A high-brightness diode end-pumped Nd:YAG microchip laser, passively Q-switched by a Cr4+:YAG saturable absorber (SA), has been developed. The dependences of pulse energy and width were investigated based on theoretical verification to enhance the peak power. As a result, the peak power exceeded 1.2 MW with M2=1.04 and spectrum width Δλ<5.1 pm at a repetition rate of 100 Hz. Brightness of 98 TW/sr·cm2 was obtained with a supplied average electrical power of 2.3 W. The peak power increased up to 2.1 MW with M2=1.36. Peak power of 1.7 MW was obtained from a 2-cm-diameter×5-cm-long monolithic laser head.
©2008 Optical Society of America
A passive Q-switching technique can significantly simplify the operation and structure of solid-state lasers and improve compactness, safety and portability since it does not require additional complicated controllers, such as a high voltage power supply for electro-optic systems or a high frequency power supply for acousto-optic systems [1–3]. It can also shorten pulse width and enhance peak power by a microchip-type short cavity configuration. Moreover, a diode end-pumped laser has high beam quality and high brightness. Therefore, there are many applications for compact lasers, such as micro-processing, communication, and ranging.
However, the controllability or stability of passively Q-switched lasers is degraded compared with actively Q-switched ones. Limited peak power, which is from a few tens to hundreds of kW [4–9], prevents further applications.
In this letter, we present the details of a mega-watt level high brightness passively Q-switched laser discussed in . Since the lasing threshold should be high to increase the pulse energy of the passively Q-switched laser, we examined the dependences of the pulse energy on the SA initial transmission, the reflectivity of the output coupler and the beam area. However, since it was necessary to suppress the optical loss simultaneously, the pulse energy was improved by investigating the dependence on the SA initial transmission. Moreover, the pulse width, which is an important factor for brightness, was examined with cavity length. Finally, we have demonstrated the >2.1 MW peak power microchip laser within the electrically supplied power of 2.3 W for 100 Hz repetition frequency. The brightness of 100 TW/sr·cm2 should be the highest record with this kind of monolithic lasers.
Such high-brightness compact lasers have sufficiently reached the micro-processing application level . Moreover, polarization stabilizing, which is required for remote sensing and the generation of ultra-violet light and THz wave, will be reported as further work [12–14].
Szabo and Stein  first derived the relevant rate equations for passively Q-switched lasers. Then Degnan  and Pavel  developed a method for optimizing output pulse energy. Figure 1 shows a model of a diode end-pumped passively Q-switched microchip laser that includes a laser medium contacted optically to the SA. The laser medium is coated for high reflectivity (HR) at 1064 nm and high transmissivity (HT) at 808 nm on the pump side. The opposite face of the SA is coated for partial reflectivity R at 1064 nm as an output coupler. The surface between the laser medium and SA is coated for HR at 808 nm and HT at 1064 nm to prevent the absorption of pump light in the SA. The end-pump source is a pulse-operated diode laser that controls the repetition rate of the passively Q-switched laser and solves the problem of thermal effect. Ag and ASA are the effective areas of the resonator mode at the centers of the laser medium and SA, and wp is the pumping beam radius at the beam waist. The energy levels of the laser medium and the SA for the rate equations are a four-level system for Nd3+:YAG and a three-level system for Cr4+:YAG, respectively, which include excited state absorption (ESA) in SA. Pulse energy Ep is given by 
and pulse width tp is given by
where three parameters,
