Anisotropic model for the fabrication of Annealed and Reverse Proton Exchanged waveguides in congruent Lithium Niobate
Francesco Lenzini, Sachin Kasture, Ben Haylock, Mirko Lobino
AAnisotropic model for the fabrication ofAnnealed and Reverse ProtonExchanged waveguides in congruentLithium Niobate
Francesco Lenzini, Sachin Kasture, Ben Haylock,and Mirko Lobino ∗ Centre for Quantum Dynamics, Griffith University, Brisbane, QLD, AustraliaandQueensland Micro- and Nanotechnology Centre, Griffith University, Brisbane, QLD, Australia ∗ m.lobino@griffith.edu.au Abstract:
An anisotropic model for the fabrication of annealed andreverse proton exchange waveguides in lithium niobate is presented. Wecharacterized the anisotropic diffusion properties of proton exchange,annealing and reverse proton exchange in Z-cut and X-cut substratesusing planar waveguides. Using this model we fabricated high qualitychannel waveguides with propagation losses as low as 0.086 dB/cm anda coupling efficiency with optical fiber of 90% at 1550 nm. The splittingratio of a set of directional couplers is predicted with an accuracy of ± © 2018 Optical Society of America OCIS codes: (130.3130) Integrated optics materials; (230.7370) Waveguides.
References and links
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1. Introduction
Lithium niobate (LN) is one of the most widely used materials for the fabrication of inte-grated optical devices because of its high nonlinearity and large electro-optic coefficient forfast switching [1]. High speed modulators in LN have been standard components of opticaltelecommunication networks for decades [2] and more recently LN integrated optical deviceshave been used for the optical simulation of solid state systems [3, 4] and for quantum op-tics experiments including the generation [5] and manipulation [6] of single photons and thedemonstration of a compact quantum-key-distribution system [7].LN waveguides are fabricated mainly by two techniques: titanium indiffusion (Ti-indiffusion) [8] and proton exchange (either annealed (APE) or reverse (RPE) proton exchange)[9]. Ti-indiffused waveguides are fabricated through the deposition of a few nanometer thick Tilayer on top of the material followed by annealing at T ∼ ◦ C in a furnace. This is the stan-dard technique used for commercial modulators and Ti indiffusion has been well characterisedand reliably modeled [10]. For annealed (APE) and reverse (RPE) proton exchange waveguides,the core is fabricated by replacing lithium ions (Li + ) with hydrogen ions (H + ) by dipping thesample in a hot acid bath: this substitution increases the extraordinary refractive index anddecreases the ordinary one [11]. In APE waveguides a subsequent annealing step in air is per-formed to reduce the H + concentration and improve the optical properties of the waveguide.After proton exchange and annealing a third step of RPE is used to bury the waveguide underthe crystal surface and increase the circular symmetry of the optical mode. The main differencebetween the two techniques is that Ti-indiffused devices guide both polarizations while APEand RPE waveguides guide only light polarized along the optical axis of the crystal.APE and RPE waveguides have excellent optical properties and they have been used for abroad range of applications in classical and quantum optics including the demonstration of theighest conversion efficiency for second harmonic generation at 1550 nm reported to date [12]and the brightest single photon source based on parametric down conversion ever reported [5].Nonlinear diffusion models have been proposed for APE [13] and RPE [14, 15] processes. Themain limitations of these models are the assumptions that the diffusion of H + ions in the crystalis isotropic even if the crystal is not and that the refractive index changes linearly with H + concentration across all the different crystallographic phases [9].In this paper we report a model of the anisotropic diffusion processes involved in the fab-rication of APE and RPE waveguides by studying the H + diffusion on Z-cut and X-cut sub-strates. Using this model we derive a relation between proton concentration and refractive indexchanges as a function of the wavelength when this change is in the α -phase ( ∆ n e < + concentration with the ordinary and extraordinary refractive indexchanges, ∆ n e , o , is linear. We verify the validity of our model with the design and fabricationof channel waveguides and directional couplers for which the anisotropy in the diffusion isparticularly critical.The paper is divided into three more sections: the model of the APE and RPE fabricationsteps are described in section 2 for X-cut and Z-cut substrates, in section 3 we compare theprediction of model with the experimental results through the design and fabrication of channelwaveguides and directional couplers and section 4 is the conclusion.
