1. Introduction

Potassium tantalate niobate (KTN) crystals have been interested for more than four decades due to their large quadratic electro-optic (EO) coefficient [1, 2]. In recent years, there have been substantial progresses in all aspects of KTN materials such as material growth, device development, and real world applications. For example, in terms of material growth, high quality KTN crystals with a size (>30 cm³) have been successfully grown, which ensures the material supply for the device development [3]. In terms of device development, by taking advantage of the large quadratic EO coefficient of KTN material, low driving voltage EO modulator has been introduced [4]. Furthermore, by using the unique space-charge-controlled EO effect, low-driving voltage beam scanner has also been reported [5, 6].

However, all the currently reported EO devices based on KTN materials have only one function (e.g., EO modulation or beam scanning). To overcome the limitation of existing KTN based EO devices, in this paper, we are reporting an electric field induced dynamic EO waveguide based on KTN crystals, which can serve multiple functions (1) wave guiding, (2) fast speed light modulation, and (3) the position control of the output beam. This multi-functional device can be very useful to enhance the functionality and reduce the size of EO devices.

2. Technical approach of electric field induced dynamic optical waveguide

2.1 Quadratic electro-optic effect in KTN crystals

KTN crystal possesses the quadratic electro-optic effect. The general equation of the index ellipsoid of quadratic electro-optic effect can be written as

Due to the existence of the mixed term,$4xy{s}_{44}{E}_x{E}_y$, in Eq. (3), the major axes of ellipsoid under the external electric field, are no longer parallel to the xyz crystal axes. To eliminate the mixed term, a rotation transformation, as illustrated in Fig. 1 , can be applied in Eq. (3), as given by

 

Fig. 1 A schematic illustration of coordinate rotation.

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The new equation of ellipsoid is obtained via substituting Eq. (4) into Eq. (3).

Based on Eq. (7), one can see that for an arbitrarily linearly polarized light with an angle $\alpha$with respect to x'-axis, as shown in Fig. 2 , it can be decomposed into two polarized waves with x'- and y'- polarization axes, respectively. The refractive indices for these two polarized waves are $n_{x\text{'}}$ and $n_{y\text{'}}$, respectively. If $\alpha \ne 0^{\circ }$or $\alpha \ne {90}^{\circ }$there will be a phase delay between x'- and y'- polarized wave. Thus, a linearly polarized input light will become elliptically polarized light. To avoid the change of the polarization property of the incoming light, the polarization axis of the input polarized light needs to be along x'- and/or y'- axis. This is only possible when the direction of applied field, ${\theta }_E={\tan }^{-1}(E_y/E_x)$, keeps the same within the interested region so that one can obtain the same rotation angle, $\theta$, of the ellipse. To realize this idea, we select the central area of dipole electrodes as the interested region, to be described in detail in Section 2.2.

 

Fig. 2 A schematic illustration of the ellipse of indices in both x-y and x'-y' coordinates when the field is applied in the space.

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2.2 Design of dynamic optical waveguides based on KTN crystals

As described in Section 2.1, to maintain the polarization axis during the propagation, we select the central area of dipole electrodes as the interested region. In this case, the direction of the applied electric field is along x-axis and the rotation angle, $2\theta =0$, based on Eq. (6). In other words, x-axis and x'-axis are in the same direction. Similarly, y-axis and y'-axis are also in the same direction. Thus, if the input polarization axis is along x-axis or y-axis, its polarization state will maintain during the propagation.

