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High refractive index metastable phases in proton exchanged H:LiTaO3 optical waveguides
November 2000
Materials Letters 46 Ž2000. 189–192 www.elsevier.comrlocatermatlet
High refractive index metastable phases in proton exchanged H:LiTaO 3 optical waveguides V.V. Atuchin a,) , I. Savatinova b, C.C. Ziling a a
Institute of Semiconductor Physics, Russian Academy of Sciences, Siberian Branch, Pr. LaÕrentyeÕa 13, 630090 NoÕosibirsk 90, Russia b Institute of Solid State Physics, Bulgarian Academy of Science, 72 Tzarigradsko Chaussee BlÕd., 1784 Sofia, Bulgaria Received 6 January 2000; received in revised form 18 May 2000; accepted 19 May 2000
Abstract The properties of metastable phases in proton exchanged optical waveguides in LiTaO 3 were investigated. The temperature ranges of the transition from equilibrium at room temperature to metastable b-H x Li 1yxTaO 3 phase is determined as a function of hydrogen content. The relaxation of refractive index in meta-a-H x Li 1yxTaO 3 phase is traced. q 2000 Elsevier Science B.V. All rights reserved. PACS: 42.79.G; 77.84.D Keywords: Lithium tantalate ŽLiTaO 3 .; Ion exchange; Refractive index; Phase transition
1. Introduction Lithium tantalate ŽLT. based layers with partial hydrogen substitution for lithium by ion exchange technique are a promising waveguide medium for integrated optics needs. It is evident that the practical applicability of any waveguide system, incidentally, is defined in many respects by the stability of their optical properties, refractive index in particular. Meanwhile, in proton exchanged ŽH:LT. layers the occasional variations of extraordinary index increase D n with time t were demonstrated repeatedly at near room temperature. Over the period from a few days to 3 months the decrease of D n may be as much as )
Corresponding author. Tel.: q7-3832-343-889; fax: q7-3832332-771. E-mail address: [email protected] ŽV.V. Atuchin..
Ž1–3. = 10y3 Ž l s 0.63 mm. w1–5x. Moreover, in Ref. w1x the inmonotonous function D nŽ t . was revealed. In Ref. w3x the supposition was made that the possible cause of D n decrease with time, detected in H:LT layers with quiet D n distribution over depth, may be the existence of metastable phases with increased refractive index in solid solutions H x Li 1yxTaO 3 . A remark is in order that earlier the existence of metastable phases, for b-phase region only, was demonstrated in allied solid solutions H x Li 1yx NbO 3 w6,7x by X-ray analysis of the powders. Recently, a good correlation between the number and temperature intervals of D n variations in b-phase H:LN layers and the parameters of structure transitions from b-phase equilibrium at room temperature to metastable b-phases determined in Ref. w7x was shown experimentally w8x. Possible physical mechanisms of D n variations in H:LT layers when
00167-577Xr00r$ - see front matter q 2000 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 7 - 5 7 7 X Ž 0 0 . 0 0 1 6 6 - X
190
V.V. Atuchin et al.r Materials Letters 46 (2000) 189–192
the transition between metastable and equilibrium phase take place were discussed earlier w9x. Presently, known information on the structure of phase diagram of H x Li 1yxTaO 3 compounds is very scarce. Structural phase diagrams have been constructed for H:LT layers formed in a few typically used LT cuts w10–12x. Besides solid solution of hydrogen in LT at low x, so-called a-phase, the formation of four to five phases was detected by X-ray rocking curve measurements. Unfortunately, the concentration and temperature boundaries of these phases remain unclear. In Refs. w13,14x, watching for D n profile shape variation and transformations of OH-band structure in H:LT waveguide layers on annealing, the resemblance of H x Li 1yx MO 3 ŽM s Nb,Ta. phase diagrams was found. So, concerning H x Li 1yxTaO 3 , there are concentration regions of b-phase or b-phases with closely related parameters Ž x ) 0.20, box-type D n profile. and a-phase ŽGauss-type D n profile.. In our previous studies, the existence of metastable phases with increased D n in relative to equilibrium phase was detected in both a-and b-phase regions w5,8,9x but the temperature interval of phase transformation was traced only in a-phase w8,9x. Therefore, the main purpose of present investigation is the determination of the number and the temperatures of transformations between equilibrium and metastable phases in b-phase interval of H x Li 1yxTaO 3 solid solutions. Besides this, the stability of metastable a-phase will be tested.
