# Verdet Constant of Magneto-Active Materials Developed for High-Power Faraday Devices
## 1 Introduction
### Methods for the Thermal Effects Compensation or Reduction  
Many techniques and methods for a partial reduction or compensation of the arising thermal effects have been reported in recent years. To satisfy the high demands on the high-power FDs, it is essential to take into consideration an appropriate optical layout for compensation of the thermally-induced polarization and wavefront distortions [17; 18; 19; 20]. The needed length \(L\) for achieving the desired rotation angle \(\theta\) by a magneto-optical element (MOE) may be reduced by enhancement of the applied magnetic field [21; 22; 23; 24; 25; 26]. This leads to a reduced amount of generated heat as well as to a reduced optical path travelled through a distorted medium. Another aspect which needs to be taken into account is the optimal design of the geometry and cooling of the MOE [27; 28; 29]. One possibility is to consider the cryogenic cooling [30; 31; 32], which, on the one hand, greatly enhances both Verdet constant and thermal properties of the medium, but, on the other hand, increases the cost and technological complexity of the FD and makes the system more sensitive to temperature fluctuations. The degrading impact of the thermal effects may be substantially reduced by a careful choice of the magneto-active material used as a magneto-optical element in the FD. The common materials used for the laser FDs incorporate solid-state crystals, transparent ceramics or glass [33; 34]. Possession of a high Verdet constant and transparency at the desired wavelength are the fundamental criteria for selection of a magneto-active material as a highly promising for utilization in FDs. Historically, for the purpose of comparison between the magneto-active materials, a parameter called a magneto-optical figure of merit (FOM) was introduced as a ratio between the Verdet constant and absorption \(-V/\alpha\). However, in the context of the high-power FDs, it is more convenient to include the material thermal properties for more accurate benchmarking. The \"extended\" FOM may have the following forms [16]  
Figure 1: A simplified scheme of the physical phenomena involved in the absorption-induced thermal effects in magneto-active media. \[\mu_{Q} =\left|\frac{Vk}{\alpha Q}\right|\quad(|\xi|\geq 1)\quad, \tag{2}\] \[\mu_{Q,\xi} =\left|\frac{Vk}{\alpha Q\xi}\right|\quad(|\xi|<1)\quad,\] (3) \[\mu_{P} =\left|\frac{Vk}{\alpha P}\right|\quad, \tag{4}\]  
where \(k\) denotes the thermal conductivity; \(Q\) and \(P\) are the so-called thermo-optical constants evaluating the polarization and wavefront distortions, respectfully; and \(\xi\) is the optical anisotropy parameter. Media with a negative parameter of optical anisotropy allow compensating the thermally-induced depolarization without using a reciprocal rotator in the optically-compensating layout [35; 36; 37; 38]. The \(Q,P,\xi\) parameters are dependent on a large set of material parameters incorporating optical, thermo-optical, thermo-mechanical and elasto-optical properties [16; 17; 18]. However, it was reported multiple times, how these constants may be evaluated indirectly using different measurement methods (see, e.g., [39; 40; 41; 42; 43]). Within the scope of this manuscript, we cover in detail:  
* A method for simultaneous characterization of the Verdet constant wavelength and temperature dependence. * A brief summary of the reported room-temperature investigations of the Verdet constant for several magneto-active materials suitable for the high-power FDs. The measurement of the Verdet constant dispersion \(V(\lambda)\) at room temperature usually represents an initial step in the benchmarking process of new magneto-active materials by the FOM parameters in Equations (2)-(4). The knowledge of the temperature dependence of the Verdet constant is useful for the investigation of the FDs performance under thermal loading by a high-power laser.