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Abstract
In this paper, we propose an enhanced c-axis potassium tantalate niobate (KTN) based electro-optic (EO) deflector by compensating the performance degradation using a thermal gradient. The naturally existing composition gradient in KTN crystals prevents KTN deflectors from working at its maximum functionality at all locations along the propagation path. To overcome this fundamental limitation, we propose a KTN deflector with a temperature gradient to ensure all locations of KTN to work at the temperature having its highest permittivity. Our experimental data shows the KTN deflector with temperature gradient has near three times higher deflection angle than that of the case under uniform temperature.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Since potassium tantalite niobate (KTa1-xNbxO3, KTN) was first introduced to the world in the 1960s, it has drawn significant attention to the field of optical engineering due to its extraordinarily large quadratic electro-optic (QEO) effect. For decades, it opens a variety of applications such as optical coherence tomography (OCT), optical holograms, high-speed modulation, and rapid medical imaging [1–5]. Moreover, in 2006, the first sizable high-quality KTN bulk crystal, suitable for device fabrication, was developed by using a top-seeded solution (TSSG) technique, which accelerated practical usage of KTN based electro-optic (EO) devices, including space-charge-controlled (SCC) KTN deflectors [6–9].
The KTN crystals grown by the TSSG technique had the advantages of high crystalline symmetry, EO coefficient, and optical transmittance [10]. However, the KTN crystals grown from TSSG also have a composition gradient along the growing direction. The ratio between niobium/tantalum is changed during the crystal growing process due to the nature of the phase diagram [11]. This composition gradient causes a non-uniform refractive index distribution along the crystal growing axis (i.e., c-axis).
To ensure a high beam quality after passing through the composition gradient KTN crystal, it becomes important to select proper beam propagation direction. For example, Fig. 1(a) shows 4×4×10 mm3 long-bar KTN crystal with two different directions of the light propagation. A collimated beam with beam waist of 1.33 mm and wavelength of 635 nm is used in this experiment. The red line indicates the direction perpendicular to the c-axis, and the blue line indicates the direction parallel to the c-axis. Since the light beam along the red line experiences a transversal non-uniform gradient refractive index distribution induced by the transversal non-uniform composition gradient, it may cause a beam distortion. A circularly Gaussian-shaped incoming beam becomes a distorted line, as shown in Fig. 1(b). On the other hand, the light beam along the blue line (c-axis) does not experience a transversal non-uniform gradient refractive index distribution. It only experiences a longitudinal non-uniform gradient refractive index distribution, which has little effect on beam quality. A circularly Gaussian-shaped incoming beam largely maintains a circular shaped beam after applying voltage (Vapp), as shown in Fig. 1(c). Thus, in general, a c-axis KTN deflector has a higher beam quality.
Fig. 1. (a) A photo of 4×4×10 mm3 long-bar KTN crystal on Peltier device with a hole, (b) CCD image of the beam after passing through a KTN crystal under Vapp=1400 V in the direction perpendicular to c-axis (y-direction), and (c) CCD image of the beam after passing through a KTN crystal under Vapp=1400 V in the direction parallel to c-axis (z-direction).
Although the beam quality of c-axis KTN deflectors does not seem substantially affected by the composition gradient, the other key performance factor, deflection angle, is indeed compromised by the composition gradient because the composition gradient in KTN creates a non-uniform phase-transition temperature along the light path [12]. If we assume that the electric field is applied in the x-direction and there is no composition gradient, the electric field induced beam deflection angle in the x-direction, θ(x), can be expressed by
However, when the composition gradient exists in the KTN crystal, permittivity, ɛ, is not a constant anymore. It is a function of z, denoted as ɛ(z). In this case, Eq. (1) needs to be re-written as
Since different location z has a different Curie temperature, it becomes impossible to achieve a large ɛ(z) by using the conventional single temperature operational method.