resulted surface index increase D nŽ0. is pointed for every sample as a parameter in Fig. 1. All waveguides confine two modes Ž l s 0.63 mm.. Two cooling techniques were used in the experiment: slow Žs. cooling together with the turned off furnace in 2–3 h and quick Žq. cooling in 5–7 min Žquenching. by pulling out the samples from the heating zone to room. When the quenching regime was applied, the sample was held at specified temperature for a duration of 10 min. After the last quenching at 3208C, the sample LT3 was annealed at 4008C for 2 h to decrease the hydrogen content significantly below the lower boundary of b-phase region by diffusion. So formed waveguide confines six modes that permit the accurate index profile determination. The effective indices of waveguide modes Nm , where m is a mode number, were measured by prism coupling method at l s 0.63 mm w16x. The D n profiles on depth were reconstructed by inverse WKB-method w17x.
2. Experiment The z-cuts of LT with birefringence of n e y n o s 2.6 = 10y3 Ž l s 0.63 mm. that gives the ratio LirŽLi q Ta. s 0.494 w15x were used as a starting material. Optical waveguides were fabricated by ion exchange in melted benzoic acid ŽC 2 H 5 COOH. at T s 2408C in 8 ŽLT1. and 30 h ŽLT2, LT3.. To have a set of the samples with different D n and, respectively, different hydrogen content x in the field of b-phase the subsequent annealings were carried out. So, the LT1 was treated at 2658C for 1 h and 2958C for 1.25 h to achieve the D n value that is near the lower concentration boundary of b-phase region w14x. The sample LT2 was processed at 2658C in 3 h. The
Fig. 1. Dependence of Ž N0 y n e .q on quenching temperature: Ža. D n sŽ0. s 0.0233; Žb. D n sŽ0. s 0.0174; Žc. D n sŽ0. s 0.0139.
V.V. Atuchin et al.r Materials Letters 46 (2000) 189–192
191
3. Results and discussion In Fig. 1 the difference Ž N0 y n e .q , where n e is the substrate extraordinary index, is shown as a function of quenching temperature. For comparison, the starting level Ž N0 y n e . s is indicated by dashed line. The values of D n sŽ0. s 0.0233, 0.0174, and 0.0139 can be estimated as corresponding to x s 0.20, 0.22, and 0.25, respectively w8,14x. So, it is seen that in a hydrogen content range x s 0.20–0.25 at T s 60–1608C the transition takes place from equilibrium room temperature phase with relatively low D n to phase with increased D n. Only one transition was detected clearly. The magnitude of D n jump decreases from 3 = 10y3 to 1 = 10y3 with increasing x. The transitions retain reversible up to quenching temperature T f 2608C and in this case the starting value Ž N0 y n e . s or, in other words, D n sŽ0. can be restored by repeated short time heat treatment at some temperature from the range 100– 2608C with slow cooling. A high-rate increase of Ž N0 y n e .q at T ) 2608C is a result of activation of hydrogen diffusion into depth of the crystal because the increase of waveguide layer thickness was detected concurrently. Hydrogen concentration in the layer decreases causing D n increase w14x. Thus, in b-H x Li 1yxTaO 3 the temperature ranges of the transitions between the equilibrium phase and metastable phase are dependent on doping level and are narrower then in a-H x Li 1yxTaO 3 Ž100–2408C w9x.. The relaxation of refractive index in metastable a-phase was followed by keeping track of how D n qŽ0. magnitude decreases to D n sŽ0. with time. In accordance with present notion the value of D n sŽ0. corresponds to pure a-phase w10x or a mixture of aand k-phases w12x. The resulted curve is demonstrated in Fig. 2. Here the dashed line notes the D n sŽ0. level after cooling with furnace. The reduction of D n is described well by monotonic function without any periodic bulges detected earlier w1x. It is interesting to compare the stability of metastable phases in H x Li 1yx MO 3 ŽM s Nb, Ta. waveguide layers. Previously, a full degradation of the most high temperature meta-b-H x Li 1yx NbO 3 phase created by quenching at T s 2758C was evident even 10 days later Ž T s 208C . w8 x. As to meta-aH x Li 1yxTaO 3 phase ŽFig. 2., more then 45 days was necessary for Ž D n qŽ0. y D n sŽ0.. sinking to 60% level
Fig. 2. Relaxation of D n qŽ0. in a-H x Li 1yxTaO 3 quenched at 2408C. The level of D n sŽ0. s 0.0166 is shown by dashed line.
