1. Introduction

Local Ti⁴⁺ doping in LiNbO₃ (LN) crystal induces increase of refractive index and hence formation of optical waveguide. Since the first Ti⁴⁺ in-diffused LiNbO₃ (Ti:LN) waveguide was reported by Schmidt and Kaminow at Bell Lab [1], the waveguide has become a fundamental unit of various LN-based passive and active waveguide devices. The waveguide is of the merits of lower waveguide loss, higher thermal, electric and chemical stabilities, easily realizing rare-earth doping and retained crystalline phase. Over the past years, people has realized various types of (nonlinear) integrated optical devices on the basis of Ti:LN waveguide [2]. By utilizing the excellent electro-optic (EO) property of LN, various passive and active EO devices have been demonstrated. The passive EO devices include high-speed switch, phase/intensity modulator, TE/TM mode converter, directional coupler, Y-branch or Mach-Zehnder interferometer [2, 3] and optical filter based on EO-modulated long period waveguide grating [4]. The active EO devices concern pulsed, mode-locked, and Q-switched Ti:Er:LN waveguide lasers [5–7]. An important issue concerning these EO devices is the precise knowledge about the EO coefficients of LN. It is unclear if the Ti dopant affects the EO property of LN, and if so, it is crucial to know what is the relation to the Ti doping concentration. It is interesting and essential to carry out a systematic study on Ti doping effect on the EO property of LN. Present work aims at this aspect of study. Both clamped and unclamped EO coefficients γ₃₃ and γ₁₃ of a series of bulk Ti-doped congruent LN crystals with different doping concentrations in crystal, up to ~12 mol%, were measured by Mach-Zehnder interferometry. The coefficients are correlated with Ti⁴⁺ concentration, allowing to identify the effect of the Ti⁴⁺ doping concentration.

2. Experimental description

By using the top-seeded solution method, a series of Ti-doped LN crystals used for present study were pulled in air from the congruent melts containing different TiO₂ concentrations of 1.2, 4.0, 6.0, 10.0, 13.0 and 16.0 mol%. A detailed description for sample preparation and determination of Ti⁴⁺ doping concentration has been given in [8]. Table 1 brings together the Ti⁴⁺ concentration in each studied crystal.

Table 1. Summary of Ti⁴⁺ concentration in growth melt/crystal, interaction length (L) between applied electric field and light wave propagated in crystal, spacing d of electrodes, and the EO coefficients γ₃₃ and γ₁₃ in both cases of clamped and unclamped measurements (data in the parentheses correspond to the clamped case).

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The EO coefficients γ₃₃ and γ₁₃ were measured by Mach-Zehnder interferometric method. Figure 1 shows the schematic of measurement principle. An He-Ne laser was used as the light source. To minimize the photorefractive and photovoltaic effects on the measurement, a low light intensity of ~10² W/m² was used (too low working intensity results in poor resolution of interference fringe). After spatial filtering by a pinhole, the beam was polarized and split into two beams by a splitter. One beam, as the signal arm, impinges onto an X-cut sample plate to be measured along the direction parallel to the Y axis of the crystal [An X-Y-Z Cartesian reference frame with Z axis parallel to the optical axis c of crystal is shown in Fig. 1]. Another beam acts as the reference arm. To balance the intensities of the two interferometer arms and hence increase the contrast of the interference fringes, the reference beam was attenuated appropriately. The phase of the light wave propagated in the crystal was modulated by applying a DC voltage along the direction parallel to the optical axis c of the crystal. Both clamped and unclamped EO coefficients were measured. In the case of clamped measurements, the voltage was applied to the crystal through the 150 nm thick Al films directly coated onto the two Z-surfaces of the crystal. In the case of unclamped measurements, the crystal was positioned in an electric field formed by a pair of external Cu slab electrodes (with a dimension of X × Y × Z = 40 × 50 × 0.5 mm³) as shown in Fig. 1. The signal and reference beams were recombined by another beam splitter. The recombination generates the interference fringes. After magnified by a lens, the interference pattern was projected onto a viewing screen. The zero-order fringe in the central part of the interference pattern was monitored as a DC voltage was applied to the electrodes. From the bright-dark variation of the zero-order fringe one can obtain the half-wave voltage V_π. Based on the interference condition, one can evaluate the EO coefficient γ₃₃ = λd/(Ln_e³V_π) and γ₁₃ = λd/(Ln_o³V_π), where λ is the working wavelength, d is the spacing of the two Cu slab electrodes in the case of unclamped measurements and is the separation of the two Z-surfaces of sample plate in the case of clamped measurements, n_e and n_o are the extraordinary andordinary refractive indices, respectively, and L is the interaction length between the electric field and the light wave propagated in the crystal and is actually the sample dimension along the Y axis. Table 1 summarizes the values of the parameters d and L for each sample to be measured. All of the measurements were carried out at room temperature 25 ± 0.5 °C. For comparison, the measurements were also performed on a Z-cut pure congruent LN plate. At a fixed Ti⁴⁺ doping concentration, the EO coefficient γ₃₃ or γ₁₃ was given as a result of the average over 20 measurements of V_π.

