Rare-earth calcium oxy-borate crystal ${\mathrm{ReCa}}_4\mathrm{O}{({\mathrm{BO}}_3)}_3$ (ReCOB), is a promising optoelectronic functional material, owing to its high damage threshold, good growth habit, and wide transparent regime. It has been widely used in solid-state laser generation and nonlinear frequency conversion. Among them, the $\mathrm{Yb}:{\mathrm{YCa}}_4\mathrm{O}{({\mathrm{BO}}_3)}_3$ (Yb:YCOB) crystal has recently attracted increasing attention in all-solid-state laser applications^[1]. Due to its strong crystal-field effect, Yb:YCOB has a large energy-level splitting ($\mathrm{\Delta }E\sim 1022{\mathrm{cm}}^{-1}$) in the ground state ${{}^2\mathrm{F}}_{7/2}$, thereby reducing the lasing threshold and re-absorption loss in a quasi-three-level system^[2,3]. In addition, the fluorescence lifetime of the upper-level state ${{}^2\mathrm{F}}_{5/2}$ in Yb:YCOB is sufficiently long ($\tau =2.28\mathrm{ms}$ at 1032 nm)^[2,4], which is beneficial for energy storage and giant-energy pulse generation. Moreover, Yb:YCOB exhibits a broadband and smooth fluorescence emission from 960 to 1100 nm, thus becoming suitable for the generation of mode-locked ultrashort pulses.

To date, plenty of lasers operating in the continuous-wave (CW) mode, the $Q$-switched pulse mode, and the mode-locked ultrafast pulse, have been realized in the Yb:YCOB crystal, with temporal scales ranging from the nanosecond to the picosecond and to the femtosecond domains^[5–10]. For example, an ultrabroadband tunable CW laser at 1107 to 1100 nm was achieved by tuning an SF10 prism in the cavity^[11]. A nanosecond pulse with giant energy up to 5.3 mJ was realized at 1020 nm using an acousto-optical (AO) $Q$-switch^[9]. Meanwhile, a 35 fs pulse with a central wavelength at 1055 nm and a 75 fs pulse with a central wavelength at 1048 nm, were obtained in Yb:YCOB using SESAM^[6] and Kerr-lens mode-locking^[12], respectively. These results show that Yb:YCOB is a good gain medium for solid-state laser applications with various time scales.

However, in the framework of traditional laser theory, the laser wavelengths of Yb:YCOB were limited at 1.02–1.10 µm because the available laser wavelength was constrained by the spontaneous fluorescence spectrum. In 2022, our group proposed a novel multiphonon-assisted lasing to extend the laser wavelengths of Yb:YCOB exceeding 1.1 µm, where a CW tunable laser at 1110–1465 nm was demonstrated. The active phonon energy for multiphonon-assisted lasing in a Yb:YCOB crystal located at 476 cm^−1[13]. At present, the highest CW laser output power was 3.95 W at 1130 nm and 2.06 W at 1140 nm^[14], respectively. In addition, the temporal characteristics of the multiphonon-assisted laser at the nanosecond scale were investigated. We realized the passively $Q$-switched laser operation at 1126 nm, utilizing a ${\mathrm{Cr}}^{4+}:\mathrm{YAG}$ as the saturable absorber, with a pulse duration of 29 ns and a repetition rate of 2.3 kHz. The corresponding pulse energy was 204 µJ^[15].

In order to further increase the pulse energy and investigate the temporal dynamic behavior of the multiphonon-assisted laser, for the first time, we performed a compact AO $Q$-switched Yb:YCOB laser operating at 1130 nm. In this Letter, a customized quartz AO $Q$-switch was applied to modulate the repetition rate from 0.1 to 1 kHz. At a low repetition rate, a narrow pulse width of 466.1 ns was realized with a peak power of 1.76 kW and a maximum single pulse energy of 0.82 mJ. This value increased four times compared to the passively $Q$-switched Yb:YCOB laser at 1126 nm. This work indicated that multiphonon-assisted Yb:YCOB lasing has a great capacity for giant nanosecond pulse energy generation.

Figure 1 depicts the configurational setup of the laser experiment. An InGaAs laser diode (LD) served as the pump source (Lotuxs pluto-30), with a fiber core diameter of 105 µm and a numerical aperture (NA) of 0.22. The center wavelength of the LD was stabilized at 976 nm in the total range of the pump power, which is matchable with the absorption peak of the Yb:YCOB crystal. After passing through a coupling-lens group with an amplification ratio of 1:2, the focused spot diameter on the laser crystal was 210 µm. The gain medium was a Y-cut 15% (atomic fraction) Yb:YCOB crystal grown by the Czochralski method with a size of $3\mathrm{mm}\times 3\mathrm{mm}\times 6\mathrm{mm}$. Two crystal facets were polished. To ensure efficient heat dissipation, the laser crystal was enveloped by indium platinum and placed in a copper heat sink at 10°C.

