Aug 15, 1996 - Received February 12, 1996. A direct measurement of the birefringence of a planar waveguide obtained by Na1 âK1 ion exchange was.
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Direct measurement of birefringence in ion-exchanged planar waveguides E. Fazio, W. A. Ramadan,* and M. Bertolotti Dipartimento di Energetica, Universita` Roma La Sapienza, Instituto Nazionale di Fisica Materia – Gruppo Nazionale Elettronica Quantistica e Plasmi, via Scarpa 16, I-00161, Roma, Italy
G. C. Righini Istituto di Ricerca sulle Onde Elettromagnetiche, Consiglio Nazionale delle Ricerche, via Panciatichi 64, I-50127 Firenze, Italy Received February 12, 1996 A direct measurement of the birefringence of a planar waveguide obtained by Na1 – K1 ion exchange was performed with a double Lloyd interferometer. The results are compared with those obtained by a roundrobin test involving the same sample. Birefringence of as much as Dn s2.0 6 0.2d 3 1023 was measured. 1996 Optical Society of America
In ion-exchanged glass waveguides birefringence of the material can be produced by the mechanical stresses induced by the substitution of K1 ions for Na1 ions.1,2 This birefringence was predicted.3 Many groups of researchers have already measured it by using indirect testing, for example, by measuring the dispersion of the propagating TE and TM modes inside the waveguide.4,5 However, all these methods can measure only the effective indices from which the real index prof ile can be derived. A direct measurement instead should be able to measure the index prof ile directly. We report direct measurement of the birefringence of an ion-exchanged planar waveguide by using a double Lloyd interferometer.6 The waveguide under test was previously characterized by a roundrobin test that involved seven European and Canadian laboratories.7 The operative principle of the experiment is the measurement of the interference between light rays totally ref lected by the sample and those that arrive directly from the source, as sketched in Fig. 1. The total ref lection could occur at the surface of the sample or inside it, according to the incidence angle and the refractive-index variation induced by the ion substitution. The light transmitted by the surface follows curved optical paths inside the modified region of the material until the total ref lection condition is reached at some depth; then the light emerges from the surface following a similar path. This total ref lection process induces in the light ray a phase shift that depends on the depth reached at the turning point, whose measurement permits reconstruction of the refractive-index prof ile of the modif ied region. Moreover, if different polarizations of light suffer different phase shifts, this means that different optical paths have been followed or that a birefringence of the material is present. The optical path length followed by the light ray inside the material can be calculated according to the equation8 Z Z nkˆ ? dr nds , (1) L
L
0146-9592/96/161238-03$10.00/0
where s is the curved coordinate along the optical path. From Eq. (1), substituting the vector k for unitary ˆ we can derive the accumulated phase shift vector k, that is due to travel. To calculate it we chose a Gaussian prof ile for the refractive index: nszd ns 1 Dn expf2szyzh d2 g ,
(2)
where zh is a parameter related to the slope of the index variation. The Gaussian profile was used for a comparison with the round-robin results.7 Now it is necessary to account for material birefringence: the indiffusion of substitutional ions in the glass induces mechanical stresses of compression along the plane of the surface4 or along planes parallel to it inside the material. Modif ications of the refractiveindex prof ile can be found according to the stress optic. In other words, the glass becomes optically anisotropic as a positive uniaxial material whose optical axis is orthogonal to the surface. From the experimental data the ordinary and extraordinary refractive indices can be calculated; remember that at each depth both the extraordinary and the ordinary refractive indices vary. In particular, because the incidence plane coincides with the principal plane of the uniaxial material, the refractive-index prof ile obtained with normally polarized light describes the behavior of n0 szd. Instead, the refractive index seen by the parallel polarization (i.e., extraordinary polarization) can be calculated, at each depth and for each propagation angle, according to the
Fig. 1. Ray paths in the double Lloyd interferometric system. 1996 Optical Society of America
August 15, 1996 / Vol. 21, No. 16 / OPTICS LETTERS
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was a soda-lime glass microscope slide (Gold Star type) with unperturbed refractive index n 1.5102 at 632.8 nm, manufactured by Chance Propper, Ltd. The recorded interference patterns for light polarized parallel and orthogonal to the incidence plane are shown, respectively, in Figs. 3(a) and 3(b) (circles and dashed curves) together with the theoretical f its. We fitted the experimental data by using the following parameters: Dnordinary 7.65 3 1023 , Fig. 2. Experimental setup: the light from He – Ne laser 1 is enlarged by a spatial filter. After polarization control (pol. control) it is focused by a cylindrical lens a few tens of micrometers above the sample, which is kept inside an index-matching liquid. On the CCD interference occurs between the light rays totally ref lected by the sample and the direct ones. The interference pattern is then digitalized and recorded by a PC. The inclination of the sample is checked by the ref lection of the He – Ne laser 2 beam.
ordinary
zh
7.75 mm,
Dnextraordinary 9.40 3 1023 , extraordinary
zh
9.20 mm .
