PMN-PT) Using a Polarization-Independent Electro-Optical Laser Beam Steerer

applied sciences

Article Determining the Quadratic Electro-Optic Coefﬁcients for Polycrystalline Pb(Mg1/3Nb2/3)O3-PbTiO3 (PMN-PT) Using a Polarization-Independent Electro-Optical Laser Beam Steerer

Abtin Ataei * , Paul McManamon, Cullen Bradley, Michael Wagner and Edward Ruff

School of Engineering, University of Dayton, Dayton, OH 45469, USA; [email protected] (P.M.); [email protected] (C.B.); [email protected] (M.W.); [email protected] (E.R.) * Correspondence: [email protected]

Abstract: A polarization-independent electro-optical (EO) laser beam steerer based on a bulk relaxor

ferroelectric polycrystalline Pb(Mg1/3Nb2/3)O3-PbTiO3 (PMN-PT) was developed in this study to steer light ranging from visible to mid-IR wavelengths. A large number of the resolvable spots was achieved with this EO steerer. A Fourier-transform infrared (FTIR) spectroscopy was employed to determine the refractive index of the polycrystalline PMN-PT over a wide range of optical wavelengths. Besides measuring the transmission of this material, the capacitance bridge analysis was used to characterize the effect of temperature on the dielectric constant of PMN-PT. The performance of the steerer over a variety of wavelengths was simulated using COMSOL Multiphysics. The deflection angle for the wavelengths of 532, 632.8, 1550, and 4500 nm was measured in the lab in terms of mrad.mm/kV at two different temperatures and compared to the simulation results. The Citation: Ataei, A.; McManamon, P.; quadratic Kerr electro-optic coefficient and the halfwave electric field were determined for those four Bradley, C.; Wagner, M.; Ruff, E. Determining the Quadratic wavelengths at two different temperatures. The results showed polycrystalline PMN-PT has a large Electro-Optic Coefficients for quadratic EO coefficient for visible light, almost as large in the near IR, but drops significantly in the Polycrystalline mid-IR. No significant temperature dependency for the EO coefficients was observed for any of those

Pb(Mg1/3Nb2/3)O3-PbTiO3 (PMN-PT) four wavelengths. Using a Polarization-Independent Electro-Optical Laser Beam Steerer. Keywords: relaxor ferroelectrics; Kerr effect; beam steerer; polycrystalline PMN-PT; halfwave electric Appl. Sci. 2021, 11, 3313. https:// ﬁeld; Fourier-transform infrared (FTIR) spectroscopy; mid-IR doi.org/10.3390/app11083313

Academic Editor: Shujun Zhang 1. Introduction Received: 10 March 2021 The electro-optic (EO) effect refers to producing birefringence in an optical medium in Accepted: 5 April 2021 Published: 7 April 2021 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, Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in observed in crystals with a lack of centrosymmetry such as transparent ferroelectric crystals. published maps and institutional affil- The latter is called the nonlinear EO effect, or Kerr effect, observed in almost all transparent iations. 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 piezoelec- Copyright: © 2021 by the authors. tric and pyroelectric effects, and their performance is temperature-dependent [4,5]. After Licensee MDPI, Basel, Switzerland. This article is an open access article a specific temperature, called the Curie temperature, where the dielectric constant peaks, distributed under the terms and the material becomes paraelectric, and the Kerr effect becomes dominant [1,5]. Although conditions of the Creative Commons all transparent materials show a Kerr effect, this effect is very significant in some liquids Attribution (CC BY) license (https:// like nitrobenzene and nitrotoluene and some homogenous solid crystals such as the poly- creativecommons.org/licenses/by/ crystalline PMN-PT [5] and paraelectric KTN crystal [6,7], which is the ferroelectric KTN 4.0/). heated above its Curie temperature.

Appl. Sci. 2021, 11, 3313. https://doi.org/10.3390/app11083313 https://www.mdpi.com/journal/applsci Appl. Sci. 2021, 11, 3313 2 of 27

A large Kerr effect is also observed in metal, organic polymeric nanoparticles, and quantum dots [8–10]. Quantum dots are metallic nanoparticles smaller than 10 nm. Thakur and Van Cleave 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 [3,5,7,12–14]. 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. 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 Table1, where n is the refractive index, ε 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 n3r/ε in Table1 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 LiNbO3, not only the EO coefficient varies with wavelength and temperature but also changes by modulation frequency [4,18]. As seen in Table1, 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. Appl. Sci. 2021, 11, 3313 3 of 27

Table 1. The properties of some materials with linear electro-optic (EO) response.

Material n ε r (pmV−1) n3r/ε (pmV−1) Ferroelectrics

LiNbO3 2.26 29 31 12.339 LiTaO3 2.23 43 31 7.995 KNbO3 2.23 55 64 12.904 BaTiO3 2.4 1800 1670 12.826 SBN75 (Sr0.75Ba0.25Nb2O6) 2.3 1550 1340 10.519 SBN60 (Sr0.6Ba0.4Nb2O6) 2.3 750 216 3.504 Ferroelectric KTN (KTa0.35Nb0.65O3) 2.3 10,000 8000 9.734 KBN (K2BiNb5O15) 2.4 510 346 9.379 3+ 4+ KBN (K2BiNb5O15) Ce :Ce 2.4 509 370 10.049 BSTN 2.4 345 200 8.014 BSKNN-2 2.35 800 380 6.164 BSKNN-3 2.301 800 420 6.396 SCNN 2.321 1740 1200 8.623 BBO (BaB2O4) 1.67 6.7 2.7 1.877 Semiconductors GaAs 3.5 13.2 1.2 3.898 InP 3.29 12.6 1.45 4.098 CdTe 2.82 9.4 6.8 16.223 Bi12SiO20 2.54 56 5 1.463 Bi12GeO20 2.55 47 3.4 1.200

Casson et al. calculated the EO coefficient of LiTaO3 in four different wavelengths by measuring the deflection angle of a horn-shaped EO scanner [12]. They concluded that the EO coefficient of LiTaO3 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. Although the beam after a deflection in an EO steerer can be expanded in a tele- scope, that will decrease the deflection angle proportional to that beam magnification as follows [11]: θ θ = 1 (1) 2 M

where θ2 is the deflection angle after expansion by the factor of M, and θ1 is the deflection angle before beam expansion. Therefore, deflecting an 80 µm beam to 125 mrad is equiva- lent to deflecting a 6 mm beam to 1.67 mrad. The factor that remains constant is sometimes called an angle/aperture product [3]. Instead of the deflection angle, which is not a complete metric for beam steerers, we describe the number of the resolvable spots instead as the metric for light beam steerers as follows [1]: θ N = (2) θbeam Appl. Sci. 2021, 11, 3313 4 of 27

where θ is the deflection angle depending on the geometry, optical, crystallography properties of the crystal, the type of EO effect, and the strength of the external electric field, and θbeam is the beam divergence angle in far-field, which is calculated as [1]

λ θbeam = (3) πw0

where λ is the wavelength of the light, and w0 is the radius of the beam, which can usually be up to half of the crystal height (H) or width (W) as

Max w0 = 0.5 × Min{W, H} (4)

The first EO steerer was introduced by Fowler et al. in 1964 using KH2PO4 as the EO crystal [21]. This crystal is paraelectric with tetragonal symmetry at room temperature. Although its Curie temperature is below −150 ◦C, which makes its optical properties almost temperature-independent, this crystal is soluble in the water. In addition, a very large voltage should be applied to provide enough phase delay, making it impractical. Chen et al. employed potassium tantalate niobate as a single EO crystal in their EO scanners [22]. The most used single crystal in EO steerers is LiTaO3. Hisatake et al., Scrymgeour et al., Casson et al., and many more used LiTaO3 in their EO scanners [12,13,17,20,23,24]. Because both of those two crystals are single ferroelectric crystals, their dipole orientations must be adjusted by applying more than 21 kV/mm voltage. In addition, multiple prism-shaped domains must be created to steer a small beam to a few degrees by applying more than 14 kV/mm on the crystal. Furthermore, those crystals are temperature-dependent [5,15], and their EO scanners were polarization-dependent. Polarization dependency makes the scanners deflect the light if it is only polarized in a certain direction. Therefore, polarization dependency limits these scanners’ application even in one dimension and makes it impossible to steer the light in two dimensions in one crystal. Nakamura and Nakamura et al. developed an EO scanner based on the Kerr effect and space-charge-controlled electrical conduction using paraelectric KTN [7,25]. They heated a 0.5 mm thick small KTN single-crystal slab with uniform titanium electrodes up to a few degrees above its Curie temperature to inject electrons into the crystal, taking advantage of the crystal’s high permittivity at around its Curie temperature [6]. They reported deflecting an 80 µm beam to 125 mrad by applying 500 V/mm, resulting in less than 20 resolvable spots [7]. Although this scanner uses another physical effect besides the EO effect and has the lowest applied voltage reported so far, it has several limitations. First, KTN does not have an excellent transmission in near IR and mid-IR. Moreover, adjusting the temperature in this scanner is crucial to ensure the KTN is in its paraelectric region and the permittivity is high enough to inject the electrons. In addition, using a crystal at its maximum dielectric constant will result in high loss and slow response. Furthermore, because it is impossible to inject electrons in thick dielectrics, the crystal must always be a fraction of a millimeter thick or less, which significantly limits its beam size and number of resolvable spots. The structure of the scanner and its polarization dependency not only limit its ability to steer the beam to one dimension in many applications but also makes it impossible to steer the beam to both dimensions in one crystal. The only way to steer the light in two dimensions using this scanner is to steer the light to one dimension in a crystal first, then flip the polarization of the light by a halfwave plate and focus it on another crystal to steer it into the other dimension. This inefficient and lengthy procedure does not offer a compact two-dimensional beam steering, limits the deflection angle in both dimensions, and may cause beam clipping and distortion from hitting the crystal wall boundary. In addition to the index change, the deflection angle of an EO steerer depends on the effective length-to-width ratio of the EO crystal [1,2,13,14,24,26]. Since long single EO crystals are usually not available, the crystals’ effective width is reduced to increase the Appl. Sci. 2021, 11, 3313 5 of 27

deflection angle in some studies. McManamon and Ataei suggested cutting the EO crystal like a fishtail [11]. Fang et al. suggested a trapezoid-shaped and horn-shaped crystal to maximize the effective length-to-width ratio and maximize the deflection angle [24]. However, cutting and machining the EO crystal increases the cost of the EO beam steerer. Therefore, if a long EO medium were available, the optimum shape would be a long rectangular shape. Polycrystalline Pb(Mg1/3Nb2/3)O3-PbTiO3 (PMN-PT) exhibits a much higher EO effect compared to LiNbO3 and LiTaO3 and is transparent from visible to mid-IR. This ceramic is relatively inexpensive and available in a larger size [5,19]. In this study, the refractive index of polycrystalline PMN-PT was determined using the Fourier-transform infrared (FTIR) spectroscopy as well as its transmission over a wide range of optical frequencies. A capacitance bridge analysis was performed to characterize the effect of temperature on the dielectric constant of this ceramic as well. A polarization-independent beam steerer was designed using polycrystalline PMN-PT. Its performance was simulated using COMSOL Multiphysics and measured in the lab for the wavelengths of 532, 632.8, 1550, and 4500 nm. The quadratic Kerr EO coefficient and the halfwave electric field for each wavelength were determined by measuring the deflection angle and refractive index associated with each wavelength. The effect of temperature on the EO coefficient in a finite temperature range was also investigated.

