Abstract

A direct measurement of the birefringence of a planar waveguide obtained by Na+ – K+ ion exchange was performed with a double Lloyd interferometer. The results are compared with those obtained by a round-robin test involving the same sample. Birefringence of as much as Δn = (2.0 ± 0.2) × 10−3 was measured.

© 1996 Optical Society of America

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References

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  1. A. Brandenburg, J. Lightwave Technol. LT-4, 1580 (1986).
    [CrossRef]
  2. J. Albert, G. L. Yip, Electron. Lett. 23, 737 (1987).
    [CrossRef]
  3. R. V. Ramaswamy, R. Srivastava, J. Lightwave Technol. 6, 984 (1988).
    [CrossRef]
  4. K. Tsutsumi, H. Hirai, Y. Yuba, Opt. Lett. 13, 416 (1988).
    [CrossRef] [PubMed]
  5. H. Marquez, D. Salazar, A. Villalobos, G. Paez, J. M. Rincon, Appl. Opt. 34, 5817 (1995).
    [CrossRef] [PubMed]
  6. W. A. Ramadan, E. Fazio, M. Bertolotti, “Measurement of refractive index profile 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, I. Schanen, Proc. SPIE 2212, 126 (1994).
    [CrossRef]
  8. A. W. Snyder, J. D. Love, Optical Waveguide Theory (Chapman & Hall, London, 1995), pp. 668ff.
  9. See alsoA. Y. Sane, A. R. Cooper, J. Am. Ceram. Soc. 70, 86 (1987).
    [CrossRef]
  10. R. Srivastava, C. K. Kao, R. V. Ramaswamy, J. Lightwave Technol. LT-5, 1605 (1987).
    [CrossRef]
  11. E. Costa, L. Gato, M. V. Perez, C. Gomez-Reino, Pure Appl. Opt. 4, 485 (1995).
    [CrossRef]

1995

H. Marquez, D. Salazar, A. Villalobos, G. Paez, J. M. Rincon, Appl. Opt. 34, 5817 (1995).
[CrossRef] [PubMed]

E. Costa, L. Gato, M. V. Perez, C. Gomez-Reino, Pure Appl. Opt. 4, 485 (1995).
[CrossRef]

1994

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, I. Schanen, Proc. SPIE 2212, 126 (1994).
[CrossRef]

1988

R. V. Ramaswamy, R. Srivastava, J. Lightwave Technol. 6, 984 (1988).
[CrossRef]

K. Tsutsumi, H. Hirai, Y. Yuba, Opt. Lett. 13, 416 (1988).
[CrossRef] [PubMed]

1987

J. Albert, G. L. Yip, Electron. Lett. 23, 737 (1987).
[CrossRef]

See alsoA. Y. Sane, A. R. Cooper, J. Am. Ceram. Soc. 70, 86 (1987).
[CrossRef]

R. Srivastava, C. K. Kao, R. V. Ramaswamy, J. Lightwave Technol. LT-5, 1605 (1987).
[CrossRef]

1986

A. Brandenburg, J. Lightwave Technol. LT-4, 1580 (1986).
[CrossRef]

Albert, J.

J. Albert, G. L. Yip, Electron. Lett. 23, 737 (1987).
[CrossRef]

Bertolotti, M.

W. A. Ramadan, E. Fazio, M. Bertolotti, “Measurement of refractive index profile of planar waveguides by using a double Lloyd’s interferometer,” Appl. Opt. (to be published).

Brandenburg, A.

A. Brandenburg, J. Lightwave Technol. LT-4, 1580 (1986).
[CrossRef]

Brauer, A.

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, I. Schanen, Proc. SPIE 2212, 126 (1994).
[CrossRef]

Cooper, A. R.

See alsoA. Y. Sane, A. R. Cooper, J. Am. Ceram. Soc. 70, 86 (1987).
[CrossRef]

Costa, E.

E. Costa, L. Gato, M. V. Perez, C. Gomez-Reino, Pure Appl. Opt. 4, 485 (1995).
[CrossRef]

Dannberg, P.

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, I. Schanen, Proc. SPIE 2212, 126 (1994).
[CrossRef]

Fazio, E.

W. A. Ramadan, E. Fazio, M. Bertolotti, “Measurement of refractive index profile of planar waveguides by using a double Lloyd’s interferometer,” Appl. Opt. (to be published).

Gato, L.

E. Costa, L. Gato, M. V. Perez, C. Gomez-Reino, Pure Appl. Opt. 4, 485 (1995).
[CrossRef]

Gomez-Reino, C.

E. Costa, L. Gato, M. V. Perez, C. Gomez-Reino, Pure Appl. Opt. 4, 485 (1995).
[CrossRef]

Gonella, F.

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, I. Schanen, Proc. SPIE 2212, 126 (1994).
[CrossRef]

Hirai, H.

Kao, C. K.

R. Srivastava, C. K. Kao, R. V. Ramaswamy, J. Lightwave Technol. LT-5, 1605 (1987).
[CrossRef]

Linares, J.

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, I. Schanen, Proc. SPIE 2212, 126 (1994).
[CrossRef]

Love, J. D.

A. W. Snyder, J. D. Love, Optical Waveguide Theory (Chapman & Hall, London, 1995), pp. 668ff.

Marquez, H.

Mazzi, G.

