1. Introduction

A very compact and high peak power laser is attractive for various applications based on laser induced plasma breakdown requiring a high degree of movability, such as laser ignitor [1,2], laser peening [3] of metallic bridges, long-distance laser induced breakdown spectroscopy (LIBS) [4], robotic laser material processing [5] and ultrasonic technique [6]. Giant pulse microchip lasers (MCLs) with a high peak power based on short sub-ns pulse duration are therefore strong candidate lasers for such applications. MW peak power of MCL, comparable to the peak power of fs lasers with <1 uJ pulse energy (E) and <1 ps pulse duration (τ), can easily create laser induced plasma in almost all materials.

The unique properties of MCL such as sub-ns pulse duration as well as single axial mode [7] are advantageous for the pump source of efficient nonlinear optics processes because of a good balance between high intensity for nonlinearity and long interaction time to use the parametric gain length of nonlinear materials [8–11]. On the other hand, the sub-ns pulse duration shorter than the steady-state stimulated Brillouin scattering (SBS) buildup time resulted in the three-order high conversion efficiency of THz-generation in LiNbO₃ as well as the high pump intensity [12,13]. Sub-ns pulse duration is also energy-efficient for cascade-ionization based air-breakdown because of the lower breakdown threshold fluence than the longer ns pulses [14].

Peak power scale of MCL was realized by mainly introducing quasi-continuous-wave (QCW) end pump and high thermal conductive laser host material such as YAG to reduce thermal effects inside the material. The high damage threshold of YAG causes the only choice of Cr:YAG as saturable absorber. In fact, almost all MCLs with MW level peak power, based on >1 mJ pulse energy and <1 ns pulse duration, were realized using Cr:YAG with a low initial transmittance of such as 30% [15–20].

Further peak power scale of MCL as well as keeping compactness is necessary for applications requiring more intense breakdown spark such as an advanced ignitor for a new generation of aircraft and spacecraft, utilizing technologies such as scramjet propulsion [21]. From a practical view point, a higher peak power allowing a wider plasma area results in a faster process speed such as for laser peening. However, the pulse duration becomes broadened during power-up by enlarging laser mode area because of the degradation of beam pattern due to transverse higher-order modes. Moreover, the degradation affects its focusability or M², which results in the failure of brightness scale [B$ = $E/{τ ${\cdot} $(λ${\cdot} $M²)²}] [19]. For pulse energy scaling from 0.69 mJ to 18.0 mJ, the pulse width and M² value were degraded from 590 ps and 1.04 to 1.34 ns and 10.53 respectively. The corresponding brightness reduction was from 95.5 TW/(sr${\cdot} $cm²) for 0.69 mJ to 10.7 TW/(sr${\cdot} $cm²) for 18.0 mJ [17,19].

Because the problem of pulse broadening and M² increase during energy scale in flat-flat cavity is inevitable even using cryogenic cooling [20], we proposed a flat-convex unstable resonator MCL because it allows a uniform donut beam pattern during energy scaling while keeping compactness. We reported a record 27.7 MW peak power unstable cavity MCL with a pulse energy of 13.2 mJ and a pulse width of 476 ps at 10 Hz [19]. A donut beam in near field changed in to a Bessel-like beam in far field, whose beam quality was estimated as a second-moment based M² of 6. The corresponding brightness was 68.0 TW/(sr${\cdot} $cm²). However, ${\sim} $30% energy concentration in ${\sim} $5 times smaller center part of Bessel-like beam in far field can further increase the brightness greater than 7 times effectively, which will be discussed later in detail.

The donut mode size can be enlarged by two ways: One way is to increase the diameter of outer ring by increasing the radius of curvature (ROC) of output cavity mirror with the same size. The other way is to increase both diameters of inner and outer ring such as keeping the same magnification m (=b/a, where a and b are the diameter of inner and outer ring respectively). The energy scale while increasing m should overcome the increasing round-trip loss (=1−m⁻²).

