furthermore, an integrated configuration is presented, which is beneficial for increasing the output power by mitigating ETU and ESA by cooling the crystal below room temperature, and for stabilizing low-temperature free-running operation. A maximum output power of 11.4 W is obtained with decreasing the crystal boundary temperature to 8 $^{\circ }C$, and at the low temperature we observe stable free-running operation with the power stability of $\pm$0.42$\%$ and frequency fluctuation of $\pm$72 MHz over three hours.
The article is organized as follows: In Section 2 we present the design and comparison of multi-segmented crystals. In Section 3, the design and integration of an all-solid-state laser based on the multi-segmented crystal is presented. In Section 4, we report the experimental results and discussions, and we conclude in Section 5.
2. Design and comparison of multi-segmented crystals
In the design of multi-segmented crystal, we optimized the doping concentration in each segment, according to an algorithm to search criteria for the optimization, reported in [21]. They found an efficient approach for optimization avoiding a large number of function evaluations. The optimization goal is to equalize the on-axis peak temperature between the segments, and to minimize the maximum temperature. Compared with other optimization criteria, this criterion shows a larger maximum absorption pump power with increasing the number of segments. According to the heat density distribution and the stationary heat conduction equation in [21], we can obtain the temperature distribution. Neglecting axial heat transfer, the z-dependent temperature distribution can be defined by the piecewise function
It is assumed that the beam is in Gaussian shape and does not vary in spot diameter with longitudinal coordinate in [24]. However, in practice the pump light is focused into the crystal, and has a top-hat profile in our setup. Variation of the beam radius is taken into account in our model. It can be described by the relation of the Gaussian beam waist,
where $w_{p0}$ is the beam waist radius of the pump light, $z_{0}$ is the position of the beam waist, and $w_p(z)$ is the beam radius of the pump light at the z position. Usually, the $M^2$ factor is large for the practical top-hat beams such as $M^2\sim 80$ via a 200 $\mu m$-diameter core fiber in our design. Thus, the temperature distribution $T(z)$ should relate to the beam radius as $T(z) \propto w^{-2}_p (z)$. Then, the Eq. (4) is modified to beAdditionally, we applied an undoped segment of 6 mm before the first doped segment, instead of a doped component for reducing thermal lens caused by the surface expansion. We combine the design of conventional composite crystal and the design of conventional multi-segmented crystals, in order to remove the large stress variation and the bulging of the end face, which is one of the major contributions of the thermal lens [26].
The multi-segmented crystal we designed is composed of a 6-mm-long undoped YVO$_4$ crystal, bonded to a 0.4$\%$ doping Nd:YVO$_4$ crystal with the length of 16 mm and followed by a 1.1$\%$ doping Nd:YVO$_4$ with the length of 8 mm. We compared our optimized crystal design with other two conventional single doped crystals. The data of three different crystal designs is shown in Table 1. All the cross sections of crystals are square with the side length of 4 mm. The Design 1, as reported in [27], is used with a 100 W pump setup, on the same order as the pump power applied in this work. We decided to use the same crystal length of 30 mm and the same total absorption efficiency of $\eta _{abs}$. It means that the length of doped segment $L=24$ mm and $\eta _{abs}=88 \%$. The Design 2 is also employed for single-frequency 1342 nm laser in a ring cavity as reported in [16].
Figure 1 shows the calculated longitudinal absorbed pump distribution for the three crystal designs at the same pump-light power. The absorbed pump distribution corresponds to the heat generation density distributions without considering the practical pump beam profile. It is obvious that the multi-segmented crystal has a more homogeneously pump distribution and lower peak values than the single-segmented crystals.
In order to evaluate the accuracy of the equivalent objective function, a 3D finite element method (FEM), based on solid heat transfer and mechanics, is employed to solve the temperature and the stress field, the parameters are referred in [28]. Figures 2(a) and 2(b) show separately the on-axis temperature distribution and the Von-Mises equivalent stress in the middle line on the side of surface of the three designs. The Von-Mises equivalent stress is calculated to describe the thermal stress with mechanical parameters reported in [29]. The maximum value of the stress in the multi-segmented crystal is lower than that in 0.5 at.% and 1 at.% crystal, and also below the fracture limit which has been reported in [30,31]. Correspond to our setup, the simulation assumes a top-hat profile pump and the same absorbed pump power of 70 W and the pump power longitudinal distribution we measured experimentally before are used. The FEM results show that the stress is dramatically reduced by employing the undoped composite, and the temperatures peak values of the two doped segments only differ by 1.9 K. The uniformity is better than that in the simpler calculation in Fig. 1, which shows that the optimization algorithm is improved with our modified model.
