1. Introduction

Extreme laser sources generating peak powers in the terawatt to petawatt range are opening new frontiers in scientific research as well as enabling practical technology. Their focused electric fields are sufficient to probe the fundamental science of light-matter interaction, generate anti-matter [1], or act as a “secondary source” (laser-driven source) of particles or x-ray and gamma-ray radiation [2]. The current record laser pulse peak intensity of 10 petawatts [3] represents over 3000 times the world’s average power consumption but lasts for only 10’s of femtoseconds (300 J/pulse) at a repetition rate of one pulse per minute.

The efficient pumping of such lasers requires both high pulse energies and high repetition rates. This class of lasers are known as high average-power pulsed lasers. At one extreme is an ultrafast (picosecond pulse, thin-disk, frequency-doubled) laser at a wavelength of 515 nm with 1.4 kW of average power resulting from 4.8 mJ pulses at a 300 kHz repetition rate [4]. However, to enable petawatt-class lasers, extreme laser shot peening [5], or extreme states of matter [6], pulse energies of tens to hundreds of joules are required. We investigate here the ability to accurately measure pulse energy of one such laser known as “Bivoj”. This diode-pumped solid-state cryogenically-cooled multi-slab laser (146 J/pulse, 10 Hz repetition rate, 10 ns pulse duration, 1.46 kW average power, 1030 nm wavelength) is operated at the HiLASE facility of the Czech Academy of Sciences (Dolní Břežany, Czech Republic) [7]. This is one of only two such lasers in existence – the other is operated at the European Xray Free Electron Laser facility XFEL [6]. There are more high average power lasers operating around 300 W [8,9] and all have ambition to grow in average power. Predictably, the combination of high pulse energy and high average power makes the characterization of the pulse energy difficult to measure by traditional means. We demonstrate here, for what we believe to be the first time, a direct measurement of this laser’s full output pulse energy with a high accuracy traceable to the international system of units (SI). We do this by measuring the momentum of its light pulses.

Traditional thermal approaches for measuring laser pulse energy (thermopile and pyroelectric detectors) are poorly suited to high-accuracy measurements. They require absorbing the incident laser’s energy and are not currently capable of tolerating high peak powers while simultaneously absorbing the high thermal load. As a result, sampling techniques have typically been used to measure a weakly-reflected fraction of the beam. The splitting ratio is usually measured at low power, where energy meters can be placed directly into the beam but can change at high power due to thermal effects of the beam splitter or polarization changes of the laser light resulting in potentially significant measurement uncertainties. Further, such thermal meters typically rely on a chain of calibration steps to provide traceability of the off-the-shelf device to the SI. Each step in this chain increases the measurement uncertainty, limiting manufacturer-reported measurement uncertainties alone to 3-5% (not including sampling uncertainties). Also, the limited availability of high-average-power pulsed lasers often requires that thermal energy meters are calibrated by very different laser sources than will actually be measured.

Here, we have overcome these limitations by measuring the output energy of a high-average-power pulsed laser by “absorbing” the momentum of the light pulse while reflecting its energy. This is done by measuring the force resulting from radiation pressure that the incident laser pulses impart to a highly reflective mirror. We conducted this demonstration on the Bivoj laser described above at pulse energies of 100 J, but which has subsequently produced pulse energies as high as 146 J [10].

Radiation-pressure-based power meters first demonstrated over a century ago [11,12] receive the light’s momentum p as it reflects from a mirror and the resulting force F on the mirror is directly proportional to the incident optical power ${\cal P}$ as

Photon momentum has already been used as a measurement proxy for extreme continuous wave (cw) laser powers up to 100 kW [14], but demonstration of its ability to measure high pulse energies is limited. An early report uses a torsion balance in vacuum to measure a 3 J pulse of unspecified duration and with upper repetition rate severely limited by the resonance frequency (unspecified) of the torsion balance [15]. The measurement reported here not only measures a much higher ∼ 100 J pulse energy but resolves individual pulse energies at a 10 Hz repetition rate. We performed the measurement described using a radiation pressure energy meter (RPEM) made by combining a radiation pressure power meter (RPPM) [13] to measure average power (average pulse energy) and a charge integrator photodiode CIPD [16,17] to electronically resolve the individual pulse energy. The RPPM is as described in [13] except with mirror and windows optimized for the 1030 nm laser wavelength. It is based on a modified commercial force balance with a readability (resolution) of 10 µg (∼98 nN). We use it here with the Bivoj laser to demonstrate record accuracy in measurements of its pulse energy.

