Efficient Direct Laser Generation by Three‐Phonon‐Assisted Transition with Yb:YCOB Crystal

Electron–phonon‐coupling effect can generate the direct lasing beyond the fluorescence spectrum of the gain medium, but the laser efficiency is still low owing to weak multiphonon‐coupling intensity. Herein, associated with the three‐phonon‐assisted electron transitions beyond 1100 nm, the tunable laser generation from 1125 to 1155 nm and highly efficient continuous‐wave lasers at 1131 and 1140 nm in a ytterbium‐doped YCa4O(BO3)3 crystal are realized, by balancing the intracavity loss and phonon‐determined gain. The maximum output power reaches to 3.95 and 2.06 W at 1131 and 1140 nm, corresponding to a slope efficiency of 52.4% and 39.1%, respectively, which represents the highest efficiency in the solid‐state lasers in this spectral range. More impressively, this phonon‐assisted vibronic laser exhibits a wide‐spectral tunability and a good output power stability. Herein, a practical laser source in the underdeveloped spectral range is provided by the results, and they are helpful for the development of multiphonon‐assisted lasers beyond the inherent fluorescence spectrum.


Introduction
Laser wavelength is an important parameter for the laser applications, and it is usually determined by the electronic transition among the inherent Stark levels of active ions. [1][2][3] Generally, the Stark splitting values of electronic levels depend on the crystal field intensity, as well as the microscopic symmetry of active doped ions and surrounding lattices. When lattice vibrations are involved, electron-phonon-coupling effect can homogeneously broaden the emission spectrum and greatly extend the laser wavelengths around fluorescence sidebands, even beyond. [4,5] Recently, we have demonstrated the direct lasing far beyond the fluorescence spectrum in ytterbium-doped YCa 4 O(BO 3 ) 3 (Yb:YCOB) crystal. [6] This strategy provides a novel route to search light in the darkness and paves new routes for the laser generation at those spectral gap without suitable active ions.
Compact tunable solid-state lasers beyond 1100 nm are in urgent demand but underdeveloped, because there are a few active rare-earth and transition-metal ions (Cr:forsterite and Ti:sapphire) with strong spontaneous emission at this spectral range. [7][8][9] For example, 1150 nm laser is an important pump source for Ho 3þ ion ( 5 I 8 ! 5 I 6 transition) to obtain 2 μm laser. [10] Also, 1100-1160 nm lasers can be easily converted to yellow-orange laser (550-580 nm) by frequency-doubling technique, thus holding important retinal repair applications in ophthalmic surgery. [11] Benefitting from the large crystal field splitting, some Nd 3þ -doped garnet crystals (Nd:YAG, Nd:LuAG) have a moderate emission cross section at this range (σ em % 10 À21 cm 2 ) due to the fluorescence branches of 4 F 3/2 ! 4 I 11/2 transition, and several 1112/1123 nm generation pumped by a laser diode (LD) have been reported with slope efficiency around 40%. [12,13] Longer wavelengths were also available in the sesquioxide materials with enhanced crystal field splitting, for example, an 1130.3 nm laser in Nd:Y 2 O 3 ceramic with a slope efficiency of 23%. [14] However, for a given Nd 3þ crystal, its laser spectrum has a poor tunability and only contains a few discrete wavelengths, thereby limiting their practical applications. Therefore, it is a great challenge to obtain direct lasing beyond 1100 nm with high efficiency and tunable capacity simultaneously.