Figure 3 illustrates the configuration of dynamic optical waveguides based on KTN crystals. Two metal contacts with a gap of 50 μm were located on top of the crystal, which generated an electric field perpendicular to the z-axis. It was also assumed that the incident wave propagates along the z-axis. To quantitatively analyze the field induced index change of the proposed dynamic optical waveguide, the electric field distribution was calculated via Finite Element Method (FEM). Figure 4 shows the calculated field distribution on x-y cross-section plane when the voltage difference between two contacts is 100 V. The arrows denote the vector of electric field,$\overrightarrow{E}=E_x(x,y)\widehat{x}+E_y(x,y)\widehat{y}$, at points, $(x,y)$, where the lengths proportionally present the magnitude of the electric field. One can observe that the field, parallel to x-axis, is dominated near the gap center, where is also the area of interest of the device. Furthermore, the gradient of field in x-direction, $E_x(x,y)$, is also displayed within the rainbow scale in unit of V/m. The rainbow plot reveals that a strong electric field along x-axis direction is existed near the central region of the electrode gap, which can induce significant refractive index change and enable the guiding effect.

 

Fig. 3 An illustration of configuration of dynamic optical waveguide based on KTN electro optical crystal.

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Fig. 4 The simulated electric field distribution is plotted in x-y cross-sectional plane when the bias voltage is 100 V. The black arrows and the rainbow color, respectively, indicate the proportional field vector, $\overrightarrow{E}(x,y)$, and the field magnitude in x-component, $E_x(x,y)$ (V/m).

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2.3 Simulation of guiding effect along z-axis at central region (i.e., x = 0)

For the z-transverse optical wave, electric field only exists in x-direction at gap center, $x=0$, as illustrated in Fig. 4. One can therefore investigate the relationship between the index change, $\Delta n_{x,y}(0,y)=n_{x,y}(0,y)-n$, and the applied field, $E_x(0,y)$ via Eq. (7). In this case, $\theta =0$and $E_y=0$. Figure 5(a) plots the electric field of the x-component,$E(0,y)$, that is also the cross-sectional plot of Fig. 4 at $x=0$, in function of the depth below the surface of the crystal, $y$. The induced index changes for H- and V-polarized waves are shown in Fig. 5(b) with $\Delta n_x(0,y)$ and $\Delta n_x(0,y)$, respectively. Here, we define H- and V- polarization as the polarization states with polarization axes along x- and y- directions, respectively. The values of quadratic electro-optic coefficients, s₁₁ = 1065 × 10⁻¹⁸ m²/V² and s₁₂ = −298 × 10⁻¹⁸ m²/V², and refractive index without presence of field, $n=2.29$, were taken in the equations [1, 2].

 

Fig. 5 (a) the electric field of x-component,$E_x(0,y)$, in the central region, and (b) the induced refractive index changes, $\Delta n_{x,y}(0,y)$for the x and y polarized light beams, respectively.

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Based on index profiles as shown in Fig. 5(b), the characteristics of z-transverse wave were quantitatively investigated for the cases without and with the external electric field. Beam Propagation Method (BPM) was employed for the calculation. It was assumed that the incident wave was a normalized Gaussian beam with a waist of 60 µm and a wavelength of 0.532 μm, respectively. The wave was launched at the center of the gap, $x=0$, and 15 µm beneath from the surface, $y=15$(μm).

First, without applying the external electric field (Voltage Off), the KTN crystal had an uniform refractive index profile, $\Delta n_x=\Delta n_y=0$, in both polarization states. Figure 6(a) depicts the calculated normalized optical field as a function of $y$ for different propagation distances: $z=0$mm (incident plane), $z=5$mm, $z=10$mm, and $z=20$mm, respectively. It can be seen that the optical field is diverged because there is no optical confinement effect in this case.

 

Fig. 6 The calculated optical field amplitude in conditions of (a) without applying voltage in both polarization states; (b) with applying voltage in H-polarization; (c) with applying voltage in V-polarization. Here, the gray color renders the area of the crystal.

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Second, optical field were calculated with external electric field (Voltage On). As the optical wave propagated in KTN, the field induced index change would influence the beam characteristics. Since the refractive index distributions were different for horizontally (H-) and vertically (V-) polarized waves as in Fig. 5(b), the guiding effects were also different for those two waves. Figure 6(b) shows the calculated normalized optical field of a H-polarized wave in propagation distances of $z=0$mm (incident plane), $z=5$mm, $z=10$mm, and $z=20$mm, respectively. It can be seen that there is almost no energy propagated beyond the distance of 5 mm in the crystal because the index was lowered by the electric field. In fact, this is the anti-guiding effect in this case.