2. Results and discussion
To overcome this performance drop in KTN deflectors caused by the composition gradient, we explore a non-uniform temperature gradient operational method by applying different operational temperatures at different z locations so that ɛ(z) can be maximized at all z locations. In some earlier studies, the temperature gradient has been adopted in KTN deflector for enabling 2D beam deflectors or controlling beam-divergence fluctuations in deflectors. [8,13] However, there has not been any experimental analysis for enhancing beam deflection angle by adopting a non-uniform temperature gradient. In this study, we focus on theoretical and experimental verification of non-uniform temperature gradient operational method, which can lead to its practical usage in beam deflecting systems.
We conducted the following experiments to prove this proposed concept of enhancing the beam deflection angle by a thermal gradient. First, we prepared a 4×4×10 mm3 long-bar type KTN crystal with a compositional gradient along the longest mm direction. All surfaces of KTN were optically polished, and a pair of Ti/Au electrodes with a thickness of 50 nm were coated at the lateral surfaces that allowed charge injection. Furthermore, the KTN crystal was placed on top of a 0.45 mm thick sapphire wafer and a Peltier module (CP60440) that was connected to a temperature controller (MODEL 325) so that the temperature of the KTN deflector could be precisely controlled.
Second, to validate the existence of composition gradient in the 4×4×10 mm3 long-bar type KTN crystal sample, the energy dispersed spectroscopy (EDS) of the sample was conducted. The measured result is shown in Fig. 2(a). As we depicted in the earlier text, there was a composition gradient along the c-axis. At the location z=0 mm, the Nb/Ta atomic concentration ratio is measured around 0.390 and set as the reference point of Fig. 2(a). From this point, we mapped the change in the concentration ratio of Nb/Ta along the z-direction, up to the location z=10 mm, where the Nb/Ta atomic concentration ratio is measured around 0.399. From Fig. 2(a), we could clearly observe composition difference along the z-direction. This resulted in different Curie temperatures at different z locations. To confirm this composition gradient induced non-uniformity in terms of Curie temperature, the polarized microscope image of the sample was taken as shown in Fig. 2(b). Indeed, different locations had different Curie temperature. At the locations of z=0 mm, 5 mm, 10 mm, the Curie temperatures (TC) are near 22 ${^\circ}{\textrm{C}}$, 25 ${^\circ}{\textrm{C}}$, and 27 ${^\circ}{\textrm{C}}$ respectively. This experimental result is consistent with the previous prediction [14]. As the concentration ratio of niobium (x) increases, the Curie temperature increases, as given by [15],
According to the Eq. (3) and Fig. 2(a), we could check the range of the Curie temperature (ΔTC) in our KTN sample is around 6 ${^\circ}{\textrm{C}}$ when the Nb/Ta atomic concentration ratio changes from 0.390 to 0.399. This theoretical result was close to our experimental result, as shown in Fig. 2(b).
Fig. 2. (a) The EDS result of 4×4×10 mm3 long bar type KTN crystals and (b) the polarized microscope images at 22 ${^\circ}{\textrm{C}}$, 25 ${^\circ}{\textrm{C}}$, and 27 ${^\circ}{\textrm{C}}$ temperatures, respectively.
Third, we quantitatively simulated the relationship between the permittivity and the operational temperature. Based on previous studies, the temperature-dependent relative permittivity, ɛr, could be described by the following equation [10,16,17],
Fig. 3. (a) Schematics of KTN with double Peltier modules to achieve temperature gradient, (b) the simulation result of relative permittivity ɛr and temperature T for the case of uniform temperature operation TL=TH=32 ${^\circ}{\textrm{C}}$, and (c) the simulation result of relative permittivity and temperature T for the case of non-uniform gradient temperature distribution, TL=24 ${^\circ}{\textrm{C}}$ and TH=32 ${^\circ}{\textrm{C}}$
At first, we assumed the case of a uniform working temperature as T=32 ${^\circ}{\textrm{C}}$. Figure 3(b) shows the computed relative permittivity and temperature distribution at different locations. One could see that the relative permittivity is the highest, ɛr=19000, at the location z=10 mm because it has a Curie temperature near TC=27 ${^\circ}{\textrm{C}}$, which is the closest to the operational temperature, T=32 ${^\circ}{\textrm{C}}$. On the other hand, the relative permittivity is the lowest, ɛr=10500, at the location z=0 mm because it has a Curie temperature near TC=22 ${^\circ}{\textrm{C}}$, which is further away from the operational temperature, T=32 ${^\circ}{\textrm{C}}$. In the second case, we assumed that a gradient temperature was applied to the KTN sample. At the location z=0 mm, a lower temperature TL=24 ${^\circ}{\textrm{C}}$ was applied. On the other hand, at the location z=10 mm, a higher temperature TH=32 ${^\circ}{\textrm{C}}$ was applied. In this case, we ensured that operational temperature was closer to Curie temperature at allocation z locations. Figure 3(c) shows the computed permittivity and temperature distribution. The result indicates that with a proper temperature condition, we could achieve a high permittivity, near ɛr=19000, at most of the locations. This could also enhance the deflection angle, as given by Eqs. (1) and (2).
