Light is a transverse electromagnetic wave: the electric and magnetic fields that constitute the light wave always fluctuate diagonally to the direction of propagation. Apart from color (energy) and momentum (propagation direction), light is also distinguished by a polarization which delineates the direction in which these electromagnetic fields oscillate.
If the electromagnetic oscillations stay in the same plane, the polarization is characterized as linear. However, this plane can also revolve coterminously to wave propagation. When this occurs, the polarization is referred to as elliptical, which can be either left-handed (anti-clockwise) or right-handed (clockwise), depending on the orientation of the rotation (circular polarization is an exceptional instance of elliptical polarization).
Figure 1. Schematic representation of the angle-resolved polarimetry imaging mode. The CL is collected by the paraboloid mirror and then filtered by the polarization analyzer which consists of a quarter-wave plate and a linear polarizer. The CCD camera records the polarization filtered image. By recording this image for six different analyzer settings the full polarization state in the detector plane can be retrieved for every emission angle. By applying a correction for the distorting effect of the paraboloid the original emission polarization from the sample can be reconstructed.
Applications of Polarization
Polarization plays a crucial part in light-matter interrelations and can be deployed to examine, for example, coherence, scattering, birefringence, and chirality. Moreover, it can be utilized to shield against specious ambient radiation and to adjust for anomalous outcomes in the collection optics. The polarization is not always consistent when light is emitted from a (nano)material. Exhaustive polarization studies are still yet to be carried out in the Fourier-plane, i.e. angle-resolved mode.
As the SPARC can undertake angle-resolved imaging, it is highly qualified to examine polarization effects as well. The Stokes formalism yields a total definition of the polarization state (i.e. linear, elliptical, circular) of the light which is emitted in the form of a Stokes vector. This stokes vector can be captured for every emission angle through the implementation of a polarization analyzer in concurrence with a 2D CCD or CMOS camera. The analyzer comprises a quarter wave plate (QWP) and linear polarizer (LP). Figure 1 shows a schematic representation of this setup [1-3].
Polarization-Filtered Hyperspectral Imaging
In order to ascertain comprehensive polarization data, six analyzer settings are required to perform the measurement. The measured Stokes vector is constituted by the polarization state at the detector. However, this polarization becomes distorted through contact with the polarization coming from the sample via the paraboloid collection optic inside of the SEM. By applying the appropriate adjustment the polarization distribution from the sample can be determined.
Wavelength sensitivity can be incorporated through bandpass filters. Figure 2 represents an example of this technique in action; the radial and azimuthal electric field amplitudes for different emission angles on a gold plasmonic bullseye grating are measured with CL polarimetry.
With the electron beam a circular plasmon wave is emitted in the center of the bullseye which is transformed by the structure into a radially polarized coaxial beam. The azimuthal component is negligibly small for this geometry. The light is linearly polarized in this instance but in principle the handedness can also be deduced if the emission is elliptically polarized .
As well as angle-resolved polarimetry, it is also possible to undertake polarization filtered hyperspectral imaging as is illustrated in References  and . This imaging modality also makes obtaining polarization-filtered nanoscale hyperspectral images practicable. To summarize, the modularity, the sensitivity, and the ability to measure the angular profile makes the SPARC the unrivalled platform for flexible polarization research at the nanoscale.
Figure 2. (a) SEM of a plasmonic bullseye grating milled into a single-crystal of gold using focused-ion-beam milling. (b) Radial and (c) azimuthal field amplitudes as function of emission angles θ and φ for central electron beam excitation of the bullseye.
- T. Coenen et al. Opt. Express. 20 (2012) 18679.
- C. I. Osorio et al. ACS Phot. DOI: 10.1021/acsphotonics.5b00596 (2015).
- B. J. M Brenny et al. Appl. Phys. Lett. 107 (2015) 201110.
- E. J. R. Vesseur et al. Nano Lett. 11 (2011) 5524.
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