- Email: [email protected]
Nonconventional characterization of single-mode planar proton-exchanged LiNbO3 waveguides by Cherenkov second harmonic generation
1 January 1999
Optics Communications 159 Ž1999. 37–42
Nonconventional characterization of single-mode planar proton-exchanged LiNbO 3 waveguides by Cherenkov second harmonic generation R. Ramponi ) , M. Marangoni, R. Osellame, V. Russo Istituto Nazionale Fisica–della Materia (INFM), Dipartimento di Fisica – Politecnico and Centro di Elettronica Quantistica e Strumentazione Elettronica (CEQSE) del Consiglio Nazionale delle Ricerche (CNR), Piazza L. da Vinci 32, 20133 Milan, Italy Received 13 July 1998; revised 28 September 1998; accepted 16 October 1998
Abstract A nonconventional characterization method for single-mode planar proton-exchanged ŽPE. LiNbO 3 waveguides is presented. The method exploits the dependence of the output angle of Cherenkov second-harmonic radiation-mode on the boundary conditions of the fundamental guided mode, and thus, in particular, on the cover refractive index. The measurement of this angle in the presence of different liquid covers of known refractive index provides sufficient information to determine both parameters of the waveguide refractive-index profile, i.e., the index change and the optical depth. The experimental results confirm the reliability of the method proposed. q 1999 Elsevier Science B.V. All rights reserved. PACS: 42.82; 42.65.K; 42.65.W Keywords: Proton-exchanged lithium niobate waveguides; Nonlinear optical waveguides; Second harmonic generation; Waveguide characterization
1. Introduction Proton-exchanged ŽPE. LiNbO 3 waveguides are of great interest in the field of nonlinear integrated optics. Indeed, these waveguides exhibit a high efficiency for Cherenkov second harmonic generation w1–4x and constitute the first fabrication step for PE annealed ŽAPE. waveguides, particularly suited for guided second harmonic generation in periodically poled structures w5,6x. Thus, these waveguides are likely to play a major role in many applications, such as frequency doubling at short wavelengths Žblue-violet.
)
Corresponding author. E-mail: [email protected]
and the realization of all optical devices based on x 2 cascading processes. Waveguides designed for nonlinear processes require a very accurate characterization, due to the strong dependence of nonlinear phenomena on the guiding-structure optical parameters w7x. The most widely used characterization technique for planar waveguides is conventional prism-coupling m-lines technique: in this technique, the propagation constants of the guided modes are determined and then the index profile is calculated by means of inverse methods w8x. However, even when the shape of the refractive index profile of the waveguide is known, at least two optical parameters have to be determined, i.e., the refractive index change Ž D n. and the optical depth Ž d ., and therefore at least two guided modes must be sup-
0030-4018r99r$ - see front matter q 1999 Elsevier Science B.V. All rights reserved. PII: S 0 0 3 0 - 4 0 1 8 Ž 9 8 . 0 0 5 8 0 - X
38
R. Ramponi et al.r Optics Communications 159 (1999) 37–42
ported: thus, this technique cannot be applied to the waveguides mostly used in the above mentioned applications, that are typically single-mode in a wide range of wavelengths. For single-mode waveguides, different techniques have been proposed, based on the detection of the near-field w9,10x, refracted near-field w11x or far-field w12x profile, on interferometric measurements w13x, and on prism-coupling characterization at different wavelengths w14x. None of these methods seem particularly suitable or accurate enough for PE-LiNbO3 single-mode planar waveguides, whose depth is often below 1 mm due to the high index change. In fact, near-field or refracted near-field techniques do not allow accurate measurements for very thin waveguides since these would require imaging or coupling objectives with a too high numerical aperture. The modified far-field method represents a significant improvement, but still not sufficiently accurate for nonlinear applications. As to interferometric measurements, the recently proposed Lloyd configuration w13x, that allows the highest precision, requires the waveguide to be dipped in a liquid with a refractive index higher than that of the guiding film, this being a serious problem in the case of PE-LiNbO3 waveguides since the film refractive index is much higher than that of all easy-to-handle Žnontoxic. liquids available. Finally, the technique based on the determination of the propagation constant of the mode at different wavelengths requires, for these constants to be correlated, an accurate knowledge of the dependence of the index change on the wavelength, which is not easy to obtain. In this paper a new method is presented for an accurate determination of the optical parameters of a single-mode planar PE-LiNbO3 waveguide. When a liquid is placed above the waveguide, it alters the effective refractive index of the fundamental guided mode and hence, as it has already been observed w15,16x, the Cherenkov secondharmonic radiation-mode output angle. By measuring this output angle for two different liquids of known refractive index, two independent informations are obtained, thus allowing the determination of both d and D n. It is worth noting that by this method the determination of the waveguide parameters at the fundamental wavelength of the guided mode, typically in the near infrared, is achieved by a plain angular measurement performed on the secondharmonic beam, and therefore in the visible.
can be obtained by modifying by a known quantity one of the parameters which affect the propagation conditions and hence n eff itself, e.g., by varying the cover refractive index n c of the waveguide. To this aim, a liquid of known refractive index is placed above the waveguide. In the case of PE-LiNbO 3 waveguides that exhibit second-order nonlinearity, n eff can be determined through the measurement of the output angle of Cherenkov second-harmonic radiation-mode. This method has been chosen since it is the most straightforward. Indeed, the determination of n eff by means of grating couplingroutcoupling angles would require the realization of a grating on the waveguide, whereas in the standard prism-coupling m-lines method it would be difficult to control the uniformity of the liquid layer below the prism; moreover, the geometrical and optical characteristics of the coupling device Žgrating or prism. should be known with high precision. It is worth recalling the basics of second harmonic generation in the Cherenkov configuration w2,3x. This process involves power transfer from a fundamental guided mode at v to a second harmonic radiation mode at 2 v propagating inside the substrate at the angle u C-int ŽFig. 1a.. This angle is given by the phase-matching condition, which, in the case of our experimental conditions, i.e., Z-cut PE-LiNbO3 waveguide where only extraordinary TM modes are supported, has the following expression:
u C - int s arccos
ž
v n eff
n 2s ,ev Ž u C - int .
