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Causes of refractive indices changes in He-implanted LiNbO3 and LiTaO3 waveguides
Nuclear Instruments and Methods in Physics Research B 168 (2000) 498±502
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Causes of refractive indices changes in He-implanted LiNbO3 and LiTaO3 waveguides V.V. Atuchin
*
Institute of Semiconductor Physics, Russian Academy of Sciences, Siberian Branch, Pr. Laverentyeva 13, 630090 Novosibirsk 90, Russia Received 7 October 1999; received in revised form 18 January 2000
Abstract The model of refractive indices changes in He-implanted LiNbO3 and LiTaO3 optical waveguides is presented. It is assumed that the changes are de®ned by the molar volume increase and spontaneous polarization decrease induced by the interaction of crystal lattice with ion beam. Ó 2000 Elsevier Science B.V. All rights reserved. PACS: 77.84.Dy; 61.80.Jh Keywords: Implantation; LiNbO3 ; LiTaO3 ; Refractive index; Molar volume; Spontaneous polarization
1. Introduction Crystals of LiNbO3 (LN) and LiTaO3 (LT) are among the most promising materials for integrated optics purposes because of their high electro-optical and nonlinear optical properties. One way to produce an optical waveguide in LN or LT is to implant the surface layer by highenergy light element ions [1]. As a result the twolayered structure is formed. In the near surface layer, where the electronic processes are dominant, the initial crystal properties are only slightly modi®ed by the interaction with ion beam. This layer works as a light guiding region. At some
*
Tel.: +7-3832-343889; fax: +7-3832-332771. E-mail address: [email protected] (V.V. Atuchin).
depth the nuclear collisions become the dominant mechanism of energy transfer and ion stopping is actively developed. Typically, a drastic index decrease happens at the depths near projected range Rp , that is the depth of the maximum concentration of the implant. Therefore, the layer with the reduced index can be formed by nuclear processes, achieving the waveguide mode con®nement between this buried layer and the surface. Commonly, low loss optical waveguides in LN and LT are formed by He implantation [2±6]. The choice is governed by the aspiration to keep the crystal structure of the implanted layer. As it was demonstrated by X-ray analysis the He-implanted LN remains in crystalline state for doses of at least 2 ´ 1016 cmÿ2 [7,8]. At the same time for heavier ions, N and Ar for instance, the full amorphization was achieved even at doses near 5 ´ 1015 cmÿ2
0168-583X/00/$ - see front matter Ó 2000 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 8 - 5 8 3 X ( 0 0 ) 0 0 0 3 8 - 0
V.V. Atuchin / Nucl. Instr. and Meth. in Phys. Res. B 168 (2000) 498±502
[9,10]. It seems likely that just because the crystal structure is conserved the He-implanted LN waveguides is characterized by comparatively high electro-optical and nonlinear optical properties [3,11]. The reconstruction of the refractive indices pro®les of He-implanted LN and LT reveals the near constant index level over guiding region and drastic index depression adjacent to Rp [6,12±14] that is typical for implanted oxides. A peculiarity of indices variations in guiding region of He-implanted LN family crystals is a dierence in sign. So, extraordinary index variation Dne in He-implanted LN (He ® LN) waveguides is positive [13] while ordinary index variation Dno in He ® LN layers [13] and both Dne;o in He ® LT layers are negative [6]. Any interpretation of the eect has not been presented till date. Earlier, only qualitative suppositions concerning possible physical mechanisms of indices variations in implanted ferroelectrics have been made, namely, by the change in lattice ion optical polarizabilities, the crystal volume variation, or the spontaneous polarization change [1,12,15]. No quantitative analysis has been carried out. The purpose of this paper is to construct the model of refractive indices changes in guiding region of He-implanted LN type crystals that permits the quantitative estimations, including the analysis of published experimental results when it is possible. 2. Model of index changes While constructing the model the following concepts were used as the basis: 1. As a result of the interaction between the highenergy light ions and the crystal lattice, the transition of LN or LT into a new state with decreased spontaneous polarization occurs in the region of electronic processes (guiding region). At the same time, there is no considerable disordering of the crystal lattice. 2. Chemical composition changes, oxygen loss for instance, are localized in the thin surface layer and do not aect signi®cantly the indices variations in the bulk of the guiding region.