2. Materials and Methods Polycrystalline PMN-PT is a transparent relaxor ferroelectric ceramic [5,15,19]. Unlike single crystals, ceramics are easier, cheaper, and faster to produce by several well-matured techniques like hot-pressing [5]. Ceramics are available in larger sizes compared to single crystals so that they can address a larger aperture. Polycrystalline PMN-PT, like other ceramics, is made of randomly arranged grains or crystals [5,19]. Although each grain may have different orientations, the ceramic’s properties are defined by the sum of many grain orientations, making the ceramic isotropic. Therefore, the optical properties of polycrystalline PMN-PT are the same in all directions, even under its Curie temperature. Applying an external electric field makes its isotropic and stable structure distorted and converted to a uniaxial medium in which the external electric field defines the optical axis [1,2,7]. Therefore, polycrystalline PMN-PT can be used as an EO beam steerer, and its EO properties can be defined by measuring and simulating the deflection angles. Since an EO steerer’s deflection angles also depend on the medium’s refractive index, the refractive index of polycrystalline PMN-PT, its dielectric constant, and its transmission should also be determined.

2.1. Determining the Refractive Index, Transmission, and Dielectric Constant of PMN-PT Ceramic To design and model an EO beam steerer based on polycrystalline PMN-PT and determine the ceramic’s EO coefﬁcient at several wavelengths and temperatures by measuring and/or simulating the deﬂection angle, the refractive index, transmission, and dielectric constant of this ceramic should be known. The refractive index was determined using FTIR spectroscopy [27–29]. The transmission was determined from Fresnel equations and compared with the data measured in the lab. The dielectric constant was found as a function of temperature through a capacitance bridge analysis (CBA).

2.2. Interference Fringes in FTIR Transmission Spectra A common, and normally undesirable, artifact of transmission spectroscopy, when applied to thin samples, is the inclusion of interference fringes within the transmission data. Whenever a sample consists of two planar partially-reflective parallel interfaces and the face separation is not insignificant, interference fringes will occur [27]. The phenomenon which gives rise to these interference fringes is the internal reflection, as depicted in Figure1. Appl. Sci. 2021, 11, x FOR PEER REVIEW 6 of 27

2.1. Determining the Refractive Index, Transmission, and Dielectric Constant of PMN-PT Ceramic To design and model an EO beam steerer based on polycrystalline PMN-PT and determine the ceramic’s EO coefficient at several wavelengths and temperatures by measuring and/or simulating the deflection angle, the refractive index, transmission, and dielectric constant of this ceramic should be known. The refractive index was determined using FTIR spectroscopy [27–29]. The transmission was determined from Fresnel equations and compared with the data measured in the lab. The dielectric constant was found as a function of temperature through a capacitance bridge analysis (CBA).

2.2. Interference Fringes in FTIR Transmission Spectra A common, and normally undesirable, artifact of transmission spectroscopy, when applied to thin samples, is the inclusion of interference fringes within the transmission data. Whenever a sample consists of two planar partially-reflective parallel interfaces and Appl. Sci. 2021, 11, 3313 the face separation is not insignificant, interference fringes will occur [27]. The phenome-6 of 27 non which gives rise to these interference fringes is the internal reflection, as depicted in Figure 1.

Figure 1. When an optical sample is structured with two parallel partially-reflective optical flats, Figure 1. When an optical sample is structured with two parallel partially-reflective optical flats, the incident light (I) contributes to both the reflected (R) and transmitted (T) intensities. The light the incident light (I) contributes to both the reflected (R) and transmitted (T) intensities. The light which is not immediately reflected (i.e., passes the first interface) can be internally reflected and ultimatelywhich is not add immediately interference reflectedto either the (i.e., reflecte passesd thelight first or transmitted interface) can light. be internallyNote that absorbance reflected and isultimately not explicitly add depicted interference in this to either illustration the reflected but is assumed light or transmitted to affect both light. reflectance Note that and absorbance transmit- is tance.not explicitly depicted in this illustration but is assumed to affect both reflectance and transmittance.

TheThe thin thin sample sample forms forms a simple a simple Fabry–Pérot Fabry–Pé rotetalon, etalon, creating creating an optical an optical resonator resonator that allowsthat allows the source the source light lightto constructively to constructively and destructively and destructively interfere interfere with withitself. itself. An im- An portantimportant parameter parameter when when analyzing analyzing a Fabry–Pérot a Fabry–Pérot etalon etalon is isthe the so-called so-called “finesse”, “finesse”, which which determinesdetermines the the fringe fringe contrast contrast of of the the system system and and is is given given as as [30] [30] 44|r|𝑟|2| F𝐹== (5)(5) (1−|𝑟|2) (1 − |r|2) where |𝑟| is the surface reflectance (for normally incident light) which is defined as where |r|2 is the surface reflectance (for normally incident light) which is defined as 𝑛(𝜈) − 1 |𝑟| = (6) n(𝑛ν()𝜈)−+11 2 |r|2 = (6) n( ) + High-finesse systems will have correspondingν ly1 high fringe contrast, which increases the likelihoodHigh-finesse that systemsFTIR spectrometers will have correspondingly with large spectral high bandwidths fringe contrast, will which resolve increases them. Greatthe likelihood effort, which that includes FTIR spectrometers extremely small with st largeep sizes spectral and bandwidthslong integration will times, resolve is them.typ- icallyGreat needed effort, for which a dispersive includes spectrometer extremely small to do step the sizessame. and long integration times, is typicallyThe frequency needed for of a the dispersive interference spectrometer fringes is to proportional do the same. to the thickness of the sample; aThe thick frequency sample will of the produce interference very fringeshigh frequency is proportional fringes to (small the thickness separation), of the while sample; a verya thick thin sample sample will will produce produce very very high low frequency frequency fringes fringes (small (large separation), separation). while The alatter very casethin helps sample to will explain produce why very characterizing low frequency thin fringes films (largeusing separation).FTIR spectroscopy The latter can case be helpsvery challenging.to explain why When characterizing the amplitudes thin of films the usinginterference FTIR spectroscopy fringes are strong, can be they very can challenging. severely When the amplitudes of the interference fringes are strong, they can severely obscure the transmission values. Typically, this is why significant effort is made to reduce the impact of any interference fringes. If, however, accurate transmission values are not the end-goal of characterization, then the fringes themselves offer valuable information about the sample material. For example, the interference fringe maxima are governed by m ν n(ν ) = (7) m m 2d

where νm is the wavenumber associated with the fringe of order number m, and d is the sample thickness [31]. If two of the three aforementioned values are known, then the third can be solved by rearranging Equation (7).

2.3. FTIR Analysis of Polycrystalline PMN-PT Sample The main objective of characterizing the PMN-PT sample using an FTIR spectrometer is to identify the positions of the interference fringe peaks superimposed on the transmission data. Once the peaks have been identiﬁed, it will still be necessary to assign the correct order number to each peak to calculate the refractive index at each frequency position Appl. Sci. 2021, 11, 3313 7 of 27

accurately. Since it is not possible to directly observe the zeroth-order fringe (fringe peak at 0 cm−1), it will be necessary to use the measured fringe spacing to extrapolate down to the zeroth-order and assign absolute order numbers to the known fringes. With this methodology in mind, it is desirable to measure as many fringe positions as possible directly. To that end, transmission data were collected using two separate FTIR spectrometers with different but overlapping analysis spectra. In general, analysis using FTIR spectrometers is as simple as collecting a background scan followed by a scan of the sample itself. For this analysis, it is features of the transmission data, not the transmission values themselves, that are the focus of inspection. Special consideration must therefore be made in an effort to make these features more prominent. The ﬁrst of these considerations was done by preparing a thin PMN-PT sample. A thin medium is much more likely to exhibit transmission interference fringes than one whose thickness is on the order of many hundreds of wavelengths. Another important consideration is the incident angle of the source on the sample. Typically, the normally incident transmission of a well-characterized medium can be calculated as [29] 1 T(ν) = (8) 1 + F sin2(2πνn(ν)d) where F is the so-called “ﬁnesse” value [30]. If the source light is incident on the sample at any angle other than normal, as occurs at the focal plane of FTIR spectrometers, then the n(ν)d term from Equation (8) must be substituted with Equation (9), which takes into account the angle of incidence. q 2 2 2 n(ν)d → n (ν) − nAir(ν) sin (θ)d (9)

It is possible to reduce this distortion by restricting the source light via an aperture placed some distance in front of the sample. While this will not collimate the incident illumination, it will limit the angular variation such that Equation (8) becomes a good ap- proximation of the transmittance values. An illustration of this modification is included in Figure2. While it is unavoidable that restricting the source illumination in this manner will reduce the system throughput, it is possible to balance the reduction of output power with the increased signal-to-noise ratio [29]. It will also be necessary to collect all background scans with the aperture installed such that it matches the restriction used during the actual material scans. Additionally, restricting the source beam spread serves to increase the interference fringe amplitudes. A significant consequence of the unrestricted beam spread in typical FTIR spectral analysis is that fringes at higher frequencies are suppressed; this modification reduces that effect [28]. Figure3 shows a direct comparison of interference fringes collected using three different aperture sizes to restrict the source beam and illustrates its effect on fringe amplitudes. Apertures were mounted within each FTIR spectrometer to limit the angle of incidence to less than ±3.0◦ from normal. Specific aperture configurations for each FTIR spectrometer are summarized in Table2. In addition to the prepared PMN-PT sample, a commercially available LiNbO3 single crystal thin sample was characterized as a control, and subsequent refractive index calculations were be compared to literature values to help support the validity of this methodology (Figure4). The LiNbO 3 sample used for this purpose is professionally polished and has a measured thickness of 508 µm. Appl. Sci. 2021, 11, x FOR PEER REVIEW 8 of 27

Appl. Sci. 2021, 11, 3313 8 of 27 Appl. Sci. 2021, 11, x FOR PEER REVIEW 8 of 27

Figure 2. A comparison of the incident ray bundles during unrestricted FTIR analysis (a) and restricted FTIR analysis (b).

Additionally, restricting the source beam spread serves to increase the interference fringe amplitudes. A significant consequence of the unrestricted beam spread in typical FTIR spectral analysis is that fringes at higher frequencies are suppressed; this modification reduces that effect [28]. Figure 3 shows a direct comparison of interference fringes collected using three different aperture sizes to restrict the source beam and illustrates its effect on fringe amplitudes. Apertures were mounted within each FTIR spectrometer to FigureFigure 2. 2. A Acomparison comparison of the of incident the incident ray bundles ray bundlesduring unrestricted during unrestricted FTIR analysis FTIR (a) and analysis re- (a) and limitstricted the angle FTIR analysisof incidence (b). to less than ±3.0° from normal. Specific aperture configurations restricted FTIR analysis (b). for each FTIR spectrometer are summarized in Table 2. Additionally, restricting the source beam spread serves to increase the interference fringe amplitudes. A significant consequence of the unrestricted beam spread in typical FTIR spectral analysis is that fringes at higher frequencies are suppressed; this modification reduces that effect [28]. Figure 3 shows a direct comparison of interference fringes collected using three different aperture sizes to restrict the source beam and illustrates its effect on fringe amplitudes. Apertures were mounted within each FTIR spectrometer to Appl. Sci. 2021, 11, x FOR PEER REVIEWlimit the angle of incidence to less than ±3.0° from normal. Specific aperture configurations9 of 27

for each FTIR spectrometer are summarized in Table 2.

