Non-centrosymmetric borate crystals, with absorption edges larger than 6.2 eV ($<200\mathrm{nm}$), such as ${\mathrm{LiB}}_3{\mathrm{O}}_5$ (LBO) and $\beta$-${\mathrm{BaB}}_2{\mathrm{O}}_4$ (BBO), are popular nonlinear optical crystals to generate and manipulate ultraviolet light [1]. Lithium tetraborate (${\mathrm{Li}}_2{\mathrm{B}}_4{\mathrm{O}}_7$, LB4), a member of the borate family, has an exceptionally high absorption edge at 7.56 eV (160 nm) [2]. This makes LB4 a promising nonlinear optical material for harmonics generation [3] from the visible regime into the deep ultraviolet regime [2]. On the other end of the spectrum its transparency ranges up to 3.5 μm [4,5], which surpasses the infrared (IR) transparency of ${\mathrm{KH}}_2{\mathrm{PO}}_4$ (KDP, 1.4 μm), BBO (2.6 μm), and LBO (3.2 μm) [6]. Especially in the range below 600 nm, the absorption coefficient remains consistently below $0.3{\mathrm{m}}^{-1}$ [7], which corresponds to an absorption limited intrinsic quality ($Q$) factor of above ${10}^8$ in a resonator made of this material [8] and is therefore important for efficient nonlinear conversion in it. Additionally, this low absorption can help mitigate thermal effects in the crystal. On top of that, among the borate crystals [3], LB4 has the highest laser damage threshold of $40{\mathrm{GW}/\mathrm{cm}}^2$ and the lowest hygroscopicity.

LB4 is a negative uniaxial crystal and belongs to tetragonal nonsymmorphic space group $C_{4v}^{12}$, with $a=b=9.479\mathrm{\AA }$ and $c=10.286\mathrm{\AA }$ of the unit cell [9,10]. Larger boules of LB4 crystal up to 10 cm in diameter with high quality and good refractive index homogeneity have been grown by the modified Bridgman technique [11,12]. The second-order nonlinear coefficients $d_{31}$ and $d_{33}$ are $0.5\mathrm{pm}/\mathrm{V}$ and 3 pm/V [13,14], respectively, comparable to those of other borate crystals and about one tenth of those of lithium niobate (LN) [6]. Because it belongs to point group 4 mm, other non-zero nonlinear coefficients are $d_{32}=d_{15}=d_{24}=d_{31}$ under Kleinman’s symmetry conditions [15]. Moreover, the Pockels electro-optic coefficients have been thoroughly investigated [15–17], where $r_{13}=r_{23}=4.03\mathrm{pm}/\mathrm{V}$, $r_{33}=3.96\mathrm{pm}/\mathrm{V}$, and $r_{42}=r_{51}=-0.11\mathrm{pm}/\mathrm{V}$. Some optic-related material parameters of crystalline LB4 are summarized in Table 1, and more detailed physical properties can be found in Refs. [6,18].Table 1.

Some Optic-Related Material Parameters of Lithium Tetraborate

These properties make LB4 an interesting base material for high-$Q$ monolithic optical resonators, such as whispering gallery mode (WGM) resonators. Surprisingly the paper by Fürst et al. [23] has been the only work reporting on an LB4 WGM resonator and using it for second harmonic generation (SHG) of ultraviolet light. They demonstrated an intrinsic $Q$ factor in the visible (pump) regime of $2\times {10}^8$. In this work, we demonstrate a one order of magnitude improvement over the previous result reaching an intrinsic $Q$ factor of $2\times {10}^9$ in the visible regime.

Crystalline WGM resonators crafted from low-loss crystalline materials exhibit exceptional light confinement near the surface through total internal reflection (TIR) [24–26]. This unique property allows for remarkably high $Q$ factors and compact mode volumes [27] spanning the whole transparency range of the used material (since TIR is broadband). Such properties make them a versatile platform for a wide range of applications in nonlinear optics and quantum optics [8,28]. In particular, the wide spanning resonance spectrum enables efficient all-resonant nonlinear conversion processes such as parametric down conversion [29], SHG [23], or, very prominently, frequency comb generation [30], to name only a few. At telecom band, crystalline WGM resonators have been well developed with $Q$ factors on the order of ${10}^9$ to ${10}^{11}$ [26,31]. However, works in the visible regime [29,32–37] have so far only reached $Q$ factors on the order of ${10}^7$ to ${10}^8$. To the best of our knowledge, there is no work on crystalline WGM resonators in the visible regime with $Q$ over $1\times {10}^9$, particularly not for materials that show ${\chi }^{(2)}$ nonlinearity.

