# Verdet Constant of Magneto-Active Materials Developed for High-Power Faraday Devices
## 1 Introduction  
### Faraday Effect and Its Applications  
The Faraday effect (or magnetic circular birefringence) is one of the fundamental magneto-optical phenomena emerging from the interaction of light and matter subjected to a magnetic field. This effect manifests itself in the magnetized medium as a circular anisotropy, which is an outcome of the longitudinal Zeeman effect-splitting of the ground and excited states of the medium in the magnetic field [1]. A linearly polarized light beam (which may be represented as a superposition of the right-hand(+) and the left-hand(\(-\)) circularly polarized waves with a definite phase difference) undergoes rotation of the polarization plane as it propagates through the medium because of the different propagation velocities of the \(+/-\) waves. This phenomenon may be conveniently described by assuming a ray coordinate system \((x^{\prime},y^{\prime},z^{\prime})\) travelling along the ray's path \(\mathcal{L}\) in the medium, with the unit vector \(\mathbf{z^{\prime}_{0}}\) in the direction of raypropagation. Considering linear (far from saturation) Faraday effect, the rotation angle distribution over the beam's cross-section may be described using the following expression  
\[\theta(x^{\prime},y^{\prime})=\int_{\mathcal{L}}V\left[\lambda,T(x^{\prime},y^{ \prime},z^{\prime})\right]\mathbf{B}(x^{\prime},y^{\prime},z^{\prime})\cdot \mathbf{z^{\prime}_{0}}\;\mathrm{d}\mathcal{L}\quad, \tag{1}\]  
where \(\mathbf{B}(x^{\prime},y^{\prime},z^{\prime})\) is the magnetic field, \(\mathbf{B}\cdot\mathbf{z^{\prime}_{0}}\) denotes the dot product of \(\mathbf{B}\) and \(\mathbf{z^{\prime}_{0}}\) vectors and \(V\) is the Verdet constant, a material parameter depending on wavelength \(\lambda\) and temperature \(T\). The sign of the rotation angle is determined by the projection of the magnetic field into the beam's propagation direction and by the sign of the Verdet constant. According to the convention, the Verdet constant is considered negative if the medium rotates the polarization clockwise and if the laser beam propagation is parallel to the magnetic field. By assuming constant temperature, constant magnetic field parallel to the beam of monochromatic light, Equation (1) simplifies into the familiar expression \(\theta=VBL\), where \(L\) is the distance travelled in the medium.  
There are vast possibilities for utilization of the Faraday rotation in technological and scientific applications. For instance, it can be used for magneto-optical devices for polarization-manipulation-based processing of an optical signal (e.g., modulators, switches, rotators or optical isolators [1; 2; 3; 4; 5]), magneto-optical current sensors [6], gravitational wave detection experiments [7] or magnetic splitting of ultrashort laser pulses in plasmas [8]. Within this broad scientific community dealing with the development of the Faraday devices (FDs), a great effort is dedicated to the investigation of the FDs for high-power laser systems. The high-power lasers have made several remarkable advancements in the recent years [9; 10; 11], leading to highly demanding criteria on new architectures, materials, and other related laser technologies. The FDs are used in the laser systems particularly for the multi-pass amplification and regenerative amplifiers as well as for optical isolation of one part of the system from another by eliminating possible harmful back-reflections. This makes the FDs indispensable components of any high-power laser system.