1. Introduction

LiNbO₃ (LN) is an important optical material for (nonlinear) integrated optics. Its excellent electro-optic, acousto-optic, and nonlinear optical properties, together with the possibility of using well-established technique to produce high-quality waveguide of low loss, have led to the development of high functionality devices and optical integrated circuits. However, the these devices suffer from serious photorefractive damage. Besides Mg²⁺ [1], some other optical-damage-resistant dopants have been reported. These include divalent Zn²⁺ [2], trivalent Sc³⁺ [3,4], Tm³⁺ [5] and In³⁺ [6], and tetravalent Hf⁴⁺ [7], Zr⁴⁺ [8,9] and Sn⁴⁺ [10]. Among them, Sc³⁺ doping requires a relatively low optical-damage-resistant threshold concentration C_th = 2 mol% for an LN with a Li₂O content of 48.5 mol%, and the threshold is about 2.5 times lower than that of Mg²⁺ doping, ~5 mol%. Moreover, as the composition approaches the stoichiometry, the threshold lowers to 0.4 mol% [4]. Low threshold of optical-damage-resistant dopants is required to improve the material homogeneity and the optical quality of crystal when codoped with rare-earth ions, such as Er³⁺, and to increase the diffusivity and solid solubility of codoped rare earth ions. In addition, a near-stoichiometric (NS) LN displays some properties better than the congruent material, such as larger electro-optic and nonlinear coefficients, lower coercive electric field needed for periodical poling of ferroelectric microdomain. Ti⁴⁺ diffused LN (Ti:LN) waveguide is a basic unit of LN-based passive and active 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. An NS Ti:LN doped with Sc³⁺ (Ti:Sc:LN) would be a promising component for developing various optical-damage-resistant active or passive devices. The realization of the NS Ti:Sc:LN waveguide would open up some new applications and construct a supporting platform for the development of related active and passive devices. Towards such a long-term goal, we should firstly demonstrate how to fabricate an NS Ti:Sc:LN single-mode strip waveguides. Seeing that a Sc³⁺-doped LN plate is attained not as easily as an undoped one, as an alternative, Sc³⁺ can be incorporated into the crystal by thermal diffusion method. A congruent Ti:Sc:LN strip waveguide can be fabricated at first by Ti⁴⁺ diffusion following Sc³⁺-diffusion-doping in an initially congruent LN substrate. The two-step process considers that Sc³⁺ diffuses definitely slower than Ti⁴⁺ [11, 12] and its profile must entirely cover the waveguide to satisfy the optical-damage-resistant demand. After Ti⁴⁺ diffusion, post Li-rich vapor transport equilibration (VTE) is carried out to bring the waveguide to an NS composition. In the previous work, Sc³⁺ diffusion properties [13] and Ti⁴⁺/Sc³⁺ co-diffusion characteristics [12] have been studied. Here, we demonstrate the fabrication and characterization of an NS Ti:Sc:LN strip waveguide.

2. Experimental description

The NS Ti:Sc:LN waveguide was fabricated starting from a congruent LN with a technological process in sequence of Sc³⁺ diffusion doping, Ti diffusion and post Li-rich VTE. Figure 1(a) depicts the fabrication procedure of the waveguide.

 

Fig. 1 (a) Fabrication procedure, (b) image, and (c) near-field patterns of TE and TM modes at 1547 nm wavelength of 8-μm-wide NS Ti:Sc:LN strip waveguide.

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The sample surface can be divided into three parts: undoped area, Sc³⁺-only doped part and Sc³⁺/Ti⁴⁺-diffused array waveguide part. After each annealing stage, the surface refractive index at the three surface parts were measured. On the surface part with the waveguide array, the measurements were carried out by aligning the light beam perpendicular to the strip waveguide axis to avoid the excitation of waveguide mode, which may affect the result. The refractive index was measured at the 1553 nm wavelength using a Metricon 2010 prism coupler. Both ordinary and extraordinary indices were measured.

The near-field mode was measured by endface butt-coupling technique. A polarized light emitted from a 1547 nm single-frequency laser was coupled into the waveguide via endface butt-coupling between a section of polarization-maintaining fiber and a channel waveguide. The magnified near-field image of guided mode was projected onto an infrared Hamamatsu digitizing video camera (Vidicon 1000) through a Nikon microscopic objective lens.

