1. Introduction

Compact, passively Q-switched microchip lasers are attractive for many applications, such as, microprocessing, remote sensing, laser ignition, etc., due to their short pulse-width and high peak power characteristics [1–12]. The high peak power of microchip lasers can also be used for efficient wavelength conversion to the green and UV wavelengths for a variety of applications [13–15]. However, Nd:YAG microchip lasers normally use [100] cut Cr⁴⁺:YAG as the saturable absorber for passive Q-switching. This generates a laser output with unstable polarization that is not suitable for efficient wavelength conversion, if we want megawatt, or higher, peak power giant pulse generation.

Sakai et al. suggested the use of [110] cut Cr⁴⁺:YAG to obtain a stable, linearly polarized megawatt level output with quasi-continuous-wave (QCW) pumping to avoid thermal problems [16,17]. In a [100] cut Cr⁴⁺:YAG, the transmission dependence on the angle between the polarization direction and the crystallographic axis shows equal transmission peaks at an interval of 90°. Hence, there is no preferred direction of polarization. However, in a [110] cut Cr⁴⁺:YAG, the transmission is maximum when the polarization direction is parallel to the <001> crystallographic axis. Using [110] cut Cr⁴⁺:YAG, linearly polarized oscillation is possible in this preferred direction of polarization. However, this concept has so far been verified only at low pulse energies (< 1 mJ) [16,17].

In this paper, we report the realization of stable, linearly polarized, high pulse energy (3 mJ) using [110] cut Cr⁴⁺:YAG. Its second harmonic generation (SHG), under proper conditions described in this paper, results in > 6 MW peak power at 532 nm with a conversion efficiency of 85%. To the best of our knowledge, this is the first report of pulse generation with megawatt level peak output power at 532 nm from a compact microchip laser. The conversion efficiency achieved is comparable to the high efficiencies (80~90%) recently achieved with giant flash-pumped Nd:Glass lasers [18].

2. Laser structure

A schematic of the laser structure is shown in Fig. 1 . A 4 mm-thick 1.1 at. % [111] cut Nd:YAG crystal (Scientific Materials Corp.) was pumped in the QCW regime by a fiber-coupled 120 W, 808 nm laser diode (600 μm core diameter, 0.22 NA, JOLD-120-QPXF-2P of Jenoptik) at 100 Hz. A 30% initial transmission [110] cut Cr⁴⁺:YAG crystal (Scientific Materials Corp.) was used for passive Q-switching. A flat coupler with a transmission of 50% was used at the output. The total cavity length was 11 mm. A TE cooler was used to maintain the Nd:YAG and Cr⁴⁺:YAG crystal temperature at 25°C. The complete laser structure had dimensions of 60 mm x 52 mm x 61 mm and was air-cooled.

 

Fig. 1 Schematic of laser structure.

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3. Fundamental wavelength characteristics

Using the laser structure described above, we could obtain stable, linearly polarized laser oscillation at 1064 nm. An output pulse train of 3 mJ, 365 ps pulses at 100 Hz was obtained for 100 W, 300 μs width, 100 Hz, QCW pumping. This resulted in a peak power of 8.2 MW. The polarization of the output beam was stable and the ratio between the normal modes was better than 100:1.

The output beam diameter was 1 mm approximately and the M² factor was measured to be 3.4. We aimed for maximum output energy, rather than an ideal Gaussian beam.

4. Second harmonic generation

We chose LiB₃O₅ (Lithium Triborate, LBO) crystal (dual-band anti-reflection coating @ 532 nm and 1064 nm, Quality Thin Films, Inc.) for SHG due to its high enough damage threshold and a relatively large angular acceptance bandwidth that permits efficient SHG with multi-mode laser radiation. We performed SHG in the critical phase matching (CPM) regime, since any crystal temperature control mechanism would increase the size of the green laser and, so, diminish the size-advantage offered by compact microchip lasers.

At high optical intensities, when pump depletion is to be considered, SHG efficiency, η, in the absence of phase mismatch and walk-off can be expressed as:

For SHG, we used Type I LBO crystals cut at θ = 90°, φ = 12.5° and having lengths of 5 mm and 10 mm.

The 1064 nm beam was input to the LBO through a lens, as shown schematically in Fig. 2 . We used lenses of focal lengths 100 mm, 88.3 mm, 75.6 mm and 66.3 mm, which resulted in a spot diameter, 2w₀, and confocal parameter (2 x Rayleigh Range, Z_R) given in Table 1 .

 

Fig. 2 Schematic of SHG experiment.

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Table 1. Spot Diameter and Confocal Length for Focusing Lenses Used in Experiment

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The results obtained using a 5 mm-long LBO crystal are shown in Fig. 3 . The figure shows the conversion efficiency obtained when the fundamental beam is focused to spot diameters of 0.82 mm and 0.62 mm. The dashed line shows the theoretical conversion efficiency obtained from Eq. (1) for a spot diameter of 0.62 mm. The difference of the experimental values from the values under ideal phase-matching conditions for a cw plane wave is due to the phase mismatch and spatial/temporal profile effects. Since we are operating in the CPM regime, it is difficult to achieve complete phase matching.