Fig. 2. Comparison of the three crystals simulations on-axis temperature (a) and VON-MISES equivalent stress on side surface (b).
In order to explore the thermal performance of our optimized multi-segmented crystal design, we investigated the thermal lens of different crystals by experiments. Thermal lensing is a result of crystal optical path shift, which follows a quadratic dependence in radius. It is caused by temperature gradients, stress and thermal induced end-face bulging. We measured the thermal lens dioptric power (inverse focal length) using a probe beam. It is similar to the method reported by [27,32,33]. Applying this method, the thermal lens with and without an active laser process can both be measured. However, this method is based on simple geometrical optics and not very easily applicable to end-pumped lasers. To improve on this method, we measure the divergence of the probe beam, based on Gaussian beam optics, which is similar to a method for measuring low absorption coefficients [34]. A fiber-coupled linearly polarized laser source at 1064 nm is used as probe source in our setup. The thermal lens at 1064 nm can be used to estimate for that at 1342nm, since the calculated values of the refractive index temperature derivatives at these two wavelengths are almost identical in undoped YVO$_4$ [35], which is the dominant parameter determining the value of thermal lens. The polarization of the probe laser radiation is linear and parallel to the c-axis of the laser crystal. Its wavelength can pass cavity mirrors with less attenuation because the mirrors are anti-reflection (AR) coated at 1064 nm to avoid laser operating at this wavelength. The beam waist is 500 $\mu m$ in the crystal. We measure the divergence angle by fitting the Gaussian beam profiles at multiple distances, using a beam profiler and a translation stage. Note that the probe laser is amplified when pumping. However, the induced error on the thermal lens influenced by the gain is ignored in our design compared with measurement errors.
The setup is presented in Fig. 3. The pump source is a fiber-coupled diode emitting up to 100 W at 888 nm. Special coating mirror $M_5$ is high reflection (HR) coated at 888 nm and AR coated at 1342 nm and 1064 nm. The pump light is focused into the crystal. The Nd:YVO$_4$ crystal is wrapped in indium foil and placed in a water-cooled copper mount. The crystal sits inside a four-mirror bow-tie cavity, which is resonant at 1342 nm as described in next section. A mechanical shutter is inserted into the cavity to control the laser action. Two optical filters (Filters 1 and Filters 2) are used to block the residual 888 nm light and 1342 nm light. The $M^2$ measurement system (Thorlabs Inc.) includes a beam profiler and a translation stage. Fully automated measurements and alignment accessories ensure the measurements process without off-axis and tilt. The system is not only applied for measuring $M^2$, but also can measure beam divergence and diameter. To ensure the accuracy of the measured far field divergence, the measurement is placed far away from the crystal. A large beam radius will be detected if the focal length is short. A lens with the focal length of 400 mm is chosen to decrease the beam size.
We investigated the probe beam divergence which changes with pump power due to the variation of the cavity mode by thermal lensing in the laser crystal. The position of the pump waist is at approx. 1/3 of the crystal length from the pump input surface. The waist of a Gaussian beam focusing by a thin lens is given by
where $w_0$ and $w_0^{'}$ are the beam waist radius of the Gaussian beam before and after a lens, respectively. And $l$ is the distance between the $w_0$ and the lens, $\lambda$ is the wavelength of the probe light, $F$ is the focal length of the thin lens. Considering the Gaussian beam, we get the relationship between divergence and beam waist radius where $\theta _0^{'}$ is the far field divergence of the Gaussian beam. Then we get the $l$ and $w_0$ in the measurement without pump power. As a result, $F$ is obtained by measurement of the $\theta _0^{'}$. Figure 4 shows the measured dioptric power of thermal lens as a function of the absorbed pump power without and with laser operation, respectively. The error bars only include measurement statistical errors, corresponding to a 95% confidence interval [36]. The slopes of fitted lines are 0.194, 0.278, 0.379 $m^{-1}/W$ in lasing case and 0.134, 0.200, 0.321 $m^{-1}/W$ in non-lasing case, respectively. It is shown that the dioptric power of thermal lens with our multi-segmented crystal is much smaller that of other two single doped crystals both for lasing and non-lasing case.Fig. 4. Thermal lens dioptric power of three crystals as a function of absorbed power with non-lasing and lasing.
