Figure 1 . Schematic set-ups of (a) IR dual-comb polarimetry
(IR-DCP) and (b) FTIR polarimetry. The measurement principle is outlined
on the right side. Typical measurement parameters are parallel-polarized
(ss, pp) and cross-polarized (sp, ps) transmission T (reflection R) and
absolute/relative phases Δ in dependence of the azimuthal angle
(αi). See text for further methodical details.
The dual-comb system (IRis-F1, IRsweep AG, Switzerland, schematic in
Fig. 1(a)) comprises two QCL frequency combs (FC 1 and FC 2). FC 1
probes the sample, whereas FC 2 works as the local oscillator.
Polarizers (P1, P2, P3) and beamsplitters (BaF2, Specac,
England) are used for controlling incident and output power and
polarization states, as well as beam propagation and recombination. P1
regulates the incident power (typically about 0.75 mW at the sample), P2
sets the incident polarization, and P3 acts as an analyzer. Further
polarizers (not shown) control the power incident on the reference
detector and ensure polarization matching of local oscillator beam and
sample beam. The sample was placed between P2 and P3 on a rotational
mount. The beam diameter at the sample position was about 3 mm (FWHM,
Gauss).
The operating principles of dual-comb spectroscopy have been described
previously33-35. Briefly, FC 1 and FC 2 deliver
frequency combs with inter-line spacings (frep,1and frep,2 ) of about 10 GHz. When FC 1 and FC 2
are overlaid on a high-bandwidth mercury-cadmium-telluride (MCT)
detector, a heterodyne beating corresponding to
Δfrep =frep,1 – frep,2 ≈ 2 MHz
can be recorded in the time-domain. Conducting a Fourier transform on
this signal allows for the individual frequency contributions to be
resolved. The reference detector is used to correct for amplitude and
frequency noise of the free-running QCLs. For a given polarizer
configuration, measuring the difference between a set-up without and one
with a sample gives the complex transmission txy, the
angle of which yields the absolute phase. The theoretical time
resolution is 1/Δfrep 35,36however, for data-handling and signal-to-noise reasons, the spectrometer
is typically operated at a time resolution of 4
µs35,36. In the present study, the integration time
was 65 µs. A transmission geometry at 0° incidence angle was used. For
universality reasons, and to avoid confusion with the sample azimuthal
settings in degrees (0° = horizontal orientation; 90° = vertical
orientation), we use the following notation for polarizer/analyzer
settings: (i) ss for parallel polarizers in horizontal direction, (ii)
pp for parallel polarizers in vertical direction, (iii) sp and ps for
crossed polarizers. Note that, for non-depolarizing samples, the ss-,
pp-, sp- and ps-polarized measurements are directly related to the Jones
matrix and specific combinations of the respective Mueller-matrix
elements,37 which enables the analysis of complex
dielectric functions (real and imaginary part).38
The FTIR polarimeter (Fig. 1(b)) is coupled to an FTIR IFS 55
spectrometer (BRUKER, Germany) serving as a radiation source. A
Jacquinot aperture (A) of 1.85 mm results in a spot size on the sample
of about 4.5 mm (FWHM). The sample was placed on a rotational mount.
Polarizers (KRS5, Specac, England) P1 and P2 act as polarizer and
analyzer, respectively. A liquid-nitrogen-cooled photovoltaic MCT
detector (Kolmar Technologies, USA) was used. A retarding element (R)
was additionally inserted for sensitive phase measurements. The opening
angle was about ±3.5°. Measured experimental quantities are the relative
phase Δ = Δpp – Δss and the
polarization dependent transmission
Tpp = |tpp|2and
Tss = |tss|2at 0° incidence angle. |tpp| and
|tss| represent the amplitudes of the
respective pp- and ss-polarized complex transmission coefficients (for
incidence angles larger than 0°, pp is parallel and ss is perpendicular
to the optical incidence plane), and Δ is the phase shift between them.
Further details are found in Refs.38,39 for the
ellipsometric method and in Ref.39 for the employed
set-up.