2. Modelling of the refractive index profile evolution in APE and RPE planar waveg-uides on X-cut and Z-cut substrates
Lithium niobate is a uniaxial crystal whose optical axis is commonly referred to as the Z axis. Inorder to characterize the diffusion parameters of APE and RPE processes parallel and orthogo-nal to this direction we fabricated several planar waveguides on X-cut and Z-cut substrates. Theeffective refractive indices of the guided modes n e f f were measured using the prism couplingtechnique [16] with a precision of ± ± ◦ angular resolution of our set-up.The optimal diffusion parameters were estimated by minimizing the root-mean-square (rms)error between the measured n e f f and those calculated using the nonlinear diffusion model forH + in LN. For the extraordinary and ordinary refractive indices of bulk LN we used dispersioncurves given in [17] at a temperature T =22 ◦ C.Only the the extraordinary refractive index n e increases during proton exchange while theordinary index n o decreases. For this reason APE and RPE waveguides guide only one polar-ization which is TM mode for a Z-cut substrate and TE for X-cut. Nevertheless the ordinaryrefractive index change ∆ n o = − ∆ n e / Proton exchange (PE) was performed by dipping the LN sample in a pure benzoic acid bathheated to 168.5 ◦ C. Temperature uniformity is critical for the homogeneity of the fabricationof multiple devices on a single substrate. Our PE reactor is a custom made oil-based heatingmantle with internal stirring to improve uniformity.After PE the samples have a superficial layer at higher refractive index loaded with H + ions.The guiding layer is formed by different crystallographic phases, with a portion of the protonsoccupying interstitial sites not contributing to an increase in the refractive index [11, 15, 18].A soft annealing (SA) step in air at T=210 ◦ C follows the PE causing the movement of theinterstitial H + ions to active substitutional sites with a consequent increase in the area of therefractive index profile. The area A = ∆ n e × d e is calculated assuming a step-like refractiveindex profile of depth d e and index change ∆ n e . Figure 1 shows the evolution of the areas A and n e - boundary A ( m ) t (h) SA X-cut0.1010.1130.1170.1050.1030.1090.1070.1110.1150.119 n e n e - boundary n e t (h) SA Z-cut 18 0.0850.080.0750.070.0650.06 A ( m ) (b) Fig. 1. Evolution of the refractive index change ∆ n e and area A = ∆ n e × d e as a function ofthe SA time for 3 h proton exchanged samples. Circles are experimental data points for (a)X-cut and (b) Z-cut samples. Solid line is plotted as guide to the eye. of the refractive index changes, ∆ n e , with SA time for X-cut and Z-cut planar waveguides thatwere proton exchanged for 3 h. After each SA step the n e f f of the modes were measured byprism coupling and the values of d e and ∆ n e was retrieved using the inverse-WKB method. Forboth samples there is a fast increase of A in the first hours of SA until it saturates to a constantvalue: this indicates that all interstitial H + have moved to active substitutional sites. For theZ-cut sample the index change starts to decrease very slowly when ∆ n e reaches the boundarybetween the κ and β phase corresponding to values below 0 .
105 at λ =635 nm [19]. Whilefor Z-cut samples soft annealing acts as a self-stopping process [14, 15], for X-cut the diffusionproceeds much faster and the values of ∆ n e shown by the last three data points of Fig. 1(a)clearly indicates that the crystal is entering in the κ phase, where a different relation betweenproton concentration and ∆ n e has to be employed.In our fabrication we stop the SA when the refractive index change, ∆ n e , reaches the bound-ary between κ and β at 0 . t SA andthe PE time t PE are proportional and given by [14, 15]: t SA , X = . t PE for X-cut samples, (1) t SA , Z = t PE for Z-cut samples, (2)Equations (1) and (2) are valid for a large interval of PE times, ranging from 1 h to around10 h. For Z-cut samples, when PE time was larger than 10 h the temperature for SA was in-creased to a maximum of 230 ◦ C and the new SA time calculated as: t SA ( T ) = t SA ( T ) exp (cid:18) E a k b T − E a k b T (cid:19) , (3)where T is the new temperature of choice for SA, T = ◦ C is the temperature used forderiving relations (1)-(2), k b is the Boltzmann constant, and E a (cid:39) β phase [15].Relations (1)-(3) have been used to estimate the evolution of the waveguide depth with PEtime with d e ranging from 0.5 µ m to 2 µ m. Figure 2 shows the measured evolution of d e withPE time for X-cut and Z-cut waveguides fitted with the linear diffusion law d e = (cid:112) D PE , X / Z t PE [19]. From our measurement we found that the diffusion coefficients for the two different sub-strates are: D PE , X = .