499
3. The guiding region is a homogeneous layer in the optical and structure properties. A suciently high Dn uniformity through the depth up to near Rp region was demonstrated earlier experimentally for Ar [15], He [1,12,13,16] and H [17]. The homogeneity of d-spacing over guiding region of He ® LN layers was observed in [8]. The refractive indices changes in LN family crystals can be considered as a combined eect of four possible mechanisms: DnR ± due to variation of optical refraction, DnV ± due to molar volume change, DnP ± due to variation of the spontaneous polarization P, and Dne ± due to elasto-optic eect [18±21]. The ®rst and second components are governed by Lorenz±Lorentz law, and the third one by the known model [22]. Since there is no ion stopping in the electronic processes region and, correspondingly, the crystal chemical composition in the guiding region remains unchanged, the molecular refraction of the medium is the same as for the starting material and the component DnR is 0 for this part of the modi®ed layer. As it was recently demonstrated experimentally for He ® LN layers the surface stress contribution Dne , as a ®rst approximation, can also be neglected for the layers under consideration [13]. Thus, the values Dne;o are de®ned by the following set of equations: Dne;o DnPe;o DnVe;o :
1
Assuming the conservation of the oxygen-octahedral structure of LN or LT after ion implantation with doses of at least up to 2 ´ 1016 cmÿ2 for He the components DnPe;o can be written as [22] 2
DnPe n3e g33 P k =2 k 2 Dne ; 2
DnPo n3o g13 P k =2 k 2 Dno ;
2
where P is the spontaneous polarization magnitude of the unimplanted crystal, the factor k is the ratio P ÿ P =P , and P is the spontaneous polarization of the guiding region, gij are the quadratic electro-optical coecients, and ne;o are the refractive indices of unimplanted crystal. The expressions for the components DnVe;o can be derived from the Lorenz±Lorentz formula under the conditions Dne;o ne;o as
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V.V. Atuchin / Nucl. Instr. and Meth. in Phys. Res. B 168 (2000) 498±502
DnVe;o ÿDV n2e;o ÿ 1 n2e;o 2=6ne;o V ÿDVBe;o ;
3
where V is a molar volume of the crystal, and DV is the change of the volume induced by implantation. Now, substituting Eqs. (2) and (3) in the ®rst equation of system (1), we get the relation DV k 2 Dne ÿ Dne =Be :
4
Further, using Eqs. (2)±(4) the second equation of system (1) can be transformed to the form k 2 Dno Dne Bo =Be = Dno ÿ Dne Bo =Be :
5
This relation gives the possibility to estimate the spontaneous polarization variation employing only the experimental data for Dne;o and some unimplanted crystal parameters. 3. Model veri®cation Thus, the refractive indices changes in the guiding region are governed mainly by the balance between DnPe;o and DnVe;o . Recall that DnPe;o > 0 with decreasing spontaneous polarization and in all cases DnPe > DnPo because g33 > g13 for LN family crystals. At the same time, the components DnPe;o are negative when DV > 0 (molar volume increase). Now it is reasonable to test the deductions of the model by other experimental results when possible. 3.1. He ! LN The LN parameters used in calculations are P 0.71 C/m2 [23], g33 0.090 m4 /C2 and g13 0.026 m4 /C2 [22], ne 2.2012 and no 2.2866 (congruent LN, k 0.633 lm). In [13], the Y-cut of LN implanted by 2 ´ 1016 cmÿ2 He ions with energy of 1.5 MeV was characterized by the nearsurface magnitudes Dne 0.014 and Dno )0.009. Then, from Eq. (5) we have the estimation k 0.36. Thus, the decrease of spontaneous polarization in the electronic process region or, in other words, in guiding part of He-implanted LN layers is only partial. In accordance with the known model [22] it means the presence of signi®cant
electro-optical and nonlinear optical eects in the medium. So, it would be reasonable to compare the value of k calculated above from refractive index data with the available experimental results on electro-optical and nonlinear optical properties of He ® LN waveguides. The electro-optical coecients after He implantation were estimated in [3] by Mach±Zenderin interference arrangement. The substrate orientation, dose, and exact ion energy were not reported but the depth of the layer was pointed as 2 lm. For this Rp the energy of He ions can be evaluated as near 1 MeV [3,13]. The measured values were 30% for r33 and 60% for r13 in reference to pure LN magnitudes. In accordance with the model [22] the electro-optical coecients in oxygen-octahedral ferroelectrics are in direct proportion to spontaneous polarization with the combination of some material constants as the coecient. So, if we relate the rij variations totally to spontaneous polarization decrease, then we have k 0.7±0.4. Recently the SHG capabilities of He-implanted (2 ´ 1016 cmÿ2 , 2 MeV) Y-cut LN waveguides were examined [11] by the re¯ection technique [24] with pumping at k 0.53 lm to minimize the penetration depth. A second-harmonic signal of about 75% of that of the substrate was detected in nearsurface part of the modi®ed layer. So, next time attributing the nonlinearity drop to spontaneous polarization decrease only, we have k 0.25 0.03. The pointed error bars are governed mainly by possible uncertainties (10%) in relative SH intensity measurements by the method used [24]. Thus, the spontaneous polarization decrease estimated from the electro-optical and nonlinear optical properties is closely related to the drop deduced from refractive indices changes. 