/
Ž 2.1 .
v where n eff is the effective index of the coupled guided mode, and n2s,ev is the extraordinary refractive index of the substrate as seen by the Cherenkov beam, which depends on u C-int according to the well-known index-ellipsoid.
2. Operation principle As already stated above, optical characterization of single-mode planar waveguides requires the determination of the index profile shape and of the profile parameters. When the profile shape is known, which is the case of PE-LiNbO 3 waveguides that exhibit an almost step-index profile w17x, to obtain the two parameters D n and d, the measurement of the effective index n eff of the single guided mode is not sufficient. A second independent n eff
Fig. 1. Cherenkov second harmonic generation scheme for a waveguide with air as the cover Ža. and with a liquid sample as the cover Žb.. The Cherenkov beam direction is indicated with a continuous line in the first case Ž u C-ext . and with a dashed line in the second Ž u C-ext,i ..
R. Ramponi et al.r Optics Communications 159 (1999) 37–42
Referring to Fig. 1a, it can be seen that the Cherenkov angle that can be measured is actually the external one, u C-ext , that is related to u C-int by Snell’s refraction law:
u C -ext s arcsin Ž
n 2s ,ev
Ž u C - int . sin u C - int .
Ž 2.2 .
Eqs. Ž2.1. and Ž2.2. provide the relation between u C-ext , which is the measured quantity, and the effective refractive v . The effective index in index of the fundamental mode n eff turn depends on the refractive index of the waveguide cover, by means of the well-known characteristic equation: 2 k0 d
n fv,o n fv,e
(Ž n
v 2 y f ,e
.
v 2 Ž neff . y 2F f – s y 2F f – c s 2 mp
and d, are estimated by finding the zero of the following function: f Ž D n e ,d . s Ž D u 1meas y D u 1calc Ž D n e ,d . .
F f – s s arctan
n fv,o n fv,e
Ž nsv,e n sv,o .
2
)
2
2
v Ž n eff . y Ž n sv,e . 2 v 2 Ž n fv,e . y Ž n eff .
Ž 2.3a . F f – c s arctan
n fv,o n fv,e
Ž n cv .
2
)
2
2
v Ž n eff . y Ž n cv . 2 v 2 Ž n fv,e . y Ž neff .
Ž 2.3b .
Eq. Ž2.3. contains the parameters of the waveguide to be v v y n s,e together with the determined, i.e., d and D n e s n f,e parameters known or measured, i.e., n c and n eff . Two independent equations can then be obtained by writing Eq. Ž2.3. for two different covers, where the two corresponding n eff are obtained by means of two different u C-ext measurements. In principle, the two measurements could be performed with air as the first cover and a liquid as the second one. However, from the experimental point of view, the determination of the absolute value of u C-ext requires a precise zero-setting that is not easy to obtain. It is more convenient to use air as the reference cover, with the corresponding Cherenkov output beam giving the relative zero-line, and to measure the variation of the Cherenkov output angle in the presence of two different liquid covers with respect to that line, as shown in Fig. 1b. The measured quantity is then: D u imeas s u C - ext y u C - ext ,i
Ž 2.4 .
where u C-ext is the Cherenkov output angle with air as the cover, whereas u C-ext,i , with i s 1, 2, are the Cherenkov output angles in the presence of the two different liquid covers. Once the two independent D u imeas have been measured, the values of the two waveguide parameters, D n e
2
q Ž D u 2meas y D u 2calc Ž D n e ,d . . D u 1calc
2
Ž 2.5 .
D u 2calc
where and are the Cherenkov angle variations calculated for the two covers of known refractive index when the waveguide parameters are D n e and d. Actually, to achieve a higher accuracy in the determination of D n e and d, a larger number k of independent D u imeas can be measured with different liquids, and the corresponding function f
Ž 2.3 . where d is the waveguide depth, the subscripts ‘o’ and ‘e’ stand for ordinary and extraordinary, n fv is the refractive index of the film, m is the order of the mode, and F f – s and F f – c are the phase-shifts due to the total reflection at the boundaries film–substrate and film–cover, respectively:
39
k
Ý Ž D u imeas y D u icalc Ž D ne ,d . .
f Ž D n e ,d . s
2
,
is1
i s 1, . . . ,k
Ž 2.5X .
minimized. It is worth pointing out that in the above equations, the ordinary index change D n o is also involved, but it is not explicitly indicated since it is proportional to the extraordinary one w17x. The characterization method here described can be used for any guiding structure exhibiting Cherenkov second harmonic generation Ži.e., nonlinear waveguide on nonlinear substrate, linear waveguide on nonlinear substrate, nonlinear waveguide on linear substrate., at any fundamental wavelength where the phase-matching condition is fulv filled Ž n eff - n2s v , from Eq. Ž2.1.. and giving a second harmonic in the substrate transparency range. The method is particularly suitable for PE-LiNbO3 waveguides since they give efficient second harmonic generation in the Cherenkov regime w1x. Moreover, in these waveguides, very thin and with a high index change, the cover refractive index affects significantly n eff w18x, thus resulting in large and easily detectable D u meas when a liquid is placed above the waveguide instead of air. It is worth noting that the determination of D n e and d does not require the knowledge of any parameter related to the coupling conditions Že.g., prism refractive index and base angle, coupling angle, etc...