In the case that a pump beam size is smaller than an available mode size, which is geometrically determined by a ROC of output cavity mirror, an energy scale can be possible by increasing the pump size up to the available mode size if the pump power density can overcome the increasing round-trip loss. However, it was difficult to improve the pulse energy of 13.2 mJ [19] even using about two times higher pump power of 1.5 kW. Therefore, we change Gaussian-like pump to uniform intensity pump, which allows the higher intensity near the edge of pump beam, to overcome the increasing round-trip loss. As a result, we demonstrate further peak power and brightness improvement such as a new record peak power of 59.2 MW and a successful brightness scale up to 88.9 TW/(sr${\cdot} $cm²) with a pulse energy of 24.1 mJ, a pulse width of 407 ps, and M² of 7.67 at 20 Hz.

2. Experimental method

Figure 1 shows the schematic experimental setup. The unstable cavity was composed of a flat input mirror (M_i) and a convex output mirror (M_o), containing a monolithic Nd:YAG/Cr⁴⁺:YAG ceramics (Baikowski Japan Co., Ltd.) with a dimension of 6${\times} $6${\times} $7 mm³. The Nd-doping rate and the initial transmittance of Cr⁴⁺:YAG was 1.1 at.% and 30%, respectively. The pump side surface of M_i was anti-reflection (AR) coated at 808 nm and the laser medium side surface was dual coated for AR at 808 nm for end-pump and for high-reflection (HR) at 1064 nm for laser oscillation. M_o was a HR coating in a diameter of 2 mm on the convex surface of a half-inch plano-convex lens (SL) with a radius of curvature of 52 mm. Both surfaces were AR coated at 1064 nm except the part of M_o. The detailed cavity design was reported elsewhere [19]. The monolithic ceramics was tightly set in a metal holder using an indium sheet and was thermoelectrically air cooled.

 

Fig. 1. Schematic of the experimental setup, where LD is the diode laser, OS is the optical system for uniform power pumping in a square or hexagon shape, M_i(o) is the input (output) cavity mirror, and SL is the substrate plano-convex lens of M_o. The square pump beam patterns around working distance (d${\approx} $20 mm) beyond OS are shown in dashed line.

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A QCW fiber-coupled diode laser (LD, Dilas diodenlaser GmbH., Germany; λ₀= 808 nm, P₀= 1.5 kW, τ_max= 0.5 ms) was used as the pump source. The core diameter of the fiber was 0.8 mm. Two similar types of optical system (OS) over conventional telescope were used to end pump the gain medium in uniform power area of square or hexagon. The OS was composed of such as a collimation lens for fiber, a fly-eye lens and square or hexagon rod for beam homogenizing, and zoom lens to control the homogenized beam size.

The pump beam sizes of ∼3 mm side for square and ∼3.2 mm minimal diameter for hexagon were used at the working distances of ∼20 mm, where the power difference in the pump areas is less than 5%. The square pump beam patterns around working distance are shown in Fig. 1. The patterns were captured by a CMOS camera with a 4f lens system to image the photoluminescence area of a 0.1 mm thick Nd:YAG ceramics excited by the strong pump in the short working distance.

A convex lens was used to collimate the diverging laser beam beyond SL. Three HR mirrors were used to deliver the laser beam to an energy sensor (Ophir Optronics Solution Ltd., Israel) as separating a residual pump beam. Another CMOS camera (Cinogy Technologies, Germany) was set to capture the near field laser beam. A beam quality M² tool (Cinogy Technologies, Germany) with a software of RayCi was used to determine 2^nd moment beam width and M² value. The pulse width was measured using a photodetector with a rise time of about 30 ps and a 33 GHz oscilloscope (Keysight Technologies, USA). A power reduced whole laser beam was focused into the photodetector.

