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Direct measurement of ordinary refractive index of proton exchanged LiNbO3 waveguides
Optics Communications92 (1992) 40-44 North-Holland
OPT ICS COMMUNICATIONS
Direct measurement of ordinary refractive index of proton exchanged LiNbO3 waveguides J. Olivares, M.A. Diaz-Garcia and J.M. Cabrera DepartamentoFisicaAplicada C-IV, UniversidadAut6noma de Madrid, CantoBlanco, MadridES-28049, Spain
Received 13 April 1992
A method for the direct measurementof ordinary refractiveindex no of proton-exchangedLiNbO3waveguidesis proposedand demonstrated. Valuesof Anoare givenfor a variety of guides (X-cut, Y-cut,differentlithium benzoateconcentrations,annealed or unannealed). The relationAno=0.007-0.40Anc holds for all Anovalues, exceptfor unannealed guides prepared in pure benzoicacid that showAnorelativelyhigher.The usefulnessoftbe methodfor the experimentalstudy ofanisotropicguidespresenting hybrid leakymodesis shown. 1. Introduction
Interest in proton exchanged (PE) LiNbO3 waveguides is quickly increasing because of a number of advantages in real devices. (i) The refractive index change of these guides is greater and sharper than that of Ti in-diffused guides, allowing higher circuit integration. (ii) The sensitivity to optical damage is several orders of magnitude lower [ 1,2]. (iii) The fabrication procedure is simple, cheap and well known so that the refractive index profile can be precisely controlled [3,4]. (iv) The first and best waveguide lasers have been produced on these guides [ 5 ], and second harmonic generation is actually achieved [6] by several phase matching methods. In appropriate conditions the exchange process resuits in an increase ( + 0.12) of the extraordinary refractive index and a decrease (about - 0 . 0 4 ) of the ordinary index, so that only extraordinary modes can be guided in these structures. This fact implies the occurrence of anisotropic modes of particular complexity for angles different from 0 ° or 90 ° between the optical axis and the propagating direction. These are the so-called hybrid leaky guided modes [7], whose extraordinary component is confined (guided) and, at the same time, the ordinary component radiates to the substrate. This phenomenon has important consequences for phase matching in second 40
harmonic generation and other devices based on material birefringence. Extraordinary refractive index changes Ane have been well determined from the experimental effective indices of guided modes for different types of PE-guides by common methods. On the other hand, the determination of ordinary index changes Ano induced by the proton exchange process is rather poor, in spite of the relevance mentioned above, mainly due to the fact that ordinary polarization cannot be guided in these PE-layers. Changes in ordinary index Ano have been estimated from three indirect measurements. By combining Ti in-diffusion and proton exchange processes, DeMicheli et al. [8] have inferred a value A n o = - 0 . 0 4 . By combining He + implantation with proton exchange Glavas et al. [ 9 ] have estimated the ordinary index profile and given a similar value for Ano. Finally, in order to satisfactorily explain anisotropic propagation, Nutt [ 10 ] has assumed the same value given in ref. [8], and Digonnet et al. [ 11 ] have found the value Ano= - 0 . 0 6 in Mg doped crystals. However, no direct measurement of Ano in PE-guides, free of possible cross effects with our fabrication procedures, has been published to date.
0030-4018/92/5 05.00 © 1992 ElsevierSciencePublishers B.V. All fights reserved.