Table 2. Aperture size and spacing used for each FTIR spectrometer to amplify interference fringe amplitude.

Spectrometer Aperture Diameter (mm) Aperture Distance (mm) Maximum Angle of Incidence (°) Thermo Scientific 6.0 60.0 2.862 Perkin Elmer 5.0 54.75 2.614

In addition to the prepared PMN-PT sample, a commercially available LiNbO3 single crystal thin sample was characterized as a control, and subsequent refractive index calculations were be compared to literature values to help support the validity of this method- FigureFigure 3. Reducing 3. Reducing the theaperture aperture diameter, diameter, thereby thereby reducing reducing the the maximum maximum angle angle of of incidence, incidence, serves ology (Figure 4). The LiNbO3 sample used for this purpose is professionally polished and servesto amplify to amplify the magnitudethe magnitude of the of interferencethe interference fringes. fringes. has a measured thickness of 508 μm.

Figure 3. Reducing the aperture diameter, thereby reducing the maximum angle of incidence, serves to amplify the magnitude of the interference fringes.

(a) (b)

Figure 4. The LiNbO3 single crystal control sample (a) and prepared PMN-PT sample (b) arranged Figure 4. The LiNbO3 single crystal control sample (a) and prepared PMN-PT sample (b) arranged with millimeter scales for reference. with millimeter scales for reference. Using Equation (7), it was estimated that the interference fringes of the prepared PMN-PT sample have a period of approximately 5 cm−1. With this in mind, the FTIR spectrometers were configured with a scanning resolution of 0.25 cm−1 to produce well-defined fringes in the final transmission spectrum. Additionally, the transmission values were averaged over thirty-two scans to increase waveform smoothness. While a scan resolution of 0.25 cm−1 is sufficient to capture the fringe waveforms, for the purpose of calculating the refractive index, the fringe peak positions must be known more precisely. To that end, the transmission spectra were mathematically characterized with a polynomial fit to more precisely interpolate the location of the fringe peaks. Peak locations measured using this method were expected to have an accuracy of at least two decimal places (0.01 cm−1 → 0.0001 m−1), supporting an index of refraction calculation out to four decimal places. An example of the fringe peak fitting is depicted in Figure 5.

Figure 5. The accuracy of interference fringe peak location measurements is increased by interpolation via a polynomial fit. Appl. Sci. 2021, 11, x FOR PEER REVIEW 9 of 27

Table 2. Aperture size and spacing used for each FTIR spectrometer to amplify interference fringe amplitude.

Spectrometer Aperture Diameter (mm) Aperture Distance (mm) Maximum Angle of Incidence (°) Thermo Scientific 6.0 60.0 2.862 Perkin Elmer 5.0 54.75 2.614

Appl. Sci. 2021, 11, 3313 9 of 27

Table 2. Aperture size and spacing used for each FTIR spectrometer to amplify interference fringe amplitude.

Aperture Diameter Aperture Distance Maximum Angle of Spectrometer(a) (b) (mm) (mm) Incidence (◦) FigureThermo 4. The LiNbO Scientiﬁc3 single crystal control 6.0 sample (a) and prepared 60.0 PMN-PT sample ( 2.862b) arranged with millimeterPerkin Elmerscales for reference. 5.0 54.75 2.614

UsingUsing Equation Equation (7), (7), it itwas was estimated estimated that that the the interference interference fringes fringes of ofthe the prepared prepared PMN-PTPMN-PT sample sample have have a period a period of approximately of approximately 5 cm 5−1. cm With−1. this With in thismind, in the mind, FTIR the spec- FTIR trometersspectrometers were configured were configured with a scanning with a scanning resolution resolution of 0.25 cm of−1 0.25 to produce cm−1 to well-defined produce well- fringesdefined in the fringes final intransmission the final transmission spectrum. Ad spectrum.ditionally, Additionally, the transmission the transmission values were values av- eragedwere over averaged thirty-two over thirty-two scans to increase scans to waveform increase waveform smoothness. smoothness. WhileWhile a scan a scan resolution resolution of of0.25 0.25 cm cm−1 −is1 sufficientis sufficient to capture to capture the the fringe fringe waveforms, waveforms, for for thethe purpose purpose of ofcalculating calculating the the refractive refractive index, index, the the fringe fringe peak peak positions positions must must be be known known moremore precisely. precisely. To To that that end, end, the the transmissi transmissionon spectra spectra were were mathematically mathematically characterized characterized withwith a polynomial a polynomial fit fitto tomore more precisely precisely interp interpolateolate the the location location of ofthe the fringe fringe peaks. peaks. Peak Peak locationslocations measured measured using using this this method method were were expe expectedcted to tohave have an an accuracy accuracy of ofat atleast least two two decimaldecimal places places (0.01 (0.01 cm cm−1 →−1 0.0001→ 0.0001 m−1), m supporting−1), supporting an index an index of refraction of refraction calculation calculation out to outfour to decimal four decimal places. places. An example An example of the offrin thege fringepeak fitting peak fittingis depicted is depicted in Figure in Figure 5. 5.

FigureFigure 5. The 5. The accuracy accuracy of ofinterference interference fringe fringe peak peak lo locationcation measurements measurements is increasedincreasedby by interpolation interpo- lationvia avia polynomial a polynomial fit. fit. Once the fringe positions have been measured using the polynomial fit method, it is still necessary to assign absolute fringe order numbers. The absolute fringe order for each peak is extrapolated via a linear fit to the zeroth-order. Fringe peak spacing in the frequency domain is nearly linear such that plotting the relative fringe order numbers against the fringe frequency position allows for an accurate determination of the offset from zero (i.e., 0 cm−1). This extrapolation process is depicted in Figure6. Of all the critical values necessary for accurate refractive index calculations, proper assignment of the fringe order numbers has the largest impact on the dispersion curve [32]. Successful determination of the fringe order numbers is aided by a large data set; it is at this point that the near-IR and mid-IR collections are integrated, extending the reach of the extrapolation closer to zero. If the assignment is trusted to be accurate, the index of refraction at each fringe peak location is calculated by rearranging Equation (7) as m n(νm) = (10) 2νmd

where νm, m, and d are the known values. Appl. Sci. 2021, 11, x FOR PEER REVIEW 10 of 27

Once the fringe positions have been measured using the polynomial fit method, it is still necessary to assign absolute fringe order numbers. The absolute fringe order for each peak is extrapolated via a linear fit to the zeroth-order. Fringe peak spacing in the frequency domain is nearly linear such that plotting the relative fringe order numbers against the fringe frequency position allows for an accurate determination of the offset from zero (i.e., 0 cm−1). This extrapolation process is depicted in Figure 6. Of all the critical values necessary for accurate refractive index calculations, proper assignment of the fringe order numbers has the largest impact on the dispersion curve [32]. Successful determination of the fringe order numbers is aided by a large data set; it is at this point that the near-IR and mid-IR collections are integrated, extending the reach of the extrapolation closer to zero. If the assignment is trusted to be accurate, the index of refraction at each fringe peak location is calculated by rearranging Equation (7) as Appl. Sci. 2021, 11, 3313 𝑛(𝜈) = 10(10) of 27

where 𝜈, 𝑚, and 𝑑 are the known values.

FigureFigure 6. 6. TheThe measured measured fringe fringe position position was was used used to to extrapolate extrapolate the the zeroth-order zeroth-order fringes fringes (at (at 0 0 cm cm−1−) 1) toto assign assign absolute absolute fringe fringe order order numbers numbers to to each each fringe fringe position. position.

2.4.2.4. The The Optical Optical Transmission Transmission Sp Spectrumectrum of of Polycrystalline Polycrystalline PMN-PT PMN-PT ForFor the the transparent transparent dielectric dielectric slab slab with with a athickness thickness of of d, d, a arefractive refractive index index of of nn withwith consideringconsidering a anormally normally incident incident s-polarized s-polarized plane plane wave wave with with a vacuum a vacuum wavelength wavelength of 𝜆0 of, usingλ0, using Fresnel’s Fresnel’s equation, equation, the complex the complex amplitude amplitude of the reflected of the reflected and transmitted and transmitted beam at 0 0 thebeam slab’s at frontside the slab’s (𝜌 frontside and 𝜏) and (ρ and the τones) and at the the onesslab’s at backside the slab’s (𝜌′ backside and 𝜏′) are (ρ calculatedand τ ) are ascalculated [2] as [2] ρ = (1 − n)/(1 + n) (11) 𝜌 = (1 − 𝑛)/(1 +𝑛) (11) τ = 2/(1 + n) (12) ρ0 =𝜏(n − = 12/(1)/(n + + 𝑛)1 ) (12)(13) 0 = ( + ) 𝜌′τ = (𝑛2n/ n− 1)/(𝑛1 +1) (13)(14) If φ is the phase shift associated with a single path of the beam through the slab (φ = knd = 2πndλ0), the total reflection𝜏′r =and 2𝑛/(𝑛 total transmission + 1) t of the slab considering(14) all partial reflections and transmissions at the two sides will be If ϕ is the phase shift associated with a single path of the beam through the slab (ϕ=

knd = 2 nd/), the total reflection 𝑟 and∞ total transmissionm 𝑡0 of0 2theiφ slab considering all 0 0 φ 0 φ2 ττ ρ e partial reflections andr =transmissionsρ + ττ ρ e2i at the twoρ ei sides= willρ + be (15) ∑ 02 2iφ m=0 1 − ρ e

∞ 2m ττ0eiφ t = ττ0eiφ ρ0eiφ = (16) ∑ 02 2iφ m=0 1 − ρ e If the slab is thin enough to ignore absorption, the total transmission of the slab can be calculated as !2 ττ0ρ0e2iφ T = 1 − ρ + (17) 1 − ρ02e2iφ By determining the refractive index spectrum using FTIR, the optical transmission spectrum of PMN-PT ceramic can be calculated by Equation (17). In order to verify the calculation results, the experimental set-up shown in Figure7 was developed in the lab. A 1.5 mm × 5 mm × 5 mm polycrystalline PMN-PT slab was polished and used as the sample in that set-up. The transmission of that PMN-PT slab is measured by dividing the intensity of 532 nm, 632.8 nm, and 1550 nm lights, measured by the power meter, with the slab in its place by the intensity without the slab in the pathway. Appl. Sci. 2021, 11, x FOR PEER REVIEW 11 of 27

𝜏𝜏𝜌𝑒 𝑟 = 𝜌 + 𝜏𝜏′𝜌′𝑒 (𝜌′𝑒) =𝜌+ (15) 1−𝜌𝑒

𝜏𝜏𝑒 𝑡 = 𝜏𝜏′𝑒 (𝜌′𝑒) = (16) 1−𝜌𝑒 If the slab is thin enough to ignore absorption, the total transmission of the slab can be calculated as 𝜏𝜏𝜌𝑒 𝑇=1−(𝜌+ ) (17) 1−𝜌𝑒 By determining the refractive index spectrum using FTIR, the optical transmission spectrum of PMN-PT ceramic can be calculated by Equation (17). In order to verify the calculation results, the experimental set-up shown in Figure 7 was developed in the lab. A 1.5 mm × 5 mm × 5 mm polycrystalline PMN-PT slab was polished and used as the sample in that set-up. The transmission of that PMN-PT slab is measured by dividing the Appl. Sci. 2021, 11, 3313 intensity of 532 nm, 632.8 nm, and 1550 nm lights, measured by the power meter, with11 the of 27 slab in its place by the intensity without the slab in the pathway.