are introduced. Here, T0 is the initial transmission of SA, hν is the photon energy at 1064 nm, γg and γSA are the inversion reduction factors  of the gain and SA, σg, σSA and σESA are the laser stimulated emission, the SA absorption cross section and the ESA cross section, Lg is the round-trip optical loss, δf=ngf/ngi is the ratio of the final and initial population inversion density ngf and ngi, and δt=ngt/ngi is the ratio of population inversion density when the total photon number is maximum ngt and ngi. Then δf is calculated as a solution to
Similarly, δt is calculated as a solution to
3. Experimental results and analysis for cavity design
3.1 Laser set up
The dependences of pulse energy and width were investigated to improve the brightness of passively Q-switched lasers. In this case, the laser medium and output coupler were separated from SA to exchange crystals easily. A 1.4-at.%-doped, 10-mm-long Nd3+:YAG crystal coated for HR at 1064 nm and HT at 808 nm on the pump side was used as the laser medium. The opposite face was coated for HR at 808 nm and HT at 1064 nm. Cr4+:YAG crystals with an initial transmission of T0=30%, 65% and 80%, both surfaces of which were HT-coated at 1064 nm, were used for the SA (SCIENTIFIC MATERIALS Co.). When the output coupler with a reflectivity of R=80% was used in , the pulse energy was limited to 0.326 mJ. In consideration of Eq. (1), the reflectivity of R=56%, which is lower than the conventional value, was selected. The cavity length was changed from 20 to 50 mm (optical length lc was from 31 to 60 mm) to investigate the dependence of the pulse width. A fiber-coupled diode laser with a core diameter of φc=400 µm, NA=0.22 and a center wavelength of λp=808 nm was used as the end-pump source. The repetition frequency of the passively Q-switched laser was easily controlled at 100 Hz by a pulse-operated diode laser. The pulse operation stabilized the repetition rate and solved the problem of thermal effect. The pulse width of the diode laser was 400 µs, which is about twice the lifetime of the upper level of the laser medium, to obtain maximum pulse energy, although the efficiency of the pump energy to the output pulse energy decreased. The peak power of the diode laser was adjusted in the range of 10 to 27 W so that only one pulse oscillated in pumping time. The pumping beam radius was constant at wp=370 µm to fix the beam areas, Ag=ASA=2.0×10-3 cm2, in each T0. Only the TE coolers were used to control the temperatures of the cavity and the pump source.
3.2 Dependence of pulse energy on initial transmission of SA
The dependence of the pulse energy Ep on the initial transmission of SA T0 with a cavity length of 20 mm (optical length lc=31 mm) was investigated to improve the brightness of the passively Q-switched lasers as shown in Fig. 2. The curve in this figure was calculated with Eq. (1), where σg=2.3×10-19 cm2, σSA=4.3×10-18 cm2, σESA=8.2×10-19 cm2 , γg=2  and γSA=1 . Estimation of the effective areas of the resonator mode from the beam radius and the M2 factor provided by the Shack-Hartman method (CLAS-2D, WaveFront Sciences Inc.) showed that Ag=ASA=2.0×10-3 cm2 as pumping beam radiuses were constant at wp=370 µm. Round-trip optical losses at laser medium Lg were determined as 1%. The experimental result and calculation clarifies that the high concentration of Cr4+:YAG improves the pulse energy of the passively Q-switched laser. The pulse energy was 13% higher than the calculation with Eq. (1) as T0=30%.
3.3 Dependence of pulse width on cavity length
Pulse width, which is an important factor to enhance the peak power and the brightness of passively Q-switched lasers, was investigated. The dependence of pulse width tp on optical cavity length lc with T0=30% is shown in Fig. 3, which shows that the pulse width is in proportion to lc. The line indicates the calculation with Eq. (2). The physical length limit as lc=24 mm shows that the optical length cannot be shortened any more by the relation of the lengths of the laser medium and the SA.
As a result, we chose T0=30% and lc=30 mm for the high brightness laser with limited pump energy, and a pulse energy of Ep=0.58 mJ and pulse width of tp=920 ps, indicating a peak power of 0.63 MW, were obtained with an average supplied electrical power of 2.6 W for 100 Hz repetition frequency. The beam quality was M2=1.1 and the brightness was B=Pp/(λM2)2=46 TW/sr·cm2 with output wavelength λ=1064 nm.