098 µm h − for X-cut samples, (4) D PE , Z = .
056 µm h − for Z-cut samples. (5) PE d ( m ) e t (h) PE
20 4 6 8 10 12 14 16 18(a) (b)2 4000.511.52 d ( m ) e X-cut Z-cut
Fig. 2. Proton exchange depth d e as a function of time t PE for (a) X-cut and (b) Z-cutsample. Circles are data points fitted with the linear diffusion law d e = (cid:112) D PE , X / Z t PE shown as solid line. The depths are measured after a SA time given by Eqs. (1) and (2). Proton exchanged waveguides have high propagation losses and a second order susceptibilityalmost totally suppressed [19]. Annealing in dry atmosphere at a temperature of 328 ◦ C isperformed to decrease the local H + concentration, C , and improve the optical properties of thewaveguide in terms of propagation losses, second order nonlinearity and coupling with opticalfiber.The step-like refractive index profile obtained after PE and SA is the initial condition formodelling the annealing diffusion. The proton concentration is set to C ( y ) =1 for 0 < y < d e andto 0 for y > d e with y indicating the direction orthogonal to the air-LN interface. The kinetics ofH + ions in X-cut and Z-cut planar waveguides are modelled by the one-dimensional nonlineardiffusion equation ∂ C ∂ t = ∂∂ y (cid:18) D a , X / Z ( C ) ∂ C ∂ y (cid:19) , (6)where the dependence of the diffusion coefficient D a , X / Z on C is given by [14, 15]: D a , X / Z ( C ) = D , X / Z (cid:18) α X , Z + − α X , Z β X , Z C + γ X , Z (cid:19) . (7)For α =
0, the rational form of D a , X / Z ( C ) is the same that would be obtained by a simple inter-diffusion model for H + and Li + ions after the requirement of an electroneutrality condition[20]. The additional term α acts as an empirical correcting factor taking into account the dif-ferent values of the self diffusion coefficients of the two ion species in each phase encounteredduring annealing and RPE in a multiphase crystal. When the waveguide is in the α -phase the re-fractive index change is proportional to C and given by ∆ n e ( λ ) = δ X / Z ( λ ) C . We independently Table 1. Parameters of the diffusion coefficients and Sellmeier curves for X-cut and Z-cutLN substrates.