The minimum measurable laser pulse energy E_min using the RPPM alone is expressed as

We overcome this high minimum detection level by combining the RPPM with a silicon photodiode and a switched integrator amplifier (SIA) [16] comprising a CIPD capable of a fast and sensitive measurement of pulse energy [17]. With the laser pulsing at 10 Hz, the RPPM simply measures the average laser power (which converts to average pulse energy through Eq. (2)). The CIPD rapidly measures individual pulse energy with a simultaneous high accuracy calibration by the RPPM. This synergistic combination enables the accurate measure of the individual pulse energies.

Due to its low saturation levels, the photodiode is directed to sample only the negligible fraction of the light that is scattered from the first turning mirror (M₁) of our measurement setup (Fig. 1). The photodiode is susceptible to time-dependent speckle effects of the sampling and therefore must be preceded by an integrating sphere. At the entrance port of the integrating sphere a neutral density filter with an attenuation factor of 1000 was placed so that the maximum charge generated in the photodiode by a single laser pulse with 100 J energy was at about 10 nC. This value is well inside the SIA amplifier’s operational range [17] and about 4 orders of magnitude lower than the photodiode’s saturation level [19]. The SIA’s integration time was set to 5 ms, a fraction of the Bivoj laser’s 100 ms pulse period to sample the signal (when no laser pulse is present) for background subtraction. This produces a fast and low-noise but uncalibrated pulse energy measurement. We use the RPPM to yield a high-accuracy (albeit noisier and slower) measure of average laser pulse energy traceable to the international system of units (SI). This combination yields a calibrated CIPD response that is a fast, low-noise, and high-accuracy measure of individual pulse energies.

 

Fig. 1. Measurement of pulse energy from the “Bivoj” laser source. The laser produces pulses at 10 Hz and lasting 10 ns. In the “on” state, the laser’s final amplification stage is energized yielding up to 100 J/pulse and in the unenergized “off” state, only ∼ 3 J leakage pulses are emitted (inset). M₁, M₂, and M₃ are dielectric-coated turning mirrors, W₁ and W₂ are anti-reflection-coated windows. The optical flat samples the pulse energy for measurement by pyroelectric energy meters (PEM₂, and PEM₃) using the polarizing beam splitter (PBS) for polarization insensitivity. PEM₁ is an uncalibrated redundant monitor. RPPM is the radiation pressure power meter measuring the light’s average force F on the sensing mirror M_S. CIPD is the charge integrator photodiode sampling the light scattered from M₁. RPEM is the radiation pressure energy meter comprising RPPM and CIPD. The virtual measurement point is the location at which all meters estimate laser pulse energy.

Download Full Size | PDF

2. Experiment

Figure 1 illustrates the layout of our measurement which is designed for simultaneous comparison between our energy measurements based on the radiation pressure energy meter (RPPM + CIPD) and three conventional pyroelectric energy meters (PEM) of the type typically used for pulse energy measurement. These consist of a pickoff monitor (PEM₁, Gentec QE50LP-S-MB-D0) and two calibrated higher-energy meters (PEM₂, Gentec QE65LP-H-MB-D0, and PEM₃, Gentec QE95LP-S-MB-D0). Both PEM₂ and PEM₃ are fitted with a Gentec model QED near-lambertian diffusing attenuator as well. This mention of manufacturer and model numbers is intended to adequately identify the equipment and is not intended as an endorsement. The Bivoj laser consists of 5 amplification stages. Its laser output is modulated by energizing the last stage. The modulation depth is limited by “off” state leakage pulses (∼3 J) from previous stages (Fig. 1). Our measurements were performed with the laser putting out pulse trains with an overall square-wave modulation having a period from 60-180 s and individual pulse energies from 10 J to 100 J. Results here represent the average of typically 10 “on/off” modulation periods for each pulse energy level. The polarization state of the laser is weakly dependent on the pulse energy due to depolarization effects in the amplifier [20]. The pyroelectric radiometers and photodiode measure the pulse energy in both the “on” and “off” states. However, the RPPM measures average optical power as the differential force on the mirror between the laser’s “on” and “off” states. That is, RPPM measures the average optical power during the 30-90 s “on” state implicitly subtracting the background power of the “off” state (due to leakage pulse energy). In analysis, this leakage pulse energy value (determined as the offset energy of a linear fit between PEM and RPPM measurements) was explicitly added to the RPPM reported energies.