3.2. He ! LT The refractive indices pro®les in He-implanted LT were reconstructed in [6] on the basis of a number of mode eective indices measured at k 0.633 lm. The implantation was produced with an ion energy of 2 MeV and a dose of 2 ´ 1016 cmÿ2 . Under the conditions the indices variations
V.V. Atuchin / Nucl. Instr. and Meth. in Phys. Res. B 168 (2000) 498±502
in the guiding region were Dne 0 and Dno )0.013. For LT we have P 0.50 C/m2 [23], g33 0.090 4 m /C2 and g13 0.023 m4 /C2 [22], ne 2.1824 and no 2.1770 (k 0.633 lm) for congruent composition Li/(Li+Ta) 0.49 [19]. Further, from (5), one can ®nd k 0.39. This value is in good magnitude agreement with the spontaneous polarization decrease in LN implanted by He under nearly the same conditions. So, we can safely assume that He ® LT waveguides should display the high electro-optical and nonlinear optical properties. Furthermore, with a dose increase from 2 ´ 1016 to 7 ´ 1016 cmÿ2 the extraordinary index variation becomes negative. This transition is accompanied by further decrease of the ordinary index [6]. Alternatively, in He ® LN waveguides the Dne remains positive and increases the magnitude with increasing dose [13]. This mystery dynamics of the Dne variation in these related crystals can be readily interpreted within the framework of the model presented. It is reasonable to suppose that the spontaneous polarization decrease and the volume dilation are enhanced by dose growing. If the same dose induces the same DV in LN and LT, then the components DnVe;o are closely related in the two crystals under consideration. The relation between the polarization-dependent components DnPe in LN and LT is quite dierent. Actually, the level of Dne for LN is twice as large as that for LT due to dierence in P . Now, for any k the same for LN and LT, we have DnPe LN 2DnPe (LT) from (2). If, also, the relation jDnPe LNj > jDnVe LN; LTj > jDnPe LTj is obeyed, then the sum Dne will be positive for LN and negative for LT, as we wished to prove. The eect for the ordinary index is not such outstanding due to a less strong DnPo and in both the crystals considered the values of Dno are negative. 3.3. He ! H:LN (H:LN is a proton exchanged LN) It has been known that in He ® LN layers, Dne > 0 and Dno < 0 in the guiding region [13,16]. As
501
was shown above, there is quite large residual spontaneous polarization in the layers. Recently, the optical waveguides produced by He implantation into previously hydrogen exchanged LN layers were studied [25]. The negative Dne in reference to ne level achieved by a proton exchange procedure was measured. Thus, the sign of the extraordinary index variation induced by implantation is rigorously dependent on whether pure LN or Hx Li1ÿx NbO3 solid solution was used as a substrate material. The causes of the extraordinary index increase in the guiding region of He ® LN layers were analyzed above. As to the negative extraordinary index variation in He ® H:LN waveguides, the physical properties of H:LN layers appear to be responsible for the eect. During the experiment produced in [25] the H:LN layers were synthesized by proton exchange in pure benzoic acid. It is common knowledge that the procedure results in the so-called b-Hx Li1ÿx NbO3 phase formation with x > 0.56 [26]. This phase has the rhombohedral LN structure [27] but zero or near-zero spontaneous polarization [20,24]. Consequently, when a H:LN layer is implanted by He, the extraordinary index variation is governed only by the negative DnVe component because the positive DnPe component is zero or near zero. 4. Conclusion The analysis of available experimental results on physical properties of He-implanted optical waveguides in LN family crystals permits the consideration of the refractive indices changes in guiding region as a sum of two dominant components induced by molar volume variation and spontaneous polarization decrease. It appears that the model may be extended to more complicated cases, such as a con®ning region of implanted layers and new pairs of ion implanted and substrate, say, H and LN, when the chemical interaction is possible. References [1] P.D. Townsend, Rep. Prog. Phys. 50 (1987) 501. [2] G.L. Destefanis, P.D. Townsend, J.P. Gailliard, Appl. Phys. Lett. 32 (1978) 293.