3. The design and integration of an all-solid-state laser
The design and integration of an all-solid-state laser with our designed multi-segmented Nd:YVO$_4$ crystal is presented in Figs. 5(a) and 5(b). The pump source is a fiber-coupled diode (QPC BrightLase) emitting up to 100 W at 888 nm (NA = 0.22, 400 $\mu m$ fiber core diameter, spectral width (FWHM) of 2.1 nm). $M_5$ is HR coated at 888 nm and AR coated at 1342 nm and 1064 nm and $M_6$ is a broadband HR mirror (Thorlabs Inc). The cavity is built up in a four-mirror bow-tie ring configuration. The ring cavity avoids the spatial hole-burning in the laser crystal and eases single-frequency operation with intracavity etalons. The four mirrors ($M_1-M_4$) include two concave mirrors ($M_3$ and $M_4$) with radius of curvature of 100 mm, one flat mirror ($M_2$), and one convex meniscus mirror ($M_1$) with radius of curvature of $r_c=-$500 mm. It is designed to compensate the thermal lens to maintain the eigenmode of the cavity stable at a high pump power [14]. $M_2$ is the output coupler and has a theoretical optimum transmission. We have tested some mirrors with transmissions from 3$\%$ to 11$\%$, and among them the optimum value is found at around 9$\%$ [16]. The distance between $M_1$ and $M_2$ ($M_{1-2}$) is about 300 mm, $M_{3-4}$ is 100 mm and $M_{1-4}=M_{2-3}$ is about 210 mm. The free spectral range (FSR) of the laser cavity is about 350 MHz. A terbium gallium garnet (TGG) crystal is used as a Faraday rotator (FR), which enforces unidirectional operation in combination with a true zero-order half-wave plate (HWP). Moreover, to ensure the stable single-frequency behavior and to achieve wavelength tunability, two infrared fused silica intra-cavity etalons $E1$ and $E2$ are applied. The etalon $E1$ is of 500-$\mu m$ thickness and uncoated. The etalon $E2$ is of 4-mm thickness and coated R=28$\%$, placed in a temperature-stabilized copper mount. The flatness of etalons is high to avoid the wavefront distortion which increases the inserted loss. Further fine tuning of the laser frequency for the purpose of frequency-locking is achieved by mounting $M_3$ on piezoelectric transducers (PZTs), which include a slow PZT with a large stroke of around 12 $\mu m$ at maximum voltage of 150 V and a fast PZT with a high resonance frequency of around 300 kHz. These PZTs can adjust the length of the laser cavity and stabilize the output wavelength in a frequency-locking servo loop.
Fig. 5. The design of an all-solid-state laser with our designed multi-segmented Nd:YVO$_4$ crystal (a) and the integration laser system (b).
For laser-cooling applications, a practical and long-term stable laser system is required. Thus, we integrated the whole of the laser in an O-ring sealed aluminum box. A water-cooled base is used to control the overall temperature and a thermo electric cooler (TEC) is used to control the crystal temperature. The cooling base for TEC is made of copper and isolated from the cavity base for reducing the heat distortion. A wave meter (WM) and a scanning Fabry-Perot interferometer (FPI, Thorlabs SA200) are employed to monitor the laser frequency and longitudinal-mode behavior. The whole laser system can be frequency-locked to a reference via feedback control of the PZTs.