Since the three pyroelectric energy meters simultaneously measure the energy at different points in the beam path, corrections must be made for losses at each optical surface to scale the measured energies to the same virtual point (located between the lens and the optical flat, Fig. 1). The loss from reflection and/or transmission at each optical surface has been either measured by us or provided by the manufacturer (Table 1).

Table 1. Throughput of the optical elements in the beam path as transmission (T) and reflection (R). Values are from the manufacturer (Mfr.) or measured (Meas.) by the authors and include polarization dependence when appropriate. Standard uncertainties are included only for elements whose values were used in calculations

View Table

The energy monitor PEM₁ represents what would be used during conventional operation to sample only the fraction (0.1-0.2%) of the laser beam that leaks through the high reflectivity (∼0.999) mirror M₁. This allows pulse energy monitoring without significant reduction in the total energy delivered by the laser. The fraction of light sampled by PEM₁ is difficult to accurately measure and can be unstable due to mirror alignment uncertainties, heating, and polarization effects. The CIPD with integrating sphere homogenizer (a polytetrafluoroethylene (PTFE) sphere of inner diameter 5 cm with an approximate loss of 20 dB) as well as a -30 dB neutral density filter is positioned to collect a small and poorly-known fraction of the scattered (non-specular) light from M₁. The measured charge per pulse was averaged over the full injection period and the result compared with the RPPM measurement of average power over the same period to calibrate the CIPD for the specific geometry and pulse energy level. The RPPM is positioned so that the full beam is incident on its high reflectivity sensing mirror (M_S). This mirror is mounted to the force sensor and protected from air currents by an air shield with anti-reflection-coated windows W₁ and W₂. The small transmission loss of these windows is due to residual specular reflection.

Energy-dependent polarization effects in the laser [20] prevent simply using a large-incidence-angle Fresnel reflection from an optical flat as a way to sample the beam for thermal energy measurement – this yielded a ∼10% error over the 10-100 J energy range. Near-normal incidence angles reduce polarization sensitivity but are impractical for the large 75 mm beam extent. We instead used a polarization-diversity detection scheme (Fig. 1). The beam is sampled with an optical flat followed by a polarizing beam splitter (PBS) whose axes are aligned to the plane of incidence of the flat. The PBS feeds two pyroelectric energy meters PEM₂ and PEM₃. This allows a polarization independent measure of the energy at the virtual measurement point (Fig. 1) as

The RPPM measures the average energy in the full beam at the point of its high-reflectivity mirror. For a particular injection period, RPPM measured the average force on its sensing mirror, which was converted to an average power using Eq. (1) and to average pulse energy using Eq. (2). This value had to be corrected following Ref. [21] to the virtual measurement point (Fig. 1) by accounting not only for reflection losses from the downstream window (W₂) and lens but also taking into account the light reflected by the window back onto the RPPM’s force-sensing mirror M_S (inadvertently measuring the back-reflected light twice). The uncertainty of this correction is included in the RPPM’s expanded relative uncertainty. Due to the rise time (1/f_F= 0.83 s) of its force sensor, the RPPM had a 5 s “dead time” at the start of the injection before the force reading attained 99% of its final value. Therefore, the RPPM reported average energy for an “on” state laser injection excludes the first 5 s. For comparison, the pyroelectric energy meters and photodiode responses were averaged over the same truncated time periods.

3. Results

Figure 2 shows the average pulse energy E_PEM as measured by the pyroelectric energy meter pair (PEM₂ and PEM₃) versus the average energy E_RPPM measured by the RPPM over 10 “on” and “off” state cycles at each pulse energy level. The uncertainty for RPPM is as previously calculated [13,22] but with the measured standard deviation added in quadrature to yield a relative expanded uncertainty that ranges from ∼ 2% for energies above ∼ 40 J to ∼ 9% for the lowest pulse energies (10 J). This uncertainty was dominated by air drift and vibration noise at low energies and thermally-induced nonlinear drift [13] at high energies. The term “expanded uncertainty” indicates an expansion factor of 2 for an approximate 95% confidence interval. The uncertainty of the PEM measurement comes from both statistical and systematic uncertainties (“Type A” and “Type B”, respectively [23]) added in quadrature, including the manufacturer’s calibration uncertainty u_PEM= 0.03, the uncertainty in the reflection from the two surfaces of the flat u_flat= 0.035, and the measurement standard deviation. This yields a relative expanded uncertainty of ∼9% (independent of pulse energy).