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V.V. Atuchin / Nucl. Instr. and Meth. in Phys. Res. B 168 (2000) 498±502
[3] G.L. Destefanis, J.P. Gailliard, E.L. Ligeon, S. Valette, B.W. Farmery, P.D. Townsend, A. Perez, J. Appl. Phys. 50 (1979) 7898. [4] G.D.H. King, M.C. Bone, B.L. Weiss, D.W. Weeks, Elect. Lett. 17 (1981) 897. [5] S.A.M. Al-Chalabi, B.L. Weiss, K.P. Homewood, Nucl. Instr. and Meth. B 28 (1987) 255. [6] E. Glavas, L. Zhang, P.J. Chandler, P.D. Townsend, Nucl. Instr. and Meth. B 32 (1988) 45. [7] R.S. Lowther-Harris, S.D. Brown, P.W. Haycock, P.J. Chandler, L. Zhang, C.C. Tang, R.P. Findlay, L. Babsail, M. Rodman, J. Knight, P.D. Townsend, Nucl. Instr. and Meth. B 97 (1995) 337. [8] Y. Avrahami, E. Zolotoyabko, Nucl. Instr. and Meth. B 120 (1996) 84. [9] G. G otz, H. Karge, Nucl. Instr. and Meth. 209/210 (1983) 1079. [10] Z. Zhang, I.A. Rusakova, W.-K. Chu, Jpn. J. Appl. Phys. 38 Pt. (2) (1999) L740. [11] J. Rams, J. Olivares, P.J. Chandler, P.D. Townsend, J. Appl. Phys. 84 (1998) 5180. [12] K. Wenzlik, J. Heibei, E. Voges, Phys. Stat. Sol. A 61 (1980) K207. [13] L. Zhang, P.J. Chandler, P.D. Townsend, Nucl. Instr. and Meth. B 59/60 (1991) 1147.
[14] P. Bindner, A. Boudrioua, P. Moretti, J.C. Loulergue, Nucl. Instr. and Meth. B 142 (1998) 329. [15] D.T.Y. Wei, W.W. Lee, L.R. Bloom, Appl. Phys. Lett. 25 (1974) 329. [16] P.D. Townsend, Nucl. Instr. and Meth. 46 (1990) 18. [17] P. Moretti, P. Thevenard, K. Wirl, P. Hertel, H. Hesse, E. Kr atzig, G. Godefroy, Ferroelectrics 128 (1992) 13. [18] V.V. Atuchin, C.C. Ziling, D.P. Shipilova, N.F. Beizel, Ferroelectrics 100 (1989) 261. [19] V.V. Atuchin, Optics and Spectroscopy 67 (1989) 1309. [20] C. Ziling, L. Pokrovskii, N. Terpugov, I. Savatinova, M. Kuneva, S. Tonchev, M.N. Armenise, V.M.N. Passaro, J. Appl. Phys. 73 (1993) 3125. [21] V.V. Atuchin, C.C. Ziling, I. Savatinova, M.N. Armenise, V.M.N. Passaro, J. Appl. Phys. 78 (1995) 6936. [22] M. DiDomenico, S.H. Wemple, J. Appl. Phys. 40 (1968) 720. [23] S.H. Wemple, M. DiDomenico, I. Camlibel, Appl. Phys. Lett. 12 (1968) 209. [24] F. Laurell, M.G. Roelofs, H. Hsiung, Appl. Phys. Lett. 60 (1992) 301. [25] E. Glavas, P.D. Townsend, M.A. Foad, Nucl. Instr. and Meth. B 46 (1990) 156. [26] Yu.N. Korkishko, V.A. Fedorov, J. Appl. Phys. 82 (1997) 1. [27] C.E. Rice, J. Sol. State Chem. 64 (1986) 188.