Volume 92, number 1,2,3
OPTICS COMMUNICATIONS
2. The method
In this paper, we use the simple dark-mode reflectivity technique for a direct determination of the ordinary index change and the associated layer thickness of PE-guides. In this technique light coupling is carded out with an isosceles rutile prism through a "point contact", where a previously expanded light beam is focused. We use the decoupled orientation in which propagation direction and optic axis are parallel. For this orientation, the light sees a no in the layer smaller than that of the substrate and there exist no critical reflections but only partial reflections on the guide-substrate interface. Measurements are taken of the angular positions of the interference fringes (also called r e s o n a n c e s ) arising from those partial reflections. With the prism-coupler one has nvrism> nf (nf, layer index; air-gap is neglected) and almost grazing incidence angles (0~< 90 ° ) inside the layer are possible. For these angles the interface reflectivity is relatively higher and this improves fringe visibility. Sharpness of the layersubstrate interface of proton-exchanged structures also produces relatively high reflectivity. It has been experimentally observed as well, that fringe visibility is improved by putting a pressure onto the prism higher than the "normal" one used for the observation of real dark-modes. Fringe observation is favored by an air-gap between the prism and the guide as small as possible (high pressure). The method has been used by Chandler et al. [ 12 ] to improve the determination of index profiles of guiding layers. A simple interference analysis with the condition npmm> ns > nf (ns, substrate index) and assuming a negligible air-gap, gives "dark" fringes for angles 0m such that cos 0m= ( , ~ o / 2 n f h ) m . Here, m = 1, 2, ... is the interference order, Ao is the vacuum wavelength, and nth is the optical path across the layer. (This condition is similar to the guided mode condition except for the phase changes arising from total reflection; now, they can only be either 0 or ~ and independent on 0m). Thus, in terms of the experimental data Nm = nf sin 0,,, it can be written 2 N m = n f2 -- ( , ~ o / 2 h ) 2 m 2 .
( 1)
By plotting N 2 as a function of m 2, the values of nf and h are easily obtained. A LiNbO3 wafer (integrated optics grade) has been
15 August 1992
purchased from Photox, UK. Measured values of its refractive indices were no = 2.2865 and ne = 2.2030 at the HeNe laser wavelength (632.8 nm) used throughout the paper. Proton-exchanged waveguides have been prepared by immersing 10 X 20 X 1 mm 3 substrates (either X - o r Y-cut) in a solution of lithium benzoate in benzoic acid, for 1-24 hours (depending on samples) at 240 oC. The process has been carried out in an air atmosphere and, on finishing the immersion time, samples have quickly been withdrawn from the furnace. All optical measurements have been performed about two weeks after guide fabrication in order to get stationary profiles. The lithium benzoate concentration has been varied from 0 to 2%. Guide thicknesses and extraordinary refractive index profiles have been determined from the angular positions of the modes observed in the dark-mode patterns, using the decoupled orientation in which the propagation direction is perpendicular to the optic axis. The stepper motor rotating the sample gave an angular setting reproducibility of +0.001 °, although mode measurements only allowed a +0.0001 resolution for An~. On the other hand, since the interference fringes are broader than the mode lines, the experimental error on determining Ano was about + 0.001.
3. Results and discussion
Figure l illustrates the application of eq. ( 1 ) to a couple of X-cut samples for pure ordinary polarization (Z-propagation). Close circles (only six resonances were reliably observed in this case) correspond to an annealed guide prepared in pure benzoic acid at 241 °C for 1.58 h, whilst open circles (four resonances) stand for an annealed guide prepared with a 1% concentralion of lithium benzoate at 240°C for 10 h. Annealing treatments were carried out in air at 230°C for 13 h. Table 1 lists, for a few examples, the values obtained for Ano and ho by applying eq. ( 1 ). Data of fig. I correspond to the guides labelled 1 and 3 in the table. Typical experimental errors are of the order of + 0.001 for Ano and +0.01 ttm for ho. Values of A~, and he are also included in the table for comparison purposes (they have been obtained from the dark-mode pattern with pure extraordinary polarization for each guide). Notice the 41
Volume 92, number 1,2,3
OPTICS COMMUNICATIONS
5.10
5.00
,,_j 4.90
4.80
0
I0
20
30
40
2 1'1"I
Fig. 1. Plot of N2,, = (nfsin 0,.) 2 as a function of the squared interference order (m 2) for pure ordinary polarization. Close circles correspond to guide 1 of table 1, and open circles to guide 3 of that table.