 

Fig. 2. Comparison between pulse energy averaged over the “on” state as measured by pyroelectric energy meters (E_PEM) and the radiation pressure power meter (E_RPPM). The linear fit (solid line) yields the 1.013 calibration factor of PEM by RPPM. Error bars are expanded relative uncertainty. Residuals are the result of subtracting the linear fit from the E_PEM values expressed as a fraction.

Download Full Size | PDF

A linear fit to the data of Fig. 2 yields a calibration factor for the PEM pair of C_PEM = 1.013 where

The brackets indicate an average over the “on” state injection duration (excluding the first 5 s). This indicates that the energy estimated by our PEM pair overestimates the pulse energy by only 1.3% – well within the combined measurement uncertainty. The residuals of the PEM pulse energies with respect to a linear fit show no nonlinear behavior outside the measurement uncertainty. This level of agreement represents a final result and belies the difficulty of obtaining an accurate measurement with thermal meters for pulses at these average power levels. The PEM agreement came only after initially large disagreements between PEM and RPPM prompted re-evaluation of the k factors of Eq. (4). Some initial assumptions regarding reflectivities and transmittances of the optical elements used as attenuators in front of the PEM’s turned out to be incorrect. This illustrates the utility of the radiation pressure approach compared to thermal techniques that have large and high-uncertainty correction factors.

Figure 3 shows the photodiode measurements of integrated charge Q_CIPD versus the average pulse energy reported by RPPM (each measured over the same time duration). The slope of this curve becomes the calibration factor of the CIPD. Dividing a CIPD measurement by this calibration factor will give a traceable measure of pulse energy. This measurement yields a calibration factor following the definition of Eq. (5) of C_CIPD = 0.115 nC/J, which applies only to the exact geometry of the test but seems to be quite linear (independent of pulse energy) as quantified by the residuals.

 

Fig. 3. Average measured charge per pulse from the charge integrator photodiode (Q_CIPD) related to average energy per pulse measured by the RPPM (E_RPPM). The linear fit (solid line) denotes a 0.115 nC/J calibration factor. The lack of vertical error bars indicates that the CIPD is previously uncalibrated, RPPM uncertainty (not plotted) would have error bars within the size of the plotted symbols. Residuals are the result of subtracting the linear fit from the Q_CIPD values expressed as a fraction.

Download Full Size | PDF

Figures 2 and 3 show similarly shaped residuals (increasing at the lowest energy point). This behavior is within the measurement uncertainty and is likely due to the high uncertainty of the RPPM at 10 J.

The advantage of the RPPM-calibrated charge integrator photodiode is shown in Fig. 4 where the CIPD provides a fast, SI-traceable measurement of individual pulse energy (each data point represents the energy of a single laser pulse). The error bar represents the 0.023 relative expanded uncertainty which is the quadrature sum of the fractional fit uncertainty of the linear calibration C_CIPD (Fig. 3) which includes CIPD noise, and the uncertainty of the RPPM measurements. This indicates the overall uncertainty of individual pulse energies. But the relative features of the curve are known with at least 10x better resolution limited only by the relative statistical repeatability of the CIPD energy measurement which we estimate to be < 0.002 based on correlation with PEM noise. For example, the ∼5 J unintended rise in pulse energy over the course of the 30 s “on” modulation seen in Fig. 4 is well outside the 0.2% sensitivity of the CIPD and even above the absolute measurement uncertainty of the RPPM and caused by energy stabilization after energizing the final amplifier of the Bivoj.

 

Fig. 4. Pulse energy vs time during a 30 s train of pulses measured by the charge integrator photodiode with RPPM calibration. The error bar indicates the 0.023 relative expanded uncertainty of the scaling factor of the curve with the uncertainty of the relative changes limited only by the noise of the measurement. NOTE: The vertical axis is “cut” to illustrate the fine details of the data.