 

Fig. 1 Schematic of Mach-Zehnder interferometer for measuring the EO coefficients of Ti⁴⁺-doped LNs.

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3. Results and discussion

First of all, the accuracy of the measurement system was examined. It was done by using the system to measure a pure congruent crystal and comparing the result with those values reported in the literatures [9–12]. The physical and optical properties of congruent pure LN reported by Gooch & Housego Inc. (original Crystal Technology Inc.) show that the EO coefficients γ₃₃ (γ₁₃) @632.8 nm wavelength is 33 (10) pm/V in the unclamped case and 31 (9) pm/V in the camped case, but without the error specified [9]. In parallel, Cabrera group [10, 11] and Kitamura group [12] have also reported respectively the unclamped and clamped EO coefficients of the pure congruent LN. The Spain group has reported that the unclamped γ₃₃ is 31.5 ± 0.3 pm/V and γ₁₃ is 10.5 ± 0.1 pm/V @632.8 nm wavelength [10, 11]. The Japanese group has reported that the clamped γ₃₃ is 31.5 ± 1.4 pm/V and γ₁₃ is 10.0 ± 0.8 pm/V @632.8 nm wavelength [12]. Our measurement shows that in the unclamped case γ₃₃ = 33.0 ± 0.8 pm/V and γ₁₃ = 10.4 ± 0.3 pm/V, and in the clamped case γ₃₃ = 31.0 ± 0.8 pm/V and γ₁₃ = 10.0 ± 0.3 pm/V. By taking into account all of the possible factors (errors arising from the measurements of d, L and V_π), our data have an error of ± 3%. One can see that our results can be thought as identical to those reported previously within the error for both clamped and unclamped cases.

Next, attention is paid to the photorefractive effect on the measurement result. It is well known that the LN crystal suffers from serious photorefractive damage in visible and near infrared regions. As the photorefractive effect is actually caused by the electro-optic effect of the crystal, it is unclear if the photorefractive effect influences the experimental results under the working light intensity adopted in the measurements. So, here we exemplify the undoped congruent LN to demonstrate the working light intensity and hence the photorefractive effect on the EO coefficients. Figure 2 shows the clamped EO coefficients γ₃₃ (red balls) and γ₃₁ (green balls) measured as a function of 632.8 nm light intensity in a congruent LN crystal. The light intensity changes over three orders of magnitude. We can see that the EO coefficients hardly change as the working light intensity is below 10² W/m². Higher than 10² W/m², both coefficients reveal an increase tendency due to the photorefractive effect. This isexpected from the above-mentioned expressions for γ₃₃ and γ₃₁. The photorefractive effect induces the decrease of refractive index and the corresponding increase of half-wave voltage. In case of without considering the photorefractive effect on the refractive index, the EO coefficient is over-predicted from the measured half-wave voltage. As the light intensity in our measurements was 10² W/m², the optical damage should not take an effect on the result. In words, the EO coefficients measured using our system are convincing.