4. Experimental characterization and discussion
The characteristics of the laser include the output power, the longitudinal mode and the transverse mode, were investigated by a thermal power meter (PM), a scanning FPI and the $M^2$ measurement system, respectively. Figure 6 shows the output powers at 1342 nm as functions of the absorbed decreasing and increasing pump power at 888 nm. The maximum output power of 10.0 W was realized at room temperature of 20$^{\circ } C$ with the multi-segmented crystal, represented by red lines. Compared with the output power of 6.6 W reported in [18], we obtained a higher power in a similar configuration. The lasing threshold is high because of the thermal-lens-compensated cavity design [27]. The hysteresis behavior is observed in comparison of decreasing and increasing pump power as reported in [27,37]. The output power decreases for further increasing pump power above the lasing threshold, because a large thermal lens not only leads to a higher thermally induced diffraction loss, but also leads to a poorer mode overlap [38,39].
For improved stability and long-term operation, the laser is enclosed in a sealed housing. The housing maintains the setup in a dry air atmosphere, which allows for a new investigation of output power scaling. In a more recent investigation about influences of ETU and ESA effects at 1342 nm [12], it is shown that the output power is related to the temperature of the laser crystal. The output power can increase with lower crystal temperature, taking advantage of the temperature dependence of ETU and ESA. However, the lowest cooling temperature is limited by the dew point of the air inside the laser housing. When cooled to a temperature below the dew point, the water vapor will condense on the copper mount surface and on the crystal, harming the laser operation. The dry-air atmosphere in the integrated laser box can lower the dew point of the air. It allows us to investigate the output power with decreasing the crystal mount temperature. At the temperature of 8 $^{\circ } C$, we measure the output power with changing pump power, represented by blue lines in Fig. 6, and a new maximum power of 11.4 W is reached at a higher absorbed pump power of 76 W. The relationship between the output power and temperature is shown in Fig. 7. The maximum power increases with the decrease of the crystal temperature, the linear trend is in agreement with the description of the latest theoretical model as shown in [12]. But below the crystal temperature of 8 $^{\circ } C$, the linear trend is violated. The possible reason is that the fractional thermal load is decreased and a changing thermal lens reduces the mode overlap between pump and laser beam. The limit of our laser output power are thermal lens effects. With the increased pump power, a larger loss caused by the thermal lens does not allow further output power increasing.
The output power at 1342 nm and residual transmission of pump light at 888 nm are separated using a dichroic mirror. The pump light propagates through the mirror and is collected into a beam dump. The main part of the 1342 nm power is delivered to the power meter. A-small portion is separated into two parts using a HWP2 and a polarization beam splitter (PBS). One part is delivered to the FPI with a FSR of 1.5 GHz for monitoring the longitudinal-mode behavior. The measurement result is shown in Fig. 8(a). The achieved spectral width of 1342 nm is 12.8 MHz FWHM for a single sweep of FPI (instantaneous value). The other part is delivered to the $M^2$ measurement system for measuring the laser beam quality, result as shown in Fig. 8(b). The results reveal stable single-frequency operation and the diffraction-limited output beam with the propagation factor of $M_x^2=1.06$ and $M_y^2=1.07$ for both axes and the ellipticity of 0.88.
Fig. 8. (a) Transmission signal upon scanning the F-P interferometer with a free spectral range of 1.5 GHz. (b) $M^2$ measurement of the 1342 $nm$ laser.
The long-term free-running operating stability of the laser in three hours is shown in Figs. 9(a) and 9(b). The red lines in Fig. 9(a) and the blue lines in Fig. 9(b) represent measurement results with the crystal at room temperature of 20 $^{\circ } C$ and low temperature of 8 $^{\circ } C$, respectively. The measured free-running power stability of the laser was better than $\pm$0.39$\%$ and $\pm$0.42$\%$ by peak-to-peak fluctuation, and the frequency peak-to-peak fluctuation of the laser was less than $\pm$68 MHz and $\pm$72 MHz, respectively at room temperature and low temperature. The laser operation at low temperature shows a high stability similar as that at room temperature. We further successively lock the laser frequency to a Fabry-Perot optical reference cavity (Thorlabs SA200) using the Pound-Drever-Hall (PDH) method [40] with PZTs. We have demonstrated frequency-locking for more than 24 hours without mode hopping, which confirms the system can operate in every-day use in our laboratory.
Fig. 9. The long-term free-running stability of the power and frequency of the 1342 nm laser at room temperature of 20 $^{\circ } C$ (a) and at the low temperature of 8 $^{\circ } C$ (b).