Download Full Size | PDF

The noise of the three measurement types is shown in Fig. 5. The relative standard deviations of the photodiode and pyroelectric meters show strong correlation with each other, indicating noise in the laser pulse energy itself rather than instrument noise. At the lowest pulse energies, the RPPM measurements have standard deviations that are almost two orders of magnitude larger than the CIPD or PEMs. This is attributable to an air current noise on the sensing mirror. As expected, this relative RPPM noise falls off with increasing pulse energy and at the highest energies approaches the laser pulse energy noise (estimated from the PEM and CIPD noise). This illustrates the advantage of a combination of RPPM and CIPD to allow low noise (photodiode) measurements of pulse energy with a low, SI-traceable, uncertainty (RPPM). The inset of Fig. 5 shows the relative expanded uncertainty for RPPM compared with PEM indicating the significant improvement in measurement uncertainty afforded by a radiation pressure approach for all but the smallest pulse energies.

 

Fig. 5. Statistical noise (relative standard deviation s) of pulse energy measured by RPPM, PEM, and CIPD. Inset: expanded relative uncertainty 2U of RPPM and PEM.

Download Full Size | PDF

Finally, we consider the current pulse energy noise floor of the RPPM. As estimated above, we expect its single-pulse noise floor to be ∼ 90 J/pulse. Figure 6(a) shows the raw power reported by RPPM and the accumulated charge from the photodiode during a succession of 21 individual laser pulses (10 ns duration, 92 J average energy, 20 s separation). The much slower pulse repetition rate (0.05 Hz) allows the force sensor to achieve the required equilibrium conditions between pulses as required in [18]. Though almost lost in the noise, the RPPM signal does show a correlated spike in measured power (not converted to energy) with each laser pulse. This is clarified when the RPPM’s power readings for the pulses are overlayed, referenced to the pulse start, and averaged in Fig. 6(b). We see a definite pulse (with significant noise). The pulse energy of this noisy averaged measurement is found by integrating the power from the start of the pulse (0 s) to the point (7 s) where the average value appears to no longer be decreasing and noise begins to dominate. We find an integrated pulse energy of 108 J (a 17% error) indicating the RPPM’s single-pulse noise floor is below 100 J. It is inspiring that a commercial force balance designed for measurements up to 2 g with a 5 s settling time can identify an individual laser pulse lasting for only 10 ns.

 

Fig. 6. (a) Train of 21 pulses (92 J/pulse, 10 ns width, 0.05 Hz repetition rate). The raw power reported by RPPM (upper) correlates to the measured CIPD charge (lower), but clearly operating near the noise floor. (b) Averaged RPPM power from overlaying the 21 individual laser pulses. Error bars indicate the standard deviation of the measured power among the 21 overlapped pulses.

Download Full Size | PDF

4. Conclusions

For the first time, to our knowledge, the pulse energy output of a 1 kW average power pulsed laser source has been directly measured (without sampling) with an SI-traceable energy meter. This was made possible by directly measuring momentum of the laser pulses rather than their energy. This avoids the thermal damage mechanisms that limit the use of traditional pyroelectric or calorimetric methods for such lasers. We have demonstrated pulse energy measurements with as low as 2% relative expanded uncertainty using a radiation pressure power meter in combination with a charge-integrator photodiode. This result demonstrates a greatly simplified measurement approach with a factor of 5 improvement in measurement uncertainty (at the highest energies) over conventional thermal sampling techniques. This approach will be even more important as the average powers of petawatt-class lasers (and their pumping mechanisms) must be increased to tens to hundreds of kilowatts to enable useful secondary-source particle and radiation sources [24]. Radiation-pressure-based power metrology has already demonstrated suitability to this power range for cw lasers [22].

This preliminary demonstration also illustrates need for improvement of the measurement technique. Most compelling is the implementation of a force sensor optimized for such measurements. A higher-capacity force balance (with comparable measurement resolution) would permit heavier mirrors allowing thicker (flatter) mirrors to reduce beam distortion and enabling truly non-perturbing measurements of pulse energy during routine laser operation. The extreme field strengths of petawatt class lasers risk damage to any type of mirror. But a higher capacity force sensor could suspend the massive gratings used as the final stage of the chirped pulse amplification systems that enable such lasers. Measuring the radiation pressure force of the pulses as they diffract from the grating would reduce the damaging peak intensity while permitting measurement of pulse energies in extreme petawatt lasers.