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Synchrotron radiation-based far-infrared spectroscopic ellipsometer with full Mueller-matrix capability
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Image of FIG. 1.
FIG. 1.

Ellipsometer at U4IR beamline consists of three major components: Polarization state generation (PSG) section, sample stage with an optical cryostat, and polarization state analyzer (PSA) section. Straight red arrow shows light propagation direction from the interferometer towards ellipsometer. Sample stage and PSA section can rotate around the same vertical axis to accommodate the ellipsometric measurements at different AOIs.

Image of FIG. 2.
FIG. 2.

Schematics of the sample stage and the closed-cycle cryostat assembly. From the bottom to the top, this assembly consists of (i) 2θ-circle with a holder for the PSA chamber, (ii) θ-circle that supports the following, (iii) χ angle adjustment stage with the travel range of ±7°, (iv) X-Y-Z stage, and (v) a closed-cycle cryostat that is shown in the sample-loading position.

Image of FIG. 3.
FIG. 3.

Schematics of the light propagation between the PSG and PSA sections of the ellipsometer. PSG section consists of a retarder C1, two linear polarizer, P0 and P, and three mirrors: an off-axis parabola M1P with effective focus length of 1 m and two flat ones, M2 and M3. PSA section consists of a retarder C2, analyzing polarizer A, and a parabolic mirror M4P for light focusing on a bolometer or a CuGe detector.

Image of FIG. 4.
FIG. 4.

(a) Rotating retarder based on a single silicon prism and three gold mirrors (4 bounces). (b) Rotating retarder based on two adjacent KRS5 Fresnel rhombs (4 internal bounces). Direction of the light propagation is shown with arrows.

Image of FIG. 5.
FIG. 5.

Experimental spectra for Ψ(ω) and Δ(ω) of Si and KRS5 retarders measured for the retarder position that corresponds to the maximum value of retardation. Black horizontal lines correspond to the theoretical values of Ψ(ω) and Δ(ω) for an ideal retarder. The narrow spectral range around 3000 cm−1 is shown with dotted lines due to strong absorption in the Mylar windows.

Image of FIG. 6.
FIG. 6.

Flowchart for the calculation steps in the 4 × 4 matrix formalism.

Image of FIG. 7.
FIG. 7.

Experimental RAE data for the real ɛ1 and imaginary ɛ2 parts of the dielectric function for Dy-IG measured at T = 7 K at AOI = 75° using three sets of detectors and two sets of the spectrometer beamsplitters. Strong peaks between 80 and 700 cm−1 are optical phonons.

Image of FIG. 8.
FIG. 8.

(a) Experimental spectra of the normalized MM components m 34(ω) = −m 43(ω) (magenta dotted-dashed curve) and m 33(ω) = m 44(ω) (blue dashed curve) for Dy-IG measured at T = 5 K. The strong peaks above 80 cm−1 correspond to the optical phonons. Solid red curves show the fit results. (b)-(c) The low-frequency part of the same spectra measured with a LHe-pumped 1.6 K bolometer. The corresponding range is shown in (a) with a black dotted rectangle. (d)-(g) ɛ1,2(ω) and μ1,2(ω) functions as extracted from the fit of the MM spectra. The pure magnetic dipole excitation (magnon) is observed at 59.5 cm−1 and the pure electric dipole excitation (phonon) is observed at 81 cm−1. The magnon amplitude in the m 34(ω) = −m 43(ω) spectra in (c) has an opposite sign compared to that for the optical phonon. A number of hybrid modes that contribute to both ɛ1,2(ω) and μ1,2(ω) in (d)-(g) correspond to the weak crystal-field transitions and are marked in (b) with vertical arrows.

Image of FIG. 9.
FIG. 9.

Experimental optical spectra of TbMnO3 with crystallographic orientation of xa, yc, and zb measured in the temperature range between 5 K and 40 K. Phonon peak at ∼118.5 cm−1, electromagnon (EM) peak at 62 cm−1, and peak of excitation at 135 cm−1 (EX) are marked with arrows. (a) Real part of the pseudo-dielectric function. The normalized MM components are shown in (b) m 34(ω) = −m 43(ω) and (c) m 33(ω) = m 44(ω). (d) The difference between the off-diagonal MM components m 14(ω) and m 24(ω). Vertical arrows in (c) indicate the contribution of ɛ xx (ω), μ yy (ω), and α xy (ω) to m 34(ω) = −m 43(ω) components of the MM spectra.


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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Synchrotron radiation-based far-infrared spectroscopic ellipsometer with full Mueller-matrix capability