5. Conclusion
In conclusion, we have presented the design and operation of a Nd:YVO$_4$ laser using a novel multi-segmented crystal design. The laser is operated in the CW single-frequency regime at 1342 nm. We have compared our crystal design to two common designs using FEM simulations and thermal lens measurements. Based on the crystal design, an integrated cavity configuration is realized, and powers of up to 11.4 W are achieved by lowering the crystal temperature below room temperature. According to our FEM model, a four- or five-segments crystal possibly can be used to obtain an even more homogeneously distributed thermal field, and thus higher output powers. Based on the integrated configuration, the power stability of the laser was better than $\pm$0.39$\%$ and $\pm$0.42$\%$ by peak-to-peak fluctuation, and the frequency peak-to-peak fluctuation of the laser was less than $\pm$68 MHz and $\pm$72 MHz, respectively at room temperature and low temperature during three hours. The achieved high-power stable output power can be used to generate high-power 671 nm light with efficient frequency doubling, sufficient for running an ultracold atoms experiment with lithium atoms.
Funding
National Natural Science Foundation of China (11425417, 11705191, 61625503); Natural Science Foundation of Shanghai (18ZR1443600); Natural Science Foundation of Anhui Province (1808085QF180); Chinese Academy of Sciences; National Fundamental Research Program.
References
1. M. R. Huo, J. L. Qin, Z. H. Yan, X. J. Jia, and K. C. Peng, “Generation of two types of nonclassical optical states using an optical parametric oscillator with a PPKTP crystal,” Appl. Phys. Lett. 109(22), 221101 (2016). [CrossRef]
2. M. Milanič and B. Majaron, “Energy deposition profile in human skin upon irradiation with a 1,342 nm Nd:YAP laser,” Lasers Surg. Med. 45(1), 8–14 (2013). [CrossRef]
3. X. Y. Cui, Q. Shen, M. C. Yan, C. Zeng, T. Yuan, W. Z. Zhang, X. C. Yao, C. Z. Peng, X. Jiang, Y. A. Chen, and J. W. Pan, “High-power 671 nm laser by second-harmonic generation with 93% efficiency in an external ring cavity,” Opt. Lett. 43(8), 1666–1669 (2018). [CrossRef]
4. X. C. Yao, H. Z. Chen, Y. P. Wu, X. P. Liu, X. Q. Wang, X. Jiang, Y. Deng, Y. A. Chen, and J. W. Pan, “Observation of coupled vortex lattices in a mass-imbalance Bose and Fermi superfluid mixture,” Phys. Rev. Lett. 117(14), 145301 (2016). [CrossRef]
5. R. Delhuille, C. Champenois, M. Büchner, L. Jozefowski, C. Rizzo, G. Trénec, and J. Vigué, “High-contrast Mach–Zehnder lithium-atom interferometer in the Bragg regime,” Appl. Phys. 74(6), 489–493 (2002). [CrossRef]
6. E. A. Symons, “Lithium Isotope Separation: A Review of Possible Techniques,” Sep. Sci. Technol. (Philadelphia, PA, U. S.) 20(9-10), 633–651 (1985). [CrossRef]
7. F. Sievers, N. Kretzschmar, D. R. Fernandes, D. Suchet, M. Rabinovic, S. Wu, C. V. Parker, L. Khaykovich, C. Salomon, and F. Chevy, “Simultaneous sub-doppler laser cooling of fermionic $^6Li$ and $^{40} K$ on the $D_1$ line: Theory and experiment,” Phys. Rev. A 91(2), 023426 (2015). [CrossRef]
8. H. Müller, S. W. Chiow, Q. Long, S. Herrmann, and S. Chu, “Atom interferometry with up to 24-photon-momentum-transfer beam splitters,” Phys. Rev. Lett. 100(18), 180405 (2008). [CrossRef]
