1. Introduction

There are a large number of petawatt-class laser systems in operation or in planning stages which are being built for scientific research [1]. It is estimated that by the end of 2017, there will be more than 125 petawatts of total peak power laser capacity worldwide [2]. Most of these systems operate in single-shot mode and enable proof-of-principle demonstrations. However, a variety of industrial and discovery science applications such as secondary source generation require laser drivers that produce multi-terawatt to petawatt peak power laser pulses with high repetition rates [3]. Compression of pulses to durations above 150fs is routinely done with multilayer dielectric (MLD) gratings [4], which their high efficiency and low absorption are optimal for increased average power operation. However obtaining broad bandwidth and high damage threshold MLD gratings remains a challenge, which is why compression of pulses to sub-150fs pulse durations is typically done with gold gratings. Unfortunately, the gold coating of each compressor grating can absorb 3-5% [5] of the incident laser energy which results in heat deposition into the grating. Gratings consisting of gold-coated photoresist ridges [6] are commonly used for the compression of broad-bandwidth beams. Etching directly into the substrate to form the ridge structure is done to manufacture a more robust grating, without photoresist ridges [7,8]. Recently a new class of gold diffraction gratings has been developed at LLNL in which refractory etched dielectric ridges are fabricated from holographic lithography and overcoated with gold [9]. This new process produces an engineered, photoresist-free, ridge with increased efficiency and bandwidth when compared to gratings made from substrate etched ridges.

Thermal management in the components of a laser system poses a significant challenge for enabling rep-rated (high average power) petawatt lasers [10]. For pulse compression, control of grating temperature is critical to minimize distortions from thermal expansion; both large scale deformation of the substrate and also deformation of the groove shape. High peak power short pulse compressors require operation in vacuum which results in nearly eliminating convective cooling. Gratings are typically held with minimal contact using plastic or polymer dowel pins to reduce mounting induced stress, however this significantly limits conductive cooling. Active cooling of synchrotron beamline monochrometers has been demonstrated in order to prevent thermal expansion from degrading their resolution [11,12], but cooling has not yet been demonstrated on ultrafast laser compressors nor at the scale required for petawatt lasers. In the case of high energy lasers with meter-size gratings, the thick glass grating substrates, which are necessary for meeting requirements for polished substrate flatness, can make an actively cooled configuration challenging. Heat deposited into the gratings can cause thermal gradients and surface distortion from thermal expansion. This distortion in a pulse compressor can increase the focal spot size, pulse duration, and spatial/temporal coupling, resulting in a significant reduction of the on-target intensity. Additionally, thermal management is required to keep the gold layer at a temperature below 250C to maintain desired height and width of the grooves [12]. Thermal effects in compressors of ultrafast laser systems have been observed at laser average powers as low as a few watts [13,14]. While the BELLA laser is currently the world’s highest repetition rate PW laser (1 Hz) with an average power of ~40W [15], laser systems such as those in ELI Beamlines facility are planned to operate at higher repetition rates [16,17]. We present, to our knowledge, the first study of average power limits of pulse compressors and the first demonstration of active cooling of compressor gratings high-energy ultrafast laser systems.

2. Thermo-mechanical Model

Finite Element Analyses using ANSYS Workbench 17.0 were carried out to simulate the thermo-mechanical evolution of a single diffraction grating of a compressor under use conditions. Figure 1(a) shows a finite element model of a grating with a typical mesh. We compare the performance for 1480 lines/mm groove density gratings on two substrate materials that are being used in the fabrication of gratings in our Advanced Optical Components and Technologies Program – Schott N-BK7 (BK7) and Dow Corning Ultra-Low Expansion (ULE) 7972 glass [18]. BK7 is commonly used as the substrate material for reflective optics due to its low cost. Alternatively, ULE is a titania-silicate glass engineered for low thermal expansion near room temperature. A typical instantaneous coefficient of thermal expansion of ULE as a function of temperature is shown in Fig. 1(b) [18]. Over the temperature range of −30C to 70C, the total coefficient of thermal expansion of ULE is two orders of magnitude lower than BK7. Using ULE as the substrate can provide significant improvement in the high average power operation of the grating (as discussed in section 3). The gold coating itself is not considered in this analysis since the temperature gradients within the gold are negligible due to the high thermal conductivity and small layer thickness. The substrate dimensions (8cm thick x 50cm wide x 27cm tall) are consistent with the input grating of a pulse compressor for a laser with 40J of energy and at an angle of incidence of 57° with respect to the surface normal. The grayed area on the front surface (39cm wide x 21.3cm tall) represents the FWHM of a 20th order square supergaussian beam incident on to the grating. The model in Fig. 1(a) shows cooling bars attached to the top and bottom surfaces. The heat source input to the simulations is from absorption (from gold) of the incident laser average power distributed across the beam profile. The thermal properties associated with the contact between the grating and cooling bars is included in our analysis. Conduction of heat from the cooling bars to the external mounting hardware as well as convection are both not included as these are assumed to be negligible. In the simulations the grating is constrained at dowel pin slots located on the top and bottom surfaces (shown in Fig. 1), but is permitted to expand in the horizontal and vertical directions. The distortion from gravity is also included.