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Causes of refractive indices changes in He-implanted LiNbO3 and LiTaO3 waveguides V.V. Atuchin
*
Institute of Semiconductor Physics, Russian Academy of Sciences, Siberian Branch, Pr. Laverentyeva 13, 630090 Novosibirsk 90, Russia Received 7 October 1999; received in revised form 18 January 2000
Abstract The model of refractive indices changes in He-implanted LiNbO3 and LiTaO3 optical waveguides is presented. It is assumed that the changes are de®ned by the molar volume increase and spontaneous polarization decrease induced by the interaction of crystal lattice with ion beam. Ó 2000 Elsevier Science B.V. All rights reserved. PACS: 77.84.Dy; 61.80.Jh Keywords: Implantation; LiNbO3 ; LiTaO3 ; Refractive index; Molar volume; Spontaneous polarization
1. Introduction Crystals of LiNbO3 (LN) and LiTaO3 (LT) are among the most promising materials for integrated optics purposes because of their high electro-optical and nonlinear optical properties. One way to produce an optical waveguide in LN or LT is to implant the surface layer by highenergy light element ions [1]. As a result the twolayered structure is formed. In the near surface layer, where the electronic processes are dominant, the initial crystal properties are only slightly modi®ed by the interaction with ion beam. This layer works as a light guiding region. At some
*
Tel.: +7-3832-343889; fax: +7-3832-332771. E-mail address: [email protected] (V.V. Atuchin).
depth the nuclear collisions become the dominant mechanism of energy transfer and ion stopping is actively developed. Typically, a drastic index decrease happens at the depths near projected range Rp , that is the depth of the maximum concentration of the implant. Therefore, the layer with the reduced index can be formed by nuclear processes, achieving the waveguide mode con®nement between this buried layer and the surface. Commonly, low loss optical waveguides in LN and LT are formed by He implantation [2±6]. The choice is governed by the aspiration to keep the crystal structure of the implanted layer. As it was demonstrated by X-ray analysis the He-implanted LN remains in crystalline state for doses of at least 2 ´ 1016 cmÿ2 [7,8]. At the same time for heavier ions, N and Ar for instance, the full amorphization was achieved even at doses near 5 ´ 1015 cmÿ2
0168-583X/00/$ - see front matter Ó 2000 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 8 - 5 8 3 X ( 0 0 ) 0 0 0 3 8 - 0
V.V. Atuchin / Nucl. Instr. and Meth. in Phys. Res. B 168 (2000) 498±502
[9,10]. It seems likely that just because the crystal structure is conserved the He-implanted LN waveguides is characterized by comparatively high electro-optical and nonlinear optical properties [3,11]. The reconstruction of the refractive indices pro®les of He-implanted LN and LT reveals the near constant index level over guiding region and drastic index depression adjacent to Rp [6,12±14] that is typical for implanted oxides. A peculiarity of indices variations in guiding region of He-implanted LN family crystals is a dierence in sign. So, extraordinary index variation Dne in He-implanted LN (He ® LN) waveguides is positive [13] while ordinary index variation Dno in He ® LN layers [13] and both Dne;o in He ® LT layers are negative [6]. Any interpretation of the eect has not been presented till date. Earlier, only qualitative suppositions concerning possible physical mechanisms of indices variations in implanted ferroelectrics have been made, namely, by the change in lattice ion optical polarizabilities, the crystal volume variation, or the spontaneous polarization change [1,12,15]. No quantitative analysis has been carried out. The purpose of this paper is to construct the model of refractive indices changes in guiding region of He-implanted LN type crystals that permits the quantitative estimations, including the analysis of published experimental results when it is possible. 2. Model of index changes While constructing the model the following concepts were used as the basis: 1. As a result of the interaction between the highenergy light ions and the crystal lattice, the transition of LN or LT into a new state with decreased spontaneous polarization occurs in the region of electronic processes (guiding region). At the same time, there is no considerable disordering of the crystal lattice. 2. Chemical composition changes, oxygen loss for instance, are localized in the thin surface layer and do not aect signi®cantly the indices variations in the bulk of the guiding region.
