⇦Chinese Physics Letters, 2019, Vol. 36, No. 3, Article code 034201 Laser-Diode Pumped Passive Q-Switched Laser with Quick Tunable Pulse-Width Capability Teng Sun (孙腾), Jian-Guo Xin (辛建国)**, Yu-Chen Song (宋雨辰) Affiliations School of Information and Electronics, Beijing Institute of Technology, Beijing 100081 Received 15 November 2018, online 23 February 2019 **Corresponding author. Email: xinjgbit@163.com Citation Text: Sun T, Xin J G and Song Y C 2019 Chin. Phys. Lett. 36 034201    Abstract A laser-diode pumped passive Q-switched Nd:YAG/Cr$^{4+}$:YAG laser with quick tunable pulse-width capability is studied and experimentally demonstrated. By focusing the auxiliary controlling laser beam onto a Cr$^{4+}$:YAG crystal and thereby changing the initial transmission of the Cr$^{4+}$:YAG crystal, laser pulses with different pulse widths can be achieved. The obtained laser pulse width is tunable in the range of 550–1492 ps with a fixed cavity length of 7 mm. The laser can be used to achieve different pulse widths between two pulses in the range of sub-nanosecond to a few tens of nanoseconds. DOI:10.1088/0256-307X/36/3/034201 PACS:42.60.By, 42.60.Da, 42.60.Gd © 2019 Chinese Physics Society Article Text Tunable pulse-width lasers based on the passive Q-switched theory have attracted significant interest owing to their wide range of applications in various fields, such as laser medical treatment,[1,2] laser beam machining,[3,4] spectral analysis,[5] bioacoustics,[6] nonlinear effects research,[7-9] laser-induced breakdown,[10] laser ranging,[11] and the laser lift-off process.[12] In 2008, Kimmelma et al. reported a thermal tuning passively Q-switched Nd:YAG laser,[13] and obtained a pulse-width reduction of more than 10% by changing the absorption cross-section of the laser crystal. In 2015, Nie et al. reported a temperature-dependent passively Q-switched laser.[14] For the Nd:YAG/Cr$^{4+}$:YAG laser, the pulse width varied from 970 ps to 860 ps and the pulse energy increased from 12.4 µJ to 21 µJ with the increase of the boundary temperature from 20$^{\circ}\!$C to 120$^{\circ}\!$C. In addition, for the Nd:YVO$_{4}$ passively Q-switched laser, the pulse width was tuned from 8.7 ns to 3 ns and the pulse energy increased from 5 µJ to 23 µJ with the increase of the boundary temperature from 26$^{\circ}\!$C to 113$^{\circ}\!$C. In 2017, Lim and Taira demonstrated a monolithic Nd:YAG/Cr$^{4+}$:YAG ceramic laser with a tunable pulse width using a cavity-length control method.[15] The cavity length was adjusted by moving the output coupler fixed on a motorized translation stage. The tuning range of the pulse width was 0.5 ns to 9 ns for pulse peak powers from 0.5 MW to 6 MW with the increase of the optical cavity length from 14 mm to 270 mm. Both the temperature-dependent and mechanically controlled laser pulse-width tuning techniques are slow-tuning techniques, which strongly limit the applications, particularly to areas that require quick pulse-width tuning between two pulses. In 2005, Yang et al. reported a controllable passive Q-switched Nd:YVO$_{4}$ laser.[16,17] In this technique, the initial transmission of the Cr$^{4+}$:YAG crystal was kept unchanged, and the laser was first slightly adjusted to be under the critical operation condition for cw pumping. The controlling laser beam signal was then tuned to focus onto the Cr$^{4+}$:YAG crystal and thereby the absorption loss of the cavity was reduced. Thus the laser pulse was generated. The cavity loss changed when the population inversion already closed to the threshold. With this technique, the higher the intensity of the controlling beam is, the narrower the laser pulse is. The obtained laser pulse width is in the range of 200–120 ns with a peak power from 4.5 W to 9.4 W. In this Letter, a Nd:YAG/Cr$^{4+}$:YAG