Another interesting application for WGM resonators is low-threshold Raman lasing or stimulated Raman scattering (SRS) [38,39]. SRS, a third-order nonlinear process in which photons interact with vibrating molecules or the lattice structure of materials, results in the photons being shifted to a frequency that is offset from its original frequency by the vibrational frequency it scatters from. Since SRS was discovered in 1962 by Woodbury et al. [40,41] who realized that the extra line in their Ruby laser was from the vibration frequency of the ${\mathrm{NO}}_2$ group in liquid nitrobenzene, SRS has been applied widely in the fields of chemical spectroscopy and medical bio-molecular imaging [42] because of its sensitivity to molecular vibrations. SRS is also used widely in laser applications, not only as a frequency shifter to extend existing lasers [43–46] but also in cascaded Raman lasers [38,47,48]. A WGM Raman laser can be directly made out of any Raman-active material such as silica [44,45,47] and silicon [48] and crystalline materials like calcium fluorite (${\mathrm{CaF}}_2$) [38,46,49,50], lithium niobate [39,51], and here LB4, without the need of another cavity. LB4 has four kinds of Raman-active lattice vibrational modes based on the ${\mathrm{BO}}_3$ and ${\mathrm{BO}}_4$ groups, namely, $18{\mathrm{A}}_1+19{\mathrm{B}}_1+19{\mathrm{B}}_2+39\mathrm{E}$ [52–56], where the two strongest branches manifest at $720{\mathrm{cm}}^{-1}$ and $160{\mathrm{cm}}^{-1}$, respectively. The Raman spectra of our LB4 samples are measured using the WITec Alpha300R confocal Raman microscope at the excitation of 532 nm, and they also show two consistently strongest peaks. The one ($720{\mathrm{cm}}^{-1}$) is provided by the planar ${\mathrm{BO}}_3$ triangle groups’ ${\mathrm{A}}_1$ normal mode, and has a linewidth between 8 and $10{\mathrm{cm}}^{-1}$ [18,57], while the other ($160{\mathrm{cm}}^{-1}$) is also probably related to ${\mathrm{A}}_1$ mode but difficult to be assigned accurately [53,54]. Moreover, the Raman gain of LB4 is about 1.8 cm/GW, about two orders of magnitude larger than that of silica [58], which can decrease the SRS threshold [44,59] and motivates us to explore the Raman lasing in LB4 WGM resonators.

In this article, we report the fabrication of a millimeter sized LB4 WGM resonator, which has, to the best of our knowledge, the highest reported $Q$ factor ($2\times {10}^9$ at 517 nm) in LB4. Then we report on the first cascaded SRS in the LB4 WGM resonator under a pump of 517 nm.

We fabricated our LB4 resonator from an 800-μm-thick (001)-orientated LB4 wafer grown by our collaborators, Petra Becker and Ladislav Bohatý, in Institute of Geology and Mineralogy, Section Crystallography [18]. For fabrication we follow a now well established process for crystalline WGM resonators (for a detailed description see, for example, Ref. [60] or [61]): a precursor disc is first drilled out of the wafer using a hollow brass drill and water-based 30 μm diamond slurry. Subsequently, the disc was glued on a brass rod with hot wax and subsequently precisely shaped using single-point diamond turning [61]. We tested different rake angles from $-45°$ to $-20°$ and found that $-35°$ yields the best surface quality after cutting. At this angle the cutting surface remained still rough with numerous cracks probably due to easy crack propagation on (100) and (010) planes of LB4 [62]. Following the cutting process, the preliminary resonator underwent meticulous manual polishing using diamond slurry with decreasing grain sizes from 30 μm to 0.25 μm until no scratches or other defects were observable under a microscope. The resulting LB4 WGM resonator, as depicted in the inset of Fig. 1, with azimuthal radius $R=2.97\mathrm{mm}\pm 0.01\mathrm{mm}$ and polar radius $r=2.30\mathrm{mm}\pm 0.01\mathrm{mm}$, was cleaned and put in the experimental setup.