The resonant cavity adopted a plano-concave cavity. The incident front surface of the Yb:YCOB crystal was coated with high transmission at 976–1100 nm and high reflection at 1130–1200 nm and applied as an input mirror (M1). The end face of the crystal was polished without coating, and the Fresnel reflection from the uncoated surface is $R=6.7\%$. An output coupler (M2) was a concave mirror with a curvature radius of 200 mm and a certain transmittance $T_{\mathrm{oc}}=3\%$ at 1130–1200 nm. In addition, it was coated for high transmission at 976–1100 nm to suppress conventional Yb:YCOB lasing around 1 µm. According to our measurement, the single-pass pump absorption rate was 87% under the non-lasing condition.

A quartz AO modulator (Gooch & Housego) with a 20 mm interaction length was utilized in this study. In order to make multiphonon-lasing beyond 1.1 µm, its two end faces were coated with antireflection (AR) around 1130 nm. The applied modulation frequency was 80 MHz, accompanied by a radio frequency power of 16 W. A filter was utilized to separate the pump light and 1130 nm laser. An A.P.E. spectrometer (WaveScan, S/N S09668) was utilized to record the laser spectrum. To record the average laser output power, a power meter (Newport, Model 1916-R) was placed behind the filter. The pulse laser characteristics were assessed by a TDS-3012 digital oscilloscope (Tektronix, Inc.) with a bandwidth of 100 MHz and a sampling rate of 1.25 GS/s.

In our experiment, the transmittance of M2 was optimized as $T_{\mathrm{oc}}=3\%$. This optimal transmittance can attain a high slope efficiency and prevent the optical damage induced by the exceedingly high intra-cavity power density. Compared to our previous studies on the CW laser at 1130 nm^[14], the parameters of the resonant cavity were optimized in two aspects. (i) The compression ratio of the focus system changed from 1:1 to 1:2. The incident pump laser spot was enlarged to reduce the thermal gradient inside the laser crystal, thus reducing the thermal lens effect. (ii) The cavity length increased from 100 mm to 200 mm. A long cavity length was helpful for reducing the influence of self-pulsing when inserting the AO modulator. Without the AO switch, the cavity was 205 mm long. After inserting the AO, the optimal length of the M1-M2 cavity was 217 mm. At this time, the laser spot radius in the crystal was calculated to 65 µm.

The laser spectra for both the CW and the $Q$-switched pulse operation are depicted in Fig. 2. The CW spectrum with a center wavelength of 1131.5 nm was recorded at an absorbed pump power of 13.3 W. At an 8.6 W pump power, the pulse laser spectra were recorded at pulse repetition frequencies (PRFs) of 0.1 kHz, 0.2 kHz, 0.5 kHz, and 1 kHz, respectively. It can be observed that the laser oscillation wavelength remained unchanged under different PRF conditions, locating at 1130.7–1131 nm. In addition, we observed the weak lime light at 565 nm owing to self-frequency-doubling effect of Yb:YCOB. However, its outpower is very low ($<1\mathrm{mW}$) due to the non-phase-matching condition.

Figure 3 displays the laser performances of the Yb:YCOB at 1130 nm. First, when the absorbed pump power was 13.3 W, the maximum CW laser power was 1.06 W. The slope efficiency was 13.7%, and the lasing threshold was 6.13 W. Compared to the previous study, the slope efficiency is slightly reduced because of the low pump power intensity in this setup.

Then, by inserting an AO modulator, we realized the stable $Q$-switched laser operation, as shown in Fig. 3, with the repetition rate gradually decreasing from 1 kHz to 0.1 kHz, and the laser oscillation threshold increased from 6.13 to 6.36 W. At an absorbed pump power of 9.29 W and PRF 1 kHz, the average output power was 365 mW, which is the highest one in this $Q$-switched laser experiment. At this time, the slope efficiency was 9.7%, and the intracavity loss introduced by the AO modulator was calculated to be 5%^[15,16]. We measured the beam quality of the pulsed laser ($\mathrm{PRF}=1\mathrm{kHz}$, $P_{\mathrm{out}}=100\mathrm{mW}$) using a beam quality analyzer. The $M^2$ values are 1.72 and 2.16 along $x$- and $y$-direction, respectively.

With the decreasing PRFs, the laser efficiency becomes inefficient, leading to a gradual decline in output power. This can be attributed to the low diffraction efficiency of the AO at low PRFs. Reducing the PRF to 0.1 kHz, we obtained a laser operation with a maximum average output power of 82 mW and a slope efficiency of 2.6%.

Here, we made a comparative analysis between the traditional Yb:YCOB laser at 1020 nm and the multiphonon-assisted laser at 1130 nm. In previous reports^[9], a pulse laser operation with a pulse energy of 5.3 mJ was obtained by using an output coupling mirror with a transmittance of 60% in the AO $Q$-switched laser. The laser wavelength was located at 1020–1023 nm. Here, we demonstrated a Yb:YCOB pulsed laser with a pulse energy of 0.82 mJ at 1130 nm, indicating that the multiphonon-assisted laser also exhibits good energy storage capacity.