laser with quick tunable pulse-width capability ranging from sub-nanosecond to nanoseconds is studied and experimentally demonstrated. Unlike the signal-trigger controlled technique,[16,17] the initial transmission of the Cr$^{4+}$:YAG crystal is controlled using an auxiliary controlling laser before pumping, which means that the cavity loss is already changed from the beginning of the pumping. The output pulse width changes due to the changing of initial transmission of Cr$^{4+}$:YAG crystal. This laser can be used to produce tunable laser pulses of sub-nanoseconds. In the experiments, the obtained tunable laser pulse width is in the range of 550–1492 ps with a cavity length of 7 mm. The laser pulse energy and pulse peak power are in the range of 147–184 µJ and 267–123 kW, respectively. Using this quick-tuning laser, a series of pulses with different pulse widths ranging from sub-nanosecond to nanoseconds can be achieved by modulating the controlling laser power. For the operation of a Nd:YAG/Cr$^{4+}$:YAG passive Q-switched laser, the Cr$^{4+}$:YAG absorber should have a high initial absorption or a low initial transmission before the onset of the lasing, and once the laser intensity in the cavity is high enough to bleach the absorber, the laser pulse oscillation will be realized. The laser pulse width $t_{\rm w}$ can be expressed as[18] $$\begin{align} t_{\rm w} =\,&\frac{S_{\rm p} \eta nlY_{0+}}{c[Y_{0+} -1-\ln (Y_{0+})]},~~ \tag {1} \end{align} $$ $$\begin{align} Y_{0+} =\,&\frac{\Delta N_{0}}{\Delta N_{\rm t}}=\frac{\gamma_{0} +\gamma_{\rm sa}}{\gamma_{0} +\gamma_{\rm r} },~~ \tag {2} \end{align} $$ where $S_{\rm p}$ is the coefficient related to the pulse shape, $\eta$ is the extraction efficiency of the laser pulse, $n$ is the refractive index of the laser medium, $l$ is the round trip path length of the laser beam in the cavity, $c$ is the speed of light in vacuum, $Y_{0+}$ is the normalized inversion density, $\Delta N_{0}$ is the spatially averaged population inversion density within the cavity, $\Delta N_{\rm t}$ is the threshold spatially averaged population inversion density, and $\gamma_{\rm sa}$, $\gamma_{\rm o}$, and $\gamma_{\rm r}$ are the round trip initial absorption loss constant of the Cr$^{4+}$:YAG absorber, the optical loss constant of the output coupler of the laser, and the residual absorption loss constant after the bleaching of the Cr$^{4+}$:YAG crystal, respectively. The above loss constants are defined as follows: $$\begin{align} \gamma_{\rm sa} =\,&-2\ln (T_{\rm i}),~~ \tag {3} \end{align} $$ $$\begin{align} \gamma_{\rm o} =\,&-\ln (R),~~ \tag {4} \end{align} $$ $$\begin{align} \gamma_{\rm r} =\,&-2\ln (T_{\rm r}),~~ \tag {5} \end{align} $$ where $T_{\rm i}$ is the initial transmission of the Cr$^{4+}$:YAG crystal, $R$ is the reflectivity of the output coupler of the laser cavity, and $T_{\rm r}$ is the round trip transmission after bleaching the Cr$^{4+}$:YAG crystal. Combining Eqs. (1) and (2), the laser pulse width can be rewritten as $$\begin{align} t_{\rm w} =\frac{S_{\rm p} \eta nl(\gamma_{0} +\gamma_{\rm sa})}{c[(\gamma_{\rm sa} -\gamma_{\rm r})-(\gamma_{0} +\gamma_{\rm r})\ln (\frac{\gamma_{0} +\gamma_{\rm sa}}{\gamma_{0} +\gamma_{\rm r}})]}.~~ \tag {6} \end{align} $$ Figure 1 shows the curve obtained using Eq. (6), from which it can be seen that the laser pulse width is a function of the initial transmission of the Cr$^{4+}$:YAG crystal. The pulse width increases with the initial transmission of the absorber. This shows that any change in the initial transmission of the Cr$^{4+}$:YAG crystal will change the output laser pulse width. In the calculation of Fig. 1, $l$ is 7 mm, and $R$ is 60%.
cpl-36-3-034201-fig1.png
Fig. 1. Output pulse width versus initial transmission of the Cr$^{4+}$:YAG crystal.