3. Results and discussion

The laser characteristics of unstable cavity MCL using the uniform pump were compared with a reported unstable MCL using a Gaussian-like pump [19]. The uniform square and hexagon had a similar area with a side of ∼3 mm and a minimal diameter of ∼3.2 mm, respectively. The diameter of Gaussian-like pump using a conventional telescope with two convex lenses was ∼2.6 mm. In the case of uniform pump, the larger pump area was accepted because of the higher intensity than the Gaussian-like pump near the beam edge, overcoming the increasing round-trip loss. An improvement of pulse energy was achieved from 13.2 mJ by Gaussian-like pump to 17.0 mJ by square and 24.1 mJ by hexagon using the larger pump beam areas with uniform power distribution. The near field beam patterns were donut shapes with a center Poisson spot as shown in the inset of Fig. 2(a). Although the similar area of ∼9 mm² of square and hexagon pump, the higher energy of 24.1 mJ was obtained from hexagon pump because of a better mode matching between laser and pump. The outer ring of the donut pattern for hexagon pump was a hexagon shape. On the other hand, the lower energy of 17.0 mJ came from a worse mode matching between square pump and circular laser. The only partial inner circle of square could be the gain area. However, an instable square donut mode changing to circular donut mode was observed by adjusting cavity alignment. A stable square donut mode was possible by using a concave-convex cavity (not shown here). Note that uniform circular pump can be the best pump scheme because of the circular output cavity mirror. The circular laser mode reflected from the circular output cavity mirror can be amplified efficiently in the circular gain area. Because of the same output cavity mirror for the three cases, the beam pattern of 24.1 mJ had a lager magnification m of ∼2. The laser pulses with the three energies had similar shape as shown in the Fig. 2(a).

 

Fig. 2. (a) Measured pulse shapes using Gaussian-like (black) [19], square (blue), and hexagon (red) pump with an energy of 13.2 mJ, 17 mJ, and 24.1 mJ, respectively. Inset: the beam patterns in near field. (b) Measured pulse energies for the three pump schemes during 5 minutes. Inset: the measured pulse energy for hexagon pump during 50 minutes.

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Figure 2(b) shows the measured pulse energies during a short term of 5 minutes. The average pulse energy was 13.2 mJ, 17.0 mJ, and 24.1 mJ with a root mean square (RMS) stability of 1%, 2%, and 0.9%, respectively. The RMS stability of 24.1 mJ was increased from 0.9% to 1.6% in one order longer term of 50 minutes, as shown in the inset of Fig. 2(b). Not only the pulse energy but also the repetition rate was improved from 10 to 20 Hz by using the uniform power pump.

The polarization status for the three pulse energies was almost linear polarization even using the same ceramic of Nd:YAG/Cr⁴⁺:YAG. The polarization ratio $P = \frac{{{E_{max}} - {E_{min}}}}{{{E_{max}} + {E_{min}}}}$ was 0.997 at 10 Hz for 13.2 mJ [19], where E_{max (min)} is the measured maximum (minimum) transmitted pulse energy through a polarizer. On the other hand, the polarization ratio of pump was 0.176. A small polarization dependent loss due to a mechanical stress (or thermal effect) induced birefringence or due to a slightly tilted surface of ceramic might be a possible reason of linearly polarized laser oscillation. However, the polarization status was degraded with repetition rate increase due to thermal depolarization [22]. In the case of hexagon pump, P value was 0.967, 0.940, and 0.919 at 20, 25, and 30 Hz in 24 mJ energy level, respectively.

