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Electro-optic modulation at λ= 1.5 μm has been demonstrated for the first time to the best of our knowledge in a ridge waveguide phase modulator produced in cubic potassium sodium tantalate niobate thin films epitaxially grown on potassium tantalate substrates exploiting the large quadratic electro-optic Kerr coefficient of R 11 = 8.2×10-17 m2/V2. The relative permittivity, Kerr coefficient, and refractive index have been evaluated for the thin film crystal and are compared to the values measured in bulk crystals. The half-wave voltage times length figure of merit of the modulator has been measured to be Vπl = 38 Vcm at room temperature.
©2007 Optical Society of America
1. Introduction
In recent years, electro-optic crystals of the potassium tantalate niobate (KTN) family have attracted increased attention for integrated optics due to its large linear and quadratic electro-optic coefficients[1] and the possibility of tuning the phase transition temperature by varying the Ta:Nb ratio[2][3][4][5]. The latest achievements in this field include the growth of nonlinear optical thin films of KTN on GaAs by pulsed laser deposition[6], electro-optic devices in buried KTN waveguides[7], and a wide-angle KTN beam deflector[8]. For guided optics applications, epitaxially grown thin films promise to combine low optical losses with bulk-like dielectric and electro-optic properties as long as two requirements are met: good lattice matching at the substrate-film interface and an optically flat thin film surface. While other groups have reported KTN thin films on GaAs[6] or MgO[9] substrates, as well as KTN waveguides embedded in KTN of different composition[7], we have recently demonstrated a technique that we think combines the advantages of a good substrate-film interface and an optically flat thin film surface[10]. The liquid-phase epitaxial growth of thin films of potassium sodium niobate tantalate (KNTN) on KT substrates with an as-grown optically flat surface, slab waveguiding therein and the measurement of the optical and dielectric properties of these films have been described in this publication. By substituting a small percentage of the potassium with sodium and performing the growth at a slow growth rate, a very small relative lattice mismatch of less than 1×10-4 and an rms surface roughness of approximately 20 nm were achieved.
To the best of our knowledge, we present for the first time ridge waveguiding and electro-optic modulation in KNTN thin films on KT substrates at infrared wavelengths in this paper, exploiting the huge quadratic electro-optic coefficient in this material. In the first part of this work, the material composition and dielectric behavior around the phase transistion temperature are assured by Rutherford back scattering (RBS) and interdigital electrode impedance measurements, respectively. In a bulk KNTN crystal, the quadratic electro-optic coefficient was measured in a cryostat interferometer setup and related to the dielectric behavior of the specimen. In μm-thick epitaxial films of KNTN grown on KT, ridge waveguides were produced by photolithography and argon-ion etching. The waveguides were characterized in terms of refractive indices and propagation losses, using a mode profile reconstruction method and a scattered light intensity technique, respectively. Using photolithography, electron-beam metal deposition and lift-off techniques, side electrodes were deposited parallel to the waveguides in order to create an electro-optic phase modulator. The performance of this modulator was tested in terms of half-wave voltage Vπ and modulation frequency.
2. Materials, growth and electrical properties
Potassium tantalate niobate (KTa1-xNbxO3, abbreviated KTN) is a solid solution of the two materials, potassium tantalate (KT) and potassium niobate (KN). Depending on the ratio x between tantalum and niobium, the Curie temperature T 0 of the phase transition between the paraelectric cubic phase and the ferroelectric tetragonal phase can be gradually shifted from 0 K for pure KT (x = 0) to 710 K for pure KN (x = 1.0)[11]. KTN was studied extensively and has been epitaxially grown on a variety of substrates[9][6][7], but the quality of the substrate-film interface is largely determined by the lattice mismatch between the substrate and thin film materials and even the use of several buffer layers produced relative mismatch values in the low percent range[6]. In a recent publication[10] we haven shown that by substituting a small percentage y of the potassium with sodium, an excellent lattice matching (relative mismatch < 1×10-4) between the KT substrate and the K1-yNayTa1-xNbxO3 thin film can be achieved that results in a good interface and a thin film surface that does not require polishing to be suitable for integrated optical applications.
