Actively Q-Switching in the Intra-Cavity Pumping Mechanism for Polarized Oscillation at 2.1 μm

Q-switched and polarized Ho lasers are the ideal driving source for mid-infrared radiation via optical parametric oscillation. Although intra-cavity pumping is an efficient way to achieve the Ho laser oscillation at <inline-formula> <tex-math notation="LaTeX">$2.1~\mu \text{m}$ </tex-math></inline-formula>, which also facilitates the direct use of common diodes in a compact structure, it was demonstrated to be not suitable for Q-switching due to the saturable effect of the Ho-doped gain medium. Here, we report a RbTiOPO<sub>4</sub> Q-switched intra-cavity pumped laser via integrating the Tm-doped and Ho-doped gain medium into a composite structure and decoupling the Tm laser from the Ho laser before it was modulated by the RbTiOPO<sub>4</sub> crystal. The shortest pulse of 41 ns at repetition frequency of 1 kHz was obtained with a peak power of 7.5 kW. By competing with the intensified self-pulsing, the maximum pulse repetition frequency was found to reach 7 kHz, which was half the driving frequency of the electro-optical modulator. The results pave the way for achieving regular pulses from the intra-cavity pumping mechanism, which facilities a compact, accessible and robust pulse source at <inline-formula> <tex-math notation="LaTeX">$2.1~\mu \text{m}$ </tex-math></inline-formula>.


I. INTRODUCTION
Wavelengths above 2 µm are far away from the two-photon absorption bands of the famous non-oxide mid-infrared crystals such as ZnGeP 2 and OP:GaAs [1]. These crystals made pulse Ho lasers with emission ranges from 2.05 to 2.1 µm into excellent driving sources for nonlinear frequency conversion toward the molecular fingerprint region of 3-14 µm [2]- [4]. In addition, Ho lasers are valuable in the real world and have been widely applied in surgeries, lidar applications, atmospheric monitoring, and so on [5]- [7].
In-band pumping of the unsensitized Ho-doped gain medium with 1.9 µm lasers had become a dominant way to achieve pulse operation at 2.1 µm for the past two decades [8]- [10], as the traditional Tm, Ho co-doped mechanism had severe upconversion losses at room temperature [11], [12].
The associate editor coordinating the review of this manuscript and approving it for publication was Weidong Zhou .
However, accessibility and compactness of the in-band pumped lasers was limited by the available 1.9 µm pump sources such as Tm-doped bulk or fiber lasers and the GaSb diode. Basically, the conventional Tm laser pumped Ho laser is a bulky cascade mechanism [13], where additional setup for the high-power Tm laser systems is required [14]. Owing to the broad emission spectrum and the significant wavelengthdrift of the mid-infrared diode lasers, delicate spectral and temperature control should be considered before pumping the Ho lasers with the expensive 1.9 µm diode [11], [15]. Hence, inserting the Tm-doped gain medium into the cavity of the Ho laser for intra-cavity pumping was recommended, which facilitated using the existing 800 nm diodes for a compact Ho laser at room temperatures [16]- [18]. However, such a mechanism was shown to be unsuitable for achieving active Q-switching, where irregular pulse trains occurred after the acousto-optic modulator was inserted and set with the driving frequencies of 5 to 15 kHz [16]. This was attributed to the VOLUME 8, 2020 This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/ saturable effect of the Ho-doped gain medium, which also led to self-pulsing of the intra-cavity pumped Ho lasers in a free-running state [19], [20].
Here, we show successful electro-optic Q-switching in the intra-cavity pumping mechanism by decoupling the Tm laser from the Ho laser before it was modulated by the RbTiOPO 4 crystal. A polarized Ho laser with a shortest pulse of 41 ns and a peak power of 7.5 kW was obtained at 2097 nm. Moreover, a half-frequency in the pulse repetition frequency was observed when increasing the driving frequency of the electro-optic modulator (EOM) above 4 kHz.

II. EXPERIMENTAL SETUP
For the compactness of the intra-cavity pumping mechanism, a single bulk composite gain medium integrated via diffusion bonding of a 3.5 at.% Tm:YAG and a 0.8 at% Ho:YAG crystal was applied. The lengths of the Tm-doped and Ho-doped regions of the Tm/Ho:YAG crystal were 10 mm and 6 mm respectively to enhance the intra-cavity resonance [17]. Figure 1 shows a schematic of the experimental configuration. The composite gain media was wrapped with indium foil and mounted into a copper heat sink for water cooling at 16 • . The pump source was a fiber-coupled 785 nm diode with a core diameter of 400 µm and a numerical aperture of 0.22, which was collimated and focused by two identical plano-convex lenses with a focal length of 35 mm. The pump waist radius inside the Tm-doped region was calculated to be approximately 230 µm. A plano-concave cavity consisting of the end-mirror (EM) and the output coupler (OC) was applied. EM was a plano-plano mirror coated for anti-reflection at 785 nm and high reflection (HR) at 1900 nm to 2100 nm; OC was a plano-concave mirror with a curvature of radius of 200 mm, which was coated for HR at Tm laser (2000nm-2020 nm) and had a transmittance of 10% at Ho laser (2090 nm-2130 nm). A spectral filter (SF) coated to HR the Tm laser (R>97%) and AR the Ho laser (Tč¿99.5%) was inserted intra-cavity for decoupling a majority of the Tm laser from the Ho laser. Between the SF and OC, a polarizer and an electro-optic modulator (EOM) consisting of two identical RbTiOPO 4 (RTP) crystals with a dimension of 3 mm×3 mm×5 mm, were placed in sequence. The quarter-wave voltage of the tandem RTP crystals was set at 2.3 kV in the experiment. The wavelength of the PQS laser was measured using a mid-IR spectrum analyzer (771A-IR, Bristol Instruments Inc.). The pulse signal was measured by an InGaAs detector (DET05D/M, Thorlabs Inc) connected with a 2 GHz bandwidth oscilloscope (MSO 2034, Tektronix Inc.).