3. Experimental setup The experimental setup is shown in Fig. 2. The laser source is a lamp-pumped 5 W cw Nd:YAG laser source at l s 1.064 mm, and power is lowered to an average value of 50 mW by using an external light-chopper, so as to avoid significant thermal heating of both the waveguide and the liquids. Indeed, the light, coupled into the waveguide by means of a rutile prism, has an average power of 17 mW, with a peak power 100 times higher. This results in a temperature increase of about 0.58C that does not affect significantly the optical characteristics of the materials involved. A mirror M mounted on a PC controlled
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R. Ramponi et al.r Optics Communications 159 (1999) 37–42
and the average value has been calculated. This value is reported in Table 1 together with the refractive index n c of each liquid. From these experimental data, the waveguide parameters D n e and d at l s 1.064 mm are calculated following the procedure described above and the following results are obtained: Fig. 2. Experimental set-up: LS, Nd:YAG laser; L, spherical lens f s 400 mm; P, rutile prism; WG, waveguide; BS, beam splitter; PM, power meter; D, diaphragm Ž1 mm.; LQ, liquid sample; M, mirror; R, rotatory stage. Dashed line: fundamental beam; continuous line: second harmonic beam.
rotator Žangular accuracy of "5 arcsec. is used to measure the Cherenkov output angle variation. The measurement is performed as follows: the laser beam is coupled into the waveguide with air as the cover, and the mirror is set orthogonally to the Cherenkov second harmonic beam: this position is taken as the reference for the following measurement of the Cherenkov angle variation. Then a drop of liquid is placed on the waveguide and the mirror set orthogonally to the new direction of the Cherenkov beam. The rotation angle of the mirror equals the Cherenkov angle variation D u meas induced by the presence of the liquid. To find the orthogonality condition, a diaphragm Ž1 mm diameter. is aligned to the Cherenkov output beam and the mirror rotated until the reflected beam passes back through the diaphragm: a beam splitter placed on the beam path between the waveguide and the diaphragm deviates part of the reflected beam, transmitted through the diaphragm, to a photodetector: when maximum intensity reading is obtained, the orthogonality condition is reached. With this set-up a precision of "0.018 in the measurement of D u meas is attained. The waveguide chosen to test the method described above is a Z-cut LiNbO 3 waveguide fabricated by proton exchange in benzoic acid. For such a waveguide the index profile is best described by a step-like function w17x: this was confirmed by a series of prism-coupling characterization measurements performed on some multimode samples exchanged for a longer time in the same bath. The waveguide used in the experimental test is single-mode from 450 nm up Žthe only supported mode being TM and of extraordinary polarization. and therefore cannot be characterized with the prism-coupling technique even at short wavelengths. The measurements of Cherenkov output angle variation have been performed with six liquids Žpurchased from Cargille Laboratories Inc., USA. of different refractive indices ranging from 1.484 to 1.745 at l s 1.064 mm. The values of the refractive indices of the liquids are given by Cargille with a tolerance of "0.0015.
D n e s 0.0890,
d s 0.451 mm,
whereas the ordinary index change is assumed w17x to be: D n o s yD n er3 s y0.0297. In Fig. 3, the experimental average values of D u meas are plotted versus n c together with the curve given by D u calc as calculated from the waveguide parameters obtained above. The good agreement between measured and calculated Cherenkov angle variations in the whole n c range demonstrates the reliability of the parameters determined. To show the capability of the method to discriminate a single pair of values D n e and d with sufficient resolution, the function f of Eq. Ž2.5X . has been studied. The function f can be represented as a surface dependent on D n e and d, but, for the sake of simplicity, only the curve Žsolid line. corresponding to the direction of minimum slope of f Ždashed line in the D n e –d plane. has been plotted in Fig. 4. Nevertheless, the minimum appears significantly sharp since f doubles for variations of "0.0015 in D n e and of "6 nm in d Žsee projections of the f curve on the vertical coordinate planes.. To evaluate the accuracy of the method in determining D n e and d, it is worth analyzing all possible sources of errors, so as to quantify their effect. Table 2 summarizes the results of this analysis, giving the estimated error magnitude for each different possible source, together with the consequent standard deviation of D n e and d, as calculated for our waveguide in the case of six liquids by applying the error propagation theory w19x. The most important errors come from the experimental error in the angle measurements and from an inaccurate knowledge of the liquid cover refractive index. The first one is reported for a single determination of D u meas for
Table 1 Experimental Cherenkov angle variations, D u me as Liquid refractive index, n c
D u me as Ždegrees.
4. Results and discussion
1.484 1.578 1.622 1.667 1.717 1.745
0.653 0.908 1.047 1.214 1.423 1.570
For each of the six liquids used, four measurements of Cherenkov angle variation D u meas have been performed
Average values of D u me as Žon four measurements. for the six refractive indices of the liquids used.
R. Ramponi et al.r Optics Communications 159 (1999) 37–42
41
Table 2 Error analysis of the method
Fig. 3. Full circles: experimental values of the Cherenkov angle variation D u me as plotted versus the refractive index n c of the liquids used. Continuous curve: Cherenkov angle variation D u calc as a function of n c calculated on the basis of the obtained D n e s 0.0890 and ds 0.451 mm.
each liquid and can be reduced by a factor N 1r2 by performing N measurements. In the experiment reported, four measurements per liquid were performed, so as to obtain an uncertainty of "0.0008 in D n e and of "3 nm in d, thus comparable to that caused in the present case by the unprecise knowledge of n c . The incidence of this error could also be reduced by using a telescope mounted on a goniometer instead of a rotating mirror to measure D u meas. As to the influence of n c , it would be possible to achieve better performances either by using liquids whose refractive index is known with higher precision or by measuring the liquid refractive index with some very accurate methods Žtypically interferometric methods w20x.. The effect of the error on the substrate extraordinary refractive index n s,e of our LiNbO 3 , which is "0.0004, can be considered very small on both D n e and d. This weak dependence of the waveguide parameters on the precision of the n s,e value is a significant advantage of this method with respect to those based on the measurement of coupling angles Žprism and grating-coupling methods.. Regarding the ordi-
Fig. 4. The continuous curve represents the function f of Eq. Ž2.5X . plotted versus D n e and d along the direction of minimum slope of f Ždashed line in the D n e – d plane.. The projections of this curve on the vertical coordinate planes are also represented with dashed lines.