Our setup to characterize the linear properties of the resonator and the Raman lasing is sketched in Fig. 1. To stabilize the optical spectrum, the WGM resonator is placed on a temperature controller. A green laser at 517 nm (EYLSA, Quantel), generated using the third harmonic of a telecom seed laser, is directed via optical fibers to a polarization controller (PC). Evanescent coupling into the LB4 resonator is achieved by focusing the laser through a gradient-index (GRIN) lens onto the inner surface of a diamond isosceles triangle prism under an angle of total internal reflection. The prism sits on a piezoelectric actuator to control the gap between the resonator and prism. Incoupling light beams are directed at an angle of $\varphi =39°$ with respect to the base of the prism near the resonator to efficiently excite the lowest-order radial modes in the resonator [63], as illustrated in Fig. 1. The resonator and the prism are put on a rotation stage to adjust the incoupling angle. Subsequent to the diamond prism, the transmitted pump signal is collected using a silicon photodiode (Si PD 1, Thorlabs PDA36A2) to measure the mode spectrum of the resonator and calibrate the input laser power in the system. Prior to reaching the PD 1, a 50:50 beamsplitter directs a portion of the outcoupled pump and Raman signal to an optical grating, spatially separating the generated cascaded signal from the pump. After the optical grating, a second silicon photodiode (Si PD 2, Thorlabs PDA36A-EC) detects the intensity of different orders of the cascaded Raman lasing. The wavelength (and hence the order) of the cascaded Raman lasing signal was determined by replacing the PD 2 with an Ocean Optics spectrometer (Jaz).

To measure the threshold of cascaded SRS accurately, the incident laser power in this system should be calibrated accurately. Here the power after the coupling prism (P1 shown in Fig. 1) was first measured and calibrated. Considering the Fresnel reflections (16.2%) for TM polarization at the diamond-air interface the incident power inside the prism is $P_0=1.19\times P_1$. The efficiency of the optical free space transmission pathway behind the prism is first calibrated when the diamond prism is positioned away from the LB4 resonator. The calibrated efficiency, determined by comparing the power received by Si PD 1 (P₂ shown in Fig. 1) with the power just behind the prism (P₁) measured using a power meter, is 0.40. Then, the power after the prism (P₁) for every measurement can be calculated using the power on Si PD1 (P₂) divided by this efficiency. Furthermore, when the prism and the LB4 resonator are coupled, the measured P₁ is approximately 3% lower on average than that when they are not coupled, indicating the effect of the coupling between the resonator and the prism on the P₁ is negligible.

The $Q$ factor of mm sized WGM resonators is limited by either scattering due to remaining roughness of the surface or by intrinsic material absorption. Radiation losses are insignificant for this size and wavelength since they scale as $e^{-2m}$ [65] where $m$ is the azimuthal mode number (number of field oscillations in one round trip of the light), which is on the order of 10,000 in our resonator. In any case, for the $Q$ factor, one can derive an upper limit from the material absorption of the used material using $Q_{\mathrm{intrinsic}}=2\pi n/(\lambda \alpha )$ ($\lambda$: wavelength; $\alpha$: absorption coefficient of the materials). For excitation at 517 nm we find very high $Q$ factors of up to $2.0\times {10}^9$ for TM type modes (electric field polarized orthogonal to the resonator surface) and $3.3\times {10}^8$ for TE type modes (orthogonal to TM). The $Q$ factor of the TM modes corresponds to a material loss of $\alpha =0.01{\mathrm{m}}^{-1}$, which agrees well with the literature [7]. The lower $Q$ factor of the TE modes might be a hint that bulk Rayleigh scattering is a significant contribution to the material loss at that wavelength: it was shown in Ref. [66] that TM modes in WGM resonators can partly suppress bulk scattering effects leading to a higher $Q$ factor. At 795 nm we find $Q$ factors of slightly above ${10}^9$ for both polarizations corresponding to a similar absorption coefficient of $\alpha =0.011{\mathrm{m}}^{-1}$ and at 1550 nm the $Q$ factor is between $6\times {10}^7$ and $7\times {10}^7$ corresponding to a significantly higher absorption coefficient of about $\alpha =0.1{\mathrm{m}}^{-1}$ compared to the visible regime. The fact that $Q$ factors of both polarizations are similar at 795 nm and 1550 nm is also other evidence for the existence of the Rayleigh scattering at 517 nm, because the scattering plays a smaller role at longer wavelengths. To the best of our knowledge absorption coefficients at 795 nm and 1550 nm have not been reported before for LB4, which, together with that at 517 nm, are listed in Table 2.