Finally, we experimentally measured the beam deflection angle, θ(x), with two simulated conditions: (i) uniform temperature and (ii) non-uniform gradient temperature distributions. In the experiment, for the light source, we used a laser diode with a wavelength of 635nm and let the laser beam travel along the c-axis of KTN crystal. After we set and saturated temperatures, DC voltage was applied from the DC power supply, and the beam deflection angle was measured at different conditions. The dashed red-line of Fig. 4 shows the result of the beam deflection angle with respect to the applied voltage, Vapp, for the case of uniform temperature condition where TL=TH=32 ${^\circ}{\textrm{C}}$. Under this uniform temperature condition, a maximum deflection angle of 8.8 mrad was obtained at Vapp=1400V. The dashed grey-line of Fig. 4 shows the result of the beam deflection angle with respect to the applied voltage, Vapp, for the case of non-uniform temperature distribution, TL=28 ${^\circ}{\textrm{C}}$ and TH=32 ${^\circ}{\textrm{C}}$. The maximum deflection angle was increased to 13 mrad at the same Vapp=1400V. For the last, the dashed blue-line of Fig. 4 shows the result of the beam deflection angle with respect to the applied voltage, Vapp, for the case of non-uniform temperature distribution, TL=24 ${^\circ}{\textrm{C}}$ and TH=32 ${^\circ}{\textrm{C}}$. Figure 4 shows that the maximum deflection angle was increased to 24 mrad at the same Vapp=1400V, which is three times of conventional uniform temperature operational case, because a high permittivity could be harnessed at all z locations, as depicted in Fig. 3(c).
Fig. 4. Experimentally measured deflection angles, θ(x), of 4×4×10 mm3 long bar type KTN crystals under different operational temperature profiles. (i) uniform temperature distribution (red-dashed line) and (ii) non-uniform gradient temperature distribution (gray, blue dashed lines).
3. Conclusion
In conclusion, we have successfully demonstrated an enhanced c-axis KTN deflector by compensating its composition gradient effect with the thermal gradient. We analyzed the physical origin of the performance drop of the composition gradient c-axis KTN deflector when the conventional uniform operational temperature was used. Since different locations had different Curie temperatures, it was impossible to harness maximum relative permittivity at all locations with uniform operational temperature. To overcome this limitation, we proposed and demonstrated that the maximum relative permittivity could be realized at all locations by harnessing a non-uniform thermal gradient temperature distribution. A 3-fold increase in the deflection angle was experimentally demonstrated. In this way, we could achieve both high beam quality, offered by c-axis configuration, and large deflection angle. This could expedite the practical applications of KTN deflectors, such as optical coherence tomography, high-speed tunable lasers, and high resolution, high-speed scanning imaging.
Funding
Office of Naval Research (N00014-17-1-2571).
Acknowledgments
This research was sponsored and partially supported by the Office of Naval Research (ONR) under Grant Number N00014-17-1-2571. The views and conclusions contained in this document are those of the authors and should not be interpreted as representing the official policies, either expressed or implied, of the Army Research Laboratory or the US Government. The US Government is authorized to reproduce and distribute reprints for Government purposes notwithstanding any copyright notation hereon.
Disclosures
The authors declare no conflicts of interest.
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