III. SUPPRESSING THE POTENTIAL PASSIVELY Q-SWITCHING
According to the criterion for a Q-switched Tm laser where the Ho-doped gain medium acted as the saturable absorber [21], we derived the condition for suppressing passive Q-switching (PQS) induced by the Ho-doped region during the EOM, that is where α Ho and g Tm are the absorption coefficient and gain coefficient of the Ho-doped and Tm-doped regions with lengths of L Ho and L Tm , respectively; A Tm and A Ho are the mode radii inside the thermal lens centers of the Tm-doped and Ho-doped regions; σ Ho Abs and σ Tm e are the absorption cross section and emission cross section of the Ho-doped and Tm-doped regions, respectively. γ is 1 for a four-level laser and 2 for a three-level laser. Here, γ is 1 for creating a low Q-switching threshold. The gain coefficient g Tm is where η QY = 1.97 is the quantum yielding of Tm 3+ ions [22], Pp is the absorbed diode pump power, λp = 785 nm is the diode wavelength, λ Tm = 2019 nm is wavelength of the Tm laser, ω p = 0.23 mm is the pump waist radius of the diode, and I Tm s = 5.9 kW/cm 2 is the saturable intensity of the Tm-doped region [23]. Figure 2 denotes the evolution in g Tm and the acceptable mode ratio A Tm / A Ho for suppressing the PQS, where α Ho , σ Ho Abs , and σ Tm e in (1) are 0.144 cm −1 , 0.17 × 10 −20 cm 2 and 0.13 × 10 −20 cm 2 respectively at 2019 nm [17]. The relationship between the thermal lens in the Tm-doped region f Tm and the absorbed diode power Pp was described as f Tm = Cω 2 p /P P with C = 21.7 kW/mm [17]. Based on the ABCD matrices model with f Tm , the evolution in A Tm /A Ho without considering the thermal lens in the Ho-doped region is denoted by the blue dashed line in Fig. 2, where potential PQS can be predicted at a diode pump power below 5.6 W. However, with the increased diode power, higher A Tm /A Ho is allowed due to the increased g Tm . Meanwhile, the real A Tm / A Ho became smaller due to the shorter thermal lens in the Ho-doped region f Ho compared with that in the Tm-doped region f Tm , under higher diode power. According to the thermal model for intracavity pumped Ho lasers [17], f Ho and f Tm were calculated to be 88 mm and 76 mm respectively, where the cavity mode distribution of the Tm laser is depicted in Fig. 2b. Since A Tm /A Ho decreased with the increased thermal lens in the Ho-doped region, the PQS tends to be well suppressed with the increased diode power, which is conducive to a stable Q-switching modulated by the EOM.

IV. RESULTS AND DISCUSSIONS A. SELF-PULSING PHENOMENON OF THE HO LASER
Before driving the EOM, maximum continuous-wave (CW) power of 1.32 W at 2097.7 nm from the OC was obtained (Fig. 3a). Besides, the leaked laser reflected by the polarizer was measured, which had a lower threshold (5.04 W) compared with the CW laser (7.05W). This was attributed to the first oscillation in the Tm laser from the cavity consisting of EM and SF, since that SF had a small transmittance of 4% of the Tm laser. Further confirmation was made by the sideleaked Tm laser wavelength of 2019 nm (Fig. 3c), which was reflected by the polarizer. The formation of a polarized Ho laser was achieved with a polarization extinction ratio of 23 dB in the horizontal direction, where no Ho laser signal was detected from the side leakage light. Owing to the saturable effect of the Ho-doped region which modulated the Tm laser and gain-switched the Ho laser consequently, irregular self-pulsing was observed in the CW Ho laser and the side-leakage Tm laser, respectively (Fig. 3d).
In a smaller scope of 50 µs/div, these trains are easily mistaken as the Q-switching signals (Fig. 4a), where the pulse repetition frequency drifted within a broad range around 30 kHz (Fig. 4b) and the pulse width drifted within a range below 1 ms (Fig. 4c) at each pulse train. Correspondingly, drifting ranges of the peak power at different diode pump powers are calculated based on Figs. 4b and 4c. As shown in Fig. 4d, the upper peak power of the random pulse increased significantly with the increased absorbed pump power, which will be high enough to interrupt the electro-optical Q-switching especially at higher driving frequency.