good agreement between "ordinary" (ho) and "extraordinary" (he) thicknesses. The capabilities of this method are better illustrated with the experimental data shown in fig. 2 for the guide labelled 3 in table 1. In fig, 2a, "effective indices" associated to the resonances measured for pure ordinary polarization (Z-propagation) have been included, together with a schematic representation of the no profile. Figure 2c shows measured effective indices of pure extraordinary modes, as well as those associated to the resonances observed when N,, is smaller than the substrate extraordinary index. A schematic representation of the ne profile is also included. (Resonances associated with ne are experimentally seen with more contrast since Ane > Ano. ) Figure 2b shows the effective indices of hybrid leaky modes and resonances as a function of the angle between optical axis (C) and the direction of propagation. Since, as mentioned above, the mode condition and eq. (1) (dark interference fringe condi-
15 August 1992
tion) differ very little, the angular dependence of each mode is seen to continue on the angular dependence of the corresponding resonance. Obviously, at the crossing point of the substrate and layer effective indices (30 ° in this figure), no resonances are experimentally observed since there exists no optical discontinuity at this angle. This figure deafly illustrates the usefulness of the method presented in this paper for a detailed study of anisotropic hybrid leaky modes. In order to complete the information on the no changes, a couple of figures more are also given. Figure 3 shows Ano, determined from the observed resonances, as a function of the lithium benzoate concentration. Values of Ano are shown for guides just exchanged and the same guides after annealing at 230 ° C for 13 h. The corresponding values of Ane have also been included for comparison purposes. A complete parallelism is not observed between Ano and Ane curves. For the guide prepared in pure benzoic acid, a ratio AnJAno,~ 2.2 is found before annealing, whilst the ratio turns out to be about 3 after annealing. A ratio clearly greater than 2.2 is also found in all guides prepared in lithium benzoate solutions, either annealed or unannealed. This indicates that the (more aggressive) pure benzoic acid treatment affects to a relatively greater extend the ordinary index than the extraordinary one. This behaviour is more clearly visualized in fig. 4. In this figure Ano has been plotted against Ane for all guides prepared in this work: X-cut, Y-cut, different benzoate concentrations, different temperatures and times of treatment, before annealing and after a first annealing (at 230°C for 13 h) and a second annealing (at 275 ° for 15 h). Two clearly different And Ano values are observed in this figure. For those data corresponding to unannealed guides fabricated in pure benzoic acid (open circles) the value of Ane/
Table 1 Numerical data for a few examples of annealed guide, ,~= 632.8 nm. Li benzoate (%)
Temperature
Time (h)
Ano
ho (~tm)
An~
(°C)
h~ (ttm)
1
0
2 3 4
0.5 1 2
241 241 240 241
1.58 7 10 23.5
0.036 0.034 0.035 0.033
3.50 2.46 2.51 1.65
0.1095 0.1055 0.1036 0.0994
3.40 2.35 2.42 1.56
Sample
42
Volume 92, number 1,2,3
OPTICS COMMUNICATIONS
no profile
15 August 1992
ne profile ~
= '" " ° I I!!!!!!!:--/ ......... /
0
I
,2.32
1""
2
30
Depth (/~m)
$0
&nile •
90
I
2
Depth ( ~ m )
Fig. 2. (a) Schematic profile or ordinary refractive index and measured values of"effective indices" nfsin 0,, of observed dark interference fringes for pure ordinary polarization. (b) Continuous lines: dependence on # (angle formed by optic axis and propagation direction) of the refractive index of the guide and the substrate; close circles: measured effective indices of observed real modes at various values; open circles: measured "effective indices" of observed interference fringes at various ¢ values. Notice that interferences are not observed at the crossing angle of substrate and guide indices. (c) Schematic profile of extraordinary refractive index and measured effective indices of real modes and interference fringes for pure extraordinary polarization. Data have been taken from guide 3 of table 1. 0.06
|
,
~,
-
~,,,, ,,,
0.05 0
.