 

Fig. 1 (a) Finite element model of a 50cm wide x 27cm tall diffraction grating fabricated at LLNL. Cooling bars are attached on the top and bottom edges. The finite element boundaries used in our model are shown. The dark gray region in the middle indicates the laser beam footprint (39cm x 21cm) projected on the grating at the 57° incidence angle. (b) The instantaneous coefficient of thermal expansion (CTE) as a function of temperature for the ULE substrate from [18].

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In our analysis we evaluated different active cooling geometries. While cooling through the back surface provides more homogeneous temperature distribution that becomes relevant for going to higher average power levels, issues such as CTE mismatch with the grating mounts, integration with existing mounting hardware, light transmission through the substrate, and substrate re-processing makes this geometry more challenging. For the analysis with active cooling, bars are attached on the top and bottom surfaces (Fig. 1) and held at a constant temperature. Computational fluid dynamics analysis of water circulated through cooling channels within the bars validated the use of the constant temperature bar condition. For the analysis with no active cooling, no bars are attached as they may cause additional deformation from mismatch in the coefficient of thermal expansion. Radiation is included as a cooling term where the substrate is assumed to have an emissivity of 0.8. To simplify this analysis the radiation emitted from the grating is not re-absorbed, which may not necessarily be the case for a grating on a glass substrate in a metal vacuum chamber. This effect should be negligible for cases where radiative cooling is not significant (i.e. low temperatures).

3. Results

3.1 Steady State Analysis for a Cooled Grating

Figure 2 shows the steady state simulation results for a grating at use conditions irradiated by a 40J Ti:Sapphire-based petawatt laser operating at 10Hz. The input to the simulations is heat flux absorbed by the gold overcoating layer. The distribution of this heat flux, shown in Fig. 2(a) corresponds to 3.5% absorption of a 400W average power laser distributed across this profile, where the peak heat flux absorbed is 164W/m². Figure 2(b) shows the grating surface temperature distribution. The rectangular black line indicates the extent (FWHM) of the input beam. The temperature at the top and bottom surfaces is uniform due to cooling bars attached here and held at a constant temperature. The temperature varies by 14C across the entire grating surface. The temperature variation results in non-uniform expansion of the substrate, where the resulting deviation, from flat, of the grating surface is shown in Fig. 2(c). In this case the grating front surface has a 47nm peak to valley (PV) variation across the beam aperture, which is on the order of the manufactured surface figure for a substrate of this size. The vertical shift in the peak of the deflection is due to the effects of gravity on the large substrate.

 

Fig. 2 (a) Estimated distribution of heat flux absorbed by a diffraction grating which is irradiated by a 400W average power laser. For this case the peak heat flux absorbed is 164 W/m² and the total absorbed power is 14W. This heat source is the input to the thermo-mechanical simulations. The grating surface (b) steady state temperature, (c) height deviation, and (d) horizontal deflection are shown for an actively top and bottom surface cooled grating in vacuum. The black lines indicate the FWHM of the beam footprint.

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The deflection of the grating along the horizontal direction is shown in Fig. 2(d), where the grooves are aligned along the vertical direction. The magnitude of this deflection is ~100nm and corresponds to a line density variation that is less than manufacturing tolerances. This effect is of interest as any deformation along this axis corresponds to spatial non-uniformities of the grating lines which can degrade the on target spatial and temporal performance. Here the variation along the vertical direction is due a combination of thermal expansion and gravity.