The surface and/or depth profiles of diffused Sc³⁺ and Ti⁴⁺ ions were analyzed by secondary ion mass spectrometry (SIMS). A time-of-flight secondary ion mass spectrometer (ToF SIMS V; ION-TOF GmbH, Münster, Germany) was used to analyze the surface Ti⁴⁺ profile and the depth profiles of all of the substrate ions ⁶Li, ⁹³Nb, ¹⁶O and the diffused ions ⁴⁵Sc and ⁴⁸Ti. The surface profile was obtained by doing surface mapping with a raster size of 135 × 135 μm². For the depth analysis, a Cs⁺-beam (~45 μm in diameter) of 32 nA at 3 keV was used to sputter a crater of 150 × 150 μm² on the strip waveguide surface and a pulsed bismuth ion beam (pulsed current: 1 pA, pulsed energy: 25 keV) was used to analyze the yields of secondary ions ⁶Li, ⁹³Nb, ¹⁶O, ⁴⁵Sc and ⁴⁸Ti as a function of time. Positive secondary ions were detected. Ions from a central area of 18 × 18 μm² inside the erosion crater rastered on the strip waveguide were detected. A low energy pulsed electron gun was used to reduce the surface charge accumulation. For the same purposes, a 50 nm thick Au film was coated onto the sample surface to be analyzed before the SIMS analysis. The trace and depth of the erosion crater were measured by a Tencor Alpha Step 200 profilometer (KLA-Tencor Corp., Milpitas, CA). The depth resolution is better than 5 nm.

3. Results and discussion

It is crucial to know if Sc³⁺ doping affects the LN refractive index, and if so, it is unclear if its contribution is comparable to the Ti⁴⁺-induced increment Δn_o (Δn_e), which is ~0.006 (0.012) at 1.5 µm wavelength for a usual congruent Ti:LN waveguide fabricated by diffusion of ~100-nm-thick Ti-strips at 1030-1060 °C for 9 h, which gives rise to a surface Ti⁴⁺ concentration 1.2 × 10²¹ ions/cm³. The contribution can be determined by comparing the index values at Sc³⁺-only doped and undoped surface parts. In the earlier work, we have studied it and concluded that the contribution is small compared to the Δn_o,e of usual congruent waveguide [13]. The conclusion is further verified by present work. The measurement, which has an error of ± 1 × 10⁻³, shows that, after the first, second and third heat treatment stages, the n_o (n_e) value at the Sc³⁺-only doped surface part is 2.2113 (2.1376), 2.2115 (2.1379) and 2.2113 (2.1262), respectively, and that at the undoped part is 2.2113 (2.1377), 2.2114 (2.1378) and 2.2112 (2.1260), respectively. We note that Sc³⁺ doping contribution is on the order of 10⁻⁴ for both cases of n_o and n_e, and is minor in both cases of congruent and NS compositions. It is also crucial to know the Li₂O content at waveguide surface. Here, the refractive index measurement method is used to evaluate the Li₂O-contents at each part of sample surface based on the Li-composition-dependent birefringence [14]. The refractive index measurement accuracy, 1.0 × 10⁻³, results in a Li₂O-content uncertainty of 0.1 mol%. First, evaluation was performed on the as-grown congruent plate, for which the index was measured to be n_o = 2.2112 and n_e = 2.1375. As expected, it has a Li₂O-content 48.6 ± 0.1 mol%, which is in good agreement with the nominal value. After the VTE process, the Li₂O-contents at the Sc³⁺-only doped and undoped surface parts are evaluated as 49.6 and 49.7 ± 0.1 mol%, respectively. Both are near-stoichiometric and can be thought as same within the error. It is impossible to obtain the Li₂O-content accurately on the surface of an individual strip waveguide on the basis of the refractive index measurement by prism coupler as the coupler is designed for a thin film and slab waveguide rather than the strip waveguide. The reason is detailed below. The working light spot of the prism coupler has a diameter of 1 mm. The width of strip waveguide under study is usually several micrometers only (8 μm here) and the waveguides separate by 200 μm each other. The area part of waveguide surface seen by the light spot is no more than 5%. Thus, the measured pattern of the light reflected from sample surface is mainly contributed from the substrate surface instead of the narrow strip waveguide surface. Moreover, the Ti⁴⁺ presence, which induces the index increase, makes it difficult to obtain the correct Li₂O-content of the strip waveguide. We have no choice but to roughly evaluate the waveguide composition by referencing the situation at the surface part away from the waveguide region. We have done the refractive index measurement on the surface part with the waveguide array. The resultant composition can be approximated as that at the surface part away from the waveguide because the effect of strip waveguide presence on the result is small as demonstrated above. The refractive indices measured at the surface part with the waveguide array are n_o = 2.2114 and n_e = 2.1264 at the 1553 nm wavelength. The corresponding birefringence yields a Li₂O content of 49.7 ± 0.1 mol%, which is the same as the values at the Sc³⁺-only doped and undoped surface parts. Although the exact Li composition at the strip waveguide surface cannot be obtained, it should not have a large difference from that of the surface part where no waveguide is defined. In words, the waveguide under study is in an NS composition environment.