Sources of errors
Error magnitude s Ž D n. s Ž d . Žnm.
Single measurement of D u me as Knowledge of n c Knowledge of n s,e Knowledge of D n o End-face angle cut
"0.018 "0.0015 "0.0004 "0.003 "0.18
0.0016 0.0010 0.0001 0.0001 0.0002
6 4.5 0.3 1 0.4
Analysis of the different sources of error of the method. The effect of each source of error on the determination of D n e and d is calculated and reported in the table in terms of standard deviation.
nary index change, since the literature does not provide any indication on the precision of the relationship giving D n o , we have assumed a tolerance of "10% on its absolute value, which should constitute an excess estimate of the possible error. Nevertheless, its influence on the waveguide parameters is also very small. Lastly, we verified that it is sufficient to control the end-face angle within "0.18 so as not to affect significantly the determination of D n e and d. When considering all possible sources of error, the resulting accuracy, with four measurements for each of the six liquids, is better than "0.0013 for D n e and "6 nm for d. A further confirmation of the goodness of our index profile parameter reconstruction, comes from the excellent agreement between the calculated effective index of the guided mode Žwith air as the cover., n eff s 2.1573, and the effective index measured by prism-coupling technique, equal to 2.1572. Actually, the number of liquids to be used and that of the measurements per liquid to be performed depends on the final accuracy required for D n e and d. In this respect, some criteria have to be taken into account: Ži. for a given number of liquids, the resulting accuracy increases when the range of refractive indices of the liquids themselves is wider; Žii. the number of liquids and that of the measurements per liquid have to be chosen so that the two main errors in the index profile reconstruction are comparable, i.e., a higher number of liquids has to be used when their refractive index is known with poor precision, whereas a higher number of measurements per liquid has to be performed when the experimental error on D u meas is important. With the errors reported above for our case, when using only the two liquids with n c s 1.484 and n c s 1.745 and performing a single measurement per liquid, the resulting uncertainty on D n e would increase to "0.0022 and that on d to "9 nm, still acceptable for many applications. It is noteworthy that the overall accuracy reached in the characterization of single-mode waveguides by the method proposed is not far from that achievable on multimode waveguides with conventional techniques Že.g., m-line spectroscopy by prism coupling.. Actually, a direct com-
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R. Ramponi et al.r Optics Communications 159 (1999) 37–42
parison of the different methods on the same waveguide would in principle be of interest, but in practice it is difficult to perform in a significant way. In fact, conventional techniques can be applied only to multimode waveguides and become more and more precise when the number of guided modes increases, since the reconstruction of the index profile benefits a higher number of measured fitting parameters. On the contrary, the Cherenkov-based characterization that we propose gives its best performances on single-mode waveguides, where maximum sensitivity is obtained, together with a good Cherenkov conversion efficiency. As a consequence, a direct comparison on single-mode waveguides is not feasible, and a direct comparison on multimode waveguides would not evidence the real potentials of the Cherenkovcharacterization on single-mode waveguides, which however are the most important in photonic devices.
5. Conclusions We have demonstrated a new accurate method for the determination of the index profile parameters of singlemode planar nonlinear waveguides, particularly suitable for PE-LiNbO 3 waveguides. The method exploits the dependence of second harmonic generation in the Cherenkov configuration on the propagation conditions as determined by the presence of different covers. It allows a nondestructive waveguide characterization, performed by means of a simple angular measurement. It does not require any knowledge of the light coupling conditions nor of the coupling device characteristics. Moreover, the waveguide parameters in the near infrared are determined by means of a measurement performed at the second harmonic frequency, that is in the visible range, with obvious advantages in terms of easiness of operation.
Acknowledgements This work was partially supported by the National Research Council through the Special Project MADESS II
and the Research Project ‘Nonlinear optical guiding structures for all-optical signal processing’ of Technological Sciences and Innovation Committee. The authors wish to thank Prof. De Silvestri and Prof. Magni for the use of the Nd:YAG laser.