FigureFigure 7. 7.SchematicSchematic of ofthe the experimental experimental set-up set-up used used for formeasuring measuring the thetransmission transmission of a of1.5 a mm 1.5 mm thickthick PMN-PT PMN-PT ceramic ceramic slab slab at atthree three different different wavelengths wavelengths (532 (532 nm, nm, 632.8 632.8 nm, nm, and and 1550 1550 nm). nm). Those Those threethree measurements measurements were were used used to to verify verify the the three three points points of of the the tr transmissionansmission spectrum spectrum calculated calculated by byEquation Equation (17) (17) using using the the refractive refractive indices indices deﬁned defined by by the the FTIR FTIR method. method.

2.5.2.5. The The Experimental Experimental Set-up Set-up for for Dielectric Dielectric Constant Constant Measurements Measurements InIn this this study, study, impedance impedance measurements measurements we werere performed performed to to determine determine the the dielectric dielectric constantconstant of of the the device device under under test test (DUT) (DUT) as we wellll as variousvarious otherotherelectrical electrical properties. properties. Special Spe- cialAC AC bridge bridge circuits circuits are are used used to accuratelyto accurately measure measure the the complex complex impedance impedance values values for for the theDUT. DUT. More More speciﬁcally, specifically, capacitance capacitance bridges bridge suchs such as theas the Schering Schering Bridge Bridge (Figure (Figure8) were 8) used to assess the capacitance values of the DUT and subsequently calculate the dielectric were used to assess the capacitance values of the DUT and subsequently calculate the constant as dielectric constant as e C κ = e = m = m (18) Appl. Sci. 2021, 11, x FOR PEER REVIEW r e𝜖 𝐶C 12 of 27 0 0 𝜅=𝜖 = = (18) where Cm and C0 are the capacitances of the DUT𝜖 and the𝐶 air-gapped specimen cell, respectively.

where 𝐶 and 𝐶 are the capacitances of the DUT and the air-gapped specimen cell, respectively.

FigureFigure 8. TheThe capacitance capacitance bridge bridge circuit circuit is isa auseful useful AC AC bridge bridge circuit circuit that that allows allows for forthe theprecise precise measurementmeasurement ofof impedanceimpedance valuesvalues throughthrough balancingbalancing (unifying)(unifying) thethe voltagesvoltages atat nodesnodes BB andand D.D.

ImplementationImplementation of of the the capacitance capacitance bridge bridge is is greatly greatly simplified simpliﬁed through through the the use use of ad- of advancedvanced LCR LCR measurement measurement devices. devices. These These meters meters are purpose-built are purpose-built to measure to measure the induct- the inductanceance (L), capacitance (L), capacitance (C), (C),and andresistance resistance (R) (R)of ofconnected connected devices devices using using a a variable ACAC source.source. ManyMany LCRLCR metersmeters utilizeutilize fourfour BNC connectionsconnections toto independently measuremeasure currentcurrent andand voltage.voltage. These four connections cancan bebe conﬁguredconfigured asas anan auto-balancingauto-balancing bridgebridge circuitcircuit whichwhich quicklyquickly andand automaticallyautomatically determinesdetermines thethe capacitancecapacitance valuevalue forfor aa DUTDUT (Figure(Figure9 ).9). For the calculations of the dielectric constant, a thin unpolished sample of PMN-PT (approximately 12 mm × 10 mm × 0.5 mm) was characterized using a capacitance bridge apparatus. Capacitance values of the PMN-PT sample at multiple temperatures were compared to “open-cell” capacitance to determine the dielectric constant as a function of temperature.

Figure 9. Connection configuration when using an LCR meter as a capacitance bridge to test the capacitance of a device under test (DUT).

For the calculations of the dielectric constant, a thin unpolished sample of PMN-PT (approximately 12 mm × 10 mm × 0.5 mm) was characterized using a capacitance bridge apparatus. Capacitance values of the PMN-PT sample at multiple temperatures were compared to “open-cell” capacitance to determine the dielectric constant as a function of temperature. The PMN-PT samples for dielectric measurement require uniformity but can be unpolished. Beginning with one of the thin slices taken from the bulk sample segment, the pointed ends were removed. Additionally, it was necessary to remove the outer edge of the sample due to poor homogeneity in this area which is a result of the hot-press manufacturing process. Following the sample shaping, conductive silver paint was applied to the two parallel faces to serve as electrodes for impedance measurements (Figure 10). Appl. Sci. 2021, 11, x FOR PEER REVIEW 12 of 27

Figure 8. The capacitance bridge circuit is a useful AC bridge circuit that allows for the precise measurement of impedance values through balancing (unifying) the voltages at nodes B and D.

Implementation of the capacitance bridge is greatly simplified through the use of ad- vanced LCR measurement devices. These meters are purpose-built to measure the inductance (L), capacitance (C), and resistance (R) of connected devices using a variable AC Appl. Sci. 2021, 11, 3313 source. Many LCR meters utilize four BNC connections to independently measure current12 of 27 and voltage. These four connections can be configured as an auto-balancing bridge circuit which quickly and automatically determines the capacitance value for a DUT (Figure 9).

Figure 9. ConnectionConnection configuration conﬁguration when when using using an an LCR LCR me meterter as as a capacitance a capacitance bridge bridge to totest test the the capacitance of a device under test (DUT).

TheFor the PMN-PT calculations samples of the for dielectric dielectric constant, measurement a thin requireunpolished uniformity sample of but PMN-PT can be unpolished.(approximately Beginning 12 mm × with 10 mm one × of 0.5 the mm) thin was slices characterized taken from using the bulk a capacitance sample segment, bridge the pointed ends were removed. Additionally, it was necessary to remove the outer edge apparatus. Capacitance values of the PMN-PT sample at multiple temperatures were com- of the sample due to poor homogeneity in this area which is a result of the hot-press Appl. Sci. 2021, 11, x FOR PEER REVIEWpared to “open-cell” capacitance to determine the dielectric constant as a function of13 tem- of 27 manufacturing process. Following the sample shaping, conductive silver paint was applied perature. to the two parallel faces to serve as electrodes for impedance measurements (Figure 10). The PMN-PT samples for dielectric measurement require uniformity but can be unpolished. Beginning with one of the thin slices taken from the bulk sample segment, the pointed ends were removed. Additionally, it was necessary to remove the outer edge of the sample due to poor homogeneity in this area which is a result of the hot-press manufacturing process. Following the sample shaping, conductive silver paint was applied to the two parallel faces to serve as electrodes for impedance measurements (Figure 10).

(a) (b)

Figure 10. The dielectric sample waswas preparedprepared fromfrom a a bulk bulk sample sample thin thin slice slice (a (),a), and and silver silver paint paint was was applied applied to to each each face face to toserve serve as as electrodes electrodes (b ).(b).

TheThe conductive coating coating applied applied to to either face should help to ensu ensurere that the electric fieldﬁeld is is distributed distributed evenly evenly across across the the area area of of the the sample. sample. The The capacitance capacitance bridge bridge can can be implementedbe implemented using using a high-accura a high-accuracycy inductance inductance capacitance capacitance resistance resistance (LCR) (LCR) meter meteroper- atingoperating at 1 kHz. at 1 kHz. Again,Again, LiNbO 3 single crystal samplessamples servedserved asasa a control control group group to to support support the the validity valid- ityof thisof this methodology. methodology. Due Due to the to birefringentthe birefringent nature nature of LiNbO of LiNbO3 single3 single crystals, crystals, the dielectric the dielectricconstant constant of the material of the material is orientation-dependent. is orientation-dependent. For thoroughness, For thoroughness, the capacitance the capaci- bridge tancemethod bridge was method used to was calculate used to the calculate dielectric the constant dielectric for constant both x-cut for both (11) andx-cut z-cut (11) and (33) LiNbO samples at room temperature. Literature values for the dielectric constants of x-cut z-cut (33)3 LiNbO3 samples at room temperature. Literature values for the dielectric con- and z-cut LiNbO crystals are given as 85.2 and 28.7, respectively [33]. If the dielectric stants of x-cut and3 z-cut LiNbO3 crystals are given as 85.2 and 28.7, respectively [33]. If the dielectricconstant ofconstant a material of a ismaterial known, is an known, estimate an ofestimate the capacitance of the capacitance can be calculated can be calculated as as A C = e e (19) m 0 r d𝐴 𝐶 =𝜖 𝜖 (19) 𝑑 where A and d are the area and thickness of the material, respectively, the resulting wherecalculations 𝐴 and for 𝑑 the are expected the area capacitance and thickness values of the of thema twoterial, LiNbO respectively,3 samples the are resulting summarized cal- culationsin Table3 ,for which the expected also includes capacitance the physical values parameters of the two needed LiNbO for3 samples Equation are (19).summarized in Table 3, which also includes the physical parameters needed for Equation (19).

Table 3. Expectation values for the capacitance measurements of x-cut and z-cut lithium niobate (LiNbO3) single crystal samples.

Parameter LiNbO3 (x-cut) LiNbO3 (z-cut) Area (cm2) 1.6445 1.0 Thickness (mm) 1.0 0.5 Calculated Capacitance (pF) 124.0 50.8

With expected capacitance values for the LiNbO3 samples in hand, measurements can be made using the LCR meter. Electrical connections are established with the samples by inserting them between conductive plates that are wired directly to the LCR meter terminals. Measuring the capacitance with the LiNbO3 sample between the plates establishes the material capacitance, Cm. To measure the open-cell capacitance, C0, the LiNbO3 sample is removed, and the plates are held apart by the thickness of the sample with the same area of overlap. These two measurements cannot be immediately used for calculating the dielectric constant. They must first be corrected for the open circuit capacitance of the LCR meter. Separating the two conductive plates by a sufficient distance results in a small capacitance measurement that acts as the relative zero of the system. To correct the material and open-cell measurements, this open circuit value simply needs to be subtracted from both measurements. Following these steps, the necessary capacitance values Appl. Sci. 2021, 11, 3313 13 of 27

Table 3. Expectation values for the capacitance measurements of x-cut and z-cut lithium niobate

(LiNbO3) single crystal samples.