It is worthwhile to note that the real Li₂O content in the Sc³⁺-doped layer is not so high because some Sc³⁺ ions enter into Li⁺ sites (Sc_Li) and others enter into Nb⁵⁺ sites as its concentration C_Sc is above the threshold C_th according to the commonly accepted defect model for LN, and this is the case for the sample studied here because the C_Sc at the sample surface, as shown later, is 3.7 mol% that is far above the C_th ( = 0.4 mol% for an NS LN [4]). Each Sc_Li requires additional two Li vacancies (V). The real composition in the Sc³⁺-doped layer should consider the ratio R = ([Li_Li] + [Sc_Li] + [V_Li])/([Nb_Nb] + [Sc_Nb]), where the sign [X_Y] denotes the concentration of X ion on Y site. The above-mentioned 49.6 mol% Li₂O content only implies that the R value in the Sc³⁺-doped layer is equivalent to that of a pure LN having a Li₂O content 49.6 mol%. The real Li₂O content there is smaller than 49.6 mol%. One can anticipate that Li₂O content in the waveguide should have an even lower value as Ti⁴⁺ enters both Li and Nb sites too [15].

Figure 1(b) shows the waveguide surface image (1000 × ). The waveguide has a smooth and flat surface. The end-fire experiment shows that the waveguide well supports single-mode (at 1.5 μm wavelength) under both transverse electric (TE) and magnetic (TM) polarizations. Figure 1(c) shows the TE and TM mode patterns. Figures 2(a) and 2(b) show the TE- and TM-mode light intensity profiles along the width direction x and depth direction y. The light intensity of the guided mode follows a Gauss function A_xexp[-2(x/W_x)²] in the x direction and a Hermite-Gauss function A_yy²exp[-2(y/W_y)²] in the y direction. The black lines represent the Gauss or Hermite-Gauss fit. The mode size W_x × W_y is 5.7 × 4.5 μm² for the TE mode and 4.9 × 4.1 μm² for the TM mode. As expected, the confinement to the TM mode is considerably stronger than that to the TE mode because Ti-induced refractive index increment Δn_e >Δn_o [for a Z-cut LN substrate, TM (TE) mode concerns Δn_e (Δn_o)].

 

Fig. 2 TE- and TM-mode light intensity profiles along (a) x and (b) y directions of 8-μm-wide NS Ti:Sc:LN strip waveguide.

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The waveguide loss was evaluated from the insertion loss measured at 1547 nm wavelength. The fiber-to-fiber insertion loss of the 8-μm-wide, 1.5-cm-long waveguide was measured to be 4.5/5.6 dB under the TE/TM polarizations. From the obtained mode sizes, the coupling loss between the waveguide and a single-mode fiber (with a mode field diameter of 10.3 μm) is 1.8/2.1 dB for the TE/TM mode. The total reflection loss is 0.3 dB. The measured insertion loss also includes the etalon effect, which may cause 0-2.0 dB loss in the resonator formed by the two endfaces of the waveguide and 0-0.5 dB loss in each air resonator formed by the endfaces of waveguide and fiber. The pitch of interference fringes is on the submicron order and requires a measurement accuracy of a few tens of nanometer for the resonator length. Such an accuracy is not easily achieved. So, the etalon effect cannot be determined accurately. With ignored etalon effect, the waveguide loss was evaluated as 0.4/0.7 dB/cm for the TE/TM mode.