at room temperature and only the temperature increase of up to 1008C permits to destroy the metastable phase in real time. So, the H x Li 1yxTaO 3 metastable phases are very long time living at room conditions. Furthermore, attention is drawn to the fact that D n value produced by treatment at 1008C is below D n sŽ0.. It seems likely that the cooling of sample with furnace to room temperature in 2–3 h typically is not enough to form completely the equilibrium a-phase and special treatment at T s 1008C must be applied to this end.
4. Conclusion The study of index variation attendant on metastable phase formation in H x Li 1yxTaO 3 layers showed that the temperature intervals of the transitions in both a- and b-phases regions are related. Only one transition was detected contrary to numerous transitions in b-H x Li 1yx NbO 3 phase region w8x. It was obtained that metastable a-H x Li 1yxTaO 3 phase relaxes very slowly at room temperature. To form a-phase waveguide with stable index increase the extra treatment at 1008C in 20–30 h is appropriate.
192
V.V. Atuchin et al.r Materials Letters 46 (2000) 189–192
References w1x T. Maciak, Characterization of proton exchanged optical waveguides in z cut LiTaO 3 , Int. J. Optoelectron. 7 Ž4. Ž1992. 557–563. w2x P.J. Matthews, A.R. Mickelson, Instabilities in annealed proton exchanged waveguides in lithium tantalate, J. Appl. Phys. 71 Ž11. Ž1992. 5310–5317. ˚ w3x H. Ahlfeldt, J. Webjorn, ¨ F. Laurell, G. Arvidsson, Postfabrication changes and dependence on hydrogen concentration of the refractive index of proton-exchanged lithium tantalate waveguides, J. Appl. Phys. 75 Ž2. Ž1994. 717–727. ˚ w4x H. Ahlfeldt, F. Laurell, Drift of phasematching wavelength for quasi-phasematching LiTaO 3 waveguides, Electr. Lett. 31 Ž9. Ž1995. 750–751. w5x I. Savatinova, S. Tonchev, R. Todorov, M.N. Armenise, V.M.N. Passaro, C.C. Ziling, Electro-optic effect in proton exchanged LiNbO 3 and LiTaO 3 waveguides, J. Lightwave Technol. 14 Ž3. Ž1996. 403–409. w6x C.E. Rice, J.L. Jackel, Structural changes with composition and temperature in rhombohedral Li 1y x H x NbO 3 , Mater. Res. Bull. 19 Ž5. Ž1984. 591–597. w7x C.E. Rice, The structure and properties of Li 1y x H x NbO 3 , J. Solid State Chem. 64 Ž1986. 188–199. w8x I. Savatinova, C.C. Ziling, V.V. Atuchin, Metastable states in proton exchanged layers H:LiMO 3 ŽM s Nb, Ta., Opt. Mater. 12 Ž1999. 157–162. w9x C.C. Ziling, V.V. Atuchin, I. Savatinova, S. Tonchev, M.N.
