## 1 Introduction  
The electro-optic (EO) effect refers to producing birefringence in an optical medium in response to a slowly varying external electric field compared to optical frequencies [1, 2]. The change in the medium's refractive index can be proportional to the electric field or the square of the electric field. The former is called the linear EO effect, or Pockels effect, observed in crystals with a lack of centrosymmetry such as transparent ferroelectric crystals. The latter is called the nonlinear EO effect, or Kerr effect, observed in almost all transparent materials [3]. The EO materials in which the Pockels effect or linear EO effect is dominant, and hence, they exhibit linear EO response, are called linear EO materials. Nonlinear EO materials are referred to as the materials in which the Kerr effect or nonlinear EO effect is dominant. Besides the Pockels effect, the ferroelectric transparent crystals also exhibit piezoelectric and pyroelectric effects, and their performance is temperature-dependent [4, 5]. After a specific temperature, called the Curie temperature, where the dielectric constant peaks, the material becomes paraelectric, and the Kerr effect becomes dominant [1, 5]. Although all transparent materials show a Kerr effect, this effect is very significant in some liquids like nitrobenzene and nitrotoluene and some homogenous solid crystals such as the polycrystalline PMN-PT [5] and paraelectric KTN crystal [6, 7], which is the ferroelectric KTN heated above its Curie temperature. A large Kerr effect is also observed in metal, organic polymeric nanoparticles, and quantum dots [8; 9; 10]. Quantum dots are metallic nanoparticles smaller than 10 nm. [PERSON] and [PERSON] measured the Kerr coefficient of gold nanoparticles in a glass and showed the magnitude of the Keff coefficients increases rapidly by decreasing the diameter of nanoparticles [8]. They showed the subnanometer size particles exhibit the largest Kerr coefficients of any materials. However, to reach an appreciable optical path delay (OPD), a long nano sample is required. It is also challenging to make the sample thick enough to provide a uniform external electric field and address a large aperture. Furthermore, nanoparticles' Kerr effect is very dispersive since the wavelength should be very close to the onset of the optical absorption due to surface plasmon resonance. Those facts limit the industrial application of nanoparticles, especially when a larger aperture and broader bandwidth of optical frequency are necessary. The EO effect is used to deflect light in EO beam steerers [1]. The EO steerers refract the light by imposing a phase delay due to changing the medium's refractive index [7]. The steering angle is varied by adjusting the voltage applied on the crystal to electro-optically control the phase delay across the beam cross-section [2; 11]. Therefore, a bulk EO crystal beam steerer consists of a transparent EO bulk crystal with electrodes deposited on its surface or the ferroelectric domains engineered to multiple prisms under a variable external electric field [11]. EO beam steerers offer fast and random access beam steering compared to mechanical optical beam steering methods such as polygons, microelectromechanical, or galvanic mirrors, which are limited by mechanical inertia effects. EO beam steering systems are also more efficient and have higher bandwidth than acousto-optic (AO) beam deflectors. The EO scanning method offers high optical efficiency and physical robustness [3; 5; 7; 12; 13; 14]. EO beam steerers can be arranged to meet a variety of requirements per application. Appropriate choice of the drive electronics, optical path, and especially the EO crystal must be made to address specific functional requirements. Any change in the crystal, the pattern of the electrodes, and the applied voltage can significantly affect the performance of the EO deflectors.