Parameter LiNbO3 (x-cut) LiNbO3 (z-cut) Area (cm2) 1.6445 1.0 Thickness (mm) 1.0 0.5 Calculated Capacitance (pF) 124.0 50.8

With expected capacitance values for the LiNbO3 samples in hand, measurements can be made using the LCR meter. Electrical connections are established with the samples by inserting them between conductive plates that are wired directly to the LCR meter terminals. Measuring the capacitance with the LiNbO3 sample between the plates establishes the material capacitance, Cm. To measure the open-cell capacitance, C0, the LiNbO3 sample is removed, and the plates are held apart by the thickness of the sample with the same area of overlap. These two measurements cannot be immediately used for calculating the dielectric constant. They must ﬁrst be corrected for the open circuit capacitance of the LCR meter. Separating the two conductive plates by a sufﬁcient distance results in a small capacitance measurement that acts as the relative zero of the system. To correct the material and open-cell measurements, this open circuit value simply needs to be subtracted from both measurements. Following these steps, the necessary capacitance values for both LiNbO3 samples were recorded and the dielectric constants calculated as shown in Table4.

Table 4. Measured capacitance values and resulting dielectric constants calculations for multiple

orientations of lithium niobate (LiNbO3) single crystals.

Parameter LiNbO3 (x-cut) LiNbO3 (z-cut) Material Capacitance (pF) 113.20 48.55 Open-Cell Capacitance (pF) 1.35 1.63 Calculated Dielectric Constant 83.73 29.75 Accepted Dielectric Constant 85.2 28.7 Percent Error (%) 1.73 3.66

As shown above, in Table4, the process of calculating the dielectric constant from the measured capacitances is accurate but not precise. The LCR meter used is expected to provide measurements with ±0.3% accuracy, and thus it is likely that the discrepancy is a result of human error. Precision in calculating the dielectric constant is dependent on precisely measuring the open-cell capacitance, which is strongly proportional to the separation of the conductive plates. A small difference between open-cell separation and the DUT thickness can significantly affect the final dielectric constant calculation. With this limitation in mind, it stands to reason that the calculated dielectric constant values still serve to describe the relative magnitude and not precise measurements. For dielectric characterization of the PMN-PT sample, the previous experimental setup is modified such that the measurement cell is contained within a Peltier heating stage. Recording the capacitance values at various temperatures allows for an observation of the effect of temperature on the dielectric constant of the material. The Peltier heat stage used for this experimentation is capable of maintaining temperatures between 0 ◦C and 120 ◦C without needing chilled water so that capacitance values will be measured over that range in 5 ◦C increments.

2.6. Designing an EO Beam Steerer Based on Polycrystalline PMN-PT The light steerer designed in this study was based on the EO effect in a 7.5 mm × 7.5 mm × 40 mm PMN-PT ceramic, which is considered isotropic, as discussed before. The propagation of an optical wave in a crystal can be described in terms of the relative 2 impermeability tensor as Bij = 1/nij = ε0/εij, where ε0 is the permittivity of free space and εij is the permittivity tensor. The Bij is a symmetric tensor because the εij is a symmetric Appl. Sci. 2021, 11, 3313 14 of 27

tensor for a lossless and inactive medium. The two directions of dielectric polarization and the refractive indices can be calculated by indicatrix or index ellipsoid as [1]

Bijxixj = 1 (20)

where i and j are 1, 2, and 3 and represent the principal axes of a crystal which are the directions in the crystal where the electric ﬁeld (E) and displacement vectors (D) are parallel. If we consider x, y, and z respectively for the subscripts of 1, 2, and 3, the ellipsoid index can be expanded as follows: x2 y2 z2 + + = 2 2 2 1 (21) nx ny nz

where nx, ny, and nz are the refractive indices for the incident light polarized in the directions of x, y, and z, respectively. The quantum theory of solids says the indicatrix depends on the charge distribution in the crystal. The external electric ﬁeld (E) and stress (σ) can change that distribution and result in a change in the shape, size, and orientation of the index ellipsoid speciﬁed by electro-optic and photoelastic effects on ∆Bij as follows [34]:

Bij(E) − Bij(0) = ∆Bij = rijkEk + sijkl EkEl + πijklσkl (22)

where rijk and sijkl are the Pockels electro-optic and Kerr electro-optic tensors, and πijkl is the piezo-optical tensor. Note that the stress ﬁeld is related to the strain tensor (Trs) as per Hook’s law [34]; σkl = cklrsTrs (23) and πijkl = pijrsΩrslk (24)

where pijrs and Ωrslk are elasto-optical tensor and compliances, respectively. Although the direct photoelastic effect vanishes when no direct stress is applied to the crystal (free crystal), mechanical constraints still can exist because of the converse piezoelectric effect. That is because the electric field will cause a strain by the converse piezoelectric effect, and therefore, the indicatrix will get modified by the photoelastic effect, which is called the secondary effect. The strain produced by an electric field is calculated as dkij Ek, where dkij is the piezoelectric tensor. Therefore, the primary and secondary electro-optic effects on a free crystal (σ = 0) can be calculated as Bij(E) − Bij(0) = ∆Bij = rijkEk + sijkl EkEl + pdkij Ek (25)

Because the relative impermeability tensor is symmetric for inactive and lossless medium, the i and j subscripts can be permuted. This will reduce the number of independent elements of rijk from 27 to 18 and from 81 to 36 for sijkl. The same thing is applied for piezoelectric tensor except for some factor of 2. Therefore, the change in indicatrix can be written for convenience as follows [34]:

Bij(E) − Bij(0) = ∆Bij = rijEj + sijkEjEk + (pdki)Ek (26)

where pmn = πmrcrn(m, n = 1, 2, . . . , 6) (27)

πmr = πijkl (n = 1, 2, 3) (28)

πmr = 2πijkl (n = 4, 5, 6) (29) As discussed, although each individual grain of PMN-PT ceramics is not centrosym- metric, the polycrystalline nature makes the PMN-PT ceramic isotropic and, thus, polarization- Appl. Sci. 2021, 11, 3313 15 of 27

independent. Therefore, the rij and dki in Equation (26) are zero, and the Kerr effect is the main factor in altering the refractive index. By contracting the indices as 11:1, 22:2, 33:3, 23:4, 13:5, and 12:6, the impermeability tensor becomes   B1 B6 B5 B =  B6 B2 B4  (30) B5 B4 B3

The Kerr effect tensor for an isotropic medium is given as [1]   s11 s12 s12 0 0 0  s12 s11 s12 0 0 0     s s s 0 0 0  s =  12 12 11  (31)  0 0 0 0.5(s − s ) 0 0   11 12   0 0 0 0 0.5(s11 − s12) 0  0 0 0 0 0 0.5(s11 − s12)

When a polycrystalline PMN-PT gets under a slowly varying external electric field, its molecules get aligned with the field, and the isotropic ceramic becomes birefringent, behaving like a uniaxial crystal in which the electrical field defines the optical axis. The change in impermeability tensor by applying an electric field on the PMN-PT ceramic will be

    2  ∆B1 s11 s12 s12 0 0 0 Ex 2  ∆B2   s12 s11 s12 0 0 0  Ey        ∆B   s s s 0 0 0  E2   3  =  12 12 11  z  (32)  ∆B   0 0 0 0.5(s − s ) 0 0  2E E   4   11 12  y z   ∆B5   0 0 0 0 0.5(s11 − s12) 0  2ExEz  ∆B6 0 0 0 0 0 0.5(s11 − s12) 2ExEy

Assuming the external electric ﬁeld is in the direction of the z-axis (E = Ez zˆ), the indicatrix of PMN-PT ceramic will be deﬁned as 1 1 1 x2 + s E2 + y2 + s E2 + z2 + s E2 = 1 (33) n2 12 n2 12 n2 11

x2 + y2 z2 + = 2 2 1 (34) no ne

where n0 is the refractive index associated with ordinary light, and ne is the refractive index seen by an extraordinary light propagating through the PMN-PT. Hence, if the light is polarized perpendicular to the external electric field direction, the index change it sees will be

3 2 ∆n = no − n = −0.5n s12E (35)

The EO scanner designed in this study had the light propagate perpendicular to the external electric field direction and was polarized parallel to the optical axis defined by that field. Therefore, the index change seen by the light can be described as

3 2 ∆n = ne − n = −0.5n s11E (36)

The birefringence (∆n) imposes relative phase retardation (Γ) to the light propagating through that medium by the length of L as

2π∆nL πn3s E2L Γ = = − 11 (37) λ λ Appl. Sci. 2021, 11, 3313 16 of 27

therefore, the electric ﬁeld that causes π radians of phase retardation will be s λ = Eπ 3 (38) n s11L

The external electric ﬁeld (E) is approximated as the applied voltage divided by the Appl. Sci. 2021, 11, x FOR PEER REVIEWthickness of the PMN-PT ceramic (E = V/d), which was 7.5 mm (d = 7.5 mm) thick.17 Theof 27

s11 is the Kerr coefficient of polycrystalline PMN-PT, which varies by wavelength and temperature. This coefficient can be defined by measuring the EO steerer’s deflection angle associated with each wavelength at different temperatures. The polycrystalline PMN-PT is isotropic and polarization-independent. Unlike single ferroelectric crystals, no crystallinecrystalline orientationorientation adjustmentadjustment andand nono domain-engineereddomain-engineered multi-prisms are required to provide thethe OPDOPD forfor linearlylinearly polarizedpolarized lightlight propagatingpropagating through the crystal. The most simple structure of an EO steerersteerer wewe cancan buildbuild withwith thethe PMN-PTPMN-PT ceramicceramic is a triangular prism with uniformuniform electrodes deposited on two opposite sides, as seen in Figure 1111..

Figure 11. AA triangular triangular prism-shaped prism-shaped EO EO scanner. scanner. (W (W is isthe the width, width, L is L the is thelength, length, and and H is H the is the height of the triangular prism).

Before applying the voltage on the electrodes,electrodes, accordingaccording toto Snell’sSnell’s law,law, wewe havehave

θ +𝜃+A =𝐴 =sinsin−1(nSinA(𝑛𝑆𝑖𝑛𝐴)) (39)(39) After applying the voltage, the isotropic medium becomes uniaxial. The light is po- After applying the voltage, the isotropic medium becomes uniaxial. The light is larized along the external electric field. Therefore the deflection angle change will be polarized along the external electric field. Therefore the deflection angle change will be 𝛥𝑛𝑠𝑖𝑛𝐴 𝛥𝜃 = ∆nsinA (40) ∆θ = √√1−𝑛𝑠𝑖𝑛𝐴 (40) 1 − n2sin2 A where Δn is given by Equation (36). To prevent a total internal reflection, |nSinA| must wherebe smaller∆n is than given 1. by Equation (36). To prevent a total internal reflection, |nSinA| must be smallerInstead than 1.of having a triangular prism with uniform electrodes, a rectangular prism with Insteadtriangular of having electrodes a triangular can be considered prism with. uniform The non-uniform electrodes, electrodes a rectangular should prism be with de- triangularposited on electrodesthe two opposite can be considered.sides of the Therectangular non-uniform PMN-PT electrodes ceramic should (7.5 mm be deposited × 7.5 mm on× 40 the mm) two to opposite impose sides a non-uniform of the rectangular electric PMN-PTfield distribution ceramic (7.5 and mm index× 7.5 change mm × to40 defect mm) tothe impose light. Figure a non-uniform 12 depicts electric the arbitrary field distribution electrodes on and the index rectangular change toPMN-PT defect theceramic. light. Figure 1213 depictsshows the the refraction arbitrary of electrodes the light onat the dielectric rectangular interfaces. PMN-PT ceramic. Figure 13 shows the refraction of the light at the dielectric interfaces. Because the electric field should be nonuniformly distributed to steer the light, the number of electrode interfaces (N) should be equal to or larger than 1 (N ≥ 1). Suppose the number of interfaces (N) was small and the PMN-PT ceramic length was long. In that case, the incident angle of an interface might get wide enough to enable a total internal reflection, at least at some voltages applied on the electrode. Therefore, the number of interfaces and the electrode geometry should be designed to avoid the total internal reflections and partial back-reflections.