Figure 6(c) shows the calculated optical field for a V-polarized wave in propagation distances of $z=0$mm (incident plane), $z=5$mm, $z=10$mm, and $z=20$mm, respectively. One can clearly observe the guiding effect in this case. The optical field is concentrated near the surface of the crystal where the area has higher refractive index, as depicted in Fig. 5(b). One can also see multi-mode competition due to the nature of a multi-mode waveguide.

Furthermore, by reducing the gap between two electrodes, a near single-mode waveguide could be realized for the V-polarized wave. To maintain the same level of biasing electric field, the lower 10 V biasing voltage was used for a 5 μm electrode gap. Figure 7(a) shows the calculated optical field amplitude for the V-polarized wave in propagation distances of $z=0$mm (incident plane), $z=5$mm, $z=10$mm, and $z=20$mm, respectively, when the waist of the input wave is reduced to 6 µm. One can clearly see the single-mode character in this case.

 

Fig. 7 The single-mode character is shown in the simulation when the electrode gap is reduced. (a) The distribution of field amplitude is maintained in various propagation distances. Here, the gray color renders the area of the crystal. (b) The output amplitude (z = 20 mm) is modulated in various applied voltages.

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Finally, since the amount of guiding effect can be controlled by adjusting the value of the applied voltage, dynamic and tunable optical waveguides can be enabled, which is another major advantage of the waveguides presented in this paper. For example, Fig. 7(b) shows the output field amplitude (at z = 20 mm) normalized to the input Gaussian wave for the V-polarized wave under different biasing voltages (0 V, 5 V, 10 V, and 15 V). One can clearly observe different guiding effects (different output profiles) in this case. The optical field diverged more under low biasing voltage.

3. Experimental results and discussions

3.1 Fabrication of a dynamic optical waveguide based on the KTN crystal

To validate the feasibility of our proposed dynamic optical waveguides based on KTN crystals, a multimode KTN crystal based waveguide with a gap width of 50 μm was fabricated because it was easier to fabricate multimode waveguide than that of single mode waveguide due to the larger feature size.

Following fabrication procedures were employed. First, a double-side polished KTN crystal was diced into following dimensions: 10 mm (L) × 7 mm (W) × 1 mm (D). Then, the side surfaces of the crystal were polished to lower the coupling loss. According to the previous report, electron charges could be injected into KTN crystal when the biasing voltage was relatively higher than the work function difference between KTN and metal contacts [4]. This created an electric field distribution inside the crystal, which in turn resulted in a gradient refractive index distribution inside the crystal via electro-optic Kerr effect. Although this kind of electron charge injection was beneficial for the application of electro-optic beam scanner, it might not be preferred for the application of high speed (nanosecond range) dynamic optical waveguide because the speed of electric charge injection was on the order of microsecond [4]. As described in Ref [4], the electron injection effect becomes observable under the field of 500 V/mm. In our case, since the electrode gap was 50 μm and the bias voltage was 100 V, the biasing electric field was up to 2000 V/mm that was higher than that of 500 V/mm. In order to avoid the electron injection effect that could reduce the modulation speed, a bi-layer structure was used. A thin 10-nm-thick aluminum oxide (Al₂O₃) barrier layer was conformally coated on the KTN crystal via atomic layer deposition (ALD) (Cambridge NanoTech, Inc. Savannah 200) before fabricating the metal contact. After the ALD coating, titanium (Ti)/gold (Au) contacts were fabricated by a lift-off process. A ridged bi-layer structure with a width of 50 μm was patterned by photoresists, LOR5A (Microchem Co.) and SPR3012 (Rohm and Haas Co.), which served as a shadow mask for the deposition of the metal contacts. A 10-nm-thick Ti layer and a 100-nm-thick Au layer were then evaporated on the surface of KTN (Kurt J. Lesker Co.) After removing the photoresist mask, a KTN crystal based electro optical dynamic optical waveguide was obtained. Figure 3 illustrates the schematic configuration of the fabricated device.