 

Fig. 2 Clamped EO coefficients γ₃₃ (red balls) and γ₁₃ (green balls) measured as a function of 632.8 nm light intensity in a congruent LN crystal.

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The clamped and unclamped EO coefficients γ₃₃ and γ₁₃ measured from the LNs doped with different Ti⁴⁺ concentrations are collected in Table 1 for reader’s convenience. The data in the parentheses show the clamped coefficients. To more clearly show the dependence of the EO coefficients on the Ti⁴⁺ doping concentration, the results are also illustrated in Fig. 3. Error bar is indicated for each plot. The red balls represent the clamped case and the green balls denote the unclamped case. It can be seen that both γ₃₃ and γ₁₃ reveal a degradation tendency with a rise in Ti⁴⁺ concentration and this is the case for both the clamped and unclamped coefficients. Nevertheless, the degradation is only slight for both cases of γ₃₃ and γ₁₃. In the clamped case (see the red ball plots), both γ₃₃ and γ₁₃ reveal a similar degradationdependence on the Ti⁴⁺ concentration. We note that both decrease by 6% as the Ti⁴⁺ concentration is increased from zero to 12 mol%. The decrease is definitely larger than the error 3%. The degradation is relatively obvious in the unclamped case. The γ₃₃ reduces by 13% and γ₁₃ by 14% as the Ti⁴⁺ concentration is increased from zero to 12 mol%.

 

Fig. 3 Clamped (red balls) and unclamped (green balls) EO coefficients (a) γ₃₃ and (b) γ₁₃ measured as a function of Ti⁴⁺ doping concentration in LN crystal.

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In conclusion, both γ₃₃ and γ₁₃ reveal a degradation tendency with a rise in Ti⁴⁺ concentration. This is the case for both the clamped and unclamped coefficients. Nevertheless, the degradation is no more than 15% for the considered Ti⁴⁺ concentration up to 12 mol%, which is about two times higher than that of typical single-mode LN devices used in the near infrared spectral region, ~6 mol% [5, 6]. Similar small effect was also reported by Holmes et al. [16], who have investigated just one LN sample doped with 3 mol% Ti⁴⁺ and did not observe noticeable change of both γ₃₃ and γ₁₃ too. In addition, the small effect is also consistent with the previous results that the performance of an electro-optic device based on the Ti⁴⁺-diffused LN waveguide is not influenced noticeably by the Ti⁴⁺ dopants, and the voltage used to drive an EO device based on the Ti⁴⁺-diffused LN waveguide, such as the phase modulator, is usually only a few volts.

Next, we try to give a comprehensible explanation for the small effect. Over the past years, researchers have studied the EO properties of LNs doped with Hf⁴⁺ [13], Er³⁺ [14], Mg²⁺ [15, 16], Zr⁴⁺ [17], Cr³⁺ [18, 19], Fe³⁺ [20], Zn²⁺ [21], H⁺ [22, 23], and the doping effect on the EO properties was qualitatively explained from the viewpoint of doping effect on the defect structure. In contrast, Fontana group has done more work on the subject [13], [18–21] and given more consideration on explaining the doping effect [19, 21]. They extended the general model for the EO coefficient of an inorganic crystal to the LN, and concluded that among the three possible contributions (piezo-optic effect, ionic and electronic contributions) the ionic contribution plays in a predominant role in the doping effect on the EO coefficient of LN [19]. It was suggested that the EO properties of LN originate from the deformation and polarizability of NbO₆ and LiO₆ clusters, and two processes mainly contribute to the EO effect: the deformability of the oxygen octahedron around Li ion (process 1) and the ionic and electronic polarizabilities of Nb ion (process 2). Each process can change with the contents of Nb antisites and Li ions in the crystal. In the doped LN, the role of dopant in the EO properties is related to its influence on the contents of Nb antisite and Li ion. Because the dopants are incorporated into either the Li or Nb sites, the EO properties are governed by process 1 in the former case while by process 2 in the latter case. Different dopants have different circumstances of site occupancy, cause different contributions of processes 1 and 2, and hence different change extents of EO coefficients. It is thus comprehensible that some dopants such as Cr³⁺ [18], Zn²⁺ [21] and H⁺ [22–25] cause relatively large change of EO coefficients (so does the alteration of crystal composition [18]) while other dopants such as Hf⁴⁺ [13], Er³⁺ [14], Mg²⁺ [15, 16], Zr⁴⁺ [17], Fe³⁺ [20], as well as the Ti⁴⁺ studied here have relatively weak effect. Regarding the Ti⁴⁺-doping case, the Ti⁴⁺ ions are incorporated into both Li and Nb lattice sites [26]. Processes 1 and 2 simultaneously play a role, and it is possible that the doping has a relatively weak effect.

