# Verdet Constant of Magneto-Active Materials Developed for High-Power Faraday Devices
## 2 Characterization of the Verdet Constant as a Function of Wavelength and Temperature
### Experimental Setup for the Characterization  
A simplified scheme of the experimental setup used for the characterization of the Verdet constant is depicted in Figure 2. In the experiment, a probe beam from the broadband radiation source is linearly polarized by an input high-contrast Glan polarizer (P\({}_{1}\)) and propagates through the measured material sample, which is thermally coupled to a cryostat ledge. An external magnetic field is applied on the sample, inducing a Faraday rotation of the propagating probe beam. The beam then enters the detection system, which may be realized in different configurations, as depicted in Figure 2. The reason for consideration of different detection systems is the following: the transmission ranges of the employed optical elements and the wavelengths provided by the utilized broadband source will eventually limit the effective spectral range of the measurement. The first depicted configuration for the detection system consists of another Glan polarizer (an analyzer), which could be arbitrarily rotated around the optical axis and a diffuser. The latter may be either transmissive or reflective and its purpose is to suppress the polarization dependence of the fiber couplings delivering the optical signal to the spectrometers. This configuration was used in the investigations in Refs. [45; 46; 47], and its main advantage is the relative simplicity of the setup, compared with the other configurations. Furthermore, assuming we measure the Verdet constant on a single wavelength only (we use a laser probe beam except the broadband source), the spectrometers may be exchanged with a power meter, which even more simplifies the measurement and data analysis. The other depicted configurations take advantage of using an arbitrarily rotated achromatic wave plate, half (No. 2) or quarter-wave plate (No. 3) or of an arbitrarily rotated polarizer (No. 4) in a combination with a static analyser. The latter three configurations practically cancel the problem of the polarization-sensitive fiber couplings and allow to construct different spectral ranges of the measurement, based on the availability of the listed components. The configuration with the rotating half-wave plate was quite recently demonstrated [48] (a 3D overview of the experimental setup is depicted in Figure 3a), with the effective range of the measurement covering visible, near-infrared and mid-infrared wavelengths. The other configurations are planned to be investigated in the near future. Regardless of the what type of detection system is used, the measurement is taken twice (at each of the measured temperatures), i.e., with and without applying the magnetic field. The spectra are gathered in a large number of angular steps of the rotating element of the detection system, making the measurement more robust, as compared with taking only three angular steps in the original method [44]. According to the Jones calculus, the detected intensity data need to be proportional to the angular position \(\alpha\) of the rotating element of the depicted detection systems (Nos. 1-4) as follows  
\[I_{1}(\alpha,\lambda_{i},T_{j}) \propto\cos^{2}\left[\alpha+\theta(\lambda_{i},T_{j})-\alpha_{0} \right]\quad, \tag{5}\] \[I_{2}(\alpha,\lambda_{i},T_{j}) \propto\cos^{2}\left[2\alpha+\theta(\lambda_{i},T_{j})-\alpha_{0} \right]\quad,\] (6) \[I_{3}(\alpha,\lambda_{i},T_{j}) \propto\frac{1}{2}\cos^{2}(\alpha_{0})+\frac{1}{2}\cos^{2}\left[ 2\alpha+\theta(\lambda_{i},T_{j})-\alpha_{0}\right]\quad,\] (7) \[I_{4}(\alpha,\lambda_{i},T_{j}) \propto\cos^{2}(\alpha-\alpha_{0})\cos^{2}\left[\alpha+\theta( \lambda_{i},T_{j})-\alpha_{0}\right]\quad, \tag{8}\]  
where \(I_{1-4}(\alpha,\lambda_{i},T_{j})\) denotes the measured intensity data gathered at each of the detectable wavelengths \(\lambda_{i}\) and temperatures \(T_{j}\). \(\alpha_{0}\) corresponds to the initial mutual angular position of the input polarizer and the rotating element in the detection system.