3.2 Build experimental setup for testing the dynamic optical waveguides based on KTN crystals

Figure 8 illustrates the experimental setup for testing the dynamic optical waveguide based on KTN crystal. A 532 nm diode pumped solid state (DPSS) laser (Coherent, Inc. Compass 532-200) was used as the testing light source. The laser beam was coupled into the waveguide by the focusing lens L2. A quarter wave plate (QWP), a polarizer and some other mirrors and lenses were also used in the system so that the polarization direction of the light beam entering the KTN waveguide could be controlled. Since electro-optic coefficient of KTN crystal was sensitive to the ambient temperature, the KTN waveguide was put on top of a temperature controller based on thermoelectric cooler (TEC). The temperature of TEC was set at 25°C, which was 5°C higher than this KTN’s Curie temperature (T_c) to maximize electro-optic Kerr effect. A CCD camera (SONY XC-77) was used to measure the light intensity distribution at the exit end of the KTN waveguide. Furthermore, to measure the response time of dynamic optical waveguide, a high-speed voltage pulse generator (Avtech Electrosystems, Ltd. AVL-3A-C) was utilized to quickly apply the dynamic driving electric field and a fiber coupled high speed photodetector (FEMTO Messtechnik GmbH HCA-S-200M-Si) was employed to measure the response time of the optical waveguide under dynamic driving electric field.

 

Fig. 8 A schematic illustration of experimental setup for testing the dynamic optical waveguides based on KTN crystals, including a 532 nm DPSS laser, two mirrors (M1 and M2), an objective lens (OB), a pinhole (PH), two lenses (L1 and L2), a quarter wave plate (QWP), a polarizer (P1), a KTN crystal based dynamic waveguide, and a photodetector (PD).

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3.3 Evaluate the guiding effect of dynamic optical waveguides based on KTN crystals

To measure the output light field distribution of dynamic optical waveguide based on KTN crystal, the intensity distributions at the exit end of waveguide were measured by using a long working distance microscope objective lens (Nikon ELWD 40X/0.55) and a CCD camera (SONY XC-77) for the cases with and without applying a 100 V biasing voltage.

Figure 9(a) shows the measured light intensity distribution at the exit end of the waveguide without applying the biasing voltage. Since KTN crystal is isotropic without biasing voltage, the output intensity distribution is the same for both polarization states. In comparison, the experimental result of Fig. 9(a) in the cross-sectional plot at x = 0 and the simulation result of Fig. 6(a) are similar. The slight difference is due to the multimode nature of the waveguide, which is sensitive to the launching condition.

 

Fig. 9 Experimentally measured light intensity distribution at the exit end of the dynamic optical waveguide: (a) without the biasing voltage, (b) with the biasing voltage for the H-polarized wave, and (c) with the biasing voltage for the V-polarized wave.

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Figure 9(b) shows the measured light intensity distribution at the exit end of the waveguide with a 100 V biasing voltage for the H-polarized wave. One can clearly see the difference of the light intensity distributions between the cases with and without the applied electric field. There is almost no light between two electrodes, which closes to the theoretically calculated field profile, as illustrated in Fig. 6(b).

Figure 9(c) shows the measured light intensity distribution at the exit end of the waveguide with a 100 V biasing voltage for the V-polarized wave. Again, one can clearly see the difference of the light intensity distributions between the cases with and without the applied electric field. The guiding effect is observed as well. As the plotting of Fig. 6(c), the light is concentrated near the surface, compared to H-polarized light.