w10x
w11x
w12x
w13x
w14x
w15x
w16x w17x
Armenise, V.M.N. Passaro, The influence of the cooling rate on the stability of z-cut H:LiTaO 3 waveguides, J. Phys. D: Appl. Phys. 30 Ž1997. 2698–2703. V.A. Fedorov, Yu.N. Korkishko, Crystal structure and optical properties of proton-exchanged LiTaO 3 waveguides, Ferroelectrics 160 Ž1994. 185–208. Yu.N. Korkishko, V.A. Fedorov, Integrated ferroelectrics H x Li 1y x NbO 3 , H x Li 1y xTaO 3 and Zn x r2Li 1y xTaO 3 formed by ion exchange technique: the crystal structure and optical properties, Ferroelectrics 183 Ž1996. 245–254. D.V. Maring, R.F. Tavlykaev, R.V. Ramasvamy, Yu.N. Korkishko, V.A. Fedorov, J.M. Zavada, Effect of crystal phases on refractive index profiles of annealed proton-exchanged waveguides in X-cut LiTaO 3 , Appl. Phys. Lett. 73 Ž4. Ž1998. 423–425. I. Savatinova, M. Kuneva, Z. Levi, V. Atuchin, K. Ziling, M. Armenise, Proton exchange in LiTaO 3 with different stoichiometric composition, Proc. SPIE 1374 Ž1990. 37–46. C.C. Ziling, V.V. Atuchin, I. Savatinova, M. Kuneva, Proton exchanged and post-exchange annealed LiTaO 3 waveguides, Int. J. Optoelectron. 7 Ž4. Ž1992. 519–532. V.V. Atuchin, The dependence of refractive indices on crystal stoichiometry in LiTaO 3 , Opt. Spektros. 67 Ž6. Ž1989. 1309–1312. T. Tamir ŽEd.., Integrated Optics, Springer-Verlag, 1975. V.G. Pankin, V.Yu. Pchyolkin, V.V. Shashkin, On the use of WKB method for determination of the refractive index profile in plane diffusion waveguides, Kvant. Elektron. 4 Ž7. Ž1977. 1497–1502.
Materials Letters 46 Ž2000. 189–192 www.elsevier.comrlocatermatlet
High refractive index metastable phases in proton exchanged H:LiTaO 3 optical waveguides V.V. Atuchin a,) , I. Savatinova b, C.C. Ziling a a
Institute of Semiconductor Physics, Russian Academy of Sciences, Siberian Branch, Pr. LaÕrentyeÕa 13, 630090 NoÕosibirsk 90, Russia b Institute of Solid State Physics, Bulgarian Academy of Science, 72 Tzarigradsko Chaussee BlÕd., 1784 Sofia, Bulgaria Received 6 January 2000; received in revised form 18 May 2000; accepted 19 May 2000
Abstract The properties of metastable phases in proton exchanged optical waveguides in LiTaO 3 were investigated. The temperature ranges of the transition from equilibrium at room temperature to metastable b-H x Li 1yxTaO 3 phase is determined as a function of hydrogen content. The relaxation of refractive index in meta-a-H x Li 1yxTaO 3 phase is traced. q 2000 Elsevier Science B.V. All rights reserved. PACS: 42.79.G; 77.84.D Keywords: Lithium tantalate ŽLiTaO 3 .; Ion exchange; Refractive index; Phase transition
1. Introduction Lithium tantalate ŽLT. based layers with partial hydrogen substitution for lithium by ion exchange technique are a promising waveguide medium for integrated optics needs. It is evident that the practical applicability of any waveguide system, incidentally, is defined in many respects by the stability of their optical properties, refractive index in particular. Meanwhile, in proton exchanged ŽH:LT. layers the occasional variations of extraordinary index increase D n with time t were demonstrated repeatedly at near room temperature. Over the period from a few days to 3 months the decrease of D n may be as much as )
Corresponding author. Tel.: q7-3832-343-889; fax: q7-3832332-771. E-mail address: [email protected] ŽV.V. Atuchin..
