Precision measurements of small masses, forces and high energy laser powers by photon momentum transfer

Joint research of TU Ilmenau and PTB Braunschweig on optical power measurement by means of radiation pressure

The novel force measurement system developed and built by the research team at TU Ilmenau enables direct traceability of the laser power measurement to the Planck constant of the SI system of units as well as precision generation of very small forces via photon pulse measurement.

In cooperation with the Technical University of Ilmenau, PTB has tested the suitability and accuracy of the optical power measurement method based on photon momentum. The results of the optical power measurement via the photon momentum were compared with those via a calibrated reference detector.


The TU Ilmenau and the Physikalisch-Technische Bundesanstalt are working on a joint research project on photon momentum measurement technology. Two completely different use cases from different areas of physics and engineering can be derived from this.

Firstly, the accuracy of optical power measurement of high-power laser systems can be improved, which are typically used in various fields at 100 W up to several 10 kW. For this purpose, a new class of high-power optical detector systems is already being planned and developed. The simplicity of the concept has already attracted the interest of many world-class researchers and institutions (PTB, NIST, etc.), because the expected outcomes of optical power measurement for example for 1 kW laser power are more than 100 times better than the currently used conventional measurement methods, where improvements have been incrementally minimal for several decades.

On the other hand, very small calibration forces for pico- and nano-force measurements (pN, nN) or very small masses can be generated with this novel method. The optical power of the lasers is proportional to the force value and can be measured very accurately with conventional thermal reference detectors.

The concept consists of using the radiation pressure of a laser field as an effect of the momentum transfer of the absorbed and re-emitted photons (photon momentum) from ultra-high reflection mirrors to generate very small calibration forces or to calibrate the optical power of lasers with great accuracy and precision. The calibration can be directly traced back to Planck's constant. Planck's constant is one of the natural constants used to define the base units of the International System of Units. The Planck constant (also Planck's quantum of action) describes the smallest possible amount of energy that has been theoretically known since the quantum revolution in physics in the last century.

The measuring systems currently operating are combined with other state-of-the-art measuring systems for quantum-electric quantities, which are only available in a very few high-tech measurement laboratories in the world. In this newly introduced age of quantum metrology, the measurements of quantum electrical quantities within the newly defined International System of Units are guiding many high-tech developments.

Fig. 1: 2-D geometry of laser beam reflections.

Previously appearing contributions on this topic were limited to a considerable extent because only one reflection was used. If one uses the reflection of a low-power laser beam (less than 1 mW), one needs an unimaginably high resolution for the force measurement in order to be able to implement this technology in practice. Conversely, if one uses a high-power laser of several kW, the corresponding surface would have to be extremely robust to withstand this amount of extreme light energy. There were also well-known optomechanical resonator systems that used the same effect, but only at very low optical power levels and without considering the absolute optical power losses. Prominent examples among many others are the optical resonators and microcavities often used in frequency combs to create a reference frequency domain. Another example is the LIGO project for the direct measurement of gravitational waves of cosmic origin. Gravitational wave observatories currently calibrate the displacement of mirrored test masses at the ends of interferometer arms using the photon momentum (at a single laser light reflection). In these interferometers, the absolute displacement of the mirror test masses is proportional to the absolute power (about 1 W) of the optical force generation. Consequently, the uncertainty of the interferometer displacement is directly proportional to the uncertainty of the power reflected from the mirrored test mass. The typical uncertainty of the laser power measurement is also limited here and lies between 0.15 % and 0.86 %. But for the complete operation of the LIGO, an infrared laser with a power of about 20 W is used as the light source, resulting in a total circulating power of about 100 kW in the arm.

Fig. 2: Setup for measuring the optical power via forces generated by photon moments.

In our project, the multi-reflection configuration of the laser beam is used within a macroscopic optical cavity consisting of mirrors with nearly ideal reflectivity. For example, forces of several hundred nN are generated by 20 reflections of the laser beam with only 1 W of input laser power. In contrast, the forces generated by a single laser light reflection are of the order of only a few nN. This new configuration offers better control over the measurement and calibration processes, a deterministic discretisation of the measured quantities where the limits approach the quantum mechanical domain of physics.

Fig. 3: (top) Force signals from both balances, the reflectivity of the cavity mirror is 99.995 %. (middle) Measured differential force signal from two different cavities, reflectivity of 99.5 % - red dashed line and 99.995 % black circle and blue cross. (Bottom) Optical power transmission measurements of cavities with an integrating sphere thermopile—Si photodiode detector during the photon momentum measurements; the nominal input powers are as follows: 8.57 W - blue cross, 8.77 W - black circle, and 8.69 W - red dot.
Fig. 4: The setup was developed, built and tested at the TU Ilmenau. Further metrological test investigations were carried out at PTB. Photos (left) of the force measurement setup on a vibration-isolated table in a temperature-stabilised clean room for laser radiometry at PTB, Braunschweig, and (centre, right) photo of the optical cavity with ultra-high reflection 2'' mirrors (>99.995%) adjustably suspended from the EMFC balances.

[1] S. Vasilyan, T. Fröhlich, E. Manske, “Total momentum transfer produced by the photons of a multi-pass laser beam as an evident avenue for optical and mass metrology”, Optics Express, 25, 20798-20816 (2017). DOI: 10.1364/OE.25.020798.

[2] E. Manske, T. Fröhlich, S. Vasilyan, ”Photon momentum induced precision small forces: a static and dynamic check“, Meas. Sci. Technol., 30, 105004 (2019). DOI: 10.1088/1361-6501/ab257e.

[3] S. Vasilyan, N. Rogge, T. Fröhlich, “Metrology in direct photon momentum measurement“, - In: Messunsicherheit - Prüfprozesse 2019. - Düsseldorf : VDI Verlag GmbH (2019), S. 193-205

[4] S. Vasilyan, M. López, N. Rogge “Revisiting the limits of photon momentum based optical power measurement method, employing the case of multi-reflected laser beam” Metrologia a, 58, 1, 015006 (2021). DOI: 10.1088/1681-7575/abc86e

[5] S. Vasilyan, T. Fröhlich, N. Rogge, “Deploying the high-power pulsed lasers in precision force metrology -- SI traceable and practical force quantization by photon momentum”, arXiv:2205.07042v1, (2022). DOI: 10.48550/arxiv.2205.07042.

[6] PTB-news. Photonenimpuls für die Metrologie.

[7] PTB-Mitteilungen. Optische Leistungsmessungen über Strahlungsdruck.



Dr.-Ing. Suren Vasilyan / Dr.-Ing. Norbert Rogge / Prof. Eberhard Manske / Prof. Thomas Fröhlich
Technische Universität Ilmenau

Institute of Process Measurement and Sensor Technology