Compared to Nd 3þ ions, Yb 3þ -doped crystals have a smaller quantum defect and higher laser efficiency when operating at the same lasing wavelength. In addition, Yb 3þ ion also allows tunable laser generation due to strong electron-phonon-coupling effect and large homogeneously spectral broadening. Unluckily, for most Yb 3þ lasers with 2 F 5/2 ! 2 F 7/2 transition, their crystal filed splitting is insufficiently large and the laser emission wavelengths fall in the range of 1020-1085 nm. [15] To date, only a few lasers beyond 1100 nm were reported using a birefringent filter, but their laser efficiencies were very low (<6%) due to the lowgain emission. [16,17] Therefore, Yb 3þ ions were not considered as a good candidate for lasing beyond 1100 nm in past years. Nevertheless, this limitation was broken by our proposed phonon-assisted strategy, and a milliwatt-level tunable laser output beyond 1100 nm was realized in Yb:YCOB crystal. [6] The electron-phonon-coupling process was studied from which the creation of phonons can extract energy from electronic transitions and push lasing into the long wavelength. However, associated with the solid-state theory of electron-phonon-coupling process, the electronic transition dipole moment decreases with DOI: 10.1002/adpr.202300092 Electron-phonon-coupling effect can generate the direct lasing beyond the fluorescence spectrum of the gain medium, but the laser efficiency is still low owing to weak multiphonon-coupling intensity. Herein, associated with the three-phonon-assisted electron transitions beyond 1100 nm, the tunable laser generation from 1125 to 1155 nm and highly efficient continuous-wave lasers at 1131 and 1140 nm in a ytterbium-doped YCa 4 O(BO 3 ) 3 crystal are realized, by balancing the intracavity loss and phonon-determined gain. The maximum output power reaches to 3.95 and 2.06 W at 1131 and 1140 nm, corresponding to a slope efficiency of 52.4% and 39.1%, respectively, which represents the highest efficiency in the solid-state lasers in this spectral range. More impressively, this phonon-assisted vibronic laser exhibits a wide-spectral tunability and a good output power stability. Herein, a practical laser source in the underdeveloped spectral range is provided by the results, and they are helpful for the development of multiphonon-assisted lasers beyond the inherent fluorescence spectrum.
the number of phonons involved, and a high lasing efficiency beyond the fluorescence spectrum still remains quite difficult in solid-state laser materials.
In this work, by balancing the intracavity loss and phonon-determined gain, we amplify the multiphonon-coupling intensity and realize the efficient continuous-wave (CW) laser performances in Yb:YCOB crystal. The maximum output power reaches to 3.95 W at 1131 nm, corresponding to a high slope efficiency of 52.4%. Such a high efficiency not only represents the largest one among all vibronic Yb 3þ crystals at 1131 nm, but also surpasses most of Nd 3þ crystals with inherent electronic transitions. Meanwhile, a watt-level tunable laser generation was first obtained, indicating its great potentials in some practical applications, for example, pump source, spectroscopy, sensors, etc.

Results and Discussion
The measured fluorescence spectrum and calculated emission cross section of Yb:YCOB crystal are shown in Figure 1. From this figure, it can be found that Yb:YCOB has four strong emission peaks at 976, 1020, 1026, and 1082 nm, respectively, corresponding to four Stark splitting of 2 F 7/2 level owing to the crystal field effect. The zero-phonon line at 976 nm is the highest one, indicating that the reabsorption effect has been suppressed as much as possible. The longest zero-phonon transition locates at 1082 nm and the longer wavelength fluorescence can be attributed to the phonon-assisted vibronic transitions. The dominated phonon modes in this coupling process were verified to the cooperative vibrations of "free-oxygen" motif. [6,18] It is clear that the gain cross section of Yb:YCOB at around 1131 nm is only 0.34 Â 10 À21 cm 2 , which is 1/7 times of 1082 nm (2.03 Â 10 À21 cm 2 ), and 1/20 times of that at 1026 nm (7.2 Â 10 À21 cm 2 ). Therefore, to make it lasing around 1130 nm, the conventional lasers at 1020, 1026, and 1082 nm must be suppressed.