499
3. The guiding region is a homogeneous layer in the optical and structure properties. A suciently high Dn uniformity through the depth up to near Rp region was demonstrated earlier experimentally for Ar [15], He [1,12,13,16] and H [17]. The homogeneity of d-spacing over guiding region of He ® LN layers was observed in [8]. The refractive indices changes in LN family crystals can be considered as a combined eect of four possible mechanisms: DnR ± due to variation of optical refraction, DnV ± due to molar volume change, DnP ± due to variation of the spontaneous polarization P, and Dne ± due to elasto-optic eect [18±21]. The ®rst and second components are governed by Lorenz±Lorentz law, and the third one by the known model [22]. Since there is no ion stopping in the electronic processes region and, correspondingly, the crystal chemical composition in the guiding region remains unchanged, the molecular refraction of the medium is the same as for the starting material and the component DnR is 0 for this part of the modi®ed layer. As it was recently demonstrated experimentally for He ® LN layers the surface stress contribution Dne , as a ®rst approximation, can also be neglected for the layers under consideration [13]. Thus, the values Dne;o are de®ned by the following set of equations: Dne;o DnPe;o DnVe;o :
1
Assuming the conservation of the oxygen-octahedral structure of LN or LT after ion implantation with doses of at least up to 2 ´ 1016 cmÿ2 for He the components DnPe;o can be written as [22] 2
DnPe n3e g33 P k =2 k 2 Dne ; 2
DnPo n3o g13 P k =2 k 2 Dno ;
2
where P is the spontaneous polarization magnitude of the unimplanted crystal, the factor k is the ratio P ÿ P =P , and P is the spontaneous polarization of the guiding region, gij are the quadratic electro-optical coecients, and ne;o are the refractive indices of unimplanted crystal. The expressions for the components DnVe;o can be derived from the Lorenz±Lorentz formula under the conditions Dne;o ne;o as
500
V.V. Atuchin / Nucl. Instr. and Meth. in Phys. Res. B 168 (2000) 498±502
DnVe;o ÿDV n2e;o ÿ 1 n2e;o 2=6ne;o V ÿDVBe;o ;
3
where V is a molar volume of the crystal, and DV is the change of the volume induced by implantation. Now, substituting Eqs. (2) and (3) in the ®rst equation of system (1), we get the relation DV k 2 Dne ÿ Dne =Be :
4
Further, using Eqs. (2)±(4) the second equation of system (1) can be transformed to the form k 2 Dno Dne Bo =Be = Dno ÿ Dne Bo =Be :
5
This relation gives the possibility to estimate the spontaneous polarization variation employing only the experimental data for Dne;o and some unimplanted crystal parameters. 3. Model veri®cation Thus, the refractive indices changes in the guiding region are governed mainly by the balance between DnPe;o and DnVe;o . Recall that DnPe;o > 0 with decreasing spontaneous polarization and in all cases DnPe > DnPo because g33 > g13 for LN family crystals. At the same time, the components DnPe;o are negative when DV > 0 (molar volume increase). Now it is reasonable to test the deductions of the model by other experimental results when possible. 3.1. He ! LN The LN parameters used in calculations are P 0.71 C/m2 [23], g33 0.090 m4 /C2 and g13 0.026 m4 /C2 [22], ne 2.2012 and no 2.2866 (congruent LN, k 0.633 lm). In [13], the Y-cut of LN implanted by 2 ´ 1016 cmÿ2 He ions with energy of 1.5 MeV was characterized by the nearsurface magnitudes Dne 0.014 and Dno )0.009. Then, from Eq. (5) we have the estimation k 0.36. Thus, the decrease of spontaneous polarization in the electronic process region or, in other words, in guiding part of He-implanted LN layers is only partial. In accordance with the known model [22] it means the presence of signi®cant
electro-optical and nonlinear optical eects in the medium. So, it would be reasonable to compare the value of k calculated above from refractive index data with the available experimental results on electro-optical and nonlinear optical properties of He ® LN waveguides. The electro-optical coecients after He implantation were estimated in [3] by Mach±Zenderin interference arrangement. The substrate orientation, dose, and exact ion energy were not reported but the depth of the layer was pointed as 2 lm. For this Rp the energy of He ions can be evaluated as near 1 MeV [3,13]. The measured values were 30% for r33 and 60% for r13 in reference to pure LN magnitudes. In accordance with the model [22] the electro-optical coecients in oxygen-octahedral ferroelectrics are in direct proportion to spontaneous polarization with the combination of some material constants as the coecient. So, if we relate the rij variations totally to spontaneous polarization decrease, then we have k 0.7±0.4. Recently the SHG capabilities of He-implanted (2 ´ 1016 cmÿ2 , 2 MeV) Y-cut LN waveguides were examined [11] by the re¯ection technique [24] with pumping at k 0.53 lm to minimize the penetration depth. A second-harmonic signal of about 75% of that of the substrate was detected in nearsurface part of the modi®ed layer. So, next time attributing the nonlinearity drop to spontaneous polarization decrease only, we have k 0.25 0.03. The pointed error bars are governed mainly by possible uncertainties (10%) in relative SH intensity measurements by the method used [24]. Thus, the spontaneous polarization decrease estimated from the electro-optical and nonlinear optical properties is closely related to the drop deduced from refractive indices changes. 