Figure 12. The arbitrary electrodes on the rectangular PMN-PT ceramic (top view). Appl. Sci. 2021, 11, x FOR PEER REVIEW 17 of 27

The polycrystalline PMN-PT is isotropic and polarization-independent. Unlike single ferroelectric crystals, no crystalline orientation adjustment and no domain-engineered multi-prisms are required to provide the OPD for linearly polarized light propagating through the crystal. The most simple structure of an EO steerer we can build with the PMN-PT ceramic is a triangular prism with uniform electrodes deposited on two opposite sides, as seen in Figure 11.

Figure 11. A triangular prism-shaped EO scanner. (W is the width, L is the length, and H is the height of the triangular prism).

Before applying the voltage on the electrodes, according to Snell’s law, we have 𝜃+𝐴 =sin(𝑛𝑆𝑖𝑛𝐴) (39) After applying the voltage, the isotropic medium becomes uniaxial. The light is polarized along the external electric field. Therefore the deflection angle change will be 𝛥𝑛𝑠𝑖𝑛𝐴 𝛥𝜃 = (40) √1−𝑛𝑠𝑖𝑛𝐴 where Δn is given by Equation (36). To prevent a total internal reflection, |nSinA| must be smaller than 1. Instead of having a triangular prism with uniform electrodes, a rectangular prism with triangular electrodes can be considered. The non-uniform electrodes should be deposited on the two opposite sides of the rectangular PMN-PT ceramic (7.5 mm × 7.5 mm × 40 mm) to impose a non-uniform electric field distribution and index change to defect Appl. Sci. 2021, 11, 3313 17 of 27 the light. Figure 12 depicts the arbitrary electrodes on the rectangular PMN-PT ceramic. Figure 13 shows the refraction of the light at the dielectric interfaces.

Appl. Sci. 2021, 11, x FOR PEER REVIEW 18 of 27

Figure 12.12. The arbitrary electrodes onon thethe rectangularrectangular PMN-PTPMN-PT ceramicceramic (top(top view).view).

Figure 13. The refractionFigure of the 13. light The at refraction interfaces. of the light at interfaces.

When the lightBecause hits the the electrode electric interface, field should the be region nonuni withformly a lower distributed refractive to steer index, the no light, the total internal reflectionnumber of should electrode occur. interfaces Therefore, (N) should we should be equal have to or larger than 1 (N ≥ 1). Suppose the number of interfaces (N) was small and the PMN-PT ceramic length was long. In that case,−1 the incident∆n angle of an− interface1 W might get wide enough to enable a total internalcos reflection,1 + at least≤ atα somei = tan voltages applied on the electrode. Therefore,(41) the n li number of interfaces and the electrode geometry should be designed to avoid the total Once a rayinternal is reflected reflections back fromand partial an electrode back-reflections. interface, it is considered a loss because even if it is partiallyWhen reflected the light back hits again, the itelectrode will not interface, get steered the toregion the desiredwith a lower angle. refractive There- index, fore, the total partialno total back-reflections internal reflection through should theoccur. medium Therefore, (TPBR) we should should have be minimized.

∆𝑛 𝑊 N N 𝑐𝑜𝑠 1+ ≤ 𝛼=𝑡𝑎𝑛0(!2 ) (41) nsinαi − (n +𝑛 ∆n) sin αi − θi 𝑙 TPBR = ∑ Ri = ∑ 0 (42) Once a iray=1 is reflectedi=1 nsinbackα fromi + ( ann + electrod∆n) sine interface,αi − θi it is considered a loss because even if it is partially reflected back again, it will not get steered to the desired angle. There- Finally, thefore,∆n theand total the partial ceramic’s back-reflections length should through be large the medium enough (TPBR) to give should the desired be minimized. steering angle (θ). As seen in Figure 13, Snell’s law at each interface states 𝑛𝑠𝑖𝑛𝛼 − (𝑛+∆𝑛)sin(𝛼 −𝜃 ) 𝑇𝑃𝐵𝑅 =𝑅= 0 (42) (n + ∆n) cos αj = ncos𝑛𝑠𝑖𝑛𝛼αj + (θ𝑛+∆𝑛i )sin(𝛼 −𝜃) (43) Finally, the ∆n and the ceramic’s length should0 be large enough to give the desired Assuming the deﬂection angle inside the medium (θi ) is small and ∆n n, we will have steering angle (𝜃). As seen in Figure 13, Snell’s law at each interface states 0 0 nsinθ sinα ∆nθ sinα = −∆ncosα (44) i j (𝑛+∆𝑛i j ) cos𝛼=𝑛𝑐𝑜𝑠(𝛼j +𝜃 ) (43) N Hence, the totalAssuming deﬂection the angle deflection after angleinterfaces inside the inside medium the ceramic(𝜃 ) is small will and be ∆n ≪ n, we will have N N 0 ∆n ∆n lj L∆n θ = − ∑ cot𝑛𝑠𝑖𝑛𝜃αj = − 𝑠𝑖𝑛𝛼∑⋍𝑛𝜃 =𝑠𝑖𝑛𝛼− =−∆𝑛𝑐𝑜𝑠𝛼 (45) (44) n j=1 n j=1 W Wn Hence, the total deflection angle after N interfaces inside the ceramic will be ∆𝑛 ∆𝑛 𝑙 𝐿∆𝑛 𝜃 =− cot 𝛼 =− =− (45) 𝑛 𝑛 𝑊 𝑊𝑛 The displacement of the beam (𝛿) at the output of that rectangular prism and the pivot point (pp), which is the point where the beam deflects to the angle of (𝜃’), will be 𝜃’L 𝐿∆𝑛 𝛿= =− (46) 2 2𝑊𝑛 𝛿 𝑝𝑝 = (47) 𝜃’ Appl. Sci. 2021, 11, 3313 18 of 27

Appl. Sci. 2021, 11, x FOR PEER REVIEW 19 of 27

The displacement of the beam (δ) at the output of that rectangular prism and the pivot point (pp), which is the point where the beam deflects to the angle of (θ0), will be The external deflection angle (𝜃) is related to the internal reflection angle by Snell’s θ0L L2∆n law. If 𝜃 is small enough, it can beδ calculated= = −as follows: (46) 2 2Wn 𝐿∆𝑛 𝑂𝑃𝐷 𝐿 𝜃=𝑛𝜃 =− =−δ = 𝑛 𝑠𝐸 (48) 𝑊pp = 𝑊 2𝑊 (47) θ0 As seen, for a rectangular prism PMN-PT ceramic deflector with a dimension of The external deflection angle (θ) is related to the internal reflection angle by Snell’s WXHXL (where the width is W, the height is H, and the length is L,) it is possible to grade law. If θ is small enough, it can be calculated as follows: the external electric field linearly and make an OPD in the linearly polarized light with the spot size of 𝑤 (see Equation (4))L∆ propagatingn OPD throughL the crystal. That OPD makes θ = nθ0 = − = − = n3s E2 (48) the beam deflect inside the crystal to Wthe angle ofW 𝜃’ and2W the angle11 of 𝜃 outside the crystal. By measuring the angle of 𝜃 for various wavelengths, the dispersing of 𝑠 in that ceramicAs can seen, be for determined. a rectangular prism PMN-PT ceramic deflector with a dimension of WXHXLThe (whereEO steerers’ the width deflection is W, theangle height for each is H, wavelength and the length at a is specificL,) it is voltage possible and to grade tem- peraturethe external can electric be measured field linearly by keeping and make the ligh an OPDt hittingin the the linearly camera’s polarized center by light displacing with the spot size of w0 (see Equation (4)) propagating through the crystal. That OPD makes the the camera up or down on the y-axis as seen in0 Figure 14. By making that measurement atbeam two deflect different inside image the planes crystal with to the a angledistance of θofand d apart, the angle since of theθ outside∆y ≪ d, thethe crystal.deflection By anglemeasuring for that the specific angle of wavelength,θ for various voltage, wavelengths, and temperature the dispersing can ofbes defined11 in that as ceramic can be determined. The EO steerers’ deflection angle for each∆𝑦 wavelength at a specific voltage and tem- 𝜃= (49) perature can be measured by keeping the light𝑑 hitting the camera’s center by displacing the cameraIn order up to or measure down on the the deflection y-axis as seenangle in for Figure the 14various. By making wavelengths that measurement in terms of mrad.mm/kVat two different in imagethe lab planesand calculate with a distancethe EO coefficient of d apart, for since each the wavelength∆y d, the under deflection differ- entangle temperatures, for that specific the wavelength,external electric voltage, field andapplied temperature to the ceramic can be must defined be steady as or DC. We also applied an AC external electric field ∆toy illustrate the beam’s deflection angle var- θ = (49) iation by varying the applied voltage. We uploadedd that illustrative video as the supplementary material of this paper.

Figure 14. The experimental set-up set-up for for characterization characterization of of the the EO EO beam beam steerer steerer based based on on polycrys- polycrys- talline PMN-PT. In order to measure the deflection angle for the various wavelengths in terms of 3. Results and Discussion mrad.mm/kV in the lab and calculate the EO coefficient for each wavelength under differentThe dispersion temperatures, curve the of external PMN-PT electric ceramics field defined applied in to this the ceramicstudy using must FTIR be steady spec- trometryor DC. We could also not applied be compared an AC externalto literature electric because field it to has illustrate not been the previously beam’s deflection reported. Instead,angle variation we could by validate varying theour appliedmethod’s voltage. precision We uploadedby taking thata 508 illustrative μm thick LiNbO video as3 slab the assupplementary a control sample, material defining of this its paper. dispersion curve, and comparing it to the literature. Fig- ure 15 compares the calculated refractive index values to the values reported in the liter- ature3. Results [35]. andFigure Discussion 15a indicates that the experimental and accepted refractive index data are exceptionallyThe dispersion well-matched, curve of PMN-PT and that ceramics is why the defined two curves in this in studyFigure using 15a are FTIR indistin- spec- guishable.trometry could Expanding not be comparedone-tenth of to the literature spectrum because, the slight it has notvariation been previouslyin values can reported. begin toInstead, be seen we in could Figure validate 15b. The our amount method’s of prec precisionision achieved by taking in a the 508 calculationµm thick LiNbO of the3 LiNbOslab as3 dispersiona control sample, curve indicates defining itsthat dispersion the methodology curve, and for comparing calculating it tothe the refractive literature. index Figure of the 15 PMN-PTcompares sample the calculated is quite refractive sound. The index calculat valuesed todispersion the values curve reported for the in thePMN-PT literature sample [35]. after combining the data from the NIR and MIR transmission spectra is shown in Figure 16. Appl. Sci. 2021, 11, 3313 19 of 27

Figure 15a indicates that the experimental and accepted refractive index data are excep- tionally 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 LiNbO3 dispersion curve indicates that the methodology for calculating the refractive index of the PMN-PT Appl. Sci. 2021, 11, x FORAppl. PEER Sci. 2021 REVIEW, 11, x FOR PEER REVIEW 20 of 27 20 of 27 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.