3.2 Transient Analysis for Cooled and Uncooled Gratings

We compared the performance of the actively cooled grating to a grating without cooling. For the uncooled case the substrate was also ULE and no bars were attached to avoid stress effects from thermal expansion mismatch between the substrate and the cooling bars. Figure 3(a) shows the time evolution of the surface height PV for uncooled (red lines) and the cooled conditions (blue lines). Figure 3(b) shows the peak surface temperature evolution. A line is drawn at 80nm that corresponds to a surface PV of 0.1λ. We have chosen this value as the acceptable limit for deformation as it is similar to typical flatness requirements for a manufactured grating of this size. For the uncooled grating the temperature increases over a period of days of continual operation. This long time required to reach steady state is due to the fact that the 24kg grating needs to reach a high temperature (150C) for radiation cooling to be effective while only 14W of power is absorbed. Radiative cooling alone is not sufficient to keep temperatures from exceeding 200C, which in itself can be problematic. The surface profile evolves over this time period and reaches a PV of 180nm after 2 days of continuous operation. This behavior is problematic with respect to the on-target laser performance as the focal spot and potentially the pulse duration would be continually changing. Note that for the gratings in a compressor which the beam is spatially chirped a deformable mirror cannot compensate for the thermal deformation since different wavelengths are mapped to different positions and therefore see different wavefront aberrations. In the actively cooled case the surface PV reaches a steady state value that is 4x lower than the uncooled case on a timescale that is significantly shorter.

 

Fig. 3 (a) Simulated surface PV across the beam aperture, and (b) peak surface temperature of a diffraction grating in vacuum as a function of time for a constant 14W thermal load from absorption of a 400W average power petawatt laser. The red lines are for radiation cooled only, while the blue lines are top and bottom surface cooled. A line is drawn where the surface PV exceeds 0.1λ.

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3.3 Average Power Scaling

We examined the limits of this cooling technique by running simulations with varying absorbed laser power. Since the scaling depends on the geometry for this particular cooling method the grating and beam size are kept the same as in the previous analysis. Figure 4(a) shows the surface PV across the beam aperture, and Fig. 4(b) shows the peak temperature for a grating with a ULE substrate (blue lines) and a grating with a BK7 substrate (red lines). The solid lines are for the cooled case and dashed lines are uncooled. A line is drawn at 250C which corresponds to the limit at which localized groove distortions has been observed to cause scatter and reduce diffraction efficiency in other work [12]. This analysis shows a significant advantage of using a ULE substrate due to its superior thermo-mechanical properties [18] compared to BK7. However, an uncooled ULE substrate will only operate with absorbed powers below 4.6W (130W in laser power), and also have the issues of a changing deformation over days of operation before steady state is reached as well as a high temperature (160C). The active cooling technique can extend performance nearly fivefold to withstand a 610W average power petawatt laser. Plotting these results as a function of absorbed power allows for estimating the performance of different grating technologies (gold vs. MLD), wavelengths and repetition rates. For example, the absorbed average power limit of 21W corresponds to an input laser average power of 42kW (~1.1kHz at 40J) for the case of a MLD gratings having 500ppm absorption [19] at 800nm. The absorption depends on a variety of parameters such as the substrate and coating materials, production technique, wavelength range, bandwidth, and design. Since better absorption has been achieved, we regard this absorption measurement as an upper limit in estimating the performance of current MLD grating technologies.

 

Fig. 4 (a) Surface PV across the beam aperture, and (b) peak surface temperature of a diffraction grating in vacuum as a function of total power absorbed in the grating with the fixed grating size and beam size described in Fig. 1. The red lines are simulation results for a BK7 substrate and the blue lines are results for a ULE substrate. Dotted lines are for radiative only cooling, while solid lines include top and bottom surface cooling and radiation cooling. Limits for surface PV and groove integrity are shown.