Luckily, this condition can be satisfied by a rational cavity parameter design. Based on the laser theory, the lasing thresholds (P th, i ) of each transition should be represented as Equation (1) [19] whereR i is reflectivity of the mirror for each transition, L i represents the round trip loss of each transition, l represents the length for the laser crystal, σ i represents the emission cross section of each oscillating mode, τ i is the upper laser level lifetime, hv p represents the pump photon energy, η i is the quantum efficiency of each oscillating mode, s i ðr, zÞ is the normalized cavity mode strength distribution of the each oscillating mode, and r i ðr, zÞ is the normalized pump intensity distribution in the laser cavity. In our calculations, i = 1 represents a 1130 nm mode, and i = 2, 3 are 1026 and 1082 nm mode, respectively. The s i , r i , L i , and τ i can be considered equal for i = 1, 2, 3, in a same resonant cavity. Considering the arguments of Yb:YCOB crystal and laser cavity, it was discovered that the transmission ratio of the output mirror should be less than 0.167 at 1130 and 1082 nm. Furthermore, this ratio should be less than 0.047 at 1130 and 1026 nm. Figure 2a illustrates the schematic illustration of a vibronic laser beyond 1.1 μm in Yb:YCOB crystal. The size of the sample of Y-cut Yb:YCOB crystal is 3 Â 3 Â 6 mm, with the doping concentration of 15 at%. We measured that the absorption ratio of crystal is about 87% for the single-pass configuration. The two front/end faces were polished. A plano-concave resonator is compactly used in the experiment. The front face of the crystal was coated: high transmission (HT, T > 95%) at 976-1100 nm and high reflection (HR, R > 99.9%) at 1120-1200 nm to serve as the input mirror. A concave mirror M2, as the output coupler, has the curvature radius of 100 mm and a certain transmittance (T oc = 0.1%, 1%, 3%) in the range of 1120-1200 nm. For the purpose of suppressing the high-gain oscillations at short wavelengths, M2 is also high transmittance at 1000-1100 nm. The transmittance at 1026 and 1082 nm is about 80%. Therefore, the transmission ratio of the output coupler M2 at 1130 nm and 1026/1082 nm locates at 0.001%0.04, which is less than 0.047/0.16. The coating transmission of output couplers are plotted in Figure S1, Supporting Information. The crystal sample was placed in a copper radiator and cooled down with a thermoelectric cooler. Indium foil-wrapped crystal samples were placed in a copper block and cooled down at 20°C with circulating water. A filter mirror with HT at 1100-1200 nm and HR at 976 nm is used to filter out the residual pump laser power. A 30 W fibercoupled diode laser emitting at 976 nm was used as the pump source, with a fiber-core diameter of 105 μm and a numerical aperture of 0.22.
We first investigated the thermal lens effect and its influence on the performances of Yb:YCOB laser. As we know, the increase of temperature is conducive to the enhancement of electron-phonon coupling, but at the same time, thermally induced losses caused by high-temperature should be avoided as much as possible. Both two aspects need to be balanced. The thermal lens focal length of Yb:YCOB crystal under 1130 nm laser operation was measured by using a parallel plane resonator. At the pump power of 10 W, the focal length of the thermal lens is about 12 mm. Considering the thermal lens effect  in the crystal, the laser spot size in the crystal can be adjusted by changing the cavity length in the experiment to achieve an optimal mode matching. Finally, the M1-M2 cavity length is 102-103 mm and the laser spot radius in the crystal is 47 μm. Then, we obtained a CW laser generation around 1130 nm. As depicted in Figure 2b, for T oc = 0.1%, the lasing threshold is 1.62 W. The maximum output power reaches to 266 mW with a slope efficiency of 5.5%, which is consistent with our previous report. [6] When T oc becomes 1% and 3%, the lasing threshold increases to 2.63 and 3.89 W. And the maximum output power improves to 1.68 and 3.95 W, corresponding to a high slope efficiency of 34.1% and 52.4%, respectively. This slope efficiency at fluorescence sidebands even surpasses some non-vibronic Nd 3þ -doped laser at 1123 nm, [20,21] indicating the great potential of vibronic lasers despite its low-gain emission. Figure 2c displays the laser spectrum under various output couplers. Notably, we can only obtain an efficient lasing under T oc = 0.1%, 1%, and 3%. If T oc = 5%, we did not obtain lasing around 1130 nm. It is easy to see from Equation (1) that when T oc = 5% at 1130 nm, the transmission ratio of the output coupler M2 at 1130 and 1026 nm is about 0.05, which is greater than the theoretical transmittance ratio 0.047. Therefore, the transmittance of the output coupler at 3% should be an optimal setup for 1131 nm laser in Yb:YCOB crystal.