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, I. Schanen, Proc. SPIE 2212, 126 (1994).
[CrossRef]

Noutsious, P.

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, I. Schanen, Proc. SPIE 2212, 126 (1994).
[CrossRef]

Paez, G.

Pelli, S.

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, I. Schanen, Proc. SPIE 2212, 126 (1994).
[CrossRef]

Perez, M. V.

E. Costa, L. Gato, M. V. Perez, C. Gomez-Reino, Pure Appl. Opt. 4, 485 (1995).
[CrossRef]

Ramadan, W. A.

W. A. Ramadan, E. Fazio, M. Bertolotti, “Measurement of refractive index profile of planar waveguides by using a double Lloyd’s interferometer,” Appl. Opt. (to be published).

Ramaswamy, R. V.

R. V. Ramaswamy, R. Srivastava, J. Lightwave Technol. 6, 984 (1988).
[CrossRef]

R. Srivastava, C. K. Kao, R. V. Ramaswamy, J. Lightwave Technol. LT-5, 1605 (1987).
[CrossRef]

Reino, C. G.

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, I. Schanen, Proc. SPIE 2212, 126 (1994).
[CrossRef]

Righini, G. C.

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, I. Schanen, Proc. SPIE 2212, 126 (1994).
[CrossRef]

Rimet, R.

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, I. Schanen, Proc. SPIE 2212, 126 (1994).
[CrossRef]

Rincon, J. M.

Salazar, D.

Sane, A. Y.

See alsoA. Y. Sane, A. R. Cooper, J. Am. Ceram. Soc. 70, 86 (1987).
[CrossRef]

Scaglione, A.

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, I. Schanen, Proc. SPIE 2212, 126 (1994).
[CrossRef]

Schanen, I.

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, I. Schanen, Proc. SPIE 2212, 126 (1994).
[CrossRef]

Snyder, A. W.

A. W. Snyder, J. D. Love, Optical Waveguide Theory (Chapman & Hall, London, 1995), pp. 668ff.

Srivastava, R.

R. V. Ramaswamy, R. Srivastava, J. Lightwave Technol. 6, 984 (1988).
[CrossRef]

R. Srivastava, C. K. Kao, R. V. Ramaswamy, J. Lightwave Technol. LT-5, 1605 (1987).
[CrossRef]

Tsutsumi, K.

Villalobos, A.

Yip, G. L.

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, I. Schanen, Proc. SPIE 2212, 126 (1994).
[CrossRef]

J. Albert, G. L. Yip, Electron. Lett. 23, 737 (1987).
[CrossRef]

Yuba, Y.

Appl. Opt.

Electron. Lett.

J. Albert, G. L. Yip, Electron. Lett. 23, 737 (1987).
[CrossRef]

J. Am. Ceram. Soc.

See alsoA. Y. Sane, A. R. Cooper, J. Am. Ceram. Soc. 70, 86 (1987).
[CrossRef]

J. Lightwave Technol.

R. Srivastava, C. K. Kao, R. V. Ramaswamy, J. Lightwave Technol. LT-5, 1605 (1987).
[CrossRef]

R. V. Ramaswamy, R. Srivastava, J. Lightwave Technol. 6, 984 (1988).
[CrossRef]

A. Brandenburg, J. Lightwave Technol. LT-4, 1580 (1986).
[CrossRef]

Opt. Lett.

Proc. SPIE

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, I. Schanen, Proc. SPIE 2212, 126 (1994).
[CrossRef]

Pure Appl. Opt.

E. Costa, L. Gato, M. V. Perez, C. Gomez-Reino, Pure Appl. Opt. 4, 485 (1995).
[CrossRef]

Other

A. W. Snyder, J. D. Love, Optical Waveguide Theory (Chapman & Hall, London, 1995), pp. 668ff.

W. A. Ramadan, E. Fazio, M. Bertolotti, “Measurement of refractive index profile of planar waveguides by using a double Lloyd’s interferometer,” Appl. Opt. (to be published).

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Figures (5)

Fig. 1
Fig. 1

Ray paths in the double Lloyd interferometric system.

Fig. 2
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 reflected 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 reflection of the He–Ne laser 2 beam.

Fig. 3
Fig. 3

Interference patterns and theoretical fits for (a) p and (b) s polarization.

Fig. 4
Fig. 4

Calculated index profiles as functions of depth z for ordinary (continuous curve) and extraordinary (dashed curve) polarization of the light.

Fig. 5
Fig. 5

Birefringence [Δn(z) = ne(z) – no(z)] of the ion-exchanged glass waveguide as function of depth z. The highest birefringence occurs 6–7 μm below the surface, where the stresses induced by the ion-exchanging process are stronger.

Tables (1)

Tables Icon

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

Equations (5)

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L n k ^ · d r = L n d s ,
n ( z ) = n s + Δ n exp [ ( z / z h ) 2 ] ,
n parallel ( z , θ ) = { n o 2 ( z ) cos 2 [ θ ( z ) ] + n e 2 sin 2 [ θ ( z ) ] } 1 / 2 ,
I = i = 1 [ I i + 2 j = 1 i 1 cos ( ϕ i ϕ j ) ( I i I j ) ] ,
Δ n ordinary = 7 . 65 × 10 3 , z h ordinary = 7 . 75 μ m , Δ n extraordinary = 9 . 40 × 10 3 , z h extraordinary = 9 . 20 μ m .

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