". . . .
i
,
AnD Ane
i'
0.12 0.050 0
<3 I
0.060
0.11 0.04
<1 I
0.040
,
0.03 0.0
1.0
,
0.10
2.0
0.030 0.100
% Lithium Benzoate
0.110
0.120
0.130
Ane
Fig. 3. Dependence of AnDand An©on the lithium benzoate concentration used for fabricating the guides. Before annealing (open symbols) and after annealing (close symbols). AnD is clearly s m a l l e r t h a n that c o r r e s p o n d i n g to all other guides. All o t h e r d a t a can be fitted to the straight continuous line d r a w n o n the figure whose equation is AnD = 0 . 0 0 7 - 0.40Ane.
(2)
Notice that for AnD = 0, eq. ( 2 ) gives An= = 0.018, although this extrapolation o f eq. ( 2 ) is n o t necessarily correct. M o r e likely, eq. ( 2 ) does not h o l d for these low index changes, in agreement with the highly nonlinear b e h a v i o u r previously found [4] for t h e
Fig. 4. Plot of Ant against AnDfor all guides prepared under various conditions. Open circles, pure benzoic acid (unannealed). All other are prepared with various concentrations of lithium benzoate or with pure acid after annealing. Unannealed: X-cut, close circles; Y-cut, open inverted triangles. After the first annealing treatment: X-cut, close inverted triangles; Y-cut, open squares. After the second annealing treatments: X-cut, close squares; Y-cut,open triangles. p r o t o n diffusion a n d the d e p e n d e n c e o f index on p r o t o n concentration. The extrapolated value An= = 0.018 falls in the range o f that f o u n d when using 4% benzoate concentration (An==0.03), at which a sharp change in the proton diffusion coefficient and other p r o p e r t i e s is observed [4]. D a t a for unannealed pure benzoic acid t r e a t m e n t ( o p e n circles in 43
Volume 92, number 1,2,3
OPTICS COMMUNICATIONS
fig. 4) also show the nonlinear behaviour of the exchange process. On the other hand, the plot of fig. 1 is not a straight line for unannealed guides prepared in pure benzoic acid. This indicates that the profile of Ano for these guides is not as close to a step-like profile as is the case of all other guides. This also makes less reliable the determination of Ano from eq. ( 1 ), and for this reason the error bars of Ano are larger for these data in fig. 4. (The error bars of all other data are similar to the symbol sizes. ) It was further checked that extraordinary index profiles of these guides do not actually exhibit a step-like shape as previously reported by other authors [9]. After annealing, ordinary and extraordinary profiles recover a steplike shape and, on plotting their values again in fig. 4, all fall on the straight continuous line. The different behaviour of unannealed guides fabricated with pure benzoic acid with respect to all other guides should have a counterpart on the crystallographic data of the guides. Work is under way to clarify this point. In conclusion, a simple prism-coupler method to directly measure ordinary refractive index changes in PE-LiNbO3 waveguides has been demonstrated. It is based on the measurement of the angular positions of interference fringes associated to the reflectivities of prism-guide and guide-substrate interfaces. It has been proved useful in the study of hybrid leaky modes in anisotropic PE-guides. It has been found that unannealed guides prepared in pure benzoic acid pres-
44
15 August 1992
ent relatively higher Ano than annealed guides or those prepared with lithium benzoate solutions.
Acknowledgements This work was supported by the spanish Comisi6n Interministerial de Ciencia y Tecnoloia under grants TIC88/12781.00 and TIC91/0142.