Since our last publication[10], the KNTN material composition has been modified from K0.98Na0.02Ta0.66Nb0.34O3 (called KNTN1 for future reference) to K0.95Na0.05Ta0.71Nb0.29O3 (KNTN2) to shift the phase transition closer to room temperature which significantly increases the relative dielectric permittivity and the quadratic electro-optic coefficient R, since the relative dielectric permittivity theoretically diverges at T 0 according to the Curie-Weiss law
where C is the Curie constant and T > T 0, and the quadratic electro-optic Kerr coefficient R is related to ε according to
where ε 0 ≈ 8.854 × 10-12F m-1, ε is the relative permittivity of the material and the quadratic polarization-optic coefficient g is a material parameter that is mainly determined by the oxygen octahedron in perovskites and therefore is almost constant as a function of temperature and varies only by a factor of 2-3 in different perovskites.
Fig. 1. Relative permittivity of potassium sodium niobate tantalate thin film epitaxially grown on potassium tantalate substrate as a function of temperature and frequency. Black curve shows improved material quality of present film compared to the one from our previous study[10] (gray curve).
There are two main reasons why we didn’t use KNTN with a Curie temperature above room temperature which would allow us to exploit the larger linear electro-optic Pockels coefficient r: first of all, perovskites exhibit domains in the ferroelectric phase which require poling and might give rise to scattering losses. Secondly, the waveguide phase modulator presented in this paper relies on the simultaneous propagation of both TE and TM modes in the waveguide with similar properties, which is only possible in an optically isotropic material like cubic KNTN. For future applications, work has however been started to grow ferroelectric KNTN thin films on KT substrates doped with barium, which significantly increases the electric conductivity of the KT and allows it to be used as a bottom electrode for poling and to apply the electric field to induce the electro-optic effect.
Using the growth process already described previously [10], paraelectric thin films of KNTN of a few micrometers were grown in liquid-phase epitaxy (LPE) on cubic KT substrates of typically 1 cm × 1 cm × 0.2 cm dimensions. The material quality of the thin film could be significantly enhanced through optimization of the growth parameters, as substantiated in Fig. 1. The graph shows the relative dielectric permittivity of the thin films, measured with an HP 4192 impedance analyzer connected to interdigital electrodes deposited on the thin film surface. It can be seen that the present films (in black) show a phase transition temperature of Tc ≈ -10 °C and exhibit a much higher dielectric permittivity than the previous samples (in gray). The relative dielectric permittivity reaches ε = 4000 at the phase transition temperature and ε = 2100 at room temperature. As described later in this paper, the refractive index of the thin film material could also be noticeably increased. These improvements resolve the major limitation we addressed in the last article: the distinct difference in material properties between bulk and thin film KNTN.
Fig. 2. Cryostatic interferometer setup to measure the quadratic electro-optic coefficient R 11 of potassium sodium niobate tantalate bulk crystals. Low-frequency phase oscillations are compensated by an active phase control.
The quadratic electro-optic coefficient R 11 was measured in a bulk crystal of composition KNTN1 in a cryostatic interferometer setup (depicted in Fig. 2 and described in detail in [12]) in order to relate it to the values deduced from the modulator performance. Problems were encountered from low-frequency phase variations (probably emanating from local structural changes in the material) at cryogenic temperatures that impeded a stable fixation of the working point, but this could be compensated by an active phase control (APC). The temperature dependence of R 11 measured in the interferometer setup can be used to deduce the quadratic polarization-optic coefficient g 11 and the Curie temperature T 0 according to
Figure 3 displays the measured R 11 values, the least-squares error approximation of Eq. (3) with the fit values T 0 = -81.1 °C and g 11 = 0.17 m4 C-2 and the R 11 values calculated from dielectric permittivity measurements of our last publication, showing good agreement. The Curie constant of C = 5.8 × 104 K was also taken from the permittivity data of KNTN1. The wider divergence of the curve derived from the dielectric measurements can probably be explained by the following: a bigger part of the volume of the crystal contributes to the coefficient deduced from the dielectric permittivity when compared to the more local probing of the laser beam in the interferometer, leading to a somewhat diffused phase transition. A similar effect has been observed in the past when comparing phase transition curves measured with plate versus interdigital electrodes [10]. The value of g 11 = 0.17 m4 C-2 lies between the values reported by Geusic[13] (g 11 = 0.136 m4 C-2) and Buse[14] (g 11 =0.211 m4 C-2). Note that the bulk crystal was grown with the older composition and a lower phase transition temperature, but the composition dependence of g 11 given by Buse[14] allows us to adapt the results to the new composition and therefore the lengthy process of growing good quality bulk crystals of KNTN2 composition was not performed.