In Fig. 3, the measured characteristics of MCLs with unstable resonator were compared with those of the earlier reported MW peak power level MCLs with flat-flat cavity in gray color symbols [14–20]. The MCLs with flat-flat and unstable cavity were operated at room-temperature except Ref. [20] which was based on cryogenic cooling. Figure 3(a) shows the measured pulse widths (top) and M² (bottom) as a function of pulse energy. The pulse widths at full width half maximum were 476, 452, and 407 ps for the pulse energies of 13.2 mJ (black color), 17.0 mJ (blue), and 24.1 mJ (red) respectively. To clarify the trend of pulse width and M² during energy scaling for unstable resonator, the cases of lower energies (8.8 mJ and 11.5 mJ) in the reported last work were additionally included in the same black color. The pulse width of unstable cavity did not broaden during the energy scaling in contrast to flat-flat cavity, but rather narrowed for hexagon pump. The pulse width of 407 ps was an average value with a standard deviation of 12.6 ps in 10 minutes. The narrowing may be attributed to a better alignment of cavity and mode matching between laser and pump for shorter pulse. On the other hand, the average M² $\left( { = \sqrt {M_{Maj}^2 \cdot M_{Min}^2} } \right)$ values between major and minor axis were 6.0, 7.56, and 7.67 for the pulse energies of 13.2 mJ, 17.0 mJ, and 24.1 mJ respectively. The M² values of unstable cavity were increased during energy scaling although the degree of increase is much smaller than that of flat-flat cavity. The M² values of flat-flat cavity for cryogenic cooling [20], except the highest energy data point, had similar increasing behavior. Such small increase of unstable cavity may be attributed to the increase of m or b, however, which should be confirmed with an energy scale as increasing a with the same m.

 

Fig. 3. (a) Compared pulse width (top) and M² value (bottom) between unstable (solid symbols) and flat-flat cavity (open gray symbols) as a function of pulse energy. Black, blue, and red color is for unstable cavity using Gaussian-like, square, and hexagon pump, respectively. (b) Compared peak power (top) and brightness (bottom) between unstable (solid symbols) and flat-flat cavity (open gray symbols) as a function of pulse energy. Black, blue, and red color is for unstable cavity using Gaussian-like, square, and hexagon pump, respectively. The MCLs with flat-flat and unstable cavity were operated at room-temperature except Ref. [20] which was based on cryogenic cooling.

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Figure 3(b) shows the corresponding peak power (top) and brightness (bottom). The peak power was improved from 27.7 MW for 13.2 mJ (black color) to 37.6 (blue) and 59.2 MW (red) for 17.0 and 24.1 mJ, respectively. The 59.2 MW (even 37.6 MW) is the highest peak power of MCL, to the best of our knowledge. On the other hand, the brightness scale of unstable cavity was also achieved from 68.0 TW/(sr${\cdot} $cm²) for 13.2 mJ to 88.9 TW/(sr${\cdot} $cm²) for 24.1 mJ in contrast to flat-flat cavity. This demonstration is promising further brightness scale of MCL without amplifier.

However, the brightness of unstable cavity based on second moment M² could be underestimated because of Bessel-like far field pattern. Figure 4(a) shows the cross sections of the far field patterns, as shown in the inset, for the pulse energies of 13.2 mJ in black circles, 17.0 mJ in blue squares, and 24.1 mJ in red hexagons. The position of the cross sections was normalized by their second moment beam radius (2σ). The small center part with a high intensity can increase the brightness of unstable cavity effectively. For the case of 24.1 mJ, the variation of the center part of Bessel-like beam around focal plane is shown in Fig. 4(b). The black and red open symbols were of the second moment beam radius (w) and of the radius of center part (w_eff) respectively. The w_eff was 5.75 times smaller than w, but it was slowly changed like w with a M² value of 7.67. Therefore, the w_eff had ∼4.4 times longer effective Rayleigh length (red line) than the same waist of Gaussian beam (blue line). The effective Rayleigh length can be given by ${z_{eff,R}} = \frac{{\pi w_0^2}}{{{M^2}\lambda }} = \frac{{\pi \; {{({5.75\; {w_{eff,0}}} )}^2}}}{{7.67\lambda }} \cong 4.4\frac{{\pi \; w_{eff,0}^2}}{\lambda }.$

 