References w1x T. Taniuchi, K. Yamamoto, Y. Fujii, CLEO86 paper WR3 Ž1986. p. 230. w2x R.W. Keys, A. Loni, R.M. De La Rue, J. Mod. Opt. 37 Ž1990. 545. w3x M.J. Li, M.P. De Micheli, Q. He, D.B. Ostrowsky, IEEE J. Quantum Electron. 26 Ž1990. 1384. w4x G.Y. Wang, Y. Yang, E. Garmire, Appl. Phys. Lett. 66 Ž1995. 3416. w5x P. Baldi, C.G. Trevino-Palacios, G.I. Stegeman, M.P. De ˜ Micheli, D.B. Ostrowsky, D. Delacourt, M. Papuchon, Electron. Lett. 31 Ž1995. 1350. w6x M.L. Bortz, M.A. Arbore, M.M. Fejer, Opt. Lett. 20 Ž1995. 49. w7x N.A. Sanford, J.M. Connors, J. Appl. Phys. 65 Ž1989. 1429. w8x P. Mathey, P. Jullien, Opt. Commun. 122 Ž1996. 127. w9x G.L. Yip, P.C. Noutsios, L. Chen, Appl. Opt. 35 Ž1996. 2060. w10x A. Sharma, P. Bindal, Proc. Soc. Photo-Opt. Inst. Eng. 2212 Ž1994. 152. w11x N. Gisin, R. Passy, P. Stamp, N. Hori, S. Nagano, Appl. Opt. 33 Ž1994. 1726. w12x J. Rams, J.M. Cabrera, Opt. Commun. 139 Ž1997. 205. w13x E. Fazio, W.A. Ramadan, M. Bertolotti, G.C. Righini, Opt. Lett. 21 Ž1996. 1238. w14x L.P. Shi, E.Y.B. Pun, P.S. Chung, Opt. Lett. 20 Ž1995. 1623. w15x N.A. Sanford, W.C. Robinson, Opt. Lett. 12 Ž1987. 445. w16x R. Ramponi, M. Marangoni, R. Osellame, in: A.N. Chester et al., ŽEds.., Optical Sensors and Microsystems: New Concepts, Materials and Technologies, Plenum Ž1998. in press. w17x J.F. Offersgaard, T. Veng, T. Skettrup, Appl. Opt. 35 Ž1996. 2602. w18x D. Clerc, W. Lukosz, Sensors Actuators B 11 Ž1993. 461. w19x P.R. Bevington, Data Reduction and Error Analysis for the Physical Sciences, Chaps. 4–5, McGraw-Hill Ž1969.. w20x B. Richerzhagen, Appl. Opt. 35 Ž1996. 1650.
Optics Communications 159 Ž1999. 37–42
Nonconventional characterization of single-mode planar proton-exchanged LiNbO 3 waveguides by Cherenkov second harmonic generation R. Ramponi ) , M. Marangoni, R. Osellame, V. Russo Istituto Nazionale Fisica–della Materia (INFM), Dipartimento di Fisica – Politecnico and Centro di Elettronica Quantistica e Strumentazione Elettronica (CEQSE) del Consiglio Nazionale delle Ricerche (CNR), Piazza L. da Vinci 32, 20133 Milan, Italy Received 13 July 1998; revised 28 September 1998; accepted 16 October 1998
Abstract A nonconventional characterization method for single-mode planar proton-exchanged ŽPE. LiNbO 3 waveguides is presented. The method exploits the dependence of the output angle of Cherenkov second-harmonic radiation-mode on the boundary conditions of the fundamental guided mode, and thus, in particular, on the cover refractive index. The measurement of this angle in the presence of different liquid covers of known refractive index provides sufficient information to determine both parameters of the waveguide refractive-index profile, i.e., the index change and the optical depth. The experimental results confirm the reliability of the method proposed. q 1999 Elsevier Science B.V. All rights reserved. PACS: 42.82; 42.65.K; 42.65.W Keywords: Proton-exchanged lithium niobate waveguides; Nonlinear optical waveguides; Second harmonic generation; Waveguide characterization
1. Introduction Proton-exchanged ŽPE. LiNbO 3 waveguides are of great interest in the field of nonlinear integrated optics. Indeed, these waveguides exhibit a high efficiency for Cherenkov second harmonic generation w1–4x and constitute the first fabrication step for PE annealed ŽAPE. waveguides, particularly suited for guided second harmonic generation in periodically poled structures w5,6x. Thus, these waveguides are likely to play a major role in many applications, such as frequency doubling at short wavelengths Žblue-violet.
)
Corresponding author. E-mail: [email protected]
and the realization of all optical devices based on x 2 cascading processes. Waveguides designed for nonlinear processes require a very accurate characterization, due to the strong dependence of nonlinear phenomena on the guiding-structure optical parameters w7x. The most widely used characterization technique for planar waveguides is conventional prism-coupling m-lines technique: in this technique, the propagation constants of the guided modes are determined and then the index profile is calculated by means of inverse methods w8x. However, even when the shape of the refractive index profile of the waveguide is known, at least two optical parameters have to be determined, i.e., the refractive index change Ž D n. and the optical depth Ž d ., and therefore at least two guided modes must be sup-
0030-4018r99r$ - see front matter q 1999 Elsevier Science B.V. All rights reserved. PII: S 0 0 3 0 - 4 0 1 8 Ž 9 8 . 0 0 5 8 0 - X
38
R. Ramponi et al.r Optics Communications 159 (1999) 37–42
ported: thus, this technique cannot be applied to the waveguides mostly used in the above mentioned applications, that are typically single-mode in a wide range of wavelengths. For single-mode waveguides, different techniques have been proposed, based on the detection of the near-field w9,10x, refracted near-field w11x or far-field w12x profile, on interferometric measurements w13x, and on prism-coupling characterization at different wavelengths w14x. None of these methods seem particularly suitable or accurate enough for PE-LiNbO3 single-mode planar waveguides, whose depth is often below 1 mm due to the high index change. In fact, near-field or refracted near-field techniques do not allow accurate measurements for very thin waveguides since these would require imaging or coupling objectives with a too high numerical aperture. The modified far-field method represents a significant improvement, but still not sufficiently accurate for nonlinear applications. As to interferometric measurements, the recently proposed Lloyd configuration w13x, that allows the highest precision, requires the waveguide to be dipped in a liquid with a refractive index higher than that of the guiding film, this being a serious problem in the case of PE-LiNbO3 waveguides since the film refractive index is much higher than that of all easy-to-handle Žnontoxic. liquids available. Finally, the technique based on the determination of the propagation constant of the mode at different wavelengths requires, for these constants to be correlated, an accurate knowledge of the dependence of the index change on the wavelength, which is not easy to obtain. In this paper a new method is presented for an accurate determination of the optical parameters of a single-mode planar PE-LiNbO3 waveguide. When a liquid is placed above the waveguide, it alters the effective refractive index of the fundamental guided mode and hence, as it has already been observed w15,16x, the Cherenkov secondharmonic radiation-mode output angle. By measuring this output angle for two different liquids of known refractive index, two independent informations are obtained, thus allowing the determination of both d and D n. It is worth noting that by this method the determination of the waveguide parameters at the fundamental wavelength of the guided mode, typically in the near infrared, is achieved by a plain angular measurement performed on the secondharmonic beam, and therefore in the visible.