The transmission of the Cr$^{4+}$:YAG crystal can be changed by increasing the intensity of the laser beam,[19] and the transmission can be obtained by $$\begin{align} T=\exp \Big\{\frac{\ln T_{\rm i}}{1+I/I_{\rm s}}\},~~ \tag {7} \end{align} $$ where $I$ is the intensity of the laser beam, and $I_{\rm s}$ is the saturation intensity of the absorber. From Eqs. (3) and (7), $\gamma_{\rm sa}$ can be rewritten as $$\begin{align} \gamma_{\rm sa} =2\ln \Big(\frac{1}{\exp \{\frac{\ln T_{\rm i}}{1+I/I_{\rm s}}\}}\Big).~~ \tag {8} \end{align} $$ Substituting Eq. (8) into Eq. (6), the relationship between the laser output pulse width and the light intensity of the auxiliary controlling laser beam can be obtained, as shown in Fig. 2. It can be concluded that if an auxiliary controlling laser beam is used to saturate the absorption of the Cr$^{4+}$:YAG crystal and thereby to increase the transmission of the crystal before pumping the inversion population to the maximum value in the optical cavity, the pulse width of the Q-switched laser will increase. Therefore, an auxiliary laser can be used to control the laser pulse width of the passive Q-switched laser by saturating the Cr$^{4+}$:YAG crystal and thereby change the initial transmission before pumping the inversion population of the gain medium to the maximum. It should be noted that the absorption coefficient of Cr$^{4+}$:YAG crystal depends on the wavelength, and the absorption coefficients of Cr$^{4+}$:YAG crystal used in this experiment at 1064 nm and 808 nm are 8 cm$^{-1}$ and 5.44 cm$^{-1}$, respectively. In the calculation process, the impact of the 808 nm controlling laser to the initial transmission at 808 nm should be converted to that at 1064 nm. In Eq. (8), $T_{\rm i}$ is the initial transmission at 1064 nm, and $I/I_{\rm s}$ is the 808 nm laser beam intensity.
cpl-36-3-034201-fig2.png
Fig. 2. Laser output pulse width versus light intensity of the auxiliary controlling laser beam.
cpl-36-3-034201-fig3.png
Fig. 3. Pulse-width tuning principle of initial transmission-controlled passive Q-switched laser.
Figure 3 shows the pulse-width tuning principle in our experiment. The initial transmission of the Cr$^{4+}$:YAG crystal is controlled using an auxiliary controlling laser before pumping the inversion population of the gain medium to the maximum, which means that the cavity loss is already changed from the beginning of the pumping. The output pulse width changes due to the changing of the initial transmission of Cr$^{4+}$:YAG crystal. As shown in Figs. 3(c) and 3(d), the pulse width increases with the controlling beam intensity. Figure 4 shows the experimental setup of the passive Q-switched Nd:YAG/Cr$^{4+}$:YAG laser with quick tunable pulse-width capability based on the above theoretical analysis. The pumping laser is a fiber-coupled 808 nm laser diode (obtained from BWT, Beijing) with a core diameter of 200 µm and a numerical aperture (NA) of 0.22, and this corresponds to a peak power of 30 W and a pumping pulse duration of 300 µs. A grin-lens was used to focus the pumping laser beam. A monolithic bonded Nd:YAG/Cr$^{4+}$:YAG crystal with dimensions of $3\times3\times7$ (L) mm$^{3}$ was used for the experiment. The Nd doping rate for the Nd:YAG crystal was 1.1%, and the initial transmission ($T_{\rm i}$) of the Cr$^{4+}$:YAG crystal at 1064 nm was 20%. The entrance face of this gain medium was coated for high transmission at 808 nm and high reflectivity at 1064 nm, whereas the second face was coated for a reflectivity of 60% at 1064 nm and high reflectivity at 808 nm.
cpl-36-3-034201-fig4.png
Fig. 4. Schematic of the passive Q-switched laser with quick tunable pulse-width capability.
An auxiliary 808 nm laser (obtained from BWT, Beijing), which is a fiber-coupled diode with an NA of 0.22 and a core diameter of 200 µm, was used to control the initial transmission of the Cr$^{4+}$:YAG crystal before pumping the inversion population of the gain medium to the maximum in the cavity. An optical system made up of two plano-convex lenses each with a focal length of 75 mm was used to couple the controlling beam into the Cr$^{4+}$:YAG crystal. The auxiliary controlling laser is modulated at a pulse duration of 300 µs and at a repetitive rate of 10 Hz. For changing the initial transmission of the Cr$^{4+}$:YAG, the pumping laser and controlling laser were operated at the same time with no time delay. The laser pulse widths were detected using a high-speed photo detector (DET08CFC/M InGaAs based Detector, Thorlabs, USA) with a typical rising time of 70 ps and a bandwidth of 5 GHz. The signals were displayed using a digital oscilloscope (Wavepro 7000, LeCroy, USA). The output pulse energy corresponding to 1064 nm was detected using a laser energy meter (StarLite7Z01565, Ophir, Israel), and the beam characteristics of the output laser were measured by a charge-coupled device (WinCamD-UCD12, DataRay, USA). Figure 5 shows the normalized pulse shape evolution with the variation in the auxiliary controlling laser beam intensity $I/I_{\rm s}$. For Cr$^{4+}$:YAG, the saturation intensity $I_{\rm s}$ at 808 nm is about 20.7 kW/cm$^{2}$. Because the output laser beam diameter is about 400 µm on the output surface, the beam diameter of the controlling laser focusing on the Cr$^{4+}$:YAG was adjusted to 500 µm for good results. Thus the 0–100 W controlling peak power can be converted to 0–2.46 times saturation intensity. The output pulse width of the Nd:YAG/Cr$^{4+}$:YAG passive Q-switched laser can be tuned by changing the output power intensity of the auxiliary controlling laser. The output laser pulse width increases with the power intensity of the auxiliary controlling laser beam. The tunable range of the output laser pulse width is from 550 ps to 1492 ps (full width at half maximum). The pulse duration of the pumping laser ($\tau_{\rm p}$) was fixed at 300 µs with a repetitive rate of 10 Hz. By focusing the controlling laser beam onto the Cr$^{4+}$:YAG crystal, the initial transmission of the Cr$^{4+}$:YAG laser was increased, thereby increasing the output pulse width.
