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We accurately measure the electro-optic (EO) coefficients of undoped and 1.7 mol% MgO-doped stoichiometric LiNbO3 (SLN) using high-quality crystals and a reliable AC-field applying method. The EO coefficients at the wavelength of 633 nm are determined to be r33 = 30.2 ± 0.6 pm/V and r13 = 9.1 ± 0.2 pm/V for undoped SLN, and r33 = 29.8 ± 0.2 pm/V and r13 = 9.1 ± 0.04 pm/V for MgO-doped SLN. The obtained values are found to be nearly the same with those for congruent LiNbO3.
© 2017 Optical Society of America
1. Introduction
LiNbO3 (LN) is one of the most popular electro-optic (EO) crystals which has been widely used as optical modulators and optical switches. Congruent LN (CLN), in which Li: Nb = 48.5: 51.5, has been conventionally used because of its optical homogeneity. On the other hand, stoichiometric LN (SLN) with the ratio Li: Nb = 50: 50, has been recently grown in large sizes with high quality by use of the double crucible Czochralski (DCCZ) method [1], and its various superior properties have been reported to date, including shorter absorption edges [2], lower coercive fields [3], and higher photorefractive damage threshold with lower MgO concentration than CLN [4].
However, EO coefficients of SLN, which are essential for designing various EO devices, have not been determined because large discrepancies exist between the previously reported values as shown in Table 1. Especially, the value of r33 measured by Fujiwara et al. is 20% larger than that of CLN [5], while the value of r33 obtained by de Toro et al. is smaller than that of CLN [6]. Although Fujiwara et al. used a high-homogeneity crystal grown with the DCCZ method, they applied a DC electric field to the crystal which might cause a large errors in measured r values. On the other hand, de Toro et al. developed a reliable method using an AC field, but the quality of the crystal, which was grown with the flux method, is unknown. High homogeneity of crystals is essential because large crystals are usually used for the measurements of EO coefficients.
Table 1. Previously reported EO coefficients of SLN and CLNa
It is important to accurately determine the EO coefficients for designing various EO devices using SLN even if they are larger, smaller, or the same with those of CLN. In this work, we performed accurate measurements using high-homogeneity crystals grown with the DCCZ method as well as a newly developed AC-field applying method. We determined the EO coefficients, r33 and r13, of undoped and 1.7% MgO-doped SLN at the wavelength of 632.8 nm.
2. Measurement method
The measured SLN samples were grown at Hitachi Metals, Ltd., the sizes of which were 9 mm (// X) x 10 mm (// Y) x 9 mm (// Z). Both the Z-surfaces were coated with the gold electrodes, while the input and output faces (Y-planes) were optically polished. We also measured for undoped CLN for comparison.
The measurement system was based on a Mach-Zehnder interferometer, which is shown in Fig. 1. A He-Ne laser beam (λ = 632.8 nm) was collimated and polarized parallel to the Z-axis of the sample for the measurement of r33, and to the XY-plane for the measurement of r13. The sample was placed in one branch of the interferometer with the Y-plane as the input face, and tilted by 29.0° ± 0.3° from the normal incidence to suppress the influence of multiple reflections in the sample. The modulated voltage of Vm sinΩt, which was generated from a lock-in amplifier (NF, LI5640) and amplified with a high-voltage power amplifier (TREK, 609E-6), was applied parallel to the Z-axis of the sample which induced the dynamic phase shift by the EO effect. The modulation frequency Ω was set to be 1 kHz. On the other hand, the optical-path length of the other branch was changed by a movable mirror mounted on a piezo stage (Thorlabs, NF15AP25), which caused the static phase shift, Δδ 0.
The intensity of the interference was detected with a photomultiplier tube (Hamamatsu, R943-02) after the two beams from each branch were overlapped with a half mirror and expanded with a lens. Although only a portion of the expanded beam passing through a pinhole was detected, the phase difference between the two beams was shifted within the cross section of the pinhole, which made the extinction ratio of the interference intensity low. This is shown in Fig. 2, which is the interference pattern when the movable mirror was displaced without applying the modulated voltage to the sample. The magnitude of the shift of the phase difference, Δϕ, was estimated to be 0.075 rad from the extinction ratio of this interference pattern.