References [ 1 ] J. Jackel, A.M. Glass, G.E. Peterson, C.E. Rice, D.H. Olson and J.J. Veselka) J. Appl. Phys. 55 (1984) 269. [2] E. Glavas, J.M. Cabrera and P.D. Townsend, J. Phys. D 22 (1989) 611. [3] M. De Micheli, J. Botineau, S. Neven, F. Sibillot and D.B. Ostrowsky, Optics Lett. 8 ( 1983 ) 114. [ 4 ] J. Jackel, Integrated optical circuits, SPIE Vol 1583 ( 1991 ) 54 (a recent review on proton exchanged waveguides). [ 5 ] E. Lallier, J.P. Pochole, M. Papuchon, C. Grezer-Besset, E. Pelletier, M. De Micheli, M.J. Li, Q. He and D.B. Ostrowsky, Electron. Lett. 25 (1989) 1491. [6] M. De Micheli, J. Opt. Commun. 4 (1983) 25. [ 7 ] A. Knoesen, T.K. Taylor and M.G. Moharam, J. Lightwave Technology 6 (1988) 1083. [ 8 ] M. De Micheli, J. Botineau, F. Sibillot and D.B. Ostrowsky, Optics Comm. 42 (1982) 101. [ 9 ] E. Glavas, P.D. Townsend and M.A. Foad, Nucl. Instr. Meth. Phys. Rev. B 46 (1990) 156. [ 10] A.C.G. Nutt, J. Optical Commun. 6 (1985) 8. [ 11 ] M. Digonnet, M. Fejer and R. Byer, Optics. Lett. 10 ( 1985 ) 235. [ 12] P.J. Chandler, F.L. Lama, P.D. Townsend and L. Zhang, J. Lightwave Technol. 8 (1990) 917.
OPT ICS COMMUNICATIONS
Direct measurement of ordinary refractive index of proton exchanged LiNbO3 waveguides J. Olivares, M.A. Diaz-Garcia and J.M. Cabrera DepartamentoFisicaAplicada C-IV, UniversidadAut6noma de Madrid, CantoBlanco, MadridES-28049, Spain
Received 13 April 1992
A method for the direct measurementof ordinary refractiveindex no of proton-exchangedLiNbO3waveguidesis proposedand demonstrated. Valuesof Anoare givenfor a variety of guides (X-cut, Y-cut,differentlithium benzoateconcentrations,annealed or unannealed). The relationAno=0.007-0.40Anc holds for all Anovalues, exceptfor unannealed guides prepared in pure benzoicacid that showAnorelativelyhigher.The usefulnessoftbe methodfor the experimentalstudy ofanisotropicguidespresenting hybrid leakymodesis shown. 1. Introduction
Interest in proton exchanged (PE) LiNbO3 waveguides is quickly increasing because of a number of advantages in real devices. (i) The refractive index change of these guides is greater and sharper than that of Ti in-diffused guides, allowing higher circuit integration. (ii) The sensitivity to optical damage is several orders of magnitude lower [ 1,2]. (iii) The fabrication procedure is simple, cheap and well known so that the refractive index profile can be precisely controlled [3,4]. (iv) The first and best waveguide lasers have been produced on these guides [ 5 ], and second harmonic generation is actually achieved [6] by several phase matching methods. In appropriate conditions the exchange process resuits in an increase ( + 0.12) of the extraordinary refractive index and a decrease (about - 0 . 0 4 ) of the ordinary index, so that only extraordinary modes can be guided in these structures. This fact implies the occurrence of anisotropic modes of particular complexity for angles different from 0 ° or 90 ° between the optical axis and the propagating direction. These are the so-called hybrid leaky guided modes [7], whose extraordinary component is confined (guided) and, at the same time, the ordinary component radiates to the substrate. This phenomenon has important consequences for phase matching in second 40
harmonic generation and other devices based on material birefringence. Extraordinary refractive index changes Ane have been well determined from the experimental effective indices of guided modes for different types of PE-guides by common methods. On the other hand, the determination of ordinary index changes Ano induced by the proton exchange process is rather poor, in spite of the relevance mentioned above, mainly due to the fact that ordinary polarization cannot be guided in these PE-layers. Changes in ordinary index Ano have been estimated from three indirect measurements. By combining Ti in-diffusion and proton exchange processes, DeMicheli et al. [8] have inferred a value A n o = - 0 . 0 4 . By combining He + implantation with proton exchange Glavas et al. [ 9 ] have estimated the ordinary index profile and given a similar value for Ano. Finally, in order to satisfactorily explain anisotropic propagation, Nutt [ 10 ] has assumed the same value given in ref. [8], and Digonnet et al. [ 11 ] have found the value Ano= - 0 . 0 6 in Mg doped crystals. However, no direct measurement of Ano in PE-guides, free of possible cross effects with our fabrication procedures, has been published to date.