cpl-36-3-034201-fig5.png
Fig. 5. Output pulse width with the variation in $I/I_{\rm s}$.
cpl-36-3-034201-fig6.png
Fig. 6. Output pulse width versus controlling beam laser intensity.
Figure 6 shows the comparison between the experimental pulse width and the theoretical pulse width. The experimental results are in good agreement with the theoretical results. The pulse duration of the controlling laser ($\tau_{\rm c}$) is fixed at 300 µs with a repetitive rate of 10 Hz. It can be concluded that the output laser pulse width increases with the intensity of the auxiliary controlling laser.
cpl-36-3-034201-fig7.png
Fig. 7. Output pulse energy and peak power versus output pulse width.
cpl-36-3-034201-fig8.png
Fig. 8. Beam pattern characteristics versus output pulse width.
Figure 7 shows the variations in the pulse energy and peak power with different output pulse widths. When the pulse width is tuned from 550 ps to 1492 ps, the output pulse energy increases from 147 µJ to 184 µJ and the output pulse peak power decreases from 267 kW to 123 kW. The output pulse energy and peak power are significantly correlated with the output pulse width when the pumping power is fixed at 30 W. This shows that the output laser pulse energy increases and the output peak power decreases with the increase of the controlling laser intensity under a constant pumping power condition. Figure 8 shows the beam characteristics of the output 1064 nm laser. It can be seen that the beam intensity is an ideal Gaussian distribution. The beam quality factor $M^{2}$ was kept under 1.6 by changing the output pulse width. By increasing the controlling laser beam intensity and thereby increasing the output pulse width, there will be some residual controlling beam transmission through Cr$^{4+}$:YAG to Nd:YAG. The residual controlling beam pumps the Nd:YAG with a larger gain transverse size, which results in larger transverse mode oscillation, thus the beam quality factor $M^{2}$ becomes slightly worse. Here $M^{2}$ was measured using a lens with a focal length of 75 mm. In summary, a passive Q-switched laser with quick tunable pulse-width capability ranging from sub-nanosecond to nanoseconds has been studied and experimentally demonstrated. In this laser, an auxiliary controlling laser beam is used to saturate the Cr$^{4+}$:YAG crystal and thereby to change the initial transmission of the Cr$^{4+}$:YAG crystal before pumping the inversion population of the gain medium to the maximum. The obtained laser pulse width ranges from 550 ps to 1492 ps. The obtained output laser pulse energy and pulse peak power are in the range of 147–184 µJ and 267–123 kW, respectively. The quick tunable pulse-width laser can help extend the application of tunable pulse-width lasers, particularly to fields that require quick pulse-width tuning between two pulses. References Laser-induced optical breakdown on hard and soft tissues and its dependence on the pulse duration: experiment and modelFemtosecond laser corneal ablation threshold: Dependence on tissue depth and laser pulse widthLaser drilling of advanced materials: Effects of peak power, pulse format, and wavelengthPulse width and energy influence on laser micromachining of metals in a range of 100fs to 5psLuminescence selective output characteristics tuned by laser pulse width in Tm3+ doped NaYF4 nanorodsLaser Stimulation of Auditory Neurons: Effect of Shorter Pulse Duration and Penetration DepthVariable stimulated Brillouin scattering pulse compressor for nonlinear optical measurementsEffect of pulse width on near-infrared supercontinuum generation in nonlinear fiber amplifierPulse-width and focal-volume dependence of laser-induced breakdownSPIE ProceedingsEffect of Laser Pulse Width on the Laser Lift-off Process of GaN FilmsThermal tuning of laser pulse parameters in passively Q-switched Nd:YAG lasersEnd-pumped temperature-dependent passively Q-switched lasersSub-nanosecond laser induced air-breakdown with giant-pulse duration tuned Nd:YAG ceramic micro-laser by cavity-length controlControllable Passively Q-Switched LaserOptimization of Q-switched lasers
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