To summarize, we can say that quadratic electro-optic coefficients of R 11 ≈ 2.5 × 10-15 m2 V-2 at the phase transition temperature and up to R 11 ≈ 2×10-16m2 V-2 at T = T 0+30 °C, which corresponds to room temperature for our present films, are the upper limit set by the bulk values and are by any means high enough to justify the production of an electro-optic device.
Fig. 3. Quadratic electro-optic Kerr coefficient R 11 of potassium sodium niobate tantalate bulk crystal as a function of temperature. Black points represent values measured by the interferometer setup, solid black curve indicates Curie-Weiss law and solid gray curve represents R 11 calculated from dielectric permittivity data.
3. Waveguide production and characterization
With KNTN thin films of of composition KNTN2 and good optical quality and high Kerr coefficients at hand, the next step was the production of ridge waveguides and their characterization at room temperature. To this end, waveguides of nominal widths of 3,5,7,9 and 11 μm were structured into the commercial photoresist AZ6632 and then transferred to the KNTN thin film by argon ion etching. Scanning electron microscopy (SEM), atomic force microscopy (AFM) and optical microscopy pictures confirmed an etch depth of h = 3.4±0.1 μm. After polishing of the crystal facets, infrared light from a Santec TSL-210 laser at λ = 1579 nm was coupled into the waveguides using a microscope objective. The output of the waveguide was imaged with a 100 × objective onto a Sensors Unlimited SU320MX-1.7RT infrared InGaAs CCD camera. Figure 4 shows an overlay of the waveguide cross section of a 7 μm wide ridge, uniformly illuminated from the back, and the TE mode guided in the waveguide. The inset on the left depicts the simulation of the propagating mode and will be discussed later.
Fig. 4. Waveguide profile and TE mode intensity distribution of λ = 1579 nm laser light propagating in a potassium sodium niobate tantalate thin film ridge waveguide. Left inset shows simulated mode profile with excellent agreement to measurement.
Starting from a vertical cut through the intensity distributions of the guided TE and TM modes, we employed the profile reconstruction method described previously[10] to derive the thickness d of the film and the refractive index contrast Δn between KNTN film and KT substrate. The method works by solving the Helmholtz equation for guided modes as a function of the film thickness d and the refractive index distribution n(y), and minimizing error between the measured intensity distribution and the theoretical function using a least-square error algorithm. Since the width w = 7 μm of the waveguide is much larger than the wavelength λ = 1579 nm, the intensity distribution in y direction can be approximated by a guided slab mode. The result for a TE mode is shown in Fig. 5 and shows an excellent agreement. The parameters were determined to be d = 3.4 ±0.1 μm and Δn = (11.0 ± 1.5) × 10-3.
Fig. 5. Measured light intensity (gray circles) along a vertical (y) cross section of potassium sodium niobate tantalate thin film ridge waveguide on potassium tantalate substrate. Solid curve represents the best-fitting theoretical solution of the Helmholtz equation with thin film thickness d = 3.4 ±0.1 μm and refractive index contrast Δn = (11.0±1.5) × 10-3.
Both this refractive index contrast of Δn= (11.0±1.5) × 10-3 and the result of the dielectric permittivity measurement confirm that the present thin film has dielectric and optical properties almost on par with the bulk material. Figure 6 shows the dispersion curves of bulk KT and KNTN, and the thin film values of the last (at 633 nm) and the present (at 1579 nm) thin films, indicating that bulk values could almost be reached in present films.
Using the geometry and refractive index values as reported here, we performed a simulation of the propagating TE waveguide mode with the commercial OlympIOs software package[15]. The resulting mode intensity distribution is shown on the left side of Fig. 4, demonstrating excellent consistence between measurement and simulation.
Fig. 6. Refractive index dispersion of bulk potassium tantalate (light gray solid curve), bulk potassium sodium niobate tantalate (dark gray solid curve), and epitaxial potassium sodium niobate tantalate thin film (solitary points). The thin film refractive index at λ = 1579 nm is almost equal to the bulk value. All values measured at room temperature.
The propagation losses in the waveguide were estimated by imaging the scattered light along propagation of a guided TE mode at λ = 633 nm onto an Allied Dolphin F-145B 12 bit b/w CCD camera. Since the scattered intensity is proportional to the local power in the waveguide and the linearity of the optical system including the software was assured, the measured intensity as a function of propagation distance follows an exponential decay law with the loss coefficient α in the exponent. The result of this measurement is shown in Fig. 7 and yields propagation losses of 7.8±0.5 dB/cm for λ = 633 nm. Since scattering losses decrease with increasing wavelength, the propagation loss value for infrared wavelengths is believed to be smaller. The relatively high propagation losses can be attributed to the roughness of the etched sidewalls (rms roughness approximately 55 nm) and the high refractive index contrast at these interfaces. Possible measures to reduce the losses will be discussed in section 5. In terms of both propagation constants and losses, TE and TM modes are equal within the experimental error and no mode mixing was observed, which allows for the fabrication of a waveguide phase modulator.
