Photon momentum for metrology

Although a photon does not have a mass, it does carry momentum and energy proportional to the frequency and inversely proportional to the photon’s wavelength. When a light beam consisting of a great number of photons hits a highly reflective mirror, most of these photons are reflected and only very few are absorbed. In both cases, the mirror recoils slightly due to this interaction. The major part of this recoil is generated by the reflected photons. This effect has been exploited in recent years for measuring high optical powers emitted by lasers. This method has a number of advantages compared to the traditional “thermal” approach: The measurement time is prospectively shorter, the device is more compact, and costs are lower. Moreover, the photon force transferred by lasers with a low optical power (in the mW range) can, in principle, be used for calibrating pico- and nanoforce measuring instruments (in the pN and nN ranges) or small masses, since this optical power can be measured very accurately by means of conventional thermal reference detectors.

PTB, in collaboration with the Technische Universität Ilmenau, has investigated the suitability and accuracy of this optical force measurement procedure based on photon momenta. A portable force measurement setup developed by the university was used for this purpose. This setup consists of two electromagnetic force-compensation balances and an optical cavity. The cavity is used to amplify the force by causing the mirrors to reflect the laser beam multiple times. The results of the optical power measurement using photon recoil have been compared with those obtained by means of a calibrated reference detector for an optical power range between 1 W and 10 W at a wavelength of 532 nm – which corresponds to a force of approx. 2 μN at an optical power of 10 W. The relative uncertainty of the force measurement was approx. 2.3 %, the average relative deviation between the two measurement methods was roughly 5 %.

Although the measurement uncertainties are currently still higher than those of the conventional method (approx. 1 %), this technique has a strong potential for measuring high optical powers in the kilowatt range, such as are required in industrial production, for instance. Applications are also encountered in fundamental research, e.g., in gravitational wave detectors. Here, the laser power used is factored directly into the determination of source distance and position.