Ž1–3. = 10y3 Ž l s 0.63 mm. w1–5x. Moreover, in Ref. w1x the inmonotonous function D nŽ t . was revealed. In Ref. w3x the supposition was made that the possible cause of D n decrease with time, detected in H:LT layers with quiet D n distribution over depth, may be the existence of metastable phases with increased refractive index in solid solutions H x Li 1yxTaO 3 . A remark is in order that earlier the existence of metastable phases, for b-phase region only, was demonstrated in allied solid solutions H x Li 1yx NbO 3 w6,7x by X-ray analysis of the powders. Recently, a good correlation between the number and temperature intervals of D n variations in b-phase H:LN layers and the parameters of structure transitions from b-phase equilibrium at room temperature to metastable b-phases determined in Ref. w7x was shown experimentally w8x. Possible physical mechanisms of D n variations in H:LT layers when
00167-577Xr00r$ - see front matter q 2000 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 7 - 5 7 7 X Ž 0 0 . 0 0 1 6 6 - X
190
V.V. Atuchin et al.r Materials Letters 46 (2000) 189–192
the transition between metastable and equilibrium phase take place were discussed earlier w9x. Presently, known information on the structure of phase diagram of H x Li 1yxTaO 3 compounds is very scarce. Structural phase diagrams have been constructed for H:LT layers formed in a few typically used LT cuts w10–12x. Besides solid solution of hydrogen in LT at low x, so-called a-phase, the formation of four to five phases was detected by X-ray rocking curve measurements. Unfortunately, the concentration and temperature boundaries of these phases remain unclear. In Refs. w13,14x, watching for D n profile shape variation and transformations of OH-band structure in H:LT waveguide layers on annealing, the resemblance of H x Li 1yx MO 3 ŽM s Nb,Ta. phase diagrams was found. So, concerning H x Li 1yxTaO 3 , there are concentration regions of b-phase or b-phases with closely related parameters Ž x ) 0.20, box-type D n profile. and a-phase ŽGauss-type D n profile.. In our previous studies, the existence of metastable phases with increased D n in relative to equilibrium phase was detected in both a-and b-phase regions w5,8,9x but the temperature interval of phase transformation was traced only in a-phase w8,9x. Therefore, the main purpose of present investigation is the determination of the number and the temperatures of transformations between equilibrium and metastable phases in b-phase interval of H x Li 1yxTaO 3 solid solutions. Besides this, the stability of metastable a-phase will be tested.
resulted surface index increase D nŽ0. is pointed for every sample as a parameter in Fig. 1. All waveguides confine two modes Ž l s 0.63 mm.. Two cooling techniques were used in the experiment: slow Žs. cooling together with the turned off furnace in 2–3 h and quick Žq. cooling in 5–7 min Žquenching. by pulling out the samples from the heating zone to room. When the quenching regime was applied, the sample was held at specified temperature for a duration of 10 min. After the last quenching at 3208C, the sample LT3 was annealed at 4008C for 2 h to decrease the hydrogen content significantly below the lower boundary of b-phase region by diffusion. So formed waveguide confines six modes that permit the accurate index profile determination. The effective indices of waveguide modes Nm , where m is a mode number, were measured by prism coupling method at l s 0.63 mm w16x. The D n profiles on depth were reconstructed by inverse WKB-method w17x.
2. Experiment The z-cuts of LT with birefringence of n e y n o s 2.6 = 10y3 Ž l s 0.63 mm. that gives the ratio LirŽLi q Ta. s 0.494 w15x were used as a starting material. Optical waveguides were fabricated by ion exchange in melted benzoic acid ŽC 2 H 5 COOH. at T s 2408C in 8 ŽLT1. and 30 h ŽLT2, LT3.. To have a set of the samples with different D n and, respectively, different hydrogen content x in the field of b-phase the subsequent annealings were carried out. So, the LT1 was treated at 2658C for 1 h and 2958C for 1.25 h to achieve the D n value that is near the lower concentration boundary of b-phase region w14x. The sample LT2 was processed at 2658C in 3 h. The
Fig. 1. Dependence of Ž N0 y n e .q on quenching temperature: Ža. D n sŽ0. s 0.0233; Žb. D n sŽ0. s 0.0174; Žc. D n sŽ0. s 0.0139.