Moreover, benefitting from the electronic broadening and phonon dispersion of Yb:YCOB crystal, this vibronic laser exhibits a good laser tunable capacity in this range. In tunable laser experiment, a birefringent MgF 2 filter (d = 1 mm) is inserted into  the resonant cavity along Brewster's angle and placed close to the crystal (dashed box in Figure 2a). As shown in Figure 2d, when T oc is 3%, the laser wavelength can be tuned from 1127 to 1141 nm. The maximum output power is 1.53 W at 1131 nm. With the decreased output coupler transmittance, the laser power gradually decreases and the laser tunable range becomes extended. For T oc = 1% (T oc = 0.1%), laser wavelength can be tuned from 1126.5 to 1150 nm (1125-1155 nm), respectively. The tunable laser spectra with various couplers were plotted in Figure S2, Supporting Information. This feature is better than those Nd lasers with only several discrete wavelengths (1112 or 1123 nm), [22,23] which could support some wavelength-dependent spectroscopic applications in modern photonics, for example, the tunable pump and excitation sources. Figure 3a illustrates the beam quality factor of 1131 nm laser measured by a knife-edge method. Under an output power of 3 W, this laser maintains high beam quality with M x 2 = 1.50 and M y 2 = 2.20, respectively. The asymmetric M 2 values for x and y directions can be attributed to possible thermal effects. These values are comparable to conventional Yb:YCOB lasers, for example, 1035 nm with M 2 = 1.21, [24] and 1083 nm with M 2 = 1.83. [25] The inset graph shows the 2D beam intensity profile, which has a near-Gaussian spatial pattern. The power stability of the 1131 nm laser was recorded in 30 min. As shown in  www.advancedsciencenews.com www.adpr-journal.com Figure 3b, it can be seen that the standard deviation of power fluctuation is less than 2%, indicating it good power stability. In addition, this phonon-assisted vibronic laser exhibited a wavelength-shift capacity by changing the transmittance of the output coupler. The input mirror coated on crystal remained unchanged, and the transmittance of the output mirror was changed to T oc = 8% at 1130 nm and T oc = 2.5% at 1140 nm, simultaneously. From Figure 1, it can be seen that the gain cross section of Yb:YCOB around 1140 nm is only 0.22 Â 10 À21 cm 2 . So, the transmission ratio of the output mirror should be less than 0.65 at 1140 and 1130 nm. In our setup, the transmittance ratio is 0.31, which is less than 0.65. With this new output coupler, we obtained a watt-level CW laser generation at 1140 nm. As shown in Figure 4a, the lasing threshold is 4.01 W. The maximum output power reaches to 2.06 W with a slope efficiency of 39.1%. Figure 4b displays the laser spectrum around 1140 nm. If combining frequency-doubling technology, we can obtain a watt-level 570 nm yellow laser, which is very useful in retinal repair surgery.
Finally, we made a comprehensive comparison among CW solid-state lasers beyond 1.1 μm. As listed in Table 1, there were some direct lasers beyond 1.1 μm realized in Nd 3þ -garnet and sesquioxide crystals. Most of laser results pumped by 808 nm LD show a limited slope efficiency below 50% due to large quantum defect. The best result of laser operation at 1112 nm was achieved in Nd:YAG crystal pumped by an 885 nm LD, with laser output power of 12.8 W and a slope efficiency of 64%. [12] In addition, a Nd:Lu 2 O 3 laser at 1103 nm pumped by Ti:sapphire laser exhibits a high efficiency of 63.4%. [26] Our reported laser efficiency is comparable to these two best results, but with longer laser wavelength at 1131 nm. There was also a Nd:Y 2 O 3 laser at 1130.3 nm with a slope efficiency of 23%, [14] which is lower than our Yb:YCOB laser. Therefore, this vibronic laser at fluorescence sidebands could be equally efficient, rather better, with respect to those non-vibronic lasers.
