## 3 Results and Discussion  
The dispersion curve of PMN-PT ceramics defined in this study using FTIR spectrometry could not be compared to literature because it has not been previously reported. Instead, we could validate our method's precision by taking a 508 \(\upmu\)m thick LiNbO\({}_{3}\) slab as a control sample, defining its dispersion curve, and comparing it to the literature. Figure 15 compares the calculated refractive index values to the values reported in the literature [35]. Figure 14: The experimental set-up for characterization of the EO beam steerer based on polycrystalline PMN-PT. Figure 15a indicates that the experimental and accepted refractive index data are exceptionally well-matched, and that is why the two curves in Figure 15a are indistinguishable. Expanding one-tenth of the spectrum, the slight variation in values can begin to be seen in Figure 15b. The amount of precision achieved in the calculation of the LiNbO\({}_{3}\) dispersion curve indicates that the methodology for calculating the refractive index of the PMN-PT sample is quite sound. The calculated dispersion curve for the PMN-PT sample after combining the data from the NIR and MIR transmission spectra is shown in Figure 16.  
The PMN-PT ceramics transmission for an s-polarized wave was determined using the calculated dispersion curve (Figure 17), as discussed in the previous section. Again, because the transmission of polycrystalline PMN-PT in such a wide wavelength range was not previously reported, we could not compare the results to the values reported in the literature. Instead, the transmission of a 1.5 mm \(\times\) 5 mm \(\times\) 5 mm polycrystalline PMN-PT slab was measured in the lab (see Figure 7) for three wavelengths, and the results were compared to the calculated values as seen in Table 5. Table 5 shows the measured transmission values agree with the calculated ones within 8.8% errors or less. Figure 16: The calculated dispersion curve for the PMN-PT sample after combining the data from the NIR and MIR transmission spectra. Figure 15: A comparison of the calculated refractive index values to literature values for the lithium niobate control sample. (**a**) full-view; (**b**) zoomed-view to show differences. The absorbance or optical density, \(OD\), can be calculated from the measured transmission, \(T\), as  
\[OD=\log\left(\frac{1}{T}\right) \tag{50}\]  
The magnitudes of absorbance of the PMN-PT sample for those three wavelengths have also been approximated and given in Table 5.  
The dielectric constant was calculated for each temperature using Equation (18) after collecting the capacitance values over the range, once for material capacitance and again for open-cell capacitance. The resulting dielectric values for polycrystalline PMN-PT are graphed against temperature in Figure 18. As seen in Figure 18, the maximum dielectric constant achieved was approximately 12,000, and the peak dielectric constant is reached at or near 25 \({}^{\circ}\)C. Therefore, the Curie temperature of this ceramic is at room temperature. It should be noted that a higher dielectric constant increases the loss and reduces the speed of response. The optimum number of interfaces (N) for the 7.5 mm \(\times\) 7.5 mm \(\times\) 40 mm polycrystalline PMN-PT considering no internal reflection and minimum partial back-reflection was defined as two. Figure 19 shows the polycrystalline PMN-PT under the voltage in the lab. A 1 kV/mm DC electric field was applied to the PMN-PT ceramic electrodes to measure the deflection angle using Equation (49). A 1 kV/mm AC electric field was also applied to illustrate this scanner's beam steering, as seen in this paper's supplementary materials. This EO beam steerer was used to steer the light from visible to mid-IR without any orientation adjustment or domain-engineered multi-prisms required.