(a) (b) (a) (b) Figure 15. FigureA comparison 15. A comparison of the calculated of the calculatedrefractive index refractive values index to literature values to values literature for the values lithium for theniobate lithium control sam- Figure 15. A comparisonple. (a )of full-view; the calculated (b) zoomed-view refractive index to show values differences. to literature values for the lithium niobate control sample. (a) full-view; (b) zoomed-viewniobate tocontrol show differences. sample. (a) full-view; (b) zoomed-view to show differences.

Figure 16. The calculated dispersion curve for the PMN-PT sample after combining the data from FigureFigure 16. 16. TheThe calculated calculatedthe NIR dispersion and dispersion MIR tran curve curvesmission for for the thespectra. PMN- PMN-PTPT sample sample after after combining combining the thedata data from from thethe NIR NIR and and MIR MIR tran transmissionsmission spectra. spectra. The PMN-PT ceramics transmission for an s-polarized wave was determined using TheThe PMN-PT PMN-PTthe ceramics ceramicscalculated transmission transmission dispersion forcurve for an an s-polarized(Figure s-polarized 17), waveas wave discussed was was determined determined in the previous using using section. Again, thethe calculated calculated dispersion dispersionbecause thecurve curve transmission (Figure (Figure 17), 17of ), aspolycrystalline as discussed discussed in in thePMN-PT the previous previous in such section. section. a wide Again, Again, wavelength range becausebecause the the transmission transmissionwas not previously of of polycrystalline polycrystalline reported, PMN-PT we PMN-PT could in not in such suchcomp a awideare wide the wavelength wavelengthresults to the range range values reported in waswas not not previously previouslythe reported,literature. reported, we Instead, we could could the not transmission not comp compareare the of theresults a 1.5 results mm to the × to 5 thevaluesmm values × 5 reported mm reported polycrystalline in PMN- thein literature. the literature. Instead,PT Instead, slab the was transmission the measured transmission in of the a 1.5 oflab mm a (see 1.5 × Figure mm5 mm× ×7)5 5 mmfor mm three× polycrystalline5 mmwavelengths, polycrystalline PMN- and the results were PTPMN-PT slab was slab measured wascompared measured in the to lab the in (see the calculated labFigure (see 7)values Figure for three 7as) for seen wavelengths, three in Table wavelengths, 5. and Table the and5 resultsshows theresults werethe measured trans- comparedwere compared to the missioncalculated to the calculatedvalues values agree as values seenwith asinthe seenTable calculated in 5.Table Table ones5 .5 Table showswithin5 shows the8.8% measured errors the measured or trans-less. missiontransmission values valuesagree withThe agree absorbance the with calculated the calculatedor optical ones within onesdensity, within8.8% OD errors, 8.8% can be errorsor less.calculated or less. from the measured trans- The absorbancemission, or optical T, as density, OD, can be calculated from the measured transmission, T, as 1 𝑂𝐷 = log (50) 1 𝑇 𝑂𝐷 = log (50) The magnitudes of absorbance𝑇 of the PMN-PT sample for those three wavelengths The magnitudeshave ofalso absorbance been approximated of the PMN-PT and given sample in Table for those 5. three wavelengths have also been approximated and given in Table 5. Appl. Sci. 2021, 11, 3313 20 of 27 Appl. Sci. 2021, 11, x FOR PEER REVIEW 21 of 27

Figure 17. The calculated transmission spectrumspectrum of polycrystalline PMN-PT.PMN-PT.

Table 5. The calculated andTable measured 5. The transmission calculated and and measured absorban transmissionce of a 1.5 mm and absorbancethick polycrystalline of a 1.5 mm PMN-PT thick polycrystalline slab for three different wavelengths.PMN-PT slab for three different wavelengths. Wavelength (nm) Calculated Transmission (%) Measured Transmission (%) Error (%) Absorbance Wavelength Calculated Measured Error (%) Absorbance 532 61.8(nm) Transmission (%) 60.1 Transmission (%) 2.75 0.22 0.18 632.8 68.7532 61.8 65.8 60.14.22 2.75 0.22 1550 82.1632.8 68.7 74.9 65.88.77 4.220.13 0.18 1550 82.1 74.9 8.77 0.13 The dielectric constant was calculated for each temperature using Equation (18) after collectingThe absorbance the capacitance or optical values density, over theOD ,rang cane, be once calculated for material from the capacitance measured and transmis- again sion,for open-cellT, as capacitance. The resulting dielectric values for polycrystalline PMN-PT are graphed against temperature in Figure 18. As seen1 in Figure 18, the maximum dielectric OD = log (50) constant achieved was approximately 12,000, andT the peak dielectric constant is reached at or Thenear magnitudes 25 °C. Therefore, of absorbance the Curie of temperat the PMN-PTure of samplethis ceramic for those is at threeroom wavelengthstemperature. haveIt should also be been noted approximated that a higher and dielectric given inconstant Table5. increases the loss and reduces the speed of response.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 ◦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 × 7.5 mm × 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.

Figure 18. The dielectric constant for the PMN-PT ceramic as a function of temperature. The peak dielectric constant of 11,688.9 is reached at room temperature, approximately 25 °C. Appl. Sci. 2021, 11, x FOR PEER REVIEW 21 of 27

Figure 17. The calculated transmission spectrum of polycrystalline PMN-PT.

Table 5. The calculated and measured transmission and absorbance of a 1.5 mm thick polycrystalline PMN-PT slab for three different wavelengths.

Wavelength (nm) Calculated Transmission (%) Measured Transmission (%) Error (%) Absorbance 532 61.8 60.1 2.75 0.22 632.8 68.7 65.8 4.22 0.18 1550 82.1 74.9 8.77 0.13

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 Appl. Sci. 2021, 11, x FOR PEER REVIEWconstant achieved was approximately 12,000, and the peak dielectric constant is reached22 of 27 at or near 25 °C. Therefore, the Curie temperature of this ceramic is at room temperature. Appl. Sci. 2021, 11, 3313 21 of 27 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 × 7.5 mm × 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. The deflection angle for the wavelengths of 532, 632.8, 1550, and 4500 nm was measured in the lab in terms of mrad.mm/kV at 25 °C and 40 °C temperatures. The results are given in Table 6. The measured deflection angles and the calculated refractive indices can define the EO coefficients of the polycrystalline PMN-PT using Equation (48). This EO beam steerer was also modeled in COMSOL Multiphysics to simulate its performance and compare it to the measured values. The calculated EO coefficients, the refractive indices, and the measured permittivity were used as the COMSOL model’s inputs. The voltage and electric field distribution, the birefringence, and deflection angles were the COMSOL model outputs, as seen in Figures 20–22. As seen in Table 6, the measured deflection angles for four wavelengths at 25 °C and 40 °C temperatures could also define the number of resolvable spots using Equation (2). The EO coefficients and the refractive indices can define the halfwave electric field using Equation (38). The halfwave electric field for the three different wavelengths at 25 °C and FigureFigure 18. 18. The dielectric constant for the PMN-PT ceramic as a function of temperature. The peak 40 °C wasThe also dielectric measured constant in the for lab. the As PMN-PT seen in ceramic Table as6, athe function results of are temperature. comparable The to peak the dielectricdielectric constant constant of of 11,688.9 11,688.9 is is reached reached at at room room temperature, temperature, approximately approximately 25 25 °C.◦C. calculated values.

FigureFigure 19.19.Light Light deflectiondeflection testtest withwith thethe 7.57.5 mmmm × 7.57.5 mm mm ×× 4040 mm mm polycrystalline polycrystalline PMN-PT PMN-PT with with voltage electrodes. voltage electrodes. TableThe 6. The deflection measured angle and calculated for the wavelengths wavelength an ofd 532, temperature-dependent 632.8, 1550, and 4500 parameters nm was of mea- the suredEO beam in thesteerer lab based in terms on polycrystalline of mrad.mm/kV PMN-PT. at 25 ◦C and 40 ◦C temperatures. The results are given in TableParameter6. The measured deflection Unit angles and 532 the nm calculated 633 nm refractive 1550 nm indices 4500 nm can define theThe EO refractive coefficients index of the polycrystalline- PMN-PT 2.4744 using2.4635 Equation 2.4573 (48). This2.4619 EO beamThe steerer measured was deflection also modeled angle at in25 COMSOL°C mrad.mm/kV Multiphysics 63.35 to simulate 61.6 its performance 54.88 8.68 and compareThe measured it to the deflection measured angle values. at 40 °C The calculated mrad.mm/kV EO coefficients, 62.66 60.96 the refractive 54.37 indices, 8.59 andThe themeasured measured halfwave permittivity electric field at were 25 °C used * as V/ theμm COMSOL0.124 model’s0.136 inputs. 0.228 The voltageNA andThe electric measured field halfwave distribution, electric field the at 40 birefringence, °C * V/μm and deflection0.128 angles0.141 were0.232 the COMSOLNA Number of resolvable spots at 25 °C - 1403 1146 417 23 modelNumber outputs, of resolvable as seen inspots Figures at 40 °C 20 –22. - 1388 1135 413 22 The EO coefficient (s11) at 25 °C m2/V2 1.57 × 10−15 1.55 × 10−15 1.39 × 10−15 2.18 × 10−16 The EO coefficient (s11) at 40 °C m2/V2 1.55 × 10−15 1.53 × 10−15 1.37 × 10−15 2.16 × 10−16 The calculated halfwave electric field at 25 °C * V/μm 0.122 0.135 0.224 0.960 The calculated halfwave electric field at 40 °C * V/μm 0.123 0.136 0.225 0.965 The calculated deflection angle at 25 °C mrad.mm/kV 65.85 63.51 56.85 8.91 The calculated deflection angle at 40 °C mrad.mm/kV 64.91 62.96 55.96 8.78 * The optical path was 1.5 mm. Appl.Appl. Sci. Sci.Appl. 2021 2021, Sci. 11, ,11 2021x ,FOR x ,FOR11 PEER, 3313 PEER REVIEW REVIEW 23 23of 27of 2722 of 27

(a)( a) (b)( b)

Figure 20. (a) Voltage (b) electric field (Ez) simulationz of the EO steerer based on PMN-PT ceramic under 1 kV/mm at 25 ◦ FigureFigure 20. (a 20.) Voltage(a) Voltage (b) electric (b) electric field ﬁeld (E ) (Esimulationz) simulation of the of theEO EOsteerer steerer based based on onPMN-PT PMN-PT ceramic ceramic under under 1 kV/mm 1 kV/mm at at25 25 C °C °usingC usingusing a COMSOL a COMSOL a COMSOL model. model. model.