0030-4018/92/5 05.00 © 1992 ElsevierSciencePublishers B.V. All fights reserved.
Volume 92, number 1,2,3
OPTICS COMMUNICATIONS
2. The method
In this paper, we use the simple dark-mode reflectivity technique for a direct determination of the ordinary index change and the associated layer thickness of PE-guides. In this technique light coupling is carded out with an isosceles rutile prism through a "point contact", where a previously expanded light beam is focused. We use the decoupled orientation in which propagation direction and optic axis are parallel. For this orientation, the light sees a no in the layer smaller than that of the substrate and there exist no critical reflections but only partial reflections on the guide-substrate interface. Measurements are taken of the angular positions of the interference fringes (also called r e s o n a n c e s ) arising from those partial reflections. With the prism-coupler one has nvrism> nf (nf, layer index; air-gap is neglected) and almost grazing incidence angles (0~< 90 ° ) inside the layer are possible. For these angles the interface reflectivity is relatively higher and this improves fringe visibility. Sharpness of the layersubstrate interface of proton-exchanged structures also produces relatively high reflectivity. It has been experimentally observed as well, that fringe visibility is improved by putting a pressure onto the prism higher than the "normal" one used for the observation of real dark-modes. Fringe observation is favored by an air-gap between the prism and the guide as small as possible (high pressure). The method has been used by Chandler et al. [ 12 ] to improve the determination of index profiles of guiding layers. A simple interference analysis with the condition npmm> ns > nf (ns, substrate index) and assuming a negligible air-gap, gives "dark" fringes for angles 0m such that cos 0m= ( , ~ o / 2 n f h ) m . Here, m = 1, 2, ... is the interference order, Ao is the vacuum wavelength, and nth is the optical path across the layer. (This condition is similar to the guided mode condition except for the phase changes arising from total reflection; now, they can only be either 0 or ~ and independent on 0m). Thus, in terms of the experimental data Nm = nf sin 0,,, it can be written 2 N m = n f2 -- ( , ~ o / 2 h ) 2 m 2 .
( 1)
By plotting N 2 as a function of m 2, the values of nf and h are easily obtained. A LiNbO3 wafer (integrated optics grade) has been
15 August 1992
purchased from Photox, UK. Measured values of its refractive indices were no = 2.2865 and ne = 2.2030 at the HeNe laser wavelength (632.8 nm) used throughout the paper. Proton-exchanged waveguides have been prepared by immersing 10 X 20 X 1 mm 3 substrates (either X - o r Y-cut) in a solution of lithium benzoate in benzoic acid, for 1-24 hours (depending on samples) at 240 oC. The process has been carried out in an air atmosphere and, on finishing the immersion time, samples have quickly been withdrawn from the furnace. All optical measurements have been performed about two weeks after guide fabrication in order to get stationary profiles. The lithium benzoate concentration has been varied from 0 to 2%. Guide thicknesses and extraordinary refractive index profiles have been determined from the angular positions of the modes observed in the dark-mode patterns, using the decoupled orientation in which the propagation direction is perpendicular to the optic axis. The stepper motor rotating the sample gave an angular setting reproducibility of +0.001 °, although mode measurements only allowed a +0.0001 resolution for An~. On the other hand, since the interference fringes are broader than the mode lines, the experimental error on determining Ano was about + 0.001.
3. Results and discussion
Figure l illustrates the application of eq. ( 1 ) to a couple of X-cut samples for pure ordinary polarization (Z-propagation). Close circles (only six resonances were reliably observed in this case) correspond to an annealed guide prepared in pure benzoic acid at 241 °C for 1.58 h, whilst open circles (four resonances) stand for an annealed guide prepared with a 1% concentralion of lithium benzoate at 240°C for 10 h. Annealing treatments were carried out in air at 230°C for 13 h. Table 1 lists, for a few examples, the values obtained for Ano and ho by applying eq. ( 1 ). Data of fig. I correspond to the guides labelled 1 and 3 in the table. Typical experimental errors are of the order of + 0.001 for Ano and +0.01 ttm for ho. Values of A~, and he are also included in the table for comparison purposes (they have been obtained from the dark-mode pattern with pure extraordinary polarization for each guide). Notice the 41
Volume 92, number 1,2,3
OPTICS COMMUNICATIONS
5.10
5.00
,,_j 4.90
4.80
0
I0
20
30
40
2 1'1"I
Fig. 1. Plot of N2,, = (nfsin 0,.) 2 as a function of the squared interference order (m 2) for pure ordinary polarization. Close circles correspond to guide 1 of table 1, and open circles to guide 3 of that table.
