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We report on type-I phase-matched second harmonic generation (SHG) in three nonlinear crystals: DKDP (98% deuteration), YCOB (XZ plane), and LBO (XY plane), of 8 J, 10 Hz cryogenic gas cooled Yb:YAG laser operating at 1029.5 nm. DKDP exhibited an efficiency of 45% at a peak fundamental intensity of 0.24 GW/cm2 for 10 Hz operation at 10 ns. At the same intensity and repetition rate, YCOB and LBO showed 50% and 65% conversion efficiencies, respectively. Significant improvement in conversion efficiency, to a maximum of 82%, was demonstrated in LBO at 0.7 GW/cm2 and 10 Hz, generating output energy of 5.6 J at 514.75 nm, without damage or degradation. However, no improvement in conversion efficiency was recorded for YCOB at this increased intensity. Additionally, we present theoretically calculated temperature maps for both 10 J and 100 J operation at 10 Hz, and discuss the suitability of these three crystals for frequency conversion of a 100 J, 10 Hz diode pumped solid state laser (DPSSL).
© 2016 Optical Society of America
1. Introduction
Real-world applications exploiting ultra-high intensity light-matter interactions will require development of lasers and technology capable of operating at high pulse energy and repetition rate. These applications include laser particle acceleration, active real time imaging and new medical therapies, which are reliant on efficient high energy femtosecond (fs) laser pulses for generation of particles (protons etc.) or secondary radiation (x-rays, γ-rays etc.) at repetition rates of 10s of Hz [1–3]. The next generation of ultra-high intensity laser facilities, such as ELI-Beamlines [4] operating at petawatt (PW) levels (with fs pulse widths) will require high energy nanosecond (ns) pump lasers operating in the green at wavelengths near 500 nm, coinciding with the peak in the absorption spectrum of Ti:sapphire [5], or suitable for pumping optical parametric chirped pulse amplification (OPCPA) nonlinear crystals [6].
Ytterbium doped ns solid-state lasers are ideal for high energy and high repetition rates laser operation, owing to their long fluorescence lifetime (ms), high thermal conductivity (YAG host) and suitability for diode laser pumping. However, their lasing wavelength near 1 µm is not suitable for Ti:Sapphire or conventional OPCPA schemes (generating fs pulses near 800 nm). This gap in wavelength is bridged by second harmonic generation (SHG) of 1 µm lasers using nonlinear crystals. SHG of such lasers has been reported for many nonlinear crystals [7,8], however, few SHG experiments with high energy 1 µm lasers at high repetition rates have been reported in the literature. For example, the HALNA group reported 12.5 J at 527 nm at a repetition rate of 10 Hz using CLBO with conversion efficiency of 71.5% [9]. The Mercury project at LLNL reported 22 J at 10 Hz and 15 ns using a YCOB crystal with an conversion efficiency of 50% [10]. However, limited data is available in the literature for large aperture (> 60 mm square) SHG in nonlinear crystals for high energy multi-hertz pulse rate lasers.
In previous publications we have presented a scalable concept for a diode pumped solid state laser (DPSSL) based on cryogenic gas cooled multi-slab Yb:YAG amplifier technology, with the potential of generating kilojoule pulse energies [11,12]. Recently, we have demonstrated a scaled-down prototype cryogenic gas cooled amplifier system (named DiPOLE) generating pulse energies of 10.8 J at 10 Hz repetition rate with a 10 ns pulse duration and wavelength of 1029.5 nm [13]. In this paper, we report on type-I phase-matched SHG in three nonlinear crystals: DKDP, YCOB, and LBO using the output of DiPOLE at pulse energies up to 8 J at 10 Hz. Additionally, we present calculations and proof-of-principle experimental results to determine the suitability of these nonlinear crystals for SHG of a 1029.5 nm, 100 J, 10 Hz DPSSL working in the Central Laser Facility (CLF) [14].
2. Theoretical calculations
2.1. Crystal parameters and efficiency calculations
Three non-linear crystals, namely, DKDP, YCOB and LBO were selected for SHG of the DiPOLE laser output at 1029.5 nm, with the aim to identify the crystal capable of delivering maximum conversion efficiency for high energy operation at 10 Hz repetition rate. Crystal lengths for maximising conversion efficiency for the type-I interaction were estimated using the SNLO software programme [15]. Table 1 shows the crystal parameters and variables used as input to this model [16–21].