X-cut Z-cut D ( µ m /h) 0.334 A 5.063e-3 D ( µ m /h) 0.414 A 4.646e-3 α α β µ m) 0.217 β µ m) 0.272 γ γ .45 0.6 0.75 0.9 1.05 1.2 1.35 1.5 1.65 1.80.070.0750.080.0850.090.0950.10.105 X-cutZ-cut ( m) (a) y( m) boundary n e (b)t a y( m) boundary n e (c)t a Fig. 3. (a) Sellmeier fitting (solid lines) and experimental data of the wavelength depen-dence of the refractive index change coefficient δ for ( • ) X-cut and ( (cid:4) ) Z-cut. (b) Simulatedevolution of the refractive index change ∆ n e during annealing for an X-cut planar waveg-uide calculated from Eq. (6). The waveguide had a PE depth d e = 0.822 µ m and wasannealed for t a = 36 h, 44 h and 59 h. (c) Same as (b) but for Z-cut with d e = 0.798 µ m and t a = 25 h, 34 h and 48 h. characterize the coefficient δ X / Z ( λ ) for the two substrates because the stresses experienced bythe crystal during the high temperature diffusion processes are different for Z-cut and X-cutwaveguides and this may affect the final value of ∆ n e [11]. Equation (6) is integrated using asemi-implicit finite difference algorithm [21] with 0 < y < y max and 0 < t < t a . The boundaryconditions are ∂ C ∂ y = y =
0, meaning that there is no H + flux at the LN-air interface, andfor y = y max we used a transparent boundary condition in order to simulate an infinitely thicksubstrate. This is necessary in order to avoid the use of large integration window since for large t a the refractive index profiles have a long tail that extends for tens of microns.We fabricated several planar waveguides on the two different substrates with proton exchangedepth d e ranging from 0.5 µ m to ∼ µ m and monitored their evolution during annealing bymeasuring the n e f f of the modes. The values of the parameters D , X / Z , α X / Z , β X / Z , γ X / Z and δ X / Z were determined by minimizing the root-mean-square error between the measured effec-tive indices, n mease f f , and the ones calculated with a mode solver and the refractive index profileobtained from Eq. (6), n calce f f . The wavelength dependence of δ was determined by interpolatingthe data acquired at the wavelengths 1550 nm, 780 nm, 635 nm and 532 nm with the one poleSellmeier equation δ ( λ ) = (cid:113) A + B λ − C . Table 1 shows the parameters of the diffusion and thecoefficients of the Sellmeier equations obtained from the minimization of the rms error ∆ n e f f .The Sellmeier curves are shown in Fig. 3(a), while Fig. 3(b) and (c) show the evolution ofthe refractive index profile during annealing for an X-cut with a PE depth d e = 0.822 µ m anda Z-cut waveguide with d e = 0.798 µ m. Table 2 shows the values of the rms error ∆ n e f f of themodel for these two waveguides characterised by the first four guided modes at λ =635 nm. Table 2. Root-mean-square error ∆ n e f f = (cid:114) ∑ m = (cid:16) n calce f f , m − n mease f f , m (cid:17) / n e f f for waveguides shown in Fig. 3(b) and (c). All data refers to the wavelength λ =635 nm. X-cut Z-cut t a (h) ∆ n e f f × − t a (h) ∆ n e f f × −
36 0.6 25 1.444 1.8 34 1.059 1.2 48 1.6 y( m) n e boundary (b) t RPE y( m) n e boundary (a) t RPE
Fig. 4. (a) Simulated evolution of the refractive index change during RPE for an X-cutplanar waveguide calculated form Eq. (6). The waveguide had a PE depth d e = 1.653 µ mand was annealed for t a = 24 h and reverse proton exchanged for t RPE = 8 h and 11.5 h. (b)Same as (a) but for a Z-cut sample with d e = 1.926 µ m, t a = 17 h and t RPE = 10.8 h and15.6 h.
The asymmetry in the refractive index profile of APE waveguides (see Fig.3(b),(c)) generatesan asymmetry in the intensity profile of the guided modes that reduces the coupling efficiencywith optical fibre and the mode overlap in frequency conversion processes. Furthermore themodes of APE waveguides overlap with the PE dead layer which has suppressed nonlinearity.This problem is overcome with RPE which buries the waveguides through the back substitutionof Li + for H + at the surface of the crystal.Reverse Proton Exchange is performed after annealing by dipping the sample in an eutecticmelt of LiNO : KNO : NaNO (mole percent ratio of 37 . . .