Figure 4 illustrates the pulse width of the Yb:YCOB laser under different PRFs and absorbed pump power. The pulse widths were in the microsecond (sub-nanosecond) range when the laser was running at PRFs higher than 0.5 kHz. With the increasing pump power, the pulse duration exhibited a rapid decrease followed by a progressive reduction until reaching a steady state value^[17]. At 1 kHz, the pulse duration dropped from an original value of 1.5 µs (close to the lasing threshold) to 736 ns at a maximum absorbed pump power of 9.2 W. At this time, the maximum single pulse energy was 0.36 mJ. Similarly, at the PRF of 0.1 kHz, the pulse width decreased from 834 ns to 466 ns. The highest single pulse energy was 0.82 mJ. This value improved four times compared to the passively $Q$-switched Yb:YCOB laser using ${\mathrm{Cr}}^{4+}:\mathrm{YAG}$ ($\sim 204\mathrm{\mu J}$ at 1126 nm)^[18].

The laser pulse sequence and single pulse profile were monitored by an oscilloscope with a high sampling rate. Figures 5(a) and 5(c) illustrate the pulse train at the PRF of 1 kHz and 0.1 kHz, measured at the pump absorbed power of 9.2 W and 8.6 W, respectively. It was observed that the pulse sequence for each PRF in time was very stable due to the precise setting of the laser pulse repetition rate. Furthermore, the amplitude volatility between the pulse sequence and the single pulse was calculated to be about 10 %, which is caused by the thermal effect^[19]. In addition, Figs. 5(b) and 5(d) exhibit the corresponding single pulse. The rising edge and the falling edge of the laser single pulse were basically symmetric, indicating the active $Q$-switching conditions (e.g.,  output coupling transmittance) in laser experiment are suitable^[20]. The pulse contrast ratio of the Yb:YCOB laser is about ${10}^{1.1}–{10}^{1.5}$ with a pulse duration of 466–736 ns.

For a traditional actively $Q$-switched laser, it can be comprehended by referring to a rate-equation model^[21,22]. Here, we applied this model to the multiphonon-assisted laser in the Yb:YCOB crystal under different PRFs. The pulse energy in an actively $Q$-switched laser can be represented as $$E=\frac{h\nu A}{2\sigma \gamma }\ln \left(\frac{1}{R}\right)\ln \left(\frac{n_i}{n_f}\right),$$(1)where $h\nu$ represents the photon energy, $\gamma$ is the inversion reduction factor, $A=\pi {\omega }^2$ represents the laser spot cross-sectional area, and $\omega$ is the pump laser spot radius. $\sigma$ refers to the stimulated emission cross section, and $R$ is the reflectivity of the output mirror. The initial inverted population $n_i$, given by $K\tau P_{\text{in}}(1-e^{-1/f\tau })$, is prior to pulse formation. The residual inverted population after the pulse is $n_f$, expressed as $n_i{e}^{-2\sigma ni(\ln (1/R)+L)}$^[23,24]. For the Yb:YCOB laser at 1130 nm, the parameters used for calculation are $R=97\%$, $h\nu =1.76\times {10}^{-19}\mathrm{J}$, $\gamma =2$^[25], $\omega =105\mathrm{\mu m}$, and $\sigma =0.34\times {10}^{-21}{\mathrm{cm}}^2$^[14]. Additionally, $\tau =2.65\mathrm{ms}$^[2] represents the fluorescence lifetime, $f$ denotes the PRF of the AO $Q$-switch, and $K=1.972\times {10}^{-26}$ is the pumping constant^[21,26]. The calculated results are listed in Table 1, encompassing $P_{\mathrm{avr}}$ (average output power), $E_{p,\text{cal}}$ (theoretical pulse energy), $E_{p,\exp }$ (experimental pulse energy), $t_p$ (pulse width), and $P_p$ (peak power). We can find that the theoretical pulse energy was well consistent with the experimental results, suggesting the multiphonon-assisted lasing can be described by the rate-equation model.

In summary, we demonstrated an AO $Q$-switched laser operating at 1130 nm in a Yb:YCOB crystal for the first time, to the best of our knowledge. The stable nanosecond pulse laser was obtained from 1 kHz to 0.1 kHz. The maximum pulse energy and peak power were 0.82 mJ and 1.76 kW, respectively. These results revealed the great potential of the Yb:YCOB crystal for high-energy-pulsed lasers application with extended wavelengths by electron-phonon coupling effect. Meanwhile, the experimental results can be well explained by the rate-equation model, indicating that the electron-phonon coupled laser is a natural extension of the traditional laser emitting among pure electronic levels. In the future, AO $Q$-switched yellow-orange lasers can be expected by using the self-frequency doubling effect of the Yb:YCOB crystal^[27,28].