Abstract

A novel measurement technique based on phase-stepping microinterferometry is proposed for the refractive-index profiling of planar waveguides fabricated by ion exchange in glass. The sample preparation simplicity and easy instrumental implementation, together with high accuracy and improved resolution, are argued.

© 1994 Optical Society of America

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References