B. EXPLORING THE ACTIVELY Q-SWITCHING
Starting the EOM and setting the driving frequency (DF) between 1 kHz and 5 kHz, a regular pulse train occurred at an absorbed diode power around 7.3 W (Fig. 1b). Figure 5a depicts the evolution in average Ho laser power with the increased pump power, where the maximum output power of 711 mW was obtained at a DF of 5 kHz. Decreasing the DF from 5 kHz to 1 kHz, the fitted slope efficiency decreased slightly from 13% to 11.4%, owing to the saturation in the power curve under the low DF. This saturation was caused by the increased EOM period for energy storage, where severe thermal lensing in the Ho-doped region occurred due to the intensified nonradiative transition [8]. Hence, the maximum average output powers were saturated VOLUME 8, 2020 at 318 mW and 352 mW, respectively, under the DF of 1 kHz and 2 kHz. Although a higher DF is conducive to relieving the thermal lens and increasing the output power, the halffrequency was observed at DFs of 4 kHz and 5 kHz, where the pulse repetition frequency (PRF) became half of the DF at the beginning of a stable pulse train. After increasing the diode power to 9.6 W and 10.2 W, respectively, for the DFs of 4 kHz and 5 kHz, the PRF could follow the DF. However, the halffrequency remained unchanged during the Q-switching processes at DFs between 7 kHz and 14 kHz (Fig. 6a, see Fig. 7a also for the pulse train at a DF of 14 kHz). Hence, this halffrequency is attributed to the insufficient accumulated pump intensity of the Tm laser at each EOM period, especially under low diode power or at the high DF. Neither a one-third DF frequency, nor a one-quarter DF frequency, was observed in a stable pulse train at the DF above 7 kHz, where the formation of these pulses is considered to be prohibited by the above twice EOM losses at each pulse period.
Before a stable pulse train, there existed a transition area where standard deviation (SDEV) of the PRF and the pulse width decreased from hundreds of Hz to below 1 Hz and from tens of nanoseconds to below 5 ns, respectively, as shown by the error bars in Figs. 5(a), 5(b), 6(a), and 6(b). With the measured PRF and pulse width, the evolutions in peak power of the Ho laser under different DFs are depicted in Figs. 5(c) and 6(c). Maximum peak power of 7.5 kW was obtained at PRF of 1 kHz, which corresponds to the shortest pulse with width of 41 ns. Compared with the smooth evolution in the pulse width, a step change occurred at the transition point between the half frequency and the full frequency of the DF, which was followed by a decrement in the peak power (Fig. 5c). Non-stable pulse behavior [the same as Fig. 3c was observed at a DF of 14 kHz when the diode power was increased above 10.2 W. Together with the observed threshold powers for stable Q-switching at different DFs (Figs. 5a and 6a), these are attributed to the competition between a regular pulse and the self-pulsing. Peak power of the Q-switching pulse should overwhelm that from random self-pulsing under the same pump power for a regular pulse train (Figs. 6c). However, the calculated peak powers from a regular pulse at PRF of 7 kHz (Fig. 7c) already fell within the estimated selfpulsing region (Fig. 6c). Hence, it was a challenge to obtain regular pulses at higher PRFs above 7 kHz, where the thermal stability of the current experimental configuration would need to be improved to achieve higher output power with shorter pulse widths to suppress the synchronously intensified self-pulsing.
Pulse delay with an increased DF was observed (Figs. 5b-5d), where the time separation between the falling edge of the driving signal and the front edge of the laser pulse increased from 350 ns at a DF of 1 kHz, to 610 ns at a DF of 7 kHz, at corresponding maximum output powers. As with the half-frequency, this delay was caused by the insufficient accumulated Tm laser power within each period of the lasing pulse, which also led to the broaden pulse width from 40 ns to 70 ns [21]. Near diffraction-limit beam quality with M 2 x = 1.43 (horizontal direction) and M 2 y = 1.52 (vertical direction) was measured at the maximum average power of 720 mW at PRF of 6 kHz (Fig. 7e). During the Q-switching process, the output wavelength was stabilized at 2097.3±0.5 nm (Fig. 7f).

V. CONCLUSION
In conclusion, actively Q-switching in the intra-cavity pumping mechanism has been demonstrated here for realizing polarized pulse radiation at 2.1 µm, which was shown to be impossible due to the saturable effect of the Ho-doped gain medium. 16 Regular pulse trains with PRF from 1 kHz to 7 kHz were obtained after suppressing the inherent selfpulsing caused by the saturable effect of the Ho-doped gain medium, where the shortest pulse, with a width of 41 ns and a peak power of 7.5 kW was obtained. In addition, half-frequency and pulse delay with the increased DF were observed due to the insufficient energy accumulation during the shorter pulse period at a higher DF. The results pave the way for achieving regular pulses from the intra-cavity pumping mechanism, which facilities a compact, accessible, and robust pulse source at 2.1 µm.