It was predicted in recent years that a non-chiral particle in an evanescent optical field (such as one generated by total internal reflection) is able to acquire linear momentum perpendicular to the plane of incidence from the spin component of the incoming light. When the helicity of the light is flipped, this momentum changes direction. This particular kind of spin-momentum coupling has attracted keen interest in the physics community, due to a fundamental connection with the Belinfante–Rosenfeld energy-momentum tensor which emerged in quantum field theory in 1940. Many theoretical papers have been published exploring the interaction between this momentum with matter, yet only a qualitative confirmation of the existence of the resulting force has been thus far experimentally reported in the lab.
A true test of the theory is an experimental challenge as the spin-momentum force does not act in isolation. Rather, it is merely a weak component of a 3D force vector whose magnitude is typically more than one hundred times larger in the other two directions. More generally, all three components of this force vector are predicted to change as the incident light’s pure polarization state is altered. Thus, measuring this spin-momentum force in context, that is, measuring both the magnitude and the direction of the composite vector force, using a probe whose geometry can be analytically modeled, is the only way to quantitatively determine the magnitude of the spin momentum force and unambiguously test the theory.
In our manuscript we report a series of such measurements. We have built a floating-probe force microscope using a micron-sized polystyrene sphere held in an optical tweezer. The instrument is capable of femtonewton force sensitivity and piconewton range with simultaneous, time-synchronized position readouts in the three orthogonal directions. To test the theory we take the incident light along two different closed paths on the Poincare polarization sphere. We record both the direction and magnitude of the 3D vector force acting on the trapped probe and compare against theoretical predictions. Remarkable agreement was found between theory and experiment.
This work represents a significant advancement in the systematic study of exotic optical forces. The volume-scanning capabilities of the force microscope can enable, among other applications, the 3D mapping of a vector force field with high resolution and dynamic range. As such, our results can be of interest to researchers in other fields studying microscopic interactions.
Image caption: The figure illustrates the interaction of the trapped
floating probe with the polarization- and amplitude-modulated evanescent field.