Figure 3(a) shows the Ti⁴⁺ profile (magenta balls) on the waveguide surface. The experimental data can be well fitted by a sum of two error functions. The fitting expression and parameter values are indicated (W is the initial Ti-strip width). The diffusion width d_x is 8.6 ± 0.2 µm. A mean lateral Ti⁴⁺ diffusivity is evaluated as 1.15 ± 0.03 μm²/h. Figure 3(b) shows the depth profiles of ⁶Li, ⁹³Nb, ¹⁶O, ⁴⁵Sc and ⁴⁸Ti in the waveguide. One can see that both the Ti⁴⁺ and Sc³⁺ profiles can be well fitted by a Gaussian function, indicating that the diffusion reservoir, which is shared by Ti⁴⁺ and Sc³⁺, has been exhausted. The fitting expressions are indicated. The Ti⁴⁺- or Sc³⁺-concentration profile can be written as C_{Ti, Sc}(y) = C₀^{Ti, Sc}exp[-(y/d_{Ti, Sc})²], where C₀^{Ti, Sc} is the surface Ti⁴⁺ or Sc³⁺ concentration and d_Ti (d_Sc) is the 1/e Ti⁴⁺ (Sc³⁺) diffusion depth having a value of d_Ti = 5.8 ± 0.1 μm (d_Sc = 7.2 ± 0.1 μm). The mean bulk diffusivity is 0.47 ± 0.02 (0.41 ± 0.01) μm²/h for Ti⁴⁺ (Sc³⁺). In the congruent LN, Sc³⁺ diffuses definitely slower than Ti⁴⁺ due to their difference in ionic radius (0.8 Ǻ for Sc³⁺ and 0.6 Ǻ for Ti⁴⁺) [12]. For the diffusion system concerned here, however, both ions show similar diffusivities. Moreover, the Sc³⁺ (Ti⁴⁺) diffusivity is considerably larger (lower) than the value of their respective single diffusion case [13], [16], [17]. These characteristics are associated with the multiple annealing stages, Ti⁴⁺-assisted Sc³⁺ diffusion [12] and post VTE, which causes composition increase and hence Sc³⁺ or Ti⁴⁺ diffusivity decrease [18]. It is worthwhile to mention that the Ti⁴⁺ and/or Sc³⁺ out-diffusion does not occur during the VTE process. In the early stage of VTE, the Ti⁴⁺ and Sc³⁺ continuously diffuse deeper and their profiles become slightly broader. As the VTE is prolonged, Li⁺ ions diffuse fast into the bulk (Li⁺ diffuses 10³-fold faster than Ti⁴⁺ or Sc³⁺). The waveguide layer quickly reaches to the NS composition. Consequently, the mobilities of Ti⁴⁺ and Sc³⁺ degrade largely. Both ions cannot diffuse out of crystal.

 

Fig. 3 (a) Surface Ti⁴⁺ profile and (b) depth profiles of ⁶Li, ⁹³Nb, ¹⁶O, ⁴⁵Sc and ⁴⁸Ti.

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Based on the law of mass conservation, the Ti⁴⁺ surface concentration is determined as C₀^Ti = (16.6 ± 0.5) × 10²⁰ ions/cm³, equivalent to (9.0 ± 0.4) mol%. The Sc³⁺ surface concentration is determined as C₀^Sc = (6.9 ± 0.2) × 10²⁰ ions/cm³, equivalent to (3.7 ± 0.1) mol%.