The corresponding prof iles are shown in Fig. 4. The birefringence parameter, def ined as Dnszd ne szd 2 no szd, is shown in Fig. 5. The largest birefringence occurs not where the highest ion concentration is present,
index ellipsoid nparallel sz, ud hno 2 szd cos2 fuszdg 1 ne 2 sin2 fuszdgj1/2 , (3) where uszd is the propagation angle at depth z. Finally, the interference of light is obtained by the superposition of the laser rays going straight from the source with those totally ref lected by the sample, whose phase shift can be calculated by Eqs. (3) and (2) inside Eq. (1); the fringe pattern can be described by the relation I
` X
"
i1
Ii 1 2
i21 X
q
cossfi 2 fj d sIi Ij d
# ,
(4)
j 1
where Ii and fi are the intensity and the phase, respectively, of the ith ray. In the present case we limited the calculation to the f irst four beams: in fact a larger number of rays would only increase the computer time without strongly improving the interference f itting. This is caused by the relative intensity decrease induced by the transmission and ref lection Fresnel coefficients at the sample– liquid interface. The experiment was performed with the setup shown in Fig. 2. A He –Ne laser beam was enlarged with a spatial f ilter with 303 magnification and focused by a cylindrical lens approximately 80 mm above the sample. This focusing provided for a linearly diverging light source close to the sample, which was put inside a cell f illed with a high-refractive-index liquid to ensure a totalref lection regime. The light ref lected from the waveguide and the one coming straight from the focal point of the cyclindrical lens interfered on a digitizing CCD camera. The image of the interference pattern was then processed by a digitizing controller and recorded by a PC. More details of the experimental arrangement can be found in Ref. 6. The sample was produced by K1 – Na1 ion exchange in a 100% KNO3 bath for 9 h at 395 ±C. The substrate
Fig. 3. Interference patterns and theoretical fits for (a) p and (b) s polarization.
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Table 1. Comparison between Effective Indices of Propagating Modes of the Waveguide Measured by a Round-Robin Testa with Those Calculated by the Present Method Method Round robin Present research a
TE0
TE1
TE2
TE3
TE4
TM0
TM1
TM2
TM3
TM4
1.5170 1.5163
1.5145 1.5142
1.5126 1.5124
1.5111 1.5111
– –
1.5183 1.5171
1.5156 1.5150
1.5132 1.5132
1.5116 1.5117
1.5104 1.5108
Ref. 7.
Fig. 4. Calculated index prof iles as functions of depth z for ordinary (continuous curve) and extraordinary (dashed curve) polarization of the light.
calculated according to the WKB method.8,10,11 Four TE and f ive TM modes were calculated from our profiles, too, whose effective indices are also given, for compari- son, in Table 1. Reasonable agreement with the values obtained in the round-robin test was found. In conclusion, we have described the application of a double Lloyd interference method that permits the refractive-index profiles of planar waveguides to be measured at different depths below the surface. The application of the method to an ion-exchanged glass waveguide already measured by a round-robin test by different techniques revealed reasonable agreement between results. In particular, this interferometric method permitted a direct measurement of the birefringence of the exchanged layer of the glass, which, because of the ion-exchanging process, becomes anisotropic, behaving as a uniaxial material with its optical axis normal to the surface. Unlike for the classical uniaxial crystal, in the present case the values of the ordinary and the extraordinary refractive indices are not constant but, of course, depend on the depth z inside the glass. The measured Dn was, at maximum, of the order of s2.0 6 0.2d 3 1023 . *On leave from the Department of Physics, Faculty of Sciences, University of Mansoura, Damietta, Egypt. References
Fig. 5. Birefringence fDnszd ne szd 2 no szdg of the ionexchanged glass waveguide as function of depth z. The highest birefringence occurs 6 – 7 mm below the surface, where the stresses induced by the ion-exchanging process are stronger.
i.e., at the surface sz 0d, but where the mechanical stresses inf luence the material more, which occurs in the present case 6 –7 mm below the surface.9 The calculated error is ,10% of Dnszd. This sample was measured previously by the roundrobin test, and it was found that the waveguide supported four TE and f ive TM modes, whose effective indices are listed in Table 1. To compare these results with the prof iles calculated here the propagating modes and the effective indices seen by the modes were
1. A. Brandenburg, J. Lightwave Technol. LT-4, 1580 (1986). 2. J. Albert and G. L. Yip, Electron. Lett. 23, 737 (1987). 3. R. V. Ramaswamy and R. Srivastava, J. Lightwave Technol. 6, 984 (1988). 4. K. Tsutsumi, H. Hirai, and Y. Yuba, Opt. Lett. 13, 416 (1988). 5. H. Marquez, D. Salazar, A. Villalobos, G. Paez, and J. M. Rincon, Appl. Opt. 34, 5817 (1995). 6. W. A. Ramadan, E. Fazio, and M. Bertolotti, ‘‘Measurement of refractive index prof ile of planar waveguides by using a double Lloyd’s interferometer,’’ Appl. Opt. (to be published). 7. S. Pelli, G. C. Righini, A. Scaglione, G. L. Yip, P. Noutsious, A. Brauer, P. Dannberg, J. Linares, C. G. Reino, G. Mazzi, F. Gonella, R. Rimet, and I. Schanen, Proc. SPIE 2212, 126 (1994). 8. A. W. Snyder and J. D. Love, Optical Waveguide Theory (Chapman & Hall, London, 1995), pp. 668 ff. 9. See also A. Y. Sane and A. R. Cooper, J. Am. Ceram. Soc. 70, 86 (1987). 10. R. Srivastava, C. K. Kao, and R. V. Ramaswamy, J. Lightwave Technol. LT-5, 1605 (1987). 11. E. Costa, L. Gato, M. V. Perez, and C. Gomez-Reino, Pure Appl. Opt. 4, 485 (1995).