In a WGM resonator, the SRS threshold is proportional to the mode volume and $1/Q^2$ [59]. Alongside the previously mentioned azimuthal mode number $m$, a WGM is characterized by the radial mode number $q$ and the polar mode number $p$, where $q$ is the number of field maxima along the radial direction and $p+1$ the number of field maxima along polar direction. We want to identify the so called fundamental modes ($q=1$, $p=0$) since they have the smallest mode volume, consequently corresponding to the lowest SRS thresholds. The easiest way to do that is as follows [67]. First, the coupling angle is adjusted to the smallest value where a spectrum of the resonator can be obtained. The fundamental mode is part of the spectrum since it has the smallest propagation constant (corresponding to the smallest coupling angle). Modes with polar mode number $p=0$ are typically identified as those with better coupling efficiency due to better spatial overlap between the beam coupled out of the resonator and the reflected pump from the prism [61]. Higher-order polar modes ($p>0$) can be sorted out by their two-lobe emission pattern [61,67]. The radial mode number $q$ of the remaining modes can be determined by measuring their FSR: a larger FSR is linked to a higher $q$ number. This is because the $q$ changes the effective circulating length (or the effective refractive index) of modes, and therefore the FSR, which in turn helps us identify a mode’s $q$ number. The FSR can be obtained by a modulating frequency method [64]. After comparing the theoretical FSRs calculated from the dispersion equation [68] for WGM resonators with the experimental values, we find the fundamental mode has the smallest FSR of 9.739 GHz and a coupling contrast of 32%.

To investigate the conversion from the pump power to the Raman Stokes lines, we focus on the fundamental mode by decreasing the sweeping range of the laser around that mode, and gradually increase the pump power, while the pump on PD 1 and the signal on PD 2 are observed simultaneously. During this measurement the resonator is slightly overcoupled to compensate for early pump depletion. The coupling $Q$ was $4.8\times {10}^8$ and hence the total $Q$$3.9\times {10}^8$. The coupling depth during the measurement was about 32%. Upon reaching a certain pump power level, signal peaks appear on Si PD 2. Cascaded Raman lasing is confirmed by measuring the spectrum on the Ocean Optics spectrometer and a multimode optical fiber, which replaces PD 2 in Fig. 1. The process is briefly described as follows: the first generated Raman-shifted photons are resonantly enhanced in the resonator and serve as the pump for the subsequent stages of Raman lasing. This process cascades and hence generates multiple higher-order Stokes lasing.

Cascaded SRS in a cavity was first observed in ${\mathrm{CCl}}_4$ droplets using pulsed lasing by Qian and Chang in 1986 [69], just one year after their initial observation of SRS in liquid droplets [70]. Subsequently, in 2003, Min et al. [47] first observed five cascaded SRSs in a solid silica microsphere with a pump power of about 0.9 mW and also applied coupled modes theory for its theoretical analysis. Since then, cascaded SRS has garnered significant attention and has been demonstrated in various types of resonators. For example, eight Stokes peaks were observed in ${\mathrm{CaF}}_2$ resonators [38], two Stokes peaks in racetrack silicon microrings [48], five Stokes peaks in ${\mathrm{As}}_2{\mathrm{S}}_3$ microspheres [71], and two Stokes peaks in both aluminum nitride microrings [72] and silicon carbide microresonators [73], among others.

In our LB4 WGM resonator, when the incoupled pump power is increased up to 10 mW, cascaded SRS peaks with a wavenumber difference of about $720{\mathrm{cm}}^{-1}$ up to the fourth order are observed using the Ocean Optics spectrometer, as shown in Fig. 3. The leftmost peak in Fig. 3 is the pump laser at 517 nm. The SRS peaks are located at 537.1 nm, 558.8 nm, 582.4 nm, and 608.2 nm. The inset in Fig. 3 shows a photograph of the cascaded SRS signal captured with a USB camera after the optical grating. We also observed $168{\mathrm{cm}}^{-1}$ branched cascaded SRS and did not choose to characterize it, because we find the first order of this branch, due to a smaller wavenumber difference, is masked by the strong pump, of which the threshold cannot be characterized properly.

The first-order SRS peak is identified using the spectrometer and its power is measured with the Si PD 2 at different incoupled powers. Figure 4 shows the power of the first Raman line versus the incoupled pump power $P_{\mathrm{in}}$. The incoupled power denotes the power coupled into the resonator, i.e., the product of mode contrast and the incident power inside the prism (P₀). The linear fitting (the gray area in Fig. 4) indicates a threshold power of 0.71 mW for our LB4 resonator. In comparison, the Raman lasing thresholds for other crystalline WGM resonators stand at 0.9 mW for the LN WGM resonator [39] and 8.1 mW for the magnesium fluoride (${\mathrm{MgF}}_2$) WGM resonator [74]. To date, the lowest threshold in a WGM-resonator-based Raman laser is 3 μW in a ${\mathrm{CaF}}_2$ resonator with a significantly better $Q$ factor [38].