 

Fig. 3 SHG characteristics for 5 mm-long LBO.

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For tighter focusing to a spot diameter of 0.54 mm, the optical intensity of the output 532 nm beam exceeded 2.1 GW/cm², and the anti-reflection (AR) coating on the output side of the LBO crystal got damaged.

Next, we used a 10 mm-long LBO crystal. The results of SHG are shown in Fig. 4 . While the results for spot diameters of 0.82 mm and 0.72 mm are as expected, we find that the conversion efficiency saturates quickly when the fundamental beam is focused to a spot diameter of 0.62 mm.

 

Fig. 4 SHG characteristics for 10 mm-long LBO.

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In order to examine this case further, we plotted the SHG output with time, as shown in Fig. 5 . It is seen that for a spot diameter of 0.82 mm, the SHG output is stable with time. However for a spot diameter of 0.62 mm, the SHG output drops after about 7~8 s. This seems to be a thermal effect that causes dephasing between the fundamental and the second harmonic beam, reducing the conversion efficiency. Hence, although the conversion efficiency is higher for tighter focusing at low intensity, it saturates as the input power intensity increases. We attribute this saturation to a combination of pump depletion, spatial mismatch and thermal dephasing.

 

Fig. 5 Plot of output power with time showing thermal dephasing. The maximum value on the time axis is 5 min.

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As a consequence, for a 10 mm-long LBO, we found that focusing the fundamental beam to a spot diameter of 0.72 mm was most suitable. The results for this spot diameter are shown in Fig. 6 . We obtained 1.7 mJ pulse energy with 265 ps pulse width. This resulted in a peak power of 6.26 MW at 532 nm for an input peak power of 7.39 MW at 1064 nm. The SHG conversion efficiency is 85%. The M² factor of the 532 nm beam was measured to be 3.

 

Fig. 6 SHG conversion characteristics under optimum conditions.

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5. Discussion

For a given input fundamental beam, the parameters that can be chosen to optimize the wavelength conversion efficiency are the nonlinear crystal length and the spot diameter to which the fundamental beam is focused.

Theoretical analysis has been carried out by several authors to determine the optimum focusing conditions. If the ratio of the crystal length, L, to the confocal parameter, 2Z_R, is defined as the focusing parameter,ξ, Bjorkholm has derived the optimum focusing parameter, for maximum SHG, as ξ = π/2 [19]. Boyd and Kleinman took the effect of double refraction into account, and derived the optimum focusing parameter to lie between 1.39 and 2.84, depending on the effect of double refraction [20].

However, with the availability of high peak power lasers, enabling high SHG efficiencies, pump depletion assumed importance. The effect of pump depletion was taken into account by Shen and Siegman in their analytical approach using fast-Hankel-transforms [21]. They concluded that, as the intensity of the fundamental beam increases, causing greater pump depletion, maximum SHG efficiency requires progressive weaker focusing, with the optimum focusing parameter, ξ, reducing to even less than 1. Defining an intensity parameter, K = (LZ_R/2Z_Q²)^{1/ 2}, where depletion length Z_Q = k_ω /(ω_ω²d_eff μ₀E_ω), with μ₀ = permeability of free space and E_ω = peak fundamental electric field, they plotted SHG efficiency against the focusing parameter, ξ, for different values of the intensity parameter, K.

In our case, for the optimum results shown in Fig. 6, L = 10 mm, Z_R = 10.7 mm and E_ω = 9.24x10⁷ V/m, for an input peak power of 7.39 MW. Taking d_eff = 0.83 pm/V and n = 1.6 for LBO, the intensity parameter, K, is calculated to be 1.3 and the focusing parameter, ξ, is 0.47. This is in quite good agreement with the plot given by Sheng and Siegman [21]. The conversion efficiency obtained by us is higher than that shown in their plot, because our beam is relatively flat-topped as compared to the ideal Gaussian beam assumed by Sheng and Siegman. In a flat-topped beam, even the wings of the beam will contribute to the second harmonic generation to some extent, whereas they will not do so for an ideal Gaussian beam.

Next, we have found that, for the pulse energies being used by us, thermal effects become significant in LBO, even at a low repetition rate of 100 Hz. As expected, the significance of this effect depends on the length of the crystal. We do not observe significant thermal dephasing for the shorter crystal length of 5 mm, whereas, it becomes important for a crystal length of 10 mm.

While determining the spot diameter to which the fundamental beam is focused, care has also to be taken of the optical damage threshold. LBO crystal has a high damage threshold (> 20 GW/cm²). However, its AR coating is vulnerable to damage at much lower intensities at 532 nm (~2 GW/cm², in our case).

6. Conclusion

We have demonstrated multi-megawatt peak power output at 532 nm from a microchip laser. This could be achieved by using a [110] cut Cr⁴⁺:YAG crystal for passive Q-switching, in order to obtain a stable, linearly polarized output at 1064 nm. The laser output was then frequency doubled using Type I LBO to achieve 85% conversion efficiency, giving 1.7 mJ, 265 ps pulses at 100 Hz. This results in a peak power of 6.26 MW. This is a step forward in giant micro-photonics [22], and should be useful for a variety of applications, such as, range finding, materials microprocessing, etc.