nd spiral antennas. Furthermore, and exploiting the unique capabilities of CL excitation, we measured the emission from metals and semiconductors. For these materials, we can separate coherent and incoherent emission mechanisms, with further applications in nanoscale materials science.

CL Polarimetry
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![image](Fig1.pdf){width="70.00000%"}

In our measurements, the $30$ keV electron beam from a scanning electron microscope (SEM) excites the sample. An aluminum paraboloid mirror collects and redirects the resulting CL emission out of the SEM. The outcoming beam is focused onto a fiber-coupled spectrometer or projected onto a 2D CCD array [@coenen_NL11; @coenen_APL11; @Sapienza_NM12], as shown in Fig. \[Fig1\](a). The wave-vector distribution of the CL emission can be retrieved from the CCD image, as every transverse point in the beam corresponds to a unique emission angle, in a procedure analogous to other Fourier imaging techniques [@Lieb_JosaB04; @Kosako_NP10; @curto10; @Aouani_NL11; @Sersic_NJP11; @Belacel_NL13].

Measuring polarization for all emission angles of CL presents several challenges. First, it requires determining the relative phase difference between field components, a task not achievable with only linear polarizers as in Ref. [@coenen_OE12]. Second, the paraboloid mirror performs a non-trivial transformation on the signal as it propagates from the sample to the detector plane. The shape of the mirror introduces a rotation of the vector components of light due to the coordinate transformation and, consequently, a change in the main polarization axes. In addition, the angle and polarization-dependent Fresnel coefficients of the mirror modify the polarization of the light upon reflection  [@Bruce_OPT06; @Bruce_04]. As a function of the angle of incidence, the mirror partially polarizes unpolarized light and transforms linearly to elliptically polarized light.

To address these challenges, we included a rotating-plate polarimeter in the beam path of our CL system, composed of a qua