4. Electro-optic phase modulator
Using the polarization-maintaining ridge waveguides described above, an integrated electro-optical phase modulator was created by depositing parallel electrodes on either side of a 7 μm wide waveguide. If light is coupled at an angle of 45° to the horizontal into the waveguide, both the TE and TM modes are excited inside the waveguide and propagate independently. By applying a voltage to the electrodes, the resulting electric field in the waveguide core shifts the phase of one polarization with respect to the other due to the electro-optic effect. This phase difference is converted into an amplitude change by an analyzer at the output. An additional compensator allows to set the working point of the modulator. A schematic of the setup is shown in Fig. 8. Microscope objectives were used to couple the light into and out of the waveguide. Electrodes consisting of 50 nm gold on top of 10 nm chromium (acting as adhesion promoter) were deposited on the thin film surface by standard photolithography processing, electron beam metal deposition, and a standard lift-off process. The distance between the electrodes is s = 16 μm, with the waveguide in the middle.
Fig. 7. Measured scattered light intensity at λ = 633 nm (gray curve) along propagation in potassium sodium niobate tantalate thin film ridge waveguide on potassium tantalate substrate. Exponential decay fit yields propagation losses of 7.8±0.5 dB/cm (black curve).
Fig. 8. Schematic of the setup used to characterize the potassium sodium niobate tantalate thin film ridge waveguide phase modulator working at λ= 1550 nm.
The half-wave voltage Vπ, defined as the voltage needed to switch the modulator from minimum to full intensity or vice versa, is the key figure of merit for a modulator and allows us to assert the electro-optic coefficient R values discussed earlier. Vπ was measured by adjusting the compensator to full darkness at the modulator output and then recording the transmitted light intensity as a function of the DC voltage applied to the electrodes. The resulting graph is shown in Fig. 9 and yields Vπ = 99 ±2 V at room temperature. Possible methods for reducing this value are discussed in section 5.
Fig. 9. Transmitted light intensity (y-axis) at λ = 1550 nm in potassium sodium niobate tantalate thin film ridge waveguide phase modulator as a function of DC voltage applied to parallel side electrodes (x-axis). Graph shows a half wave voltage of Vπ ≈ 100 V.
To calculate the electro-optic coefficient R, the strength of the electric field at Vπ = 100 V inside the waveguide core is needed. A Comsol Multiphysics model of the modulator cross-section was created (see Fig. 11) with the geometry and dielectric permittivity values obtained previously. The simulation shows that (1) the electric field is rather uniform in the waveguide core area with a value of Ex ≈ 0.7 × 106 V/m and (2) the horizontal component Ex of the electric field is about 40 times stronger than the vertical Ey. At Vπ, electric field strength and Kerr coefficients are related by
where λ = 1550 nm is the wavelength, l = 3.8 mm is the length of the electrodes and n = 2.18 is the effective mode index. In our case Ey ≪ Ex and thus, Eq. 4 is reduced to
Using Ex ≈ 0.7 × 106 V/m in the equation above yields R 11 ≈ 8.2 × 10-17m2/V2. This is about 40% of the expected bulk value and very high compared to other materials. Utilizing the following expression,
and the g 11 value obtained in section 2, which has been modified from the measured value of g 11 = 0.17 m4 C-2 for the previous composition to g 11 = 0.257 m4 C-2 for the present one according to the composition dependence given by Buse et al.[14], a relative dielectric permittivity of ε ≈ 2000 can be calculated and agrees well with the ε= 2100 measured directly. In terms of modulation speed, we were limited by the availability of amplifiers capable of generating the modulation voltage in the 100 V range. We demonstrate electro-optic modulation at f = 10 MHz as shown in Fig. 10, but since the material family of potassium tantalate niobate has proven its applicability in the GHz range[16, 17] in similar configurations, we have no reason to expect any fundamental limitation up to several GHz once the modulation voltage has been reduced by the methods described in the next section.