(a)( a) (b)( b)

(c)( c) (d)( d)

FigureFigure 21.Figure 21. The The 21.birefringence birefringenceThe birefringence simulation simulation simulation of ofthe the EO of EO thesteerer steerer EO based steerer based on based on PMN-PT PMN-PT on PMN-PT ceramic ceramic ceramic under under 1 under kV/mm1 kV/mm 1 kV/mm at at25 25°C at °Cusing 25 using◦C a using a a COMSOLCOMSOLCOMSOL model model for model for (a) ( 532a for) 532 nm, (a )nm, 532 (b )( nm,b633) 633 nm, (b )nm, 633 (c) ( 1550 nm,c) 1550 (nm,c) 1550nm, and and nm, (d )( andd4500) 4500 ( dnm.) 4500nm. nm. Appl. Sci. 2021, 11, 3313 23 of 27 Appl. Sci. 2021, 11, x FOR PEER REVIEW 24 of 27

Figure 22. 22. TheThe deflection deﬂection angle angle simulation simulation of the EO of steerer the EO based steerer on PMN-PT based onceramic PMN-PT underceramic 1 under kV/mm at 25 °C using a COMSOL model for (a) 532 nm, (b) 633 nm, (c) 1550 nm, and (d) 4500 nm. 1 kV/mm at 25 ◦C using a COMSOL model for (a) 532 nm, (b) 633 nm, (c) 1550 nm, and (d) 4500 nm. The wavelength-dependent birefringence (∆n) defines the phase retardance for those Table 6. The measured and calculatedfour wavelengths wavelength using and Equation temperature-dependent (37), as seen in Figure parameters 23. of the EO beam steerer based on polycrystalline PMN-PT.

Parameter Unit 532 nm 633 nm 1550 nm 4500 nm The refractive index - 2.4744 2.4635 2.4573 2.4619 The measured deflection angle at 25 ◦C mrad.mm/kV 63.35 61.6 54.88 8.68 The measured deflection angle at 40 ◦C mrad.mm/kV 62.66 60.96 54.37 8.59 The measured halfwave electric field at 25 ◦C * V/µm 0.124 0.136 0.228 NA The measured halfwave electric field at 40 ◦C * V/µm 0.128 0.141 0.232 NA Number of resolvable spots at 25 ◦C - 1403 1146 417 23 Number of resolvable spots at 40 ◦C - 1388 1135 413 22 ◦ 2 2 −15 −15 −15 −16 The EO coefficient (s11) at 25 C m /V 1.57 × 10 1.55 × 10 1.39 × 10 2.18 × 10 ◦ 2 2 −15 −15 −15 −16 The EO coefficient (s11) at 40 C m /V 1.55 × 10 1.53 × 10 1.37 × 10 2.16 × 10 The calculated halfwave electric field at 25 ◦C * V/µm 0.122 0.135 0.224 0.960 The calculated halfwave electric field at 40 ◦C * V/µm 0.123 0.136 0.225 0.965 The calculated deflection angle at 25 ◦C mrad.mm/kV 65.85 63.51 56.85 8.91 The calculated deflection angle at 40 ◦C mrad.mm/kV 64.91 62.96 55.96 8.78 * The optical path was 1.5 mm.

As seen in Table6, the measured deflection angles for four wavelengths at 25 ◦C and 40 ◦C temperatures could also define the number of resolvable spots using Equation (2). The EO coefficients and the refractive indices can define the halfwave electric field using ◦ Figure 23. The phase retardanceEquation versus (38). applied The electric halfwave field on electric PMN-PT field ceramic for thefor four three wavelengths different wavelengths(532, 633, 1550, at 25 C and and 4500 nm). 40 ◦C was also measured in the lab. As seen in Table6, the results are comparable to the calculated values. TheThe results wavelength-dependent show that although the birefringence EO coefficient (∆ nof) PMN-PT defines the ceramic phase is not retardance strongly for those −16 varyingfour wavelengths by the temperature, using Equation it drops (37),significantly as seen from in Figure 15.68 23× 10. for green laser (532 nm) to 2.18 × 10−16 for mid-IR (4500 nm). That resulted in reducing the number of resolva- The results show that although the EO coefficient of PMN-PT ceramic is not strongly ble spots of the EO beam steerer designed in this study from 1403 for 532 nm to 23 for 4500 varying by the temperature, it drops significantly from 15.68 × 10−16 for green laser nm at 25 °C. (532 nm) to 2.18 × 10−16 for mid-IR (4500 nm). That resulted in reducing the number of resolvable spots of the EO beam steerer designed in this study from 1403 for 532 nm to 23 for 4500 nm at 25 ◦C. Appl. Sci. 2021, 11, x FOR PEER REVIEW 24 of 27

Figure 22. The deflection angle simulation of the EO steerer based on PMN-PT ceramic under 1 kV/mm at 25 °C using a COMSOL model for (a) 532 nm, (b) 633 nm, (c) 1550 nm, and (d) 4500 nm. Appl. Sci. 2021, 11, 3313 24 of 27 The wavelength-dependent birefringence (∆n) defines the phase retardance for those four wavelengths using Equation (37), as seen in Figure 23.

Figure 23.23. TheThe phasephase retardanceretardance versus versus applied applied electric electric ﬁeld field on on PMN-PT PMN-PT ceramic ceramic for for four four wavelengths wavelengths (532, (532, 633, 633, 1550, 1550, and and 4500 nm). 4500 nm).

TheTable results7 compares show that the visiblealthough light the (633 EO coef nm)ficient and near-IR of PMN-PT light ceramic (1.55 µ m)is not deﬂections strongly varyingassociated by withthe temperature, polycrystalline it drops PMN-PT significantly measured from in this 15.68 study × to10− the16 for ones green measured laser (532 for nm)LiTaO to3 2.18by Casson × 10−16 for etal. mid-IR [12,17 (4500]. nm). That resulted in reducing the number of resolvable spots of the EO beam steerer designed in this study from 1403 for 532 nm to 23 for 4500 Table 7. Comparing the performance of polycrystalline PMN-PT to LiTaO in deﬂection light at nm at 25 °C. 3 visible and near-IR.

Deﬂection (mrad.mm/kV)

Wavelength (µm) LiTaO3 Polycrystalline PMN-PT 0.633 9.41 61.6 1.55 7.78 54.88

As seen, polycrystalline PMN-PT performs about seven times better than LiTaO3 at those two wavelengths, and yet, as shown, PMN-PT ceramic is polarization-independent and almost temperature-independent.

4. Conclusions This paper offered a robust approach for accurately measuring the dispersion curve of polycrystalline PMN-PT based on interference patterns in FTIR spectroscopy in a wide range of optical wavelengths for the first time. The dispersion curve was used to define the transmission of this ceramic. The dielectric constant of the PMN-PT ceramic was defined as a function of temperature through a capacitance bridge configuration and a high-accuracy LCR meter. The Curie temperature of PMN-PT ceramic was found close to the room temperature, where the dielectric constant peaks at about 12,000. A polarization-independent EO laser beam steerer based on a 7.5 mm × 7.5 mm × 40 mm polycrystalline PMN-PT was designed in this study to steer light from visible to mid-IR. The optimum number of interfaces for this EO beam steerer was found as two, considering no internal reflection and minimum partial back-reflections. The only EO beam steerer that does not need crystalline orientation adjustment so far was the one offered by Nakamura from NTT Photonics Laboratories in Japan [7]. However, since that steerer was based on charge injection and it is impossible to inject charges to a thick medium uniformly, the medium must be a fraction of a millimeter thick. Therefore, that EO steerer could steer only an 80 µm laser beam and resolved only 20 spots. For the first time, this paper offered an EO beam steerer, which was similarly polarization- independent and did not need any crystalline orientation adjustment, but it could resolve Appl. Sci. 2021, 11, 3313 25 of 27

up to 1400 spots. The voltage per millimeter applied on the EO medium in this paper was only two times more than the one presented by Nakamura, but the number of the resolvable spots was 70 times more. The deflection angle for the wavelengths of 532, 632.8, 1550, and 4500 nm was measured in the lab in terms of mrad·mm/kV at 25 ◦C and 40 ◦C temperatures to define the EO coefficients associated with those four wavelengths at two different temperatures for the first time. The calculated EO coefficients, refractive indices, transmission, and dielectric constant were used as inputs of a simulation model developed with COMSOL Multiphysics. The simulation model was used to calculate the voltage and electric field distribution as well as the birefringence. The EO beam steerer’s performance, including the deflection angles, was simulated and compared to the measured values. The EO coefficients and the refractive indices were used to define the halfwave electric field, and the results were compared to the measured values. The phase retardance associated with those four wavelengths was determined. The results show that the EO coefficient of PMN-PT ceramic is not strongly varying by the temperature, but it drops from 15.68 × 10−16 for green laser (532 nm) to 2.18 × 10−16 for mid-IR (4500 nm). That significant drop in the EO coefficient reduced the number of resolvable spots of the EO beam steerer, developed in this study, from 1403 to 23. Although the result shows the EO coefficient of bulk PMN-PT ceramics is an order of magnitude smaller than gold nanoparticles measured by Thakur and Van Cleave [8] at 633 nm, the bulk PMN-PT offers other benefits like higher transmission at mid-IR, very low thermal dependency, less EO dispersion and ability to address larger apertures. Comparing the polycrystalline PMN-PT with LiTaO3, which is the most used single crystal for EO beam steering, has shown that PMN-PT ceramic performs about seven times better than LiTaO3. Nevertheless, PMN-PT ceramic is polarization-independent. Therefore, unlike LiTaO3 single crystal, it does not need orientation adjustment and domain- engineered multi prisms to be used as an electro-optical beam steerer. The PMN-PT ceramic is also easier, cheaper, and faster to produce and is available in larger sizes than most EO single crystals.

Supplementary Materials: The following are available online at https://www.mdpi.com/article/ 10.3390/app11083313/s1, Video S1: Electro-optical 633 nm laser beam steering with the 7.5 mm × 7.5 mm × 40 mm polycrystalline PMN-PT under 1 kV/mm external electric field at 1 Hz. Author Contributions: Conceptualization, A.A. and P.M.; methodology, A.A.; software, A.A.; val- idation, A.A., C.B., M.W., and E.R.; formal analysis, A.A.; investigation, A.A.; resources, C.B. and M.W.; data curation, C.B., M.W., and E.R.; writing—original draft preparation, A.A. and M.W.; writing—review and editing, P.M. and E.R.; visualization, A.A. and M.W.; supervision, P.M.; project administration, P.M.; funding acquisition, A.A. and P.M. All authors have read and agreed to the published version of the manuscript. Funding: This research was supported by Igor Anisimov at AFRL/RY, Dr. Jonathan Slagle at AFRL/RX, DOD SMART program, and by Exciting Technology LLC. Institutional Review Board Statement: Not applicable. Informed Consent Statement: Not applicable. Data Availability Statement: Not applicable. Acknowledgments: The authors would like to thank Igor Anisimov at AFRL/RY and Jonathan Slagle at AFRL/RX for partially funding this research. Conflicts of Interest: The authors declare no conflict of interest. Appl. Sci. 2021, 11, 3313 26 of 27

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