Table 1. Key Parameters for DKDP, YCOB, and LBO Crystals Used in the Experiments
As shown in Table 1, YCOB and LBO have at least two times higher deff in comparison to DKDP, thus shorter crystal lengths are required to obtain similar conversion efficiencies. LBO shows a larger angular tolerance (Δθ°l) compared to the other two crystals, making it an attractive candidate for SHG in high energy systems as these tend to have large beam areas, and therefore is less sensitive to errors in the beam phase front. YCOB exhibits the largest temperature bandwidth which gives the crystal more flexibility for high average power applications. The favourable thermal properties of LBO (thermal conductivity) and YCOB (thermal conductivity and thermal acceptance) make them promising candidates for high average power applications.
Figure 1 shows the theoretical dependence of conversion efficiency on crystal length for the three crystals. All calculations and measurements were conducted with a 10 ns long, flat temporal profile fundamental pulse. However, the calculations assume a super-Gaussian (order = 10) circular spatial beam profile of diameter 18 mm and fluence of 3.08 J/cm2, whereas all experiments were done using either a 18 x 18 mm or a 10 x 10 mm super-Gaussian beam profile, with order factor of 10. Calculations indicate that 20 mm thick YCOB and LBO crystals should achieve over 86% conversion efficiency, whereas a 50 mm thick DKDP crystal with greater than 90% deuteration is required to achieve an efficiency of 70%. Owing to availability and cost constraints, 15 mm long LBO and YCOB (expected efficiencies of ~70%) crystals and a 50 mm long DKDP crystal with a deuteration level of 98% (expected efficiency of ~70%) were purchased for the experiments reported in this paper. It should be noted that the calculations do not take into account any effects of thermal dephasing.
Fig. 1 Predicted conversion efficiencies for DKDP, YCOB and LBO calculated by SNLO software for an 18 mm diameter beam and fundamental fluence of 3.08 J/cm2.
2.2 Thermal modelling for 10 J, 10 Hz SHG
In order to assess the longitudinal and transverse temperature differential in the crystals used in the experiments, heat deposition and flow were modelled using ANSYS (R15.0) package. A steady state condition was assumed in terms of energy absorbed, using the length and absorption coefficient for the particular crystal. A range of heat transfer coefficients (HTCs) were used in the model to simulate various cooling scenarios. Thermal conductivity was considered to be isotropic in all cases, calculated as the mean of the different anisotropic coefficients in the DKDP and LBO cases, as shown in Table 1. As YCOB has the same coefficient in all directions then this figure was used. To approximate conditions similar to the experiments performed, a 20 mm x 20 mm square beam with an average power of 100 W (10 J, 10 Hz) was used as the fundamental beam source. A nominal edge and face HTC of 10 W/m2/K was used, representative of simple free convective cooling from all sides in a laboratory environment. Table 2 shows the differential temperature results calculated for DKDP, YCOB and LBO. Note that the calculated temperature differential in the longitudinal ᵶ direction (ΔT) for DKDP (3.0 K) is larger than the predicted temperature bandwidth of 2.54 K for the 50 mm long crystal used in this study. YCOB appears a suitable candidate for high average power frequency conversion applications, as it shows an extremely high temperature bandwidth compared to the calculated temperature at 10 J, 10 Hz operation. Furthermore, LBO exhibits 2 times higher temperature bandwidth compared to the predicted temperature difference within the crystal at 10 Hz, also making it a favourable material for high energy, high repetition rate (10 Hz) operation. This also is indicative of a 1 kHz repetition rate.
Table 2. Thermal Modelling Input Parameters and Results for 10 J, 10 Hz SHG in DKDP, YCOB, and LBO Crystals
As an example, Fig. 2 shows a 3D steady-state temperature map calculated for the DKDP crystal over the beam area. The “ᵶ” and the “χ” axes in Fig. 2 denote the longitudinal (along beam propagation) and transverse (orthogonal to beam propagation) directions and are not the crystal axes. Given the symmetric geometry, only half the crystal is shown in Fig. 2.
