## 1 Introduction
Therefore, the design problem is to find an EO crystal, an optimized electrode arrangement, and an optimized amount of voltage to get the magnitude of desired refractive index change with sufficient speed [3]. Comparing to liquid crystals and other liquids exhibiting an EO effect, the transparent solid electro-optical oxides are the only type of materials featuring both significant and fast EO effects. Solid oxide EO beam steerers can be considered capacitors that are quickly charged with a voltage leading to a bandwidth in the range of a few MHz [3; 5; 15]. Some new and some widely used solid electro-optical oxides are listed in Table 1, where n is the refractive index, \(\epsilon\) is dielectric constant or relative permittivity, and r is the linear electro-optical coefficient [1; 2; 16]. An ideal crystal for EO devices and applications should have a high EO coefficient and high index to provide enough phase delay at a lower applied voltage. It should also have a low dielectric constant to offer a low capacitance and a fast response [3]. Therefore, a crystal with a higher n\({}^{3}\)r/\(\epsilon\) in Table 1 will be more attractive for EO devices. In addition to those criteria, an ideal EO crystal should be inexpensive and available in larger sizes to promote use for a larger aperture in order to offer a larger number of resolvable spots. Furthermore, it should have high transmission and low dependency on temperature and polarization. The refractive index and EO coefficient of EO crystals vary by wavelength and temperature [17; 18]. The dielectric constant of a crystal also varies by temperature [1; 4; 6]. For example, the EO coefficient of KD\({}^{*}\)P is almost independent of wavelength, but it varies by temperature. For LiNbO\({}_{3}\), not only the EO coefficient varies with wavelength and temperature but also changes by modulation frequency [4; 18]. As seen in Table 1, the EO coefficient of BBO is much smaller than other crystals. However, because its relative permittivity is low, it can handle ultra-high peak power or average power light fluences. In general, if an EO crystal is being used at a temperature far enough from its Curie temperature, its permittivity and EO coefficient are relatively temperature-independent. [PERSON] et al. calculated the EO coefficient of LiTaO\({}_{3}\) in four different wavelengths by measuring the deflection angle of a horn-shaped EO scanner [12]. They concluded that the EO coefficient of LiTaO\({}_{3}\) decreases from 30.2 pm/V for HeNe laser (632 nm) to 27.1 pm/V for diode laser (1558 nm). Although using the EO crystal as an EO scanner and measuring each wavelength's deflection angle is a precise method to determine the EO coefficient of that crystal, they did not consider refractive index variation with wavelength. The deflection angle depends on the EO coefficient and the cube of the refractive index, which is varied by wavelength [1]. In addition, the temperature dependencies of the EO coefficient, refractive index, and permittivity were not measured in that study. Most EO beam steering systems use transparent single ferroelectric crystals exhibiting a linear EO effect like lithium niobate and lithium tantalate to steer the light beam [12; 17]. However, the disadvantages are that those single crystals are highly temperature-dependent and have a low EO effect [5; 19]. Therefore, the applied voltage should be very high. Single ferroelectric crystals also need to be poled, and their crystalline orientation should be domain-engineered like multi-prisms [12; 17; 20]. Furthermore, single ferroelectric crystal steerers are polarization-dependent, and the number of resolvable spots is low because of the small beam size. Those issues have made the EO beam steerers impractical for many industrial applications.