good agreement between "ordinary" (ho) and "extraordinary" (he) thicknesses. The capabilities of this method are better illustrated with the experimental data shown in fig. 2 for the guide labelled 3 in table 1. In fig, 2a, "effective indices" associated to the resonances measured for pure ordinary polarization (Z-propagation) have been included, together with a schematic representation of the no profile. Figure 2c shows measured effective indices of pure extraordinary modes, as well as those associated to the resonances observed when N,, is smaller than the substrate extraordinary index. A schematic representation of the ne profile is also included. (Resonances associated with ne are experimentally seen with more contrast since Ane > Ano. ) Figure 2b shows the effective indices of hybrid leaky modes and resonances as a function of the angle between optical axis (C) and the direction of propagation. Since, as mentioned above, the mode condition and eq. (1) (dark interference fringe condi-
15 August 1992
tion) differ very little, the angular dependence of each mode is seen to continue on the angular dependence of the corresponding resonance. Obviously, at the crossing point of the substrate and layer effective indices (30 ° in this figure), no resonances are experimentally observed since there exists no optical discontinuity at this angle. This figure deafly illustrates the usefulness of the method presented in this paper for a detailed study of anisotropic hybrid leaky modes. In order to complete the information on the no changes, a couple of figures more are also given. Figure 3 shows Ano, determined from the observed resonances, as a function of the lithium benzoate concentration. Values of Ano are shown for guides just exchanged and the same guides after annealing at 230 ° C for 13 h. The corresponding values of Ane have also been included for comparison purposes. A complete parallelism is not observed between Ano and Ane curves. For the guide prepared in pure benzoic acid, a ratio AnJAno,~ 2.2 is found before annealing, whilst the ratio turns out to be about 3 after annealing. A ratio clearly greater than 2.2 is also found in all guides prepared in lithium benzoate solutions, either annealed or unannealed. This indicates that the (more aggressive) pure benzoic acid treatment affects to a relatively greater extend the ordinary index than the extraordinary one. This behaviour is more clearly visualized in fig. 4. In this figure Ano has been plotted against Ane for all guides prepared in this work: X-cut, Y-cut, different benzoate concentrations, different temperatures and times of treatment, before annealing and after a first annealing (at 230°C for 13 h) and a second annealing (at 275 ° for 15 h). Two clearly different And Ano values are observed in this figure. For those data corresponding to unannealed guides fabricated in pure benzoic acid (open circles) the value of Ane/
Table 1 Numerical data for a few examples of annealed guide, ,~= 632.8 nm. Li benzoate (%)
Temperature
Time (h)
Ano
ho (~tm)
An~
(°C)
h~ (ttm)
1
0
2 3 4
0.5 1 2
241 241 240 241
1.58 7 10 23.5
0.036 0.034 0.035 0.033
3.50 2.46 2.51 1.65
0.1095 0.1055 0.1036 0.0994
3.40 2.35 2.42 1.56
Sample
42
Volume 92, number 1,2,3
OPTICS COMMUNICATIONS
no profile
15 August 1992
ne profile ~
= '" " ° I I!!!!!!!:--/ ......... /
0
I
,2.32
1""
2
30
Depth (/~m)
$0
&nile •
90
I
2
Depth ( ~ m )
Fig. 2. (a) Schematic profile or ordinary refractive index and measured values of"effective indices" nfsin 0,, of observed dark interference fringes for pure ordinary polarization. (b) Continuous lines: dependence on # (angle formed by optic axis and propagation direction) of the refractive index of the guide and the substrate; close circles: measured effective indices of observed real modes at various values; open circles: measured "effective indices" of observed interference fringes at various ¢ values. Notice that interferences are not observed at the crossing angle of substrate and guide indices. (c) Schematic profile of extraordinary refractive index and measured effective indices of real modes and interference fringes for pure extraordinary polarization. Data have been taken from guide 3 of table 1. 0.06
|
,
~,
-
~,,,, ,,,
0.05 0
.