Fig. 2 Calculated steady-state temperature map over beam area of 50 mm thick DKDP crystal. BPD is the beam propagation direction.
2.3 Thermal modelling for 100 J, 10 Hz SHG
Successful demonstration of DiPOLE at 10 J, 10 Hz laser [13,18,21–24] has given confidence in the design of a higher energy system delivering 100 J at 10 Hz (named DiPOLE100) [14,23–25], which has been built at the CLF based on the same cryogenic gas cooled, multi-slab Yb:YAG technology at a baseline design beam size is 75 mm square [25].
Based on the calculated steady-state temperature map for DKDP thermal modelling results for the 10 J scenarios (as described in Section 2.2) for a 50 mm thick DKDP crystal clearly indicate a temperature difference outside the efficient operating regime. One way of reducing the temperature difference for operation at higher average powers is to use multiple thinner crystals arranged sequentially, increasing the surface area for cooling. To demonstrate this, a thermal model was used to predict the steady state temperature map for a 130 mm diameter and 10 mm thick DKDP crystal. The beam sized used for these calculations was 75 mm square. Table 3 details the characteristic parameters used in the model and also the calculated temperature difference values in both χ and ᵶ. The model assumes forced air cooling of the crystal faces, with a HTC of 20 W/m2/K, and the edges of the crystal held by an insulating material with a HTC of 0.01 W/m2/K. The steady state model results are shown in Fig. 3.
Table 3. Temperature Calculations for a 10-mm-thick DKDP Crystal for 100 J, 10 Hz Operation
Fig. 3 This multi-slab approach for DKDP crystal, combined with forced surface cooling, shows promise as the temperature difference in both longitudinal (ᵶ) as well as in transverse directions (χ) are within the temperature acceptance bandwidth for the crystal, which should then lead to more efficient SHG performance.
At the time of the experiment, the largest commercially available good quality LBO crystal was limited to 50 mm square aperture with 15 mm thickness, whereas larger aperture LBO up to 80 mm square has been reported [26]. The aperture and length of LBO is limited by the volume of crystal grown as well as the particular cut required. To fit the output beam of the DiPOLE100 system onto a 50 mm wide crystal, its size was reduced from 75 mm to 40 mm square, which corresponds to an increase in fluence from 1.77 J/cm2 to 6.25 J/cm2. Although an increase in the operational fluence helps to improve the conversion efficiency, it also increases the risk of optical damage. To assess whether 100 J level pulses at high repetition rate can reliably be frequency doubled with today’s LBO crystal availability, additional studies on operation at this increased fluence level were carried out. A thermal model, similar to that described in Section 2.2, was used to calculate steady state temperature maps for both YCOB and LBO crystals, with the increased thermal load associated with operating at 100 J, 10 Hz. Two different cooling scenarios were explored. The first, as described earlier, is representative of simple free convective cooling in a laboratory environment with the crystal faces and edges having a HTC of 10 W/m2/K. The second represents a crystal held by an insulator at the edges with HTC of 0.01 W/m2/K and the faces cooled by forced air with a HTC of 20 W/m2/K. Table 4 shows the results for the different scenarios. Again, both YCOB and LBO crystals show that the calculated temperature differentials in the longitudinal (ᵶ) are within the temperature bandwidth for both cooling scenarios. Therefore forced convective cooling is not required for either crystal and both are suitable candidates for 100 J, 10 Hz SHG. We plan to do extensive tests over a longer time to ensure that the crystal is in thermal equilibrium.
Table 4. Temperature Calculations for YCOB and LBO Crystals for 100 J, 10 Hz Operation
3. Experimental setup and results
The SHG experiments reported in this paper were performed utilizing the DiPOLE prototype laser system. During this study the output pulse energy up to 8 J at 10 Hz was employed, corresponding to a fluence of 2.0 J/cm2, which is consistent with the baseline design fluence for the 100 J, 10 Hz laser system. Full details of the design and performance parameters for DiPOLE have been reported elsewhere [13]. Figure 4 shows the spatial profile at the output of the DiPOLE amplifier at 8 J, 10 Hz with a fitted super Gaussian profile of order n = 10.
