A 2020 NIST meta-study demonstrated that laser power calibrations spanning 20 orders of magnitude agree within about 3% when traced either to the cryogenic radiometer (via the volt and ohm) or to the kilogram (via radiation pressure), and posed the open problem of turning radiation-pressure (photon-momentum) measurement into a complete primary-standard realization of the optical watt. Part of that agenda has since been settled: the NIST radiation pressure power meter has been demonstrated up to 140 kW at roughly 1% accuracy, and a primary electrostatic force balance combined with a multi-reflection optic has realized the watt from Planck's constant by radiation pressure at 100 W to 5 kW with 0.12% (k = 2) uncertainty at 5 kW. What remains open is the completion of this force-metrology realization at both ends: extending kilogram-independent, defining-constant-traceable laser power measurement to the tens-of-kilowatt-to-100-kW regime at uncertainties rivaling cryogenic radiometry (roughly 0.02% to 0.05%, versus 0.12% at 5 kW today), and pushing radiation-pressure power measurement below about 1 to 2 W at primary-standard-level uncertainty so the high-power photon-momentum scale can be compared directly against mid-power calorimeter and cryoradiometer standards without intermediate kilowatt calorimeter links.

Background

Optical radiometry is the science of measuring the power of light, and national metrology institutes anchor its unit, the watt of optical power, with primary standards: instruments whose calibration rests on electrical or mechanical quantities rather than on another optical detector. The lowest-uncertainty primary standard for laser power is the cryogenic radiometer, an electrical-substitution radiometer in which a blackened absorber held near liquid-helium temperature is heated alternately by the laser and by an accurately measured electrical current, so the optical power equals the substituted electrical power. NIST's laser-optimized cryogenic radiometer (LOCR) reaches a relative expanded uncertainty of 0.02% to 0.05% (coverage factor k = 2), but only at milliwatt-level power. At higher power, thermal detectors degrade, so NIST's chain from milliwatts to tens of kilowatts is stitched together from several instruments: an optical-fiber cryogenic radiometer (OFCR) and isoperibol calorimeters (constant-temperature-environment electrical-substitution calorimeters) of the C-series (roughly 100 µW to 2 W, 0.86%) and K-series (2 W to 10 kW, 1.1–1.5%), plus a flowing-water calorimeter (1 kW to 10 kW, 1.6%). In this landscape, Williams and colleagues introduced the radiation pressure power meter (RPPM), which measures laser power non-destructively by the force exerted when light reflects from a mirror: at normal incidence a beam of power P imparts a force F = 2P/c, where c is the speed of light, and the force is read by a balance calibrated with milligram-scale mass artifacts in the local gravitational field, giving traceability through the kilogram, meter, and second. Their 2020 meta-study (Metrologia 57, 015001) intercompared all of NIST's laser power standards and showed that calibration factors propagated across the full 20-decade range — from single-photon detectors to 50 kW — agree within about 3% along both the cryoradiometer path and the kilogram (radiation-pressure) path. The RPPM itself operated at 1.6% (k = 2) expanded uncertainty, was rigorously tested only up to 50 kW (with a preliminary excursion to 92 kW), and was limited below by a 1 kW floor. The meta-study drew out three open frontiers. First, the upper power limit of the RPPM had never been experimentally constrained, and testing at 100 kW and above was needed. Second, because the RPPM floor (1 kW) sat above the C-series ceiling (2 W only via the K-series link), reducing the minimum measurable photon-momentum power to below a few watts would let the RPPM be compared directly to the mid-power standards, shortening the traceability chain and its accumulated uncertainty; cavity-enhancement (multiple-reflection) optics and improved small-force sensors were identified as the promising routes. Third — the most fundamental direction — since radiation-pressure power measurement is intrinsically a force measurement, the optical watt could be realized without reference to the kilogram at all: a modified Kibble balance (the watt-balance apparatus that realizes mass from Planck's constant via electrical power, using the Josephson and quantum-Hall effects, the cesium hyperfine frequency, and dimensional metrology) or an electrostatic force balance (EFB, which realizes small forces through a voltage-dependent capacitor with capacitance measured by dimensional metrology) could measure the radiation-pressure force with traceability to the defining constants h, Δν(Cs), and c alone, eliminating the local gravitational acceleration and mass artifacts; the paper proposed such an instrument for the tens-of-kilowatt-to-100-kW range 'for uncertainties that rival those currently achievable only through cryogenic radiometry'.

Problem Statement

Complete the force-metrology realization of the optical watt that the 2020 meta-study proposed, at the two frontiers that remain open after subsequent work. Both frontiers (1) and (2) are jointly required, and each is resolved by a concrete design and analysis rather than by a demonstrated measurement: a measurement concept together with a component-level uncertainty budget, whose dominant terms are identified and which supports the claimed target uncertainty, and a measurement protocol and cross-comparison by which the design could be validated. (1) High-power, kilogram-independent end: realize laser power measurement by radiation pressure on a Kibble-balance or electrostatic-force-balance force standard whose traceability runs only to the SI defining constants (Planck's constant, the cesium hyperfine frequency, the speed of light, via electrical and dimensional metrology) with no reference to mass artifacts or local gravity, extended to the tens-of-kilowatt-to-100-kW regime — where the kilogram-traceable RPPM already operates at roughly 1% accuracy — with uncertainties rivaling those of cryogenic radiometry, i.e. approaching the 0.02%–0.05% (k = 2) class rather than the 0.12% (k = 2) so far achieved at 5 kW. (2) Low-power end: push absolute radiation-pressure (photon-momentum) laser power measurement below roughly 1–2 W — whether by multi-reflection/cavity force amplification, improved small-force transduction, or levitated-mass detection — at an uncertainty competitive with the mid-power C-series calorimeter it is compared against (roughly 0.86%, k = 2) so that the photon-momentum scale can be compared directly against the mid-power primary standards without the K-series kilowatt calorimeter as an intermediate link, thereby shortening the traceability chain. These two extensions are the low-power and high-power frontiers of the radiation-pressure program set out by the 2020 meta-study: reducing the minimum measurable photon-momentum power so the scale can be compared directly with the mid-power primary standards, and realizing a kilogram-independent, non-absorbing, force-based primary standard at the tens-of-kilowatt-to-100-kilowatt level with cryogenic-radiometer-level uncertainty.

References

  1. Williams, P. A., Spidell, M. T., Hadler, J. A., Gerrits, T., Koepke, A., Livigni, D., Stephens, M. S., Tomlin, N. A., Shaw, G. A., Splett, J. D., Vayshenker, I., White, M. G., Yung, C. S., Lehman, J. H. (2020). Meta-study of laser power calibrations ranging 20 orders of magnitude with traceability to the kilogram. Metrologia 57, 015001. DOI: 10.1088/1681-7575/ab4641. https://doi.org/10.1088/1681-7575/ab4641 (arXiv:1908.06139, https://arxiv.org/abs/1908.06139)
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