It is worthwhile to mention that the explanation depicted above is only qualitative, not so evident and intuitive. Actually, the EO properties of LN can be simply ascribed to two competitive mechanisms, i. e., the non-stoichiometric intrinsic defects and the ordering of the lattice structure, which mainly act on the congruent composition side and the stoichiometry side, respectively. Speaking more simply, the EO properties of LN is related to the extent of lattice distortion induced by crystal composition alteration and/or doping. The larger the extent of lattice distortion is and the more serious the degradation of EO coefficient is. Here, we exemplify the proton-exchange (PE) LN waveguide to demonstrate it. It is well known that the PE process results in serious degradation of EO coefficient of LN, by as much as 90% [22–25]. This is because a PE waveguide layer consists of many sub-layers with different crystalline phases, depending on the H⁺ concentration. Only a small part of PE layer which has extremely low H⁺ concentration retains the LN phase while most part of the layer is not in the LN phase. To recovery the LN phase, some measures, such as post annealing and use of lithium-benzoate-diluted PE source, have been taken to largely degrade the H⁺ concentration in the waveguide layer and render it be in α crystalline phase. The layer in the α crystalline phase has very low H⁺ concentration and hence retains the LN phase and crystal structure. Because of the little lattice distortion, the EO property of the waveguide in the α phase is thus preserved essentially. In summary, at the lower H⁺ concentration the lattice distorts slightly, the LN phase and crystal structure retain, and the degradation of EO property is slight. At the higher H⁺ concentration, the crystalline phase in most part of waveguide layer is not the LN phase, it is thus comprehensible that the EO property degrades by as much as 90%. In this way, one can readily understand the Ti⁴⁺-doping effect. Because Ti⁴⁺-doping does not change the crystalline phase and crystal structure, it is thus reasonable that the doping effect on the EO property is slight. As the lattice distortion increases with the doping concentration, it is thus comprehensible that the EO property degrades with a rise in doping concentration.

In addition, as mentioned above, the clamped and unclamped EO coefficients show definite discrepancy. This is the case for either the pure or Ti⁴⁺-doped LN. The difference should be associated with the homogeneity of applied external electric field. In the unclamped case, the dimension of the sample to be measured (< 13.4 × 5.8 mm²) is much smaller that of the Cu slab electrodes (40 × 50 mm²). This implies that in this case the samples are in a more homogeneous electric field environment. Instead, in the clamped case, the sample size is the same as that of the Al-metal films directly coated onto the sample. In this case, the electric field strength at the edge of sample is considerably weaker than that at the central part of sample. The different field homogeneities of the clamped and unclamped measurements result in different half-wave voltages and hence different EO coefficients.

4. Conclusion

We have demonstrated Ti⁴⁺-doping effect on electro-optic property of LiNbO₃ single crystal. The experimental results show that both γ₃₃ and γ₁₃ reveal a degradation tendency with the increase of Ti⁴⁺ concentration in both cases of clamped and unclamped measurements. Nevertheless, the degradation is no more than 15% for the considered Ti⁴⁺ concentration up to 12 mol%. The little effect is consistent with the previous experimental result that the performance of an electro-optic device based on Ti⁴⁺-diffused LiNbO₃ waveguide is not influenced noticeably by the Ti⁴⁺ dopants. The effect is qualitatively explained on the basis of the EO coefficient model of LN and the doping effect on the defect structure of LN. A more comprehensible explanation is given from the viewpoint of the lattice distortion extent induced by doping.