The output polarisation state from the DiPOLE amplifier was assessed by placing a cube polariser in the output beam when operating at low pulse energy. To achieve this, the seed input to the amplifier was deliberately delayed with reference to the pump so that low energy (below the damage threshold of the cube polariser) pulses were generated whilst keeping a similar level of thermal loading within the amplifier to that experienced at full output. The output beam was found to have 80% of its energy in vertical polarization and 20% in horizontal polarization. To ensure the correct polarization state for type-I phase matching either the crystal was rotated or the output fundamental beam polarisation was optimised with a combination a half-wave plate (λ/2) and a quarter-wave plate (λ/4).
3.1 SHG using 18 mm square beam
The first SHG experiments used an 18 mm square beam directly from DiPOLE, which provided a peak intensity up to 0.24 GW/cm2 (2.5 J/cm2) for pulse energy of 8 J in a 10 ns duration pulse. Figure 5 shows a schematic diagram of the SHG experimental setup. The fundamental beam was directed from mirror M1 and M2 (high reflective (HR) dielectric coated mirrors @ 1030 nm) onto the crystal under test. The crystal was positioned at a relay-image plane of the main DiPOLE amplifier to obtain the best possible near-field uniformity. Mirrors M3 and M4 were HR-coated for both 1030 nm fundamental and 515 nm second harmonic wavelengths. The focal spot of the second harmonic generation was characterized by focusing the leakage through mirror M4 onto camera Cam1, using an f = 750 mm focal length lens (L1). A BG40 coloured glass bandpass filter was used to suppress the fundamental light. Dichroic mirrors M6 and M7 (HR @ 515 nm, HT @ 1030 nm) were used to separate the fundamental from the second harmonic beam.
Fig. 5 Schematic of experimental setup, M1-M7: Mirrors; L1: Lens; W1, W2: Wedges; Cam 1: Camera; EM1, EM2: Energy meters; F1: Filter, BD1, BD2: Beam dumps.
The fundamental beam transmitted through M6 was directed into a water-filled beam dump (BD1) and the second harmonic beam reflected from M6 was directed into a second beam dump (BD2), using M7. Reflection from an uncoated wedge (W1) positioned in front of BD1 was used to monitor the unconverted fundamental signal on a calibrated energy meter EM1 (QE50LP-S-MB). The second beam dump contained a solution of Azorubin Pure (C20H12N2O7S2Na2) dye in water for adequate absorption at 515 nm. A second uncoated wedge (W2) was positioned in front of BD2 to measure the second harmonic energy. The second harmonic energy was measured by using a calibrated energy meter EM2 (QE50LP-S-MB). Figure 6(a) shows the measured SHG output energy and conversion efficiency for type-I DKDP at 10 Hz operation. Although the theoretically predicted conversion efficiency for 7 J input was 68% (dotted line), we could only measure a maximum of 42% experimentally. This discrepancy in the experimental results can be attributed to the temperature bandwidth as calculated previously in Section 2.3. To test this hypothesis, the measurements were repeated at 1 Hz repetition rate in order to reduce the thermal load. The conversion efficiency increased to 58% for a comparable fundamental energy, as shown in Fig. 6(b). The 1 Hz results are closer to the theoretically predicted performance, confirming thermal loading being the main cause of the observed low SHG conversion efficiency at 10 Hz operation.
Fig. 6 (a). Type-I phase-matched SHG output energy and conversion efficiency in DKDP crystal with 18 mm square beam at 10 Hz operation, (b) shows the performance at 1 Hz operation. In both graphs the dashed lines correspond to the theoretically calculated energy and efficiency for the experiment.
Type-I phase-matched SHG in YCOB, XZ plane (ϕ = 0 deg, θ = 150.9 deg) yielded a maximum conversion efficiency of 50% for a fundamental energy of 7 J, as shown in Fig. 7. This is below the theoretical value of 72%. The reason for this discrepancy is unclear. The residual absorption of YCOB at 1030nm and 515nm will contribute to the increase in the heat load, however, it is not expected to raise the temperature of the crystal more than 106K, outside the temperature bandwidth of the crystal and saturate the conversion efficiency. It could be attributed to either low optical quality of the crystal, the low angular acceptance of YCOB, and its large sensitivity to beam quality, or higher levels of residual absorption than expected leading to thermal dephasing. Further investigations are planned to determine absorption and scattering losses and testing of other samples from different suppliers to clarify the difference in measured and predicted conversion.