Fig. 4. (a) The cross sections of far-field patterns (inset) as a function of normalized position by the beam waist radii for 13.2, 17.0, and 24.1 mJ in black, blue, and red color, respectively. (b) Measured 2^nd moment beam radius, w (black open symbols) and effective radius, w_eff (red open) and the measured energy content ratio of center part, E_eff/E (black solid) as a function of position around a focal plane. (c) The ratio between w_eff and w at focal point, w_eff,0/w₀ (black open symbols) and the energy content ratio of center part at focal point, E_eff,0/E (black solid) and the effective M², $M_{eff}^2$ (red symbols) as a function of pulse energy. (d) The estimated effective brightness of unstable cavity (solid symbols) as a function of effective pulse energy, compared with brightness of flat-flat cavity (gray open symbols) and unstable cavity using Gaussian-like (open black), square (open blue), and hexagon pump (open red) as a function of pulse energy.

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On the other hand, the energy content of center part at focal point (E_eff,0/E) was 25% but was decreased as being far from the focal point as shown in the black solid symbols in Fig. 4(b). The E_eff,0/E and w_eff,0/w₀ were changed with different M² values as shown in Fig. 4(c). The E_eff,₀/E was 30%, 26%, and 25% and w_eff,0/w₀ was 21.8%, 17.8%, and 17.4% for M²= 6.0 (E = 13.2 mJ), 7.56 (17.0 mJ), and 7.67 (24.1 mJ), respectively. If two laser beams with the same conditions such as the same beam size on focusing lens and divergence except M² value are focused by the same lens, the beam waist sizes are determined by the different M² values, $\frac{{{w_{0,1}}}}{{{w_{0,2}}}} = \frac{{M_1^2}}{{M_2^2}}$. In the same manner, an effective M² value ($M_{eff}^2$) for unstable resonator can be defined as $M_{eff}^2 \equiv {M^2} \cdot \frac{{{w_{eff,0}}}}{{{w_0}}}$ together with an effective pulse energy of E_eff,₀. The $M_{eff}^2$ was 1.308, 1.346, and 1.333 for 13.2 mJ, 17.0 mJ, and 24.1 mJ, respectively, which is shown in the red symbols of Fig. 4(c). Then the effective brightness (B_eff) of unstable cavity can be determined as ${B_{eff}} \equiv \frac{{{E_{eff,0}}}}{{\tau {{({\lambda \cdot M_{eff}^2} )}^2}}}$. The estimated B_eff values of 430, 477, and 736 TW/(sr${\cdot} $cm²) for E_eff,0 of 3.96, 4.42, and 6.025 mJ are shown in black, blue, and red solid symbols in Fig. 4(d), respectively.

4. Conclusion

We demonstrated a record 37.6 and 59.2 MW peak power Nd:YAG/Cr⁴⁺:YAG ceramic air-cooled MCL with a pulse energy of 17.0 and 24.1 mJ and a pulse width of 452 and 407 ps at 20 Hz by using a uniform power square and hexagon pump, respectively. The higher performance with hexagon pump came from the better mode matching between pump and laser having the same hexagon donut beam in contrast to a circular donut beam for square pump. The near field donut beam was changed in to a Bessel-like beam in far field, whose beam quality was estimated as 2^nd moment M² of 7.56 and 7.67 for square and hexagon pump, respectively. By using the hexagon pump, the brightness scale of unstable resonator MCL was achieved from 68.0 TW/(sr${\cdot} $cm²) [19] to 88.9 TW/(sr${\cdot} $cm²) in spite of the M² value increase from 6.0 to 7.67. However, the highly intense center part of Bessel-like beam increased its brightness effectively more than 8 times, up to 736 TW/(sr${\cdot} $cm²) with an effective M² of ∼1.3 and an effective energy of ∼6 mJ. The effectively long Rayleigh length of the intense center part also could be advantageous for specific applications. This demonstration is very promising further brightness scale of MCL without amplifier.