can be obtained by modifying by a known quantity one of the parameters which affect the propagation conditions and hence n eff itself, e.g., by varying the cover refractive index n c of the waveguide. To this aim, a liquid of known refractive index is placed above the waveguide. In the case of PE-LiNbO 3 waveguides that exhibit second-order nonlinearity, n eff can be determined through the measurement of the output angle of Cherenkov second-harmonic radiation-mode. This method has been chosen since it is the most straightforward. Indeed, the determination of n eff by means of grating couplingroutcoupling angles would require the realization of a grating on the waveguide, whereas in the standard prism-coupling m-lines method it would be difficult to control the uniformity of the liquid layer below the prism; moreover, the geometrical and optical characteristics of the coupling device Žgrating or prism. should be known with high precision. It is worth recalling the basics of second harmonic generation in the Cherenkov configuration w2,3x. This process involves power transfer from a fundamental guided mode at v to a second harmonic radiation mode at 2 v propagating inside the substrate at the angle u C-int ŽFig. 1a.. This angle is given by the phase-matching condition, which, in the case of our experimental conditions, i.e., Z-cut PE-LiNbO3 waveguide where only extraordinary TM modes are supported, has the following expression:
u C - int s arccos
ž
v n eff
n 2s ,ev Ž u C - int .
/
Ž 2.1 .
v where n eff is the effective index of the coupled guided mode, and n2s,ev is the extraordinary refractive index of the substrate as seen by the Cherenkov beam, which depends on u C-int according to the well-known index-ellipsoid.
2. Operation principle As already stated above, optical characterization of single-mode planar waveguides requires the determination of the index profile shape and of the profile parameters. When the profile shape is known, which is the case of PE-LiNbO 3 waveguides that exhibit an almost step-index profile w17x, to obtain the two parameters D n and d, the measurement of the effective index n eff of the single guided mode is not sufficient. A second independent n eff
Fig. 1. Cherenkov second harmonic generation scheme for a waveguide with air as the cover Ža. and with a liquid sample as the cover Žb.. The Cherenkov beam direction is indicated with a continuous line in the first case Ž u C-ext . and with a dashed line in the second Ž u C-ext,i ..
R. Ramponi et al.r Optics Communications 159 (1999) 37–42
Referring to Fig. 1a, it can be seen that the Cherenkov angle that can be measured is actually the external one, u C-ext , that is related to u C-int by Snell’s refraction law:
u C -ext s arcsin Ž
n 2s ,ev
Ž u C - int . sin u C - int .
Ž 2.2 .
Eqs. Ž2.1. and Ž2.2. provide the relation between u C-ext , which is the measured quantity, and the effective refractive v . The effective index in index of the fundamental mode n eff turn depends on the refractive index of the waveguide cover, by means of the well-known characteristic equation: 2 k0 d
n fv,o n fv,e
(Ž n
v 2 y f ,e
.
v 2 Ž neff . y 2F f – s y 2F f – c s 2 mp
and d, are estimated by finding the zero of the following function: f Ž D n e ,d . s Ž D u 1meas y D u 1calc Ž D n e ,d . .
F f – s s arctan
n fv,o n fv,e
Ž nsv,e n sv,o .
2
)
2
2
v Ž n eff . y Ž n sv,e . 2 v 2 Ž n fv,e . y Ž n eff .
Ž 2.3a . F f – c s arctan
n fv,o n fv,e
Ž n cv .
2
)
2
2
v Ž n eff . y Ž n cv . 2 v 2 Ž n fv,e . y Ž neff .
Ž 2.3b .
Eq. Ž2.3. contains the parameters of the waveguide to be v v y n s,e together with the determined, i.e., d and D n e s n f,e parameters known or measured, i.e., n c and n eff . Two independent equations can then be obtained by writing Eq. Ž2.3. for two different covers, where the two corresponding n eff are obtained by means of two different u C-ext measurements. In principle, the two measurements could be performed with air as the first cover and a liquid as the second one. However, from the experimental point of view, the determination of the absolute value of u C-ext requires a precise zero-setting that is not easy to obtain. It is more convenient to use air as the reference cover, with the corresponding Cherenkov output beam giving the relative zero-line, and to measure the variation of the Cherenkov output angle in the presence of two different liquid covers with respect to that line, as shown in Fig. 1b. The measured quantity is then: D u imeas s u C - ext y u C - ext ,i
Ž 2.4 .
where u C-ext is the Cherenkov output angle with air as the cover, whereas u C-ext,i , with i s 1, 2, are the Cherenkov output angles in the presence of the two different liquid covers. Once the two independent D u imeas have been measured, the values of the two waveguide parameters, D n e
2
q Ž D u 2meas y D u 2calc Ž D n e ,d . . D u 1calc
2
Ž 2.5 .