As shown in Fig. 4, when the pump power exceeds the threshold of 0.71 mW, the first-order SRS appears and its output power linearly increases with increasing pump power. Subsequently, as the coupled pump power is increased to 2 mW (see the light orange area), the first-order output power begins distorting and slowly increases because the intracavity power of first order becomes sufficiently high to generate second-order SRS [38,45,48]. When the pump power is further increased to about 10 mW, all four orders of SRS appear and the output power of the first-order SRS stops increasing because those higher-order SRS peaks deplete it. It is noteworthy that as the pump power continues to increase, there is a slight observable decrease in the first-order output power. This decline can be attributed to pump mode distortion induced by the thermal drift associated with highly elevated pump power levels [38,75]. The temperature controller in our system is a few mm away from the resonator and is hence not fast enough to compensate for this effect. For future optimization one could use faster feedback systems such as a light-emitting diode shining on the resonator [76,77] or a second auxiliary laser coupled to the resonator [78]. Considering the reflection at each optical component and the diffraction efficiency of the optical grating (Thorlabs GH13-24V, and the optical iris after the optical grating), the observed unidirectional efficiency for the first-order SRS of fundamental mode is approximately 7.2% according to the threshold curve.

The generated Raman linewidth can be theoretically estimated by using equations from Refs. [79–81]. Using the Raman gain spectrum linewidth ($8–10{\mathrm{cm}}^{-1}$), the Raman shift ($720{\mathrm{cm}}^{-1}$), and $Q=1\times {10}^9$ at critical coupling, the theoretical fundamental linewidth of this Raman laser can be estimated to be 0.02 Hz. This is reasonable compared with the linewidth of about 3 Hz in a silica toroid with a $Q$ on the order of ${10}^8$ [79].

Our system is likely not running in single mode operation, even when only the first Raman peak is present because the Raman gain bandwidth is about 270 GHz while the resonator free spectral range is about 10 GHz. Hence, adjacent modes are expected to have very similar Raman gain and are likely to start lasing as well. One promising approach is to reduce the resonator size, thereby increasing the free spectral range (FSR) and limiting the number of modes that fall within the Raman gain bandwidth such that one cavity mode has a clear gain advantage over the adjacent ones [82]. In addition, higher-order WGMs can be suppressed using radiative dampers [83] or by introducing structural modifications such as drilled holes near the resonator rim [84]. Furthermore, the higher-order Raman lasing can be suppressed by carefully controlling the pump power as well as the coupling [85]. Other strategies such as incorporating a saturable-absorber-based narrow band filter [86,87] or using optical absorbers to introduce wavelength-selective loss (e.g., at the second-Stokes wavelength) [88,89] could also be possibly employed to suppress higher-order Raman lasing.

In conclusion, we have demonstrated the highest reported $Q$ factor of $2.0\times {10}^9$ at 517 nm in an LB4 WGM resonator. We also extracted absorption coefficients for longer wavelengths at 795 nm and 1550 nm, which, to the best of our knowledge, have not yet been reported in literature. The high $Q$ factors in the visible regime that should, according to literature, extend into the UV down to 250 nm and the ${\chi }^{(2)}$ nonlinear properties of LB4 make this crystal a very promising material for nonlinear optics in WGM resonators.

We also observed strong Raman lasing with a very low threshold of 0.71 mW, which cascades as high as fourth order covering a spectral width from the pump at 517 nm up to 608 nm. The LB4 cascaded SRS can act as a compatible laser source for many applications in spectroscopy and like sciences. Moreover, the LB4 WGM resonator also has a $Q$ factor of $1\times {10}^9$ at 795 nm, suggesting that the threshold for cascaded SRS to near infrared should be similar to that at 517 nm, which can be widely applied in biomedical imaging and remote sensing.

We also estimated the linewidth of the Raman laser theoretically. Due to the high $Q$ factor of our resonator, we expect the linewidth to be sub-Hz.

For many applications, single mode Raman lasing would be preferable. Despite we could not characterize this in this work, it is very likely that our system did not run in single mode operation since the Raman gain bandwidth is about 270 GHz while the resonator free spectral range is about 10 GHz leading to multiple cavity modes with very similar Raman gain. This can be easily solved by using smaller resonators with larger free spectral ranges. If larger lasing power is desired, the cascading of the Raman process needs to be suppressed. This could possibly be achieved by implementing a suitable absorber at the respective wavelength.

Acknowledgment. The authors acknowledge support by the University of Otago Postgraduate Publishing Bursary (Doctoral).