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4. Demonstration of Grating Active Cooling

An experiment to measure the surface deformation of a petawatt size grating under kW-class laser irradiation was carried out in order to demonstrate active cooling and benchmark the simulations. This was performed in an air environment due to the large cost of a vacuum chamber suitable for this type of experiment. Additional modeling was done with the conditions adjusted to reflect the experiment. A heat transfer coefficient of 15 Wm⁻²K⁻¹ was added to represent ambient airflow. The setup is shown in Fig. 5(a). The grating (Fig. 5(c)) is 50cm wide x 27cm tall and consists of gold coated dielectric ridge grating on a ULE substrate. Cooling bars (not shown) are attached to the top and bottom surfaces. The grating is placed in a Zygo interferometer with a 32” diameter beam to measure the surface normal reflected wavefront distortion. A baseline measurement was taken before laser irradiation in order to evaluate the change in the surface profile from the laser heating.

 

Fig. 5 (a) Diagram of the experimental setup to actively cool a petawatt size diffraction grating exposed to a kilowatt laser diode array and measure the surface deformation with a 32” diameter interferometer. (b) A photo of the laser diode beam on an absorbing beam block at the grating plane. (c) The 50cm x 27cm diffraction grating and mounting hardware where the cooling bars used in this experiment are not shown.

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A laser diode array operating near 780nm to was used to simulate the average power loading of a kW-class petawatt laser system. The beam was directed onto the grating at a 45° incidence angle delivering 610W of power onto the grating. A beam duct and a single lens were used to expand and relay image the diode laser beam onto the grating resulting in the profile shown in the visible photograph in Fig. 5(b). The setup was carefully designed so that zero order and −1 order beams were directed onto beam blocks and not directed back into the diode array or into the interferometer. The cooling bars were held to a constant temperature throughout the experiment via chilled water circulation. After the laser diode was turned on, interferometer measurements were taken at several points up until 1 hour of continuous irradiation. This is to our knowledge the first demonstration of active cooling for short pulse laser compressor gratings.

Figure 6(a) shows the measured surface profile of the grating after 1 hour of exposure to the diode laser subtracted from the baseline measurement. The black boxes represent the spatial extent of the diode beam on the grating estimated from Fig. 5(b). The surface deformation from the thermal gradient has a peak deflection of 52nm. The absorbed heat flux was adjusted to correspond to 5% absorption of the 610W input beam with the spatial profile shown in Fig. 5(b). Figure 6(b) shows the simulated grating surface profile after 1 hour of laser illumination showing similar shape and peak deflection as the experiment. The peak deflection of the measured and simulated grating surface height is plotted as a function of time in Fig. 6(c). The model results are within the measurement error of +/−10nm. The kink at 15 minutes is due to thermal diffusivity, where the grating substrate temperature increases prior to the cooling bars and there exists a time at which the thermal expansion induced strain difference between the substrate and the cooling bars changes sign. While the agreement between modeling and experiment is promising, future experiments in a vacuum environment are required for a complete evaluation of the performance of active top and bottom surface cooling.

 

Fig. 6 (a) Measured and (b) simulated surface height deviation of a diffraction grating illuminated with 610W of CW laser diode light in an air environment after 1 hour. The black boxes correspond to the extent of the diode array footprint. (c) Peak surface deflection for the experiment (red squares) and simulation (blue line) as a function of time.

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5. Conclusion

We present the first demonstration of active cooling of compressor gratings for high energy, high average power ultrafast lasers. To enable this, we have developed the capability to model the thermo-mechanical effects in petawatt size gratings such as temperature, surface profile distortion, and lateral displacement of grating grooves. Using this model we performed the first thermo-mechanical analysis of compressor gratings for high energy, short pulse laser systems. We determined that surface distortion on gold gratings on BK7 substrates contained in vacuum with no active cooling will exceed 0.1λ at laser average powers as low as 1W. The use of ULE for the substrate material allows for two orders of magnitude increase in average power (130W laser power), and actively cooling the top and bottom surface of ULE gratings can enable an additional 5x increase in average power (610W laser power). The active cooling of a ULE substrate was demonstrated with petawatt-class diffraction grating irradiated by 610W from a continuous wave laser diode array. Experimental results are in good agreement with the simulations. We have investigated the scaling of uncooled and cooled grating performance with average power for different substrate materials. We estimate that the implementation of low-absorption broad-bandwidth (supporting sub-150fs pulses) MLD gratings would further extend the average power capabilities of petawatt compressors to support average powers well above 40kW.