Next, we turn to discuss the photorefractive damage issue of the waveguide under study. To realize the optical-damage-resistant function, two requirements should be satisfied, i. e., the waveguide layer must be entirely covered by the Sc³⁺ profile as mentioned above, and the C_Sc at the 1/e waveguide depth should be above the threshold C_th. First, we pay attention to the former requirement. For the waveguide under study, the Sc³⁺ profile entirely covers the Ti⁴⁺ profile as d_Sc ( = 7.2 ± 0.1 μm) is considerably larger than d_Ti ( = 5.8 ± 0.1 μm). Speaking strictly, this requirement should be that the Sc³⁺ profile entirely covers the refractive index profile rather than the Ti⁴⁺ profile. This is because the 1/e depth of refractive index change, named dy_o (dy_e) for the ordinary (extraordinary) ray, does not always equal the d_Ti as the Ti⁴⁺-induced refractive index increment ∆n_o,e and the Ti⁴⁺ concentration C_Ti does not always follow a linear relationship. For example, for a usual congruent Ti:LN waveguide, both follow a nonlinear relation with a power index α_o = 0.53-0.55 [15], [19] for the ordinary ray, and a near or exact linearity with a power index α_e = 0.83 [15] or 1.0 [19] for the extraordinary ray. For the NS Ti:Sc:LN waveguide studied here, the α_o,_e value is unknown at present. However, we have already known the value (α_o = 0.90 and α_e = 1.0 [20]) for an NS Ti:LN waveguide fabricated by the same method and condition of Ti diffusion followed by the VTE (1100 °C/10 h), which causes similar surface Li₂O content 49.8 mol%. Since Sc³⁺ doping has little contribution to the LN refractive index, it is reasonable to consider that the α_o,_e value of the NS Ti:LN waveguide is also valid for the NS Ti:Sc:LN studied here. To reach an optical-damage-resistant waveguide, it requires d_Sc ≥ d_Ti/α_o,e^1/2. For the studied waveguide, d_Sc should be at least d_Ti/α_o^1/2 = 6.1 μm for the ordinary ray and d_Ti/α_e^1/2 = 5.8 μm for the extraordinary ray. One can see that the practical Sc³⁺ profile (d_Sc = 7.2 μm) is still considerably larger than the required for both cases of ordinary and extraordinary rays.

Subsequently, attention is paid to the latter requirement mentioned above. The nonlinearity between ∆n_o,e and C_Ti does not affect the requirement on the surface Sc³⁺ concentration, i. e. C₀^Sc ≥ eC_th (e = 2.71828). The C₀^Sc at the waveguide surface and at 1/e Ti⁴⁺ concentration depth are 3.7 mol% and C₀^Sc/e = 1.4 mol%, respectively, which are 9.3 and 3.5 times higher than C_th ( = 0.4 mol% for an NS LN [4]). Moreover, the Sc³⁺ profile shows that the depth where the Sc³⁺ concentration is above C_th can be extended from d_Sc ( = 7.2 μm) to 10.7 μm. One can see from Fig. 2(b) that the mode field depth range of 0-5 μm is indeed entirely covered by the Sc³⁺ profile part above the threshold (0.0-10.7 μm) for both cases of TE and TM modes. This implies that the studied waveguide is expected to be optical-damage-resistant. Future work should investigate the optical damage resistance of the NS Ti:Sc:LN waveguide using the holographic Bragg grating method developed for a strip waveguide [21].

Finally, based on the SIMS result, the refractive index profile in the NS waveguide studied can be modeled as n_o,e(x,y) = n_so,e + Δn_1o,eerfc(-y/d_o,e) + Δn_o,e{erf[(W/2 + x)/dx_o,e] + erf[(W/2-x)/dx_o,e]}exp[-(y/dy_o,e)²/{2erf[W/(2dx_o,e)]}, where -∞<x< + ∞, y≥0, the first term represents the substrate index, the second term reflects the Li composition (i. e., Li-rich VTE) effect on index [22], and the third term denotes the Ti-induced index increment profile. Δn_1o,e is the composition-induced maximum index change. The d_o,e, dx_o,e and dy_o,e are the width or depths of index increment profiles.

4. Conclusion

We have demonstrated NS Ti:Sc:LN strip waveguide fabricated by Sc³⁺-diffusion-doping, Ti diffusion and post Li-rich VTE. We show that the waveguide is in an NS composition environment, well supports both the TE and TM modes, shows considerable polarization dependence, is single-mode at 1.5 μm, and has a loss ≤ 0.4/0.7 dB/cm for the TE/TM mode. The Ti⁴⁺ surface profile can be fitted by a sum of two error functions and the depth profile can be fitted by a Gaussian function. The mode field profile is entirely covered by the Sc³⁺ profile part having a Sc³⁺ concentration above the threshold for both cases of TE and TM modes, implying that the waveguide is expected to be optical-damage-resistant. The NS Ti:Sc:LN strip waveguide is promising for active and passive integrated optics.