D u 2calc
where and are the Cherenkov angle variations calculated for the two covers of known refractive index when the waveguide parameters are D n e and d. Actually, to achieve a higher accuracy in the determination of D n e and d, a larger number k of independent D u imeas can be measured with different liquids, and the corresponding function f
Ž 2.3 . where d is the waveguide depth, the subscripts ‘o’ and ‘e’ stand for ordinary and extraordinary, n fv is the refractive index of the film, m is the order of the mode, and F f – s and F f – c are the phase-shifts due to the total reflection at the boundaries film–substrate and film–cover, respectively:
39
k
Ý Ž D u imeas y D u icalc Ž D ne ,d . .
f Ž D n e ,d . s
2
,
is1
i s 1, . . . ,k
Ž 2.5X .
minimized. It is worth pointing out that in the above equations, the ordinary index change D n o is also involved, but it is not explicitly indicated since it is proportional to the extraordinary one w17x. The characterization method here described can be used for any guiding structure exhibiting Cherenkov second harmonic generation Ži.e., nonlinear waveguide on nonlinear substrate, linear waveguide on nonlinear substrate, nonlinear waveguide on linear substrate., at any fundamental wavelength where the phase-matching condition is fulv filled Ž n eff - n2s v , from Eq. Ž2.1.. and giving a second harmonic in the substrate transparency range. The method is particularly suitable for PE-LiNbO3 waveguides since they give efficient second harmonic generation in the Cherenkov regime w1x. Moreover, in these waveguides, very thin and with a high index change, the cover refractive index affects significantly n eff w18x, thus resulting in large and easily detectable D u meas when a liquid is placed above the waveguide instead of air. It is worth noting that the determination of D n e and d does not require the knowledge of any parameter related to the coupling conditions Že.g., prism refractive index and base angle, coupling angle, etc...
3. Experimental setup The experimental setup is shown in Fig. 2. The laser source is a lamp-pumped 5 W cw Nd:YAG laser source at l s 1.064 mm, and power is lowered to an average value of 50 mW by using an external light-chopper, so as to avoid significant thermal heating of both the waveguide and the liquids. Indeed, the light, coupled into the waveguide by means of a rutile prism, has an average power of 17 mW, with a peak power 100 times higher. This results in a temperature increase of about 0.58C that does not affect significantly the optical characteristics of the materials involved. A mirror M mounted on a PC controlled
40
R. Ramponi et al.r Optics Communications 159 (1999) 37–42
and the average value has been calculated. This value is reported in Table 1 together with the refractive index n c of each liquid. From these experimental data, the waveguide parameters D n e and d at l s 1.064 mm are calculated following the procedure described above and the following results are obtained: Fig. 2. Experimental set-up: LS, Nd:YAG laser; L, spherical lens f s 400 mm; P, rutile prism; WG, waveguide; BS, beam splitter; PM, power meter; D, diaphragm Ž1 mm.; LQ, liquid sample; M, mirror; R, rotatory stage. Dashed line: fundamental beam; continuous line: second harmonic beam.
rotator Žangular accuracy of "5 arcsec. is used to measure the Cherenkov output angle variation. The measurement is performed as follows: the laser beam is coupled into the waveguide with air as the cover, and the mirror is set orthogonally to the Cherenkov second harmonic beam: this position is taken as the reference for the following measurement of the Cherenkov angle variation. Then a drop of liquid is placed on the waveguide and the mirror set orthogonally to the new direction of the Cherenkov beam. The rotation angle of the mirror equals the Cherenkov angle variation D u meas induced by the presence of the liquid. To find the orthogonality condition, a diaphragm Ž1 mm diameter. is aligned to the Cherenkov output beam and the mirror rotated until the reflected beam passes back through the diaphragm: a beam splitter placed on the beam path between the waveguide and the diaphragm deviates part of the reflected beam, transmitted through the diaphragm, to a photodetector: when maximum intensity reading is obtained, the orthogonality condition is reached. With this set-up a precision of "0.018 in the measurement of D u meas is attained. The waveguide chosen to test the method described above is a Z-cut LiNbO 3 waveguide fabricated by proton exchange in benzoic acid. For such a waveguide the index profile is best described by a step-like function w17x: this was confirmed by a series of prism-coupling characterization measurements performed on some multimode samples exchanged for a longer time in the same bath. The waveguide used in the experimental test is single-mode from 450 nm up Žthe only supported mode being TM and of extraordinary polarization. and therefore cannot be characterized with the prism-coupling technique even at short wavelengths. The measurements of Cherenkov output angle variation have been performed with six liquids Žpurchased from Cargille Laboratories Inc., USA. of different refractive indices ranging from 1.484 to 1.745 at l s 1.064 mm. The values of the refractive indices of the liquids are given by Cargille with a tolerance of "0.0015.
D n e s 0.0890,
d s 0.451 mm,
whereas the ordinary index change is assumed w17x to be: D n o s yD n er3 s y0.0297. In Fig. 3, the experimental average values of D u meas are plotted versus n c together with the curve given by D u calc as calculated from the waveguide parameters obtained above. The good agreement between measured and calculated Cherenkov angle variations in the whole n c range demonstrates the reliability of the parameters determined. To show the capability of the method to discriminate a single pair of values D n e and d with sufficient resolution, the function f of Eq. Ž2.5X . has been studied. The function f can be represented as a surface dependent on D n e and d, but, for the sake of simplicity, only the curve Žsolid line. corresponding to the direction of minimum slope of f Ždashed line in the D n e –d plane. has been plotted in Fig. 4. Nevertheless, the minimum appears significantly sharp since f doubles for variations of "0.0015 in D n e and of "6 nm in d Žsee projections of the f curve on the vertical coordinate planes.. To evaluate the accuracy of the method in determining D n e and d, it is worth analyzing all possible sources of errors, so as to quantify their effect. Table 2 summarizes the results of this analysis, giving the estimated error magnitude for each different possible source, together with the consequent standard deviation of D n e and d, as calculated for our waveguide in the case of six liquids by applying the error propagation theory w19x. The most important errors come from the experimental error in the angle measurements and from an inaccurate knowledge of the liquid cover refractive index. The first one is reported for a single determination of D u meas for
Table 1 Experimental Cherenkov angle variations, D u me as Liquid refractive index, n c
D u me as Ždegrees.