Moreover, some tunable lasers beyond 1.1 μm have been achieved in Yb 3þ -doped crystals by inserting a birefringent filter, but all of them suffer from a low laser power and efficiency. At present, the maximum output power was 2 W at 1116 nm in a thin-disk Yb:Lu 2 O 3 laser. [16] As summarized in Figure 5, Yb:YCOB vibronic laser at 1131 nm is the longest laser wavelength among all vibronic Yb lasers with a high lasing efficiency more than 50%. The output power at 1131 nm is about two-order magnitude higher than that of the well-known Yb-doped crystals. [27,28] More importantly, this laser has a good tunable capacity in this range. Therefore, this work represents a significant step forward for solid-state vibronic lasers and we believe that there are great opportunities in this research field.

Conclusion
In conclusion, we realized a highly efficient watt-level laser beyond 1100 nm in Yb:YCOB crystal. The maximum output power at 1131 nm is 3.95 W and the slope efficiency increases to 52.4%. Our experimental results show that the laser efficiency at fluorescence sidebands can be also comparable to those conventional lasing at strong fluorescence peaks in Yb 3þ -doped crystals. By optimizing the coating conditions of cavity mirrors, we also realized the wide tunable laser wavelengths in 1125-1155 nm. Such a tunable laser source would be a promising pump source candidate for Ho 3þ lasers and nonlinear optical conversion technique in the future. More impressively, this multiphonon-coupling strategy can be easily applicable in other laser systems (such as Pr 3þ -, Tm 3þ -, Dy 3þ -, Er 3þ -doped crystals), thus giving great opportunities to fill the inactive spectral "gap" in the visible and near-/mid-infrared regime.

Experimental Section
Fluorescence Spectrum Measurement: The fluorescence spectrum of Yb:YCOB crystal was collected by an Edinburgh fluorescence spectrometer. A 940 nm LD was used as a pump source. The wavelength step was 0.5 nm and the dwell time was 0.02 s. The excitation and emission collection-grating function were set to be 8 and 1. Every spectral line of Yb:YCOB crystal was collected with five repeats.

Laser Experimental Setup:
The size of the sample of Y-cut Yb:YCOB crystal was 3 Â 3 Â 6 mm, with the doping concentration of 15 at%. The two front/end faces were polished. A plano-concave resonator compactly was used in the experiment. The front face of the crystal was coated: HT (T > 95%) at 976-1100 nm and HR (R > 99.9%) at 1120-1200 nm to serve as the input mirror. A concave mirror M2, as the output coupler, had the curvature radius of 100 mm and a certain transmittance (T oc = 0.1%, 1%, 3%) in the range of 1120-1200 nm. For purpose of suppressing the high-gain oscillations at short wavelengths, M2 was also high transmittance at 1000-1100 nm. The transmittance at 1026 and 1082 nm was about 99%. The crystal sample was placed in a copper radiator and cooled down with a thermoelectric cooler. Indium foil-wrapped crystal samples were placed in a copper block and cooled down at 20°C with circulating water. The birefringent MgF 2 filter (d = 1 mm) was inserted into the resonant cavity along Brewster's angle and placed close to the crystal. A 30 W fiber-coupled diode laser emitting at 976 nm was used as the pump source, with a fiber-core diameter of 105 μm and a numerical aperture of 0.22. The laser output power was measured by a power meter (Newport, Model 1916-R), and the laser spectrum was recorded by a spectrometer (A.P.E. WaveScan, S/N S09668).

Supporting Information
Supporting Information is available from the Wiley Online Library or from the author.