Fig. 7 Type-I phase-matched SHG output energy and conversion efficiency in YCOB crystal with 18 mm square beam at 10 Hz operation. The dashed lines represent theoretically calculated energy and efficiency for the experiment.
Finally, type-I phase-matched SHG in LBO conversion efficiency reached 65%, as shown in Fig. 8(a), in good agreement with theoretical calculations. As the measured efficiency in this experiment does not show saturation, a further increase in efficiency should be possible at higher peak intensity by decreasing the fundamental beam size or increasing the fundamental energy for LBO.
Fig. 8 (a). Type-I phase-matched SHG output energy and conversion efficiency in LBO crystal with 18 mm square beam at 10 Hz operation. The dashed lines represent theoretically calculated energy and efficiency for the experiment. (b) Long-term SHG output energy stability for LBO crystal. Red line represents the total fundamental energy, black line is the efficiency, green line is the second harmonic generation and grey line is the unconverted energy.
To assess the energy stability of SHG output from the LBO crystal, the laser was operated for a period of ~15 minutes, equivalent to over 9000 shots at 7 J fundamental energy and 10 Hz repetition rate. The results are plotted in Fig. 8(b). The measured RMS energy stability was 1.9%. As can be seen in Fig. 8(b), the primary source of this instability was the variation in 1030 nm fundamental energy brought about by temperature variations within the DiPOLE cryogenic amplifier. The sudden increase in SHG energy after ~100 s is caused by an increase in the fundamental (user intervention) to maintain > 7 J output at the main amplifier.
3.2 Output beam quality and temporal profiles
The SHG far-field profile is shown in Fig. 9(a), Gaussian fits to horizontal and vertical lineouts yield widths of 63 µrad and 47 µrad (FWHM) in X and Y-axis. For an 18 mm square beam these values correspond to 2.5 and 1.9 times the diffraction limit, respectively. Figure 9(b) shows the temporal profile of the fundamental input to the crystal (without SHG) and the SHG output. As expected the SHG signal grows towards the trailing edge of the pulse following the rise in fundamental intensity.
Fig. 9 (a). Far-field image of the second harmonic output generated from LBO crystal, (b) Fundamental 1030 nm and 515 nm temporal profiles.
3.3 SHG using 10 mm square beam. (Fluence up to 7.2 J/cm2)
As discussed in Section 2.3, large aperture LBO crystals suitable for SHG at 100 J with a beam size of 75 mm square (1.77 J/cm2 fluence), are presently unavailable commercially. To fit within currently available crystals, the beam must be reduced to 40 x 40 mm, confidently to a fluence of 6.25 J/cm2. Figure 10 shows a schematic of the experimental setup used during these high fluence experiments. The fundamental beam was reduced in size from 18 mm to 10 mm square using a beam reducing relay-imaging telescope incorporating a vacuum spatial filter (VSF). The VSF included a 3 mm diameter pinhole that acted as a baffle to prevent reflections being fed back into the laser chain. The output beam from DiPOLE was directed towards the telescope using a pair of mirrors M1 and M2 (HR @ 1030 nm). Mirrors P-M1 and P-M2 formed a periscope to raise the beam to the correct height ready to pass through the telescope. The beam reducing telescope was formed by a pair of plano-convex lenses L1 (f = 500 mm) and L2 (f = 350 mm) on either side of VSF. Mirror M4 then directed the de-magnified fundamental beam onto the frequency conversion crystal. The telescope was arranged such that the crystal was positioned at a relay-image plane of the main DiPOLE amplifier to obtain the best possible near-field uniformity. A HWP and QWP were placed at the output of the laser and adjusted with the help of a polariser. After correction, 98% of the fundamental energy was contained in the vertical polarization state. Leakage through the second mirror M2 was used for fundamental diagnostics, where lens L3 (with a focal length of 750 mm), and L4 (f = 75 mm), de-magnified the beam by a factor of 10 to provide a near-field image on Cam1, and a third lens L5 created a focus to record the far-field on Cam 2. The SHG output and unconverted fundamental energy were measured using the same configuration described in Section 3.1.
