Partial polarization of optical beams and near fields probed with a nanoscatterer

We consider theoretically the detection of the spectral polarization characteristics of random, partially polarized optical beams and near fields by probing them with a dipolar nanoparticle. We show that measuring the polarization state of the scattered far field with a conventional waveplate-polarizer setup, possibly in several directions, results in the full 3×3 polarization matrix at the probe site. This allows us to deduce the distributions of the degree of polarization of the field and the Stokes parameters of the polarized part of the field with a resolution limited by the probe size. Regarding random near fields we show that, in analogy with a known result on beam fields, a degree of polarization of three-component light fields put forward in recent literature can in some cases be interpreted as a ratio of the intensity in the polarized part of the light to that of the total field. We demonstrate the technique by considering the probing of a Gaussian-Schell model beam and a thermally excited near field. The method extends the current scanning-probe techniques to the detection of partial polarization of random light fields and can find applications in nanophotonics and polarization optics.