V.V. Atuchin et al.r Materials Letters 46 (2000) 189–192
191
3. Results and discussion In Fig. 1 the difference Ž N0 y n e .q , where n e is the substrate extraordinary index, is shown as a function of quenching temperature. For comparison, the starting level Ž N0 y n e . s is indicated by dashed line. The values of D n sŽ0. s 0.0233, 0.0174, and 0.0139 can be estimated as corresponding to x s 0.20, 0.22, and 0.25, respectively w8,14x. So, it is seen that in a hydrogen content range x s 0.20–0.25 at T s 60–1608C the transition takes place from equilibrium room temperature phase with relatively low D n to phase with increased D n. Only one transition was detected clearly. The magnitude of D n jump decreases from 3 = 10y3 to 1 = 10y3 with increasing x. The transitions retain reversible up to quenching temperature T f 2608C and in this case the starting value Ž N0 y n e . s or, in other words, D n sŽ0. can be restored by repeated short time heat treatment at some temperature from the range 100– 2608C with slow cooling. A high-rate increase of Ž N0 y n e .q at T ) 2608C is a result of activation of hydrogen diffusion into depth of the crystal because the increase of waveguide layer thickness was detected concurrently. Hydrogen concentration in the layer decreases causing D n increase w14x. Thus, in b-H x Li 1yxTaO 3 the temperature ranges of the transitions between the equilibrium phase and metastable phase are dependent on doping level and are narrower then in a-H x Li 1yxTaO 3 Ž100–2408C w9x.. The relaxation of refractive index in metastable a-phase was followed by keeping track of how D n qŽ0. magnitude decreases to D n sŽ0. with time. In accordance with present notion the value of D n sŽ0. corresponds to pure a-phase w10x or a mixture of aand k-phases w12x. The resulted curve is demonstrated in Fig. 2. Here the dashed line notes the D n sŽ0. level after cooling with furnace. The reduction of D n is described well by monotonic function without any periodic bulges detected earlier w1x. It is interesting to compare the stability of metastable phases in H x Li 1yx MO 3 ŽM s Nb, Ta. waveguide layers. Previously, a full degradation of the most high temperature meta-b-H x Li 1yx NbO 3 phase created by quenching at T s 2758C was evident even 10 days later Ž T s 208C . w8 x. As to meta-aH x Li 1yxTaO 3 phase ŽFig. 2., more then 45 days was necessary for Ž D n qŽ0. y D n sŽ0.. sinking to 60% level
Fig. 2. Relaxation of D n qŽ0. in a-H x Li 1yxTaO 3 quenched at 2408C. The level of D n sŽ0. s 0.0166 is shown by dashed line.
at room temperature and only the temperature increase of up to 1008C permits to destroy the metastable phase in real time. So, the H x Li 1yxTaO 3 metastable phases are very long time living at room conditions. Furthermore, attention is drawn to the fact that D n value produced by treatment at 1008C is below D n sŽ0.. It seems likely that the cooling of sample with furnace to room temperature in 2–3 h typically is not enough to form completely the equilibrium a-phase and special treatment at T s 1008C must be applied to this end.
4. Conclusion The study of index variation attendant on metastable phase formation in H x Li 1yxTaO 3 layers showed that the temperature intervals of the transitions in both a- and b-phases regions are related. Only one transition was detected contrary to numerous transitions in b-H x Li 1yx NbO 3 phase region w8x. It was obtained that metastable a-H x Li 1yxTaO 3 phase relaxes very slowly at room temperature. To form a-phase waveguide with stable index increase the extra treatment at 1008C in 20–30 h is appropriate.