9. L. McDonagh, R. Wallenstein, R. Knappe, and A. Nebel, “High-efficiency 60 W TEM$_{00}$ Nd:YVO$_4$ oscillator pumped at 888 nm,” Opt. Lett. 31(22), 3297–3299 (2006). [CrossRef]
10. Y. F. Chen, L. J. Lee, T. M. Huang, and C. L. Wang, “Study of high-power diode-end-pumped Nd:YVO$_4$ laser at 1.34 $\mu m$: Influence of Auger upconversion,” Opt. Commun. 163(4-6), 198–202 (1999). [CrossRef]
11. M. Okida, M. Itoh, T. Yatagai, H. Ogilvy, J. Piper, and T. Omatsu, “Heat generation in Nd doped vanadate crystals with 1.34 $\mu m$ laser action,” Opt. Express 13(13), 4909–4915 (2005). [CrossRef]
12. Y. Y. Ma, Y. J. Li, J. X. Feng, and K. S. Zhang, “Influence of energy-transfer upconversion and excited-state absorption on a high power Nd:YVO$_4$ laser at 1.34 $\mu$m,” Opt. Express 26(9), 12106–12120 (2018). [CrossRef]
13. F. A. Camargo, T. Zanon-Willette, T. Badr, N. U. Wetter, and J. J. Zondy, “Tunable single-frequency Nd:YVO$_4$ BiB$_3$O$_6$ ring laser at 671 nm,” IEEE J. Quantum Electron. 46(5), 804–809 (2010). [CrossRef]
14. Y. H. Zheng, Y. J. Wang, C. D. Xie, and K. C. Peng, “Single-frequency Nd:YVO$_4$ laser at 671 nm with high-output power of 2.8 W,” IEEE J. Quantum Electron. 48(1), 67–72 (2012). [CrossRef]
15. U. Eismann, F. Gerbier, C. Canalias, A. Zukauskas, G. Trénec, J. Vigué, F. Chevy, and C. Salomon, “An all-solid-state laser source at 671 nm for cold-atom experiments with lithium,” Appl. Phys. B: Lasers Opt. 106(1), 25–36 (2012). [CrossRef]
16. U. Eismann, A. Bergschneider, F. Sievers, N. Kretzschmar, C. Salomon, and F. Chevy, “2.1-watts intracavity-frequency-doubled all-solid-state light source at 671 nm for laser cooling of lithium,” Opt. Express 21(7), 9091–9102 (2013). [CrossRef]
17. P. Koch, F. Ruebel, J. Bartschke, and J. A. L’huillier, “5.7 W cw single-frequency laser at 671 nm by single-pass second harmonic generation of a 17.2 W injection-locked 1342 nm Nd:YVO$_4$ ring laser using periodically poled MgO:LiNbO$_3$,” Appl. Opt. 54(33), 9954–9959 (2015). [CrossRef]
18. N. Kretzschmar, U. Eismann, F. Sievers, F. Chevy, and C. Salomon, “2.4-watts second-harmonic generation in ppZnO: LN ridge waveguide for lithium laser cooling,” Opt. Express 25(13), 14840–14855 (2017). [CrossRef]
19. Y. Y. Ma, Y. J. Li, J. X. Feng, and K. S. Zhang, “High-power stable continuous-wave single-longitudinal-mode Nd:YVO$_4$ laser at 1342 nm,” Opt. Express 26(2), 1538–1546 (2018). [CrossRef]
20. D. Kracht, R. Wilhelm, M. Frede, K. Dupré, and L. Ackermann, “407 W end-pumped multi-segmented Nd:YAG laser,” Opt. Express 13(25), 10140–10144 (2005). [CrossRef]
21. R. Wilhelm, M. Frede, and D. Kracht, “Power scaling of end-pumped solid-state rod lasers by longitudinal dopant concentration gradients,” IEEE J. Quantum Electron. 44(3), 232–244 (2008). [CrossRef]
22. R. Wilhelm, D. Freiburg, M. Frede, and D. Kracht, “End-pumped Nd:YAG laser with a longitudinal hyperbolic dopant concentration profile,” Opt. Express 16(24), 20106–20116 (2008). [CrossRef]
23. Y. J. Huang and Y. F. Chen, “High-power diode-end-pumped laser with multi-segmented Nd-doped yttrium vanadate,” Opt. Express 21(13), 16063–16068 (2013). [CrossRef]