Fig. 10 Schematic of the experimental setup to increase the fluence on LBO and YCOB crystals. M1-M7: Mirrors; L1-L5: Lenses; HWP: Half-wave Plate; QWP: Quarter-wave plate; VSF1: Vacuum spatial filter; W1, W2: Wedges; Cam 1, Cam 2: Cameras, EM1, EM2: Energy meters; BD1, BD2: Beam dumps.
As in the previous experiments the YCOB crystal was clamped on an uncooled mount and phase-matched for type-I SHG in the XZ-plane. Figure 11 shows experimental results obtained at peak intensities up to 0.6 GW/cm2 and 10 Hz pulse repetition rate along with theoretically predicted energy and efficiency curves (dotted lines). The peak intensity saturates at 0.25 GW/cm2 and has a measured conversion efficiency of 51% and there is no increase in efficiency at 0.57 GW/cm2, which is significantly less than the theoretically calculated value of 86%. Second harmonic output energy stability was measured over a period of 7.5 minutes, corresponding to 4500 pulses at 10 Hz, the results from which are shown in Fig. 11b. It should be noted that, prior to higher fluence experiments the temperature stability of the DiPOLE cryogenic amplifier was improved, which explains the absence of the oscillations seen in Fig. 8(b). As seen in Fig. 11b, initially the conversion efficiency, as well as the SHG energy, increased following a rise in fundamental energy; however, after approximately 4 minutes the efficiency began to fall and continued to drop until the end of experiment. The reason for this drop is unclear, and further experiments on YCOB are required to determine if it is thermally induced.
Fig. 11 (a). Type-I phase-matched SHG energy and conversion efficiency in YCOB crystal with 10 mm square fundamental beam at 10 Hz operation. The dashed lines represent theoretically calculated energy and efficiency. (b) Long-term SHG energy stability for YCOB crystal.
The same experimental setup was used for type-I frequency doubling in LBO (XY-plane). Figure 12(a) shows measured SHG energy and conversion efficiency along with theoretically calculated values. At a fundamental peak intensity of 0.7 GW/cm2, the second harmonic generation pulse energy reached 5.6 J at 10 Hz, corresponding to a conversion efficiency of 82%, in good agreement with theoretical predictions. The output energy was monitored for more than 8000 shots (13 minutes), at a fundamental energy of 6.25 J (Fluence (F) = 6.25 J/cm2), as shown in Fig. 12(b). The measured SHG output energy stability was 0.7% rms, consistent with the improvement in fundamental energy stability. The conversion efficiency remained stable over the duration of the experiment (stability of 0.5% rms).
Fig. 12 (a). Type-I phase-matched SHG output energy and conversion efficiency in LBO crystal with 10 mm square fundamental beam at 10 Hz operation. The dashed lines represent the theoretically calculated energy and efficiency for the experiment. (b) Long-term SHG energy stability for LBO crystal.
Table 5 summarises the experimental results obtained during SHG experiments using large aperture DKDP, YCOB and LBO crystals.
Table 5. Summary of the Calculated and Experimental SHG Results for DKDP, YCOB, and LBO Crystal Efficiencies
4. Conclusion
The SHG results show that, type-I phase-matched SHG in large aperture LBO (XY) represents the best choice for frequency conversion of high energy, high pulse repetition rate (10 Hz) lasers operating at a wavelength near 1 µm. At this stage, YCOB should not be discounted, and we plan to test crystals from different suppliers to assess whether performance limits are related to material quality issues. Results suggest that DKDP is not suitable for high average power SHG, unless a more advanced thermal management scheme such as multi-slab active gas cooling is adopted. Future improvements include installation of an adaptive optics system to improve the beam quality and to source different YCOB crystals.
Finally, to the best of our knowledge we have recorded the highest SHG conversion efficiency of 82% from a high energy (6.25 J) and repetition rate (10 Hz) at 1030 nm fundamental source. Over an extended operating period of 13 minutes (8000 shots) the conversion efficiency remained stable, with an energy stability of 0.7% rms. No sign of laser induced optical damage was observed during testing, which provides confidence that the crystal and coating are resilient to operation at these repetition rates and pulse fluences (up to 7 J/cm2).
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