192
V.V. Atuchin et al.r Materials Letters 46 (2000) 189–192
References w1x T. Maciak, Characterization of proton exchanged optical waveguides in z cut LiTaO 3 , Int. J. Optoelectron. 7 Ž4. Ž1992. 557–563. w2x P.J. Matthews, A.R. Mickelson, Instabilities in annealed proton exchanged waveguides in lithium tantalate, J. Appl. Phys. 71 Ž11. Ž1992. 5310–5317. ˚ w3x H. Ahlfeldt, J. Webjorn, ¨ F. Laurell, G. Arvidsson, Postfabrication changes and dependence on hydrogen concentration of the refractive index of proton-exchanged lithium tantalate waveguides, J. Appl. Phys. 75 Ž2. Ž1994. 717–727. ˚ w4x H. Ahlfeldt, F. Laurell, Drift of phasematching wavelength for quasi-phasematching LiTaO 3 waveguides, Electr. Lett. 31 Ž9. Ž1995. 750–751. w5x I. Savatinova, S. Tonchev, R. Todorov, M.N. Armenise, V.M.N. Passaro, C.C. Ziling, Electro-optic effect in proton exchanged LiNbO 3 and LiTaO 3 waveguides, J. Lightwave Technol. 14 Ž3. Ž1996. 403–409. w6x C.E. Rice, J.L. Jackel, Structural changes with composition and temperature in rhombohedral Li 1y x H x NbO 3 , Mater. Res. Bull. 19 Ž5. Ž1984. 591–597. w7x C.E. Rice, The structure and properties of Li 1y x H x NbO 3 , J. Solid State Chem. 64 Ž1986. 188–199. w8x I. Savatinova, C.C. Ziling, V.V. Atuchin, Metastable states in proton exchanged layers H:LiMO 3 ŽM s Nb, Ta., Opt. Mater. 12 Ž1999. 157–162. w9x C.C. Ziling, V.V. Atuchin, I. Savatinova, S. Tonchev, M.N.
w10x
w11x
w12x
w13x
w14x
w15x
w16x w17x
Armenise, V.M.N. Passaro, The influence of the cooling rate on the stability of z-cut H:LiTaO 3 waveguides, J. Phys. D: Appl. Phys. 30 Ž1997. 2698–2703. V.A. Fedorov, Yu.N. Korkishko, Crystal structure and optical properties of proton-exchanged LiTaO 3 waveguides, Ferroelectrics 160 Ž1994. 185–208. Yu.N. Korkishko, V.A. Fedorov, Integrated ferroelectrics H x Li 1y x NbO 3 , H x Li 1y xTaO 3 and Zn x r2Li 1y xTaO 3 formed by ion exchange technique: the crystal structure and optical properties, Ferroelectrics 183 Ž1996. 245–254. D.V. Maring, R.F. Tavlykaev, R.V. Ramasvamy, Yu.N. Korkishko, V.A. Fedorov, J.M. Zavada, Effect of crystal phases on refractive index profiles of annealed proton-exchanged waveguides in X-cut LiTaO 3 , Appl. Phys. Lett. 73 Ž4. Ž1998. 423–425. I. Savatinova, M. Kuneva, Z. Levi, V. Atuchin, K. Ziling, M. Armenise, Proton exchange in LiTaO 3 with different stoichiometric composition, Proc. SPIE 1374 Ž1990. 37–46. C.C. Ziling, V.V. Atuchin, I. Savatinova, M. Kuneva, Proton exchanged and post-exchange annealed LiTaO 3 waveguides, Int. J. Optoelectron. 7 Ž4. Ž1992. 519–532. V.V. Atuchin, The dependence of refractive indices on crystal stoichiometry in LiTaO 3 , Opt. Spektros. 67 Ž6. Ž1989. 1309–1312. T. Tamir ŽEd.., Integrated Optics, Springer-Verlag, 1975. V.G. Pankin, V.Yu. Pchyolkin, V.V. Shashkin, On the use of WKB method for determination of the refractive index profile in plane diffusion waveguides, Kvant. Elektron. 4 Ž7. Ž1977. 1497–1502.