Weak Measurement of the Dipolar Emitter Polarization State via its Far-Field Polarization Singularities

We investigate polarization singularities [Proc. R. Soc. A 389, 279 (1983)] in the far-field of an elliptically polarized dipole, exhibiting in general four points of purely circular polarization (C points). We reveal that... [ view full abstract ]

We investigate polarization singularities [Proc. R. Soc. A 389, 279 (1983)] in the far-field of an elliptically polarized dipole, exhibiting in general four points of purely circular polarization (C points). We reveal that the helicities of the C points and their angle of observation in the far-field bare full information on the polarization state of the dipolar emitter [arXiv:180403890]. For a highly eccentric (almost linear) dipole moment, four singularities occur along directions almost aligned with the major axis of the dipole polarization ellipse. The low overall power emitted by the dipole into the far-field in this direction prevents a direct experimental observation of the C points. 

We experimentally realize a weak-measurement technique [Phys. Rev. Lett. 60, 1351 (1988)] in a vectorial vortex polarization basis (radial and azimuthal) to create a strongly directive far-field intensity pattern [Nano Lett. 14, 2546 (2014)]. This pattern is obtained by projecting the far-field emitted light on a complex spatially varying polarization state. The extrema of the intensity distribution of the projected far-field pattern reveal the properties of the polarization singularities and, eventually, the polarization state of the dipolar emitter. The developed experimental technique also allows for precise sensing of orientation of a linear dipole moment [arXiv:180403890].

The sensitivity of our experimental scheme to tiny changes of the polarization state of a dipolar emitter suggests far-reaching applications for localization and position sensing. An experimentally induced dipole moment in a polarizable dipole-like scatterer is proportional to the local strength and orientation of the electric field. Therefore, the variation of the intensity and polarization profile in the focal volume of a tightly focused beam relate the induced dipole moment to the position of the scatterer within the focal volume. We experimentally confirm our theoretical findings utilizing a tightly focused radially polarized beam, which features a spatially varying axially symmetric distribution of transversely spinning electric fields within its focal volume. Weak measurement of the position dependent dipole moment, excited by a focused radially polarized beam in a spherical gold nanoparticle, allows us to localize the nanoparticle with deep sub-nanometer precision [M. Neugebauer, S. Nechayev et al., in preparation (2018)].