3.4 Evaluate the response time of dynamic optical waveguides based on KTN crystals

As aforementioned, a high speed electric pulse generator and a high speed photodetector were used to evaluate the response time of dynamic optical waveguide based on KTN crystal. Furthermore, the H-polarized light beam was used for the measurement. In the experiment, a 250 V voltage pulse with a fast rising time ~1 ns was applied on the electrodes. The fast speed photodetector was used to measure the light intensity as a function of time in the area beneath the central region of the electric gap. Without applying the biasing voltage, there was light in this area between two electrodes so that the output light intensity could be detected by the photodetector. However, with the applied biasing voltage, the light was more concentrated near the edge of the contacts, but central region of the gap. Thus, there was a substantial light intensity drop in the area beneath the central region of the electric gap. Figure 10 shows the experimentally measured the light intensity change as a function of time. One can clearly see that the light intensity drops significantly in the area beneath the central region of electric gap when there is a biasing electric field. The experimentally measured response time is around 15 ns, which is much faster than the reported response time of KTN crystal based beam scanner (>1 µs) because the relatively slow electron injection process is avoided by adding the thin alumina layer in our device [4]. It should also be noted that the 50 ns response time is limited by the RC time constant of the device rather than the electro-optic effect of KTN crystal itself. To validate this conclusion, the following analyses were conducted. First, the capacitance of the waveguide was precisely calculated by FEM. The calculated value was 375 pF. The impedance of the device was 50 Ω. Thus, the time constant of the waveguide system was $\tau =RC=19$ns which was very close to our experimentally measured response time. An even faster response time can be achieved by reducing the capacitance of the waveguide, which will be investigated in the future.

 

Fig. 10 The experimentally measured response time of dynamic optical waveguide based on KTN crystal.

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It may be noted that although one can also clearly observe guiding effect of V-polarized wave when bias is on (Fig. 9(c)), the difference is not that big compared to Fig. 9(a) (i.e., the case without bias voltage). On the other hand, after applying bias voltage, the propagation wave in H-polarization is blocked by the device (Fig. 9(b)). The signal is, thus, suddenly shut off obviously. That is why the authors choose V-polarization for the experiment of measuring response time.

Also, 250 V was used in the experiment of measuring response time because there could be large variations in the actual electro-optic efficient of KTN crystals. The imperfection of the crystal could substantially reduce the electro-optic coefficient. It is still an on-going effort to perfect the quality of KTN crystal in this field. In the simulation, the electro-optic coefficient from Ref [1, 2]. was used. In this case, only 100 V biasing voltage was needed for 50 μm gap electrode. However, the electro-optic efficient of the KTN crystal used in our experiment was smaller. This was why a higher (250 V) biasing voltage was used in the experiment of measuring response time so that a large enough output signal-to-noise ratio can be obtained.

4. Conclusions

In this paper, a dynamic optical waveguide based on KTN electro-optic crystal was presented. The refractive index distributions and the corresponding light field distributions for the H- and V-polarized light beams were quantitatively computed under different levels of applied external electric fields. The simulation results showed that the V-polarized light could be guided within the regions between two electrodes. The simulation results also indicated that not only the total intensity but also the distribution of the light fields could be controlled by adjusting the magnitude of the applied external electric field, which enabled the dynamic optical waveguide. The dynamic nature of the optical waveguide allowed us to quickly control the guiding effect in optical waveguides, which could be a great beneficial for many tunable optical devices such as variable optical attenuators and dynamic gain equalizers. Furthermore, a multimode dynamic waveguide was fabricated and its performance including output light intensity distribution with and without applied external electric field was quantitatively evaluated. It could be observed that the experimental results agreed relatively well with the theoretical models, which confirmed the feasibility of our proposed dynamic optical waveguide. A fast response time (tens of ns) was also experimentally observed, which was much faster than recently reported KTN crystal based optical beam scanner because the effect of slow electron injection was avoided via the Al₂O₃ barrier layer [4]. The tuning speed could also be further increased by reducing the RC time constant of the system. In the future, we will conduct more experiments to future enhance performances of the device, such as reducing the gap between two electrodes to enable the single mode operation waveguide and decreasing the capacitance of the system to realize the higher speed dynamic optical waveguide.