". . . .
i
,
AnD Ane
i'
0.12 0.050 0
<3 I
0.060
0.11 0.04
<1 I
0.040
,
0.03 0.0
1.0
,
0.10
2.0
0.030 0.100
% Lithium Benzoate
0.110
0.120
0.130
Ane
Fig. 3. Dependence of AnDand An©on the lithium benzoate concentration used for fabricating the guides. Before annealing (open symbols) and after annealing (close symbols). AnD is clearly s m a l l e r t h a n that c o r r e s p o n d i n g to all other guides. All o t h e r d a t a can be fitted to the straight continuous line d r a w n o n the figure whose equation is AnD = 0 . 0 0 7 - 0.40Ane.
(2)
Notice that for AnD = 0, eq. ( 2 ) gives An= = 0.018, although this extrapolation o f eq. ( 2 ) is n o t necessarily correct. M o r e likely, eq. ( 2 ) does not h o l d for these low index changes, in agreement with the highly nonlinear b e h a v i o u r previously found [4] for t h e
Fig. 4. Plot of Ant against AnDfor all guides prepared under various conditions. Open circles, pure benzoic acid (unannealed). All other are prepared with various concentrations of lithium benzoate or with pure acid after annealing. Unannealed: X-cut, close circles; Y-cut, open inverted triangles. After the first annealing treatment: X-cut, close inverted triangles; Y-cut, open squares. After the second annealing treatments: X-cut, close squares; Y-cut,open triangles. p r o t o n diffusion a n d the d e p e n d e n c e o f index on p r o t o n concentration. The extrapolated value An= = 0.018 falls in the range o f that f o u n d when using 4% benzoate concentration (An==0.03), at which a sharp change in the proton diffusion coefficient and other p r o p e r t i e s is observed [4]. D a t a for unannealed pure benzoic acid t r e a t m e n t ( o p e n circles in 43
Volume 92, number 1,2,3
OPTICS COMMUNICATIONS
fig. 4) also show the nonlinear behaviour of the exchange process. On the other hand, the plot of fig. 1 is not a straight line for unannealed guides prepared in pure benzoic acid. This indicates that the profile of Ano for these guides is not as close to a step-like profile as is the case of all other guides. This also makes less reliable the determination of Ano from eq. ( 1 ), and for this reason the error bars of Ano are larger for these data in fig. 4. (The error bars of all other data are similar to the symbol sizes. ) It was further checked that extraordinary index profiles of these guides do not actually exhibit a step-like shape as previously reported by other authors [9]. After annealing, ordinary and extraordinary profiles recover a steplike shape and, on plotting their values again in fig. 4, all fall on the straight continuous line. The different behaviour of unannealed guides fabricated with pure benzoic acid with respect to all other guides should have a counterpart on the crystallographic data of the guides. Work is under way to clarify this point. In conclusion, a simple prism-coupler method to directly measure ordinary refractive index changes in PE-LiNbO3 waveguides has been demonstrated. It is based on the measurement of the angular positions of interference fringes associated to the reflectivities of prism-guide and guide-substrate interfaces. It has been proved useful in the study of hybrid leaky modes in anisotropic PE-guides. It has been found that unannealed guides prepared in pure benzoic acid pres-
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ent relatively higher Ano than annealed guides or those prepared with lithium benzoate solutions.
Acknowledgements This work was supported by the spanish Comisi6n Interministerial de Ciencia y Tecnoloia under grants TIC88/12781.00 and TIC91/0142.
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