4. Results and discussion
1.484 1.578 1.622 1.667 1.717 1.745
0.653 0.908 1.047 1.214 1.423 1.570
For each of the six liquids used, four measurements of Cherenkov angle variation D u meas have been performed
Average values of D u me as Žon four measurements. for the six refractive indices of the liquids used.
R. Ramponi et al.r Optics Communications 159 (1999) 37–42
41
Table 2 Error analysis of the method
Fig. 3. Full circles: experimental values of the Cherenkov angle variation D u me as plotted versus the refractive index n c of the liquids used. Continuous curve: Cherenkov angle variation D u calc as a function of n c calculated on the basis of the obtained D n e s 0.0890 and ds 0.451 mm.
each liquid and can be reduced by a factor N 1r2 by performing N measurements. In the experiment reported, four measurements per liquid were performed, so as to obtain an uncertainty of "0.0008 in D n e and of "3 nm in d, thus comparable to that caused in the present case by the unprecise knowledge of n c . The incidence of this error could also be reduced by using a telescope mounted on a goniometer instead of a rotating mirror to measure D u meas. As to the influence of n c , it would be possible to achieve better performances either by using liquids whose refractive index is known with higher precision or by measuring the liquid refractive index with some very accurate methods Žtypically interferometric methods w20x.. The effect of the error on the substrate extraordinary refractive index n s,e of our LiNbO 3 , which is "0.0004, can be considered very small on both D n e and d. This weak dependence of the waveguide parameters on the precision of the n s,e value is a significant advantage of this method with respect to those based on the measurement of coupling angles Žprism and grating-coupling methods.. Regarding the ordi-
Fig. 4. The continuous curve represents the function f of Eq. Ž2.5X . plotted versus D n e and d along the direction of minimum slope of f Ždashed line in the D n e – d plane.. The projections of this curve on the vertical coordinate planes are also represented with dashed lines.
Sources of errors
Error magnitude s Ž D n. s Ž d . Žnm.
Single measurement of D u me as Knowledge of n c Knowledge of n s,e Knowledge of D n o End-face angle cut
"0.018 "0.0015 "0.0004 "0.003 "0.18
0.0016 0.0010 0.0001 0.0001 0.0002
6 4.5 0.3 1 0.4
Analysis of the different sources of error of the method. The effect of each source of error on the determination of D n e and d is calculated and reported in the table in terms of standard deviation.
nary index change, since the literature does not provide any indication on the precision of the relationship giving D n o , we have assumed a tolerance of "10% on its absolute value, which should constitute an excess estimate of the possible error. Nevertheless, its influence on the waveguide parameters is also very small. Lastly, we verified that it is sufficient to control the end-face angle within "0.18 so as not to affect significantly the determination of D n e and d. When considering all possible sources of error, the resulting accuracy, with four measurements for each of the six liquids, is better than "0.0013 for D n e and "6 nm for d. A further confirmation of the goodness of our index profile parameter reconstruction, comes from the excellent agreement between the calculated effective index of the guided mode Žwith air as the cover., n eff s 2.1573, and the effective index measured by prism-coupling technique, equal to 2.1572. Actually, the number of liquids to be used and that of the measurements per liquid to be performed depends on the final accuracy required for D n e and d. In this respect, some criteria have to be taken into account: Ži. for a given number of liquids, the resulting accuracy increases when the range of refractive indices of the liquids themselves is wider; Žii. the number of liquids and that of the measurements per liquid have to be chosen so that the two main errors in the index profile reconstruction are comparable, i.e., a higher number of liquids has to be used when their refractive index is known with poor precision, whereas a higher number of measurements per liquid has to be performed when the experimental error on D u meas is important. With the errors reported above for our case, when using only the two liquids with n c s 1.484 and n c s 1.745 and performing a single measurement per liquid, the resulting uncertainty on D n e would increase to "0.0022 and that on d to "9 nm, still acceptable for many applications. It is noteworthy that the overall accuracy reached in the characterization of single-mode waveguides by the method proposed is not far from that achievable on multimode waveguides with conventional techniques Že.g., m-line spectroscopy by prism coupling.. Actually, a direct com-
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R. Ramponi et al.r Optics Communications 159 (1999) 37–42
parison of the different methods on the same waveguide would in principle be of interest, but in practice it is difficult to perform in a significant way. In fact, conventional techniques can be applied only to multimode waveguides and become more and more precise when the number of guided modes increases, since the reconstruction of the index profile benefits a higher number of measured fitting parameters. On the contrary, the Cherenkov-based characterization that we propose gives its best performances on single-mode waveguides, where maximum sensitivity is obtained, together with a good Cherenkov conversion efficiency. As a consequence, a direct comparison on single-mode waveguides is not feasible, and a direct comparison on multimode waveguides would not evidence the real potentials of the Cherenkovcharacterization on single-mode waveguides, which however are the most important in photonic devices.
5. Conclusions We have demonstrated a new accurate method for the determination of the index profile parameters of singlemode planar nonlinear waveguides, particularly suitable for PE-LiNbO 3 waveguides. The method exploits the dependence of second harmonic generation in the Cherenkov configuration on the propagation conditions as determined by the presence of different covers. It allows a nondestructive waveguide characterization, performed by means of a simple angular measurement. It does not require any knowledge of the light coupling conditions nor of the coupling device characteristics. Moreover, the waveguide parameters in the near infrared are determined by means of a measurement performed at the second harmonic frequency, that is in the visible range, with obvious advantages in terms of easiness of operation.
Acknowledgements This work was partially supported by the National Research Council through the Special Project MADESS II
and the Research Project ‘Nonlinear optical guiding structures for all-optical signal processing’ of Technological Sciences and Innovation Committee. The authors wish to thank Prof. De Silvestri and Prof. Magni for the use of the Nd:YAG laser.
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