4. High brightness microchip laser
From the above result, a Cr4+:YAG with an initial transmission of T0=25% was employed to enhance the output pulse energy. Next, the length of the Nd3+:YAG laser medium was changed from 10 to 5 mm to shorten the cavity length. The pumping conditions were adjusted in accordance with the increase in the lasing threshold. The pump peak power and pulse width were 26 W and 350 µs (the average supplied electrical power was 2.3 W for 100 Hz repetition frequency), and the pumping beam radius was wp=280 µm. Figure 4 shows the pulse energy and the average power as a function of the repetition rate with a cavity length of 14 mm (optical length lc=21 mm). The pulse energy increased markedly as the repetition rate decreased due to the reduction in thermal distortion. On the other hand, the average power increased slowly and leveled off (the pulse energy decreased and the pulse width increased) as the repetition rate increased. The output pulse time shape at a repetition rate of 100 Hz is shown in Fig. 5. The pulse energy and pulse width were 0.69 mJ and 580 ps (the rise times of the oscilloscope of trO=100 ps and the detector of trD=35 ps were removed), respectively, indicating a peak power of Pp=1.2 MW. The inset shows the beam profile of the output pulse measured by the Shack-Hartman method (CLAS-2D, WaveFront Sciences Inc.). The measurement resulted in an almost single transverse mode (M2=1.04). The brightness of this laser was up to B=98 TW/sr·cm2, which is comparable to high power actively Q-switched lasers. Figure 6 presents the etalon fringe pattern measured by a pulsed laser wavelength meter (WA-4550, EXFO Electro-Optical Engineering Inc.) at a repetition rate of 100 Hz. The measured spectrum width was less than the equipment resolution limit of 5.1 pm, and there was no satellite peak around the main peak. The Free Spectral Range (FSR) of the laser with an optical cavity length of 21 mm is 7.1 GHz, which is larger than the equipment resolution of 1.3 GHz, indicating a single longitudinal mode oscillation.
In order to increase the peak power, we have changed the pumping condition as follows. The pump beam radius was wp=330 µm and the pump peak power and pulse width were 29 W and 500 µs (the average supplied electrical power was 3.6 W for 100 Hz repetition frequency). Then the peak power exceeded 2.1 MW (0.96 mJ pulse energy and 460 ps pulse width), but the M2 factor worsened to 1.36 and the brightness was limited to 100 TW/sr·cm2. Extending the pump beam area deteriorated the beam quality of the passively Q-switched laser.
Figure 7 shows an optical head that includes a laser medium contacted optically to the SA, which shortened the cavity length to 8 mm (optical length lc=15 mm) and enhanced the peak power. The pump peak power and pulse width were 28 W and 420 µs, and the pumping beam radius was wp=300 µm. A peak power of 1.7 MW (0.67 mJ energy and 400 ps pulse width) was obtained from a 2-cm-diameter×5-cm-long laser head. There are problems of beam quality in the optically contacted cavity since fine alignment of the cavity was impossible, and parallelism of the crystals needs to be improved.
The highest-brightness Nd3+:YAG microchip laser, passively Q-switched by Cr4+:YAG with supplied electricity of 2.3 W for 100 Hz repetition frequency, to our knowledge, has been demonstrated. We clarified theoretically and experimentally that a decrease in the initial transmission of SA and shortening the cavity length achieved high brightness. As a result, the maximum peak power exceeded 1.2 MW (0.69 mJ energy and 580 ps pulse width) at a repetition rate of 100 Hz with single transverse and longitudinal mode oscillation (M2=1.04 and spectrum width < 5.1 pm). Brightness of 98 TW/sr·cm2, comparable to high power actively Q-switched lasers, was obtained from a compact single cavity head without an amplifier. The pulse energy was 13% higher than calculation with Eq. (1) and the pulse width was 26% broader than calculation with Eq. (2). A peak power of 2.1 MW (0.97 mJ energy and 460 ps pulse width) was obtained by extending the pump beam area, but the M2 factor worsened to 1.36 and the brightness was limited to 100 TW/sr·cm2. We demonstrated the laser set-up that included a laser medium contacted optically to the SA, and a peak power of 1.7 MW (0.67 mJ energy and 400 ps pulse width) was obtained from a 2-cm-diameter×5-cmlong laser head. The temperature of all systems, which include a cavity and a pump source, was controlled only by TE coolers. Such high-brightness compact lasers can be used for many applications, such as processing and measurement.
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