0) at a temperatureof 328 ◦ C [22]. During this process the H + near the LN surface are removed while the otherprotons are annealed deeper into the substrate. The process is modelled using Eq. (6) withchanged boundary condition C = y =
0. In this way we model the eutectic melt as a perfectlyabsorbing layer placed at the LiNbO top surface. The parameter γ X / Z , that controls the valueof the diffusion coefficient for C →
0, plays a central role in determining the rate of the RPEprocess. In fact this rate is mainly affected by the diffusion properties of the protons at thetop surface of the crystal, that have concentration values approaching zero. For this reason thevalues of γ X / Z reported in Tab. 1 are obtained through minimization of the RPE data keepingfixed the value of the other parameters obtained by the APE characterization.Figure 4 shows the evolution of the refractive index profile during RPE for X-cut and Z-cutsubstrates and the rms in the calculation of the n e f f for these profiles is given in Tab. 3. Reverseexchange moves the peak of the profile below the LN surface causing an improvement in thesymmetry of the mode, a reduction in the surface scattering component of the propagationlosses and a pulling of the mode away from dead-layer on the surface that is created after PE. Table 3. Root-mean-square error ∆ n e f f in the calculation of the n e f f for waveguides shownin Fig. 4(a) and (b). All data refers to the wavelength λ =635 nm. X-cut Z-cut t RPE (h) ∆ n e f f × − t RPE (h) ∆ n e f f × − . Design and fabrication of channel waveguides We applied this model for the design and fabrication of straight channel waveguide and direc-tional couplers on a Z-cut substrate. The design constraints were: good coupling with opticalfiber, waveguide in the α -phase, single mode operation at 1550 nm and low propagation losses.The fabrication parameters were determined by solving the diffusion equation ∂ C ∂ t = ∂∂ y (cid:18) D a , Z ( C ) ∂ C ∂ y (cid:19) + ∂∂ x (cid:18) D a , X ( C ) ∂ C ∂ x (cid:19) , (8)with the diffusion coefficients obtained in section 2 for annealing and RPE and maximizing ourfabrication constraints. The initial condition for the annealing diffusion is the step-like refrac-tive index profile shown in Fig. 5(a) where the shaded region has a proton concentration C = w =8 µ m. The undercut diffusionof proton during PE is modelled by the empirical formula u under ( y ) = u max (cid:112) − ( y / de ) with u max = . (cid:112) ( D X / D Z ) d e (see inset in Fig. 5(a)).After our analysis we fabricated the devices using a proton exchange depth d e =1.75 µ m,annealing time t a =26 h and reverse time t RPE =14.5 h. Figure 5(b) shows the intensity profileof the waveguide output mode at 1550 nm while Fig 5(c) is the mode profile predicted by ourmodel. The overlap between measured and calculated mode is 96% and overlap between themeasured fiber and waveguide modes is 90% which is in accordance with the 90.5% predic-tion from our model. The insertion losses for a 2.8 cm long waveguide were 1.39 dB whichaccount for 0 . ± .
02 dB per facet of coupling and Fresnel losses and 0 . ± .
006 dB/cmpropagation losses.A set of 15 directional couplers with coupling lengths ranging from 1.2 mm to 18 mm werefabricated with the same parameters as the straight waveguide and a separation of 13.5 µ mbetween the centres of the waveguide in the coupling region. The anisotropy of the diffusionis critical for the modeling of this devices because the lateral diffusion of H + plays a crucialrole in the effective coupling between the waveguides. Figure 6 shows the measured splittingratios as a function of the coupling length: the data is plotted along with the a sine square fittingfunction, which gives a coupling length L c = 3.973 ± L c , est = 3.976 mm also shown in Fig. 6. The comparison between measured and simulatedsplitting ratio has a rms error of 0.06. m) x( m) y ( m ) y ( m ) (b)xywu(y) (a)Ti-mask 10(c) Fig. 5. (a) Step-like refractive index profile used as initial condition for annealing. The insetshows the undercut diffusion of H + . (b) Measured intensity profile of the guided mode at1550 nm. (c) Calculated mode from the refractive index profile obtained by solving Eq. (8).The waveguide had a channel width of w =8 µ m, d e =1.75 µ m, t a =26 h and t RPE =14.5 h. S p litti ng r a ti o Fig. 6. Splitting ratio of the directional coupler. ◦ are the experimental measurements andthe blue-dotted line is their fitting. The red solid line is the function calculated using ourmodel.
4. Conclusions
In conclusion we have derived a simple and reliable model of the anisotropic diffusion for thefabrication of APE and RPE waveguide in LN. The model was tested with the design and fabri-cation of straight waveguides and directional couplers with good agreement between measuredand calculated quantities. This model will provide a useful tool for the design and optimizationof complex integrated optical devices in LN.