The intensity of the interference is then given by
as the average of the intensity at each position of the detected beam over Δϕ, where I1 and I2 are the intensity of the branches 1 and 2 (they were set to be the same intensity), respectively. Vπ is the half-wave voltage which is defined byfor the extraordinary and the ordinary rays, respectively, where zs is the sample height, and ys(e) and ys(o) are the optical path lengths in the samples through which the extraordinary and the ordinary beams pass, respectively. ne and no are the extraordinary and the ordinary refractive indices, respectively, which we measured using the minimum deviation method with the accuracy of better than 1 x 10−4 [7]. Table 2 shows those values. d32 ( = −0.86 ± 0.02 pm/V for CLN [8]) is the piezo-electric coefficient, and we assumed that the undoped and MgO-doped SLN have the same value. It is noted that even the error of 10% in the d32 value would change the value of r by only 0.07%.Table 2. Refractive indices of LN at 632.8 nm
Equation (1) can be expanded using the Bessel functions, so that the fundamental and second-harmonic components of the interference intensity oscillating at the frequency Ω and 2Ω under the modulated voltage Vm sinΩt can be written as
Respectively. Here, J1 and J2 are the first and the second-order Bessel functions, respectively. We obtained the values of |ΔIΩ| and |ΔI2Ω| by the lock-in amplifier. Then the ratio of the amplitudes of |ΔIΩ| and |ΔI2Ω|,can be experimentally obtained without any influence of fluctuations of the laser power (about ± 3%) and the shift of the phase difference within the detected beam because (6) does not contain I1, I2, and Δϕ anymore, although the interference signal in Fig. 2 is affected by the power fluctuation. The values of Vπ(33) and Vπ(13) are then obtained and finally the r33 and r13 values are determined by use of (2) and (3), respectively.3. Experimental results
Figure 3(a) shows, as an example, the dependence of the fundamental and the second-harmonic components, |ΔIΩ| and |ΔI2Ω|, for r33 (undoped SLN) on the displacement of the movable mirror, i.e., the static phase shift Δδ 0, at the applied voltage Vm = 700 V. On the other hand, Fig. 3(b) shows those for r13 (undoped SLN) at Vm = 900 V. The experimental data and the theoretical fitting curves are in good agreement. These measurements were carried out from Vm = 200 to 1000 V. The obtained amplitude ratio between the fundamental and the second-harmonic components, ΔI2Ω, m / ΔIΩ, m, as a function of the applied voltage Vm is shown in Fig. 4, from which and (6), the half-wave voltages were obtained: Vπ(33) = 1763 ± 30 V and Vπ(13) = 5049 ± 86 V. The EO coefficients r33 and r13 of undoped SLN were then determined to be 30.2 ± 0.6 and 9.1 ± 0.2 pm/V, respectively.
Fig. 3 Dependence of the fundamental and the second-harmonic components on mirror displacement for (a) r33 (undoped SLN) at Vm = 700 V and (b) r13 (undoped SLN) at Vm = 900 V.
Fig. 4 Ratio of second-harmonic to fundamental components as a function of the applied voltage for undoped SLN and undoped CLN.
We used two samples for each measurement to check the reproducibility, and the obtained values were the same within the experimental accuracy. The main factors which determine the experimental accuracy are the measurement errors of the amplitudes ΔIΩ, m and ΔI2Ω, m. They cause the error in the obtained half-wave voltages, Vπ, by 1.7%. Other factors include the piezo-electric coefficient, the crystal lengths, the optical path lengths in the samples, and so on, the total error of which is estimated to be less than 0.2%. The overall accuracy is then less than 2%.
On the other hand, the fundamental and second-harmonic components as a function of the static phase shift for r33 and r13 of 1.7% MgO-doped SLN are shown in Figs. 5(a) and 5(b), respectively. The experimental data and the theoretical fitting curves are in good agreement. These measurements were also carried out from Vm = 200 to 1000 V. The obtained amplitude ratio between the fundamental and the second-harmonic components, ΔI2Ω, m / ΔIΩ, m, as a function of the applied voltage Vm is shown in Fig. 6. The EO coefficients r33 and r13 of 1.7% MgO-doped SLN are determined to be 29.8 ± 0.6 and 9.1 ± 0.2 pm/V, respectively.
Fig. 5 Dependence of the fundamental and the second-harmonic components on mirror displacement for (a) r33 (1.7% MgO-doped SLN) at Vm = 600 V and (b) r13 (1.7% MgO-doped SLN) at Vm = 700 V.
Table 3 summarizes the obtained values for undoped SLN, CLN and 1.7% MgO-doped SLN. The values of CLN agreed well with the standard values [9]. The r33 and r13 values of SLN were found to be nearly the same with those of CLN. The EO coefficients of 1.7% MgO-doped SLN were also found to be nearly the same with those of undoped SLN and CLN within the accuracy of the measurement. It has been reported that the differences of refractive indices of undoped and MgO-doped SLN and CLN are less than 1% [7], and that the second-order nonlinear-optical coefficients of undoped and MgO-doped SLN also agree with those of undoped CLN in the experimental accuracy (less than 5%) [10]. We suppose that this means 5% difference of the Li/Nb ratio between SLN and CLN and 1.7% inclusion of MgO have little influence on the macroscopic optical properties, and this also applies to the EO coefficients of SLN and CLN. However, SLN has an advantage that it is easier to fabricate periodically poled structures owing to its lower coercive field than CLN, so that more sophisticated devices, in which both a wavelength converter and an EO modulator are incorporated into one substrate, for example, can be fabricated using SLN. An EO device operating at wavelengths around 350 nm is also one of the applications for SLN because of its 10 nm shorter absorption edge than CLN. Then it is necessary to measure the EO coefficients at shorter wavelength region.
Table 3. EO coefficients at 632.8nm determined in this work (pm/V)
4. Conclusion
We have accurately determined the EO coefficients r33 and r13 of undoped SLN and MgO-doped SLN using high-quality samples combined with a reliable measurement method. We found that the EO coefficients of undoped and 1.7 mol% MgO-doped SLN are nearly the same with those of CLN within the accuracy of the measurement.
The measurements of the wavelength dependence of the EO coefficients including shorter wavelength region are now undertaken.
References and links
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