Fig. 10. Electro-optic modulation at f = 10 MHz in potassium sodium niobate tantalate thin film ridge waveguide phase modulator. Upper curve shows voltage applied to the side electrodes in units of half-wave voltage, lower curve shows detected light intensity.
5. Discussion
The fundamental suitability of epitaxial KNTN thin films on KT substrates for electro-optical integrated waveguide devices has been demonstrated and shows promising properties like high lateral index contrasts, allowing small devices, while maintaining excellent material interfaces and good optical surfaces. The relative dielectric permittivity and Kerr coefficients rank among the highest of all materials reported so far and all the limitations described in our previous publication[10] have successfully been addressed. However, to pave the way for real device use, two main restrictions have to be overcome: the half-wave voltage Vπ has to be diminished and the propagation losses have to be reduced. We will first discuss one approach to address both issues simultaneously and then discuss about additional measures individually. As stated in sections 3 and 4, the propagation losses mainly stem from the etched side walls of the waveguide, while the top surface is of good optical quality, and the half-wave voltage is on the order of 100 V due to the huge difference in the relative dielectric permittivity of the KNTN thin film (ε ≈ 2100) and the KT substrate (ε ≈ 240). Accordingly, we suggest a simple modification to the waveguide production process that will greatly improve both the loss and Vπ values: instead of etching ridges the full height of the thin film, the etch depth will be reduced to h = 1.4 μm, and 2 μm of the KNTN thin film will remain as a pedestal beneath the ridge. Simulations performed in OlympIOs ensure the continued monomodality of the ridge waveguide. The effects will be twofold: first of all, the propagating mode has much less interaction with the etched waveguide side walls, which reduces propagation losses and secondly, the electrodes now also reside on the thin film material which increases the electric field strength inside the waveguide core area. To illustrate this effect, both geometries were modelled in Comsol Multiphysics. The result is shown in Fig. 11 and indicates that in case (b) with shallower ridge waveguides, the electric field component Ex is 7 times stronger than in the present case (a) for the same voltage applied to the electrodes. Conversely, to achieve the same phase shift, the half wave voltage Vπ drops from 100 V to about 14 V. When also taking into account the electrode length l, the figure of merit Vπl of this suggested geometry is among the lowest values reported so far[16].
Fig. 11. Existing (a) and suggested (b) waveguide geometries to significantly reduce half-wave voltage in potassium sodium niobate tantalate thin film ridge waveguide phase modulator. Placing the electrodes on the thin film instead of on the substrate increases the electric field in the waveguide core by a factor of seven.
Other possible methods to reduce Vπ: (1) increasing the length of the waveguide and the electrodes, which may potentially increase device size, (2) biasing the modulator with a DC voltage, since Vπ decreases with a DC bias due to the quadratic electo-optic effect as demonstrated in Fig. 9, or (3) changing the material composition to shift the phase transition temperature closer to the operation temperature. In regards to reducing the losses, the etching process itself can be further optimized, or the waveguide could be covered with a thin layer, SiO2 or Si3N4 for example, to reduce the surface roughness, though it is difficult to estimate the amount of loss reduction that would be achievable by these means.
6. Conclusion
Electro-optic modulation in paraelectric epitaxially grown KNTN thin films on KT substrates at λ = 1550 nm has been reported here for the first time to the best of our knowledge, exploiting a thin film Kerr coefficient of (8.2 ± 1.1) × 10-17 m2/V2. While rather simple measures will allow for a decrease in both propagation losses and the half-wave voltage of the demonstrated ridge waveguide phase modulator, this achievement already constitutes an important step towards more sophisticated integrated optics devices, such as Mach-Zehnder modulators or cross-switches, that utilize the outstanding dielectric and electro-optic properties of the KTN material family.
Acknowledgments
We thank Jaroslav Hajfler for the expert polishing of the waveguide facets, Max Döbeli for the RBS measurements and Shanmugam Aravazhi for the bulk crystals. This work was in part supported by the TH project “Electro-optical Microring Resonators for Photonic Applications”, TH13/05-2.