3.2. He ! LT The refractive indices pro®les in He-implanted LT were reconstructed in [6] on the basis of a number of mode eective indices measured at k 0.633 lm. The implantation was produced with an ion energy of 2 MeV and a dose of 2 ´ 1016 cmÿ2 . Under the conditions the indices variations
V.V. Atuchin / Nucl. Instr. and Meth. in Phys. Res. B 168 (2000) 498±502
in the guiding region were Dne 0 and Dno )0.013. For LT we have P 0.50 C/m2 [23], g33 0.090 4 m /C2 and g13 0.023 m4 /C2 [22], ne 2.1824 and no 2.1770 (k 0.633 lm) for congruent composition Li/(Li+Ta) 0.49 [19]. Further, from (5), one can ®nd k 0.39. This value is in good magnitude agreement with the spontaneous polarization decrease in LN implanted by He under nearly the same conditions. So, we can safely assume that He ® LT waveguides should display the high electro-optical and nonlinear optical properties. Furthermore, with a dose increase from 2 ´ 1016 to 7 ´ 1016 cmÿ2 the extraordinary index variation becomes negative. This transition is accompanied by further decrease of the ordinary index [6]. Alternatively, in He ® LN waveguides the Dne remains positive and increases the magnitude with increasing dose [13]. This mystery dynamics of the Dne variation in these related crystals can be readily interpreted within the framework of the model presented. It is reasonable to suppose that the spontaneous polarization decrease and the volume dilation are enhanced by dose growing. If the same dose induces the same DV in LN and LT, then the components DnVe;o are closely related in the two crystals under consideration. The relation between the polarization-dependent components DnPe in LN and LT is quite dierent. Actually, the level of Dne for LN is twice as large as that for LT due to dierence in P . Now, for any k the same for LN and LT, we have DnPe LN 2DnPe (LT) from (2). If, also, the relation jDnPe LNj > jDnVe LN; LTj > jDnPe LTj is obeyed, then the sum Dne will be positive for LN and negative for LT, as we wished to prove. The eect for the ordinary index is not such outstanding due to a less strong DnPo and in both the crystals considered the values of Dno are negative. 3.3. He ! H:LN (H:LN is a proton exchanged LN) It has been known that in He ® LN layers, Dne > 0 and Dno < 0 in the guiding region [13,16]. As
501
was shown above, there is quite large residual spontaneous polarization in the layers. Recently, the optical waveguides produced by He implantation into previously hydrogen exchanged LN layers were studied [25]. The negative Dne in reference to ne level achieved by a proton exchange procedure was measured. Thus, the sign of the extraordinary index variation induced by implantation is rigorously dependent on whether pure LN or Hx Li1ÿx NbO3 solid solution was used as a substrate material. The causes of the extraordinary index increase in the guiding region of He ® LN layers were analyzed above. As to the negative extraordinary index variation in He ® H:LN waveguides, the physical properties of H:LN layers appear to be responsible for the eect. During the experiment produced in [25] the H:LN layers were synthesized by proton exchange in pure benzoic acid. It is common knowledge that the procedure results in the so-called b-Hx Li1ÿx NbO3 phase formation with x > 0.56 [26]. This phase has the rhombohedral LN structure [27] but zero or near-zero spontaneous polarization [20,24]. Consequently, when a H:LN layer is implanted by He, the extraordinary index variation is governed only by the negative DnVe component because the positive DnPe component is zero or near zero. 4. Conclusion The analysis of available experimental results on physical properties of He-implanted optical waveguides in LN family crystals permits the consideration of the refractive indices changes in guiding region as a sum of two dominant components induced by molar volume variation and spontaneous polarization decrease. It appears that the model may be extended to more complicated cases, such as a con®ning region of implanted layers and new pairs of ion implanted and substrate, say, H and LN, when the chemical interaction is possible. References [1] P.D. Townsend, Rep. Prog. Phys. 50 (1987) 501. [2] G.L. Destefanis, P.D. Townsend, J.P. Gailliard, Appl. Phys. Lett. 32 (1978) 293.
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