24. B. Li, X. Ding, B. Sun, Q. Sheng, J. Liu, Z. Wei, P. B. Jiang, C. Fan, H. Y. Zhang, and J. Q. Yao, “12.45 W wavelength-locked 878.6 nm laser diode in-band pumped multisegmented Nd:YVO$_4$ laser operating at 1342 nm,” Appl. Opt. 53(29), 6778–6781 (2014). [CrossRef]
25. A. M. Rodin, M. Grishin, and A. Michailovas, “Picosecond laser with 11 W output power at 1342 nm based on composite multiple doping level Nd:YVO$_4$ crystal,” Opt. Laser Technol. 76, 46–52 (2016). [CrossRef]
26. A. K. Cousins, “Temperature and thermal stress scaling in finite-length end-pumped laser rods,” IEEE J. Quantum Electron. 28(4), 1057–1069 (1992). [CrossRef]
27. F. Lenhardt, M. Nittmann, T. Bauer, J. Bartschke, and J. A. L’huillier, “High-power 888-nm-pumped Nd:YVO$_4$ 1342-nm oscillator operating in the TEM$_{00}$ mode,” Appl. Phys. B: Lasers Opt. 96(4), 803–807 (2009). [CrossRef]
28. N. Kretzschmar, “Experiments with ultracold fermi gases: quantum degeneracy of potassium-40 and all-solid-state laser sources for lithium,” Ph.D. thesis, Ecole Normale Supérieure-ENS PARIS (2015).
29. X. Y. Peng, A. Asundi, Y. H. Chen, and Z. J. Xiong, “Study of the mechanical properties of nd: Yvo 4 crystal by use of laser interferometry and finite-element analysis,” Appl. Opt. 40(9), 1396–1403 (2001). [CrossRef]
30. A. Sugiyama and Y. Nara, “Improved direct bonding method of Nd:YVO$_4$ and YVO$_4$ laser crystals,” Ceram. Int. 31(8), 1085–1090 (2005). [CrossRef]
31. R. Wilhelm, D. Freiburg, M. Frede, D. Kracht, and C. Fallnich, “Design and comparison of composite rod crystals for power scaling of diode end-pumped Nd:YAG lasers,” Opt. Express 17(10), 8229–8236 (2009). [CrossRef]
32. D. S. Sumida, D. A. Rockwell, and M. S. Mangir, “Energy storage and heating measurements in flashlamp-pumped Cr:Nd:GSGG and Nd:YAG,” IEEE J. Quantum Electron. 24(6), 985–994 (1988). [CrossRef]
33. P. J. Hardman, W. A. Clarkson, G. J. Friel, M. Pollnau, and D. C. Hanna, “Energy-transfer upconversion and thermal lensing in high-power end-pumped Nd:YLF laser crystals,” IEEE J. Quantum Electron. 35(4), 647–655 (1999). [CrossRef]
34. C. Hu and J. R. Whinnery, “New thermooptical measurement method and a comparison with other methods,” Appl. Opt. 12(1), 72–79 (1973). [CrossRef]
35. H. S. Shi, G. Zhang, and H. Y. Shen, “Measurement of principal refractive indices and the thermal refractive index coefficients of yttrium vanadate,” J. Synth. Cryst. 30, 85–88 (2001).
36. M. Krzywinski and N. Altman, “Points of significance: error bars,” Nat. Methods 10(10), 921–922 (2013). [CrossRef]
37. Q. W. Yin, H. D. Lu, J. Su, and K. C. Peng, “High power single-frequency and frequency-doubled laser with active compensation for the thermal lens effect of terbium gallium garnet crystal,” Opt. Lett. 41(9), 2033–2036 (2016). [CrossRef]
38. U. Eismann, “A novel all-solid-state laser source for lithium atoms and three-body recombination in the unitary bose gas,” Ph.D. thesis (2012).
39. Y. F. Chen, C. F. Kao, T. M. Huang, C. L. Wang, and S. C. Wang, “Influence of thermal effect on output power optimization in fiber-coupled laser-diode end-pumped lasers,” IEEE J. Sel. Top. Quantum Electron. 3(1), 29–34 (1997). [CrossRef]
40. E. D. Black, “An introduction to Pound–Drever–Hall laser frequency stabilization,” Am. J. Phys. 69(1), 79–87 (2001). [CrossRef]