References and links
1. F. S. Chen, J. E. Geusic, S. K. Kurtz, J. G. Skinner, and S. H. Wemple, “Light Modulation and Beam Deflection with Potassium Tantalate-Niobate Crystals,” J. Appl. Phys. 37, 388 (1966). [CrossRef]
2. S. Triebwasser, “Study of Ferroelectric Transitions of Solid-Solution Single Crystals of KNbO3-KTaO3,” Phys. Rev. 114, 63–70 (1959). [CrossRef]
3. R. Gutmann, J. Hulliger, and H. Wuest, “Growth of Paraelectric and Ferroelectric Epitaxial Layers of KTa1-xNbxO3 by Liquid-Phase Epitaxy,” Ferroelectrics 134, 291–296 (1992). [CrossRef]
4. R. Gutmann, J. Hulliger, and E. Reusser, “Liquid-Phase Epitaxy of Lattice-Matched KTa1-xNbxO3 Grown on KTaO3 Substrate,” J. Cryst. Growth 126, 578–588 (1993). [CrossRef]
5. H. Pierhofer, Z. Sitar, F. Gitmans, H. Wuest, and P. Gunter, “New semiconducting substrate for heteroepitaxial growth of K1-yNayTa1-xNbxO3,” Ferroelectrics 201, 269–275 (1997). [CrossRef]
6. L. A. Knauss, K. S. Harshavardhan, H. M. Christen, H. Y. Zhang, X. H. He, Y. H. Shih, K. S. Grabowski, and D. L. Knies, “Growth of nonlinear optical thin films of KTa1-xNbxO3 on GaAs by pulsed laser deposition for integrated optics,” Appl. Phys. Lett. 73, 3806–3808 (1998). [CrossRef]
7. S. Toyoda, K. Fujiura, M. Sasaura, K. Enbutsu, A. Tate, M. Shimokozono, H. Fushimi, T. Imai, K. Manabe, T. Matsuura, and T. Kurihara, “Low-driving-voltage electro-optic modulator with novel KTa1-xNbxO3 crystal waveguides,” Jpn. J. Appl. Phys. 43, 5862–5866 (2004). [CrossRef]
8. K. Nakamura, J. Miyazu, M. Sasaura, and K. Fujiura, “Wide-angle, low-voltage electro-optic beam deflection based on space-charge-controlled mode of electrical conduction in KTa1-xNbxO3,” Appl. Phys. Lett. 89, 131115-1–131115-3 (2006).
9. H. Y. Zhang, X. H. He, Y. H. Shih, K. S. Harshavardhan, and L. A. Knauss, “Optical and nonlinear optical study of KTa0.52Nb0.48O3 epitaxial film,” Optics Letters 22, 1745–1747 (1997). [CrossRef]
10. C. Herzog, S. Aravazhi, A. Guarino, A. Schneider, G. Poberaj, and P. Gunter, “Epitaxial K1-xNaxTa0.66Nb0.34O3 thin films for optical waveguiding applications,” J. Opt. Soc. Am. B 24, 829–832 (2007). [CrossRef]
11. R. Gutmann, “Liquid phase epitaxy of para- and ferroelectric KTa1-xNbxO3,” Ph.D. dissertation (ETH Zurich No. 10095, 1993).
12. C. Herzog, G. Poberaj, and P. Gunter, “Electro-optic behavior of lithium niobate at cryogenic temperatures,” submitted to Opt. Commun. (2007).
13. J. E. Geusic, S. K. Kurtz, L. G. Vanuitert, and S. H. Wemple, “Electro-Optic Properties of Some ABO3 Perovskites in Paraelectric Phase,” Appl. Phys. Lett. 4, 141 (1964). [CrossRef]
14. K. Buse, F. Havermeyer, L. Glabasnia, K. Schlomp, and E. Kratzig, “Quadratic polarization-optic coefficients of cubic KTa1-xNbxO3 crystals,” Opt. Commun. 131, 339–342 (1996). [CrossRef]
15. http://www.c2v.nl/fr_index.shtml?/products/software/olympios-software.shtml
16. K. Fujiura and K. Nakamura, “KTN optical waveguide devices with an extremely large electro-optic effect,” in Passive Components and Fiber-Based Devices, Pts 1 and 2, Y. Sun, S. S. Jian, S. B. Lee, and K. Okamoto, eds., vol. 5623 of Proceedings of the Society of Photo-Optical Instrumentation Engineers (Spie), pp. 518–532 (2005). Conference on Passive Components and Fiber-based Devices NOV 09-11, 2004 Beijing, PEOPLES R CHINA.
17. T. Itoh, M. Sasaura, S. Toyoda, K. Manabe, K. Nakamura, and K. Fujiura, “High-frequency response of electro-optic single crystal KTaxNb1-xO3 in paraelectric phase,” Conference on Lasers and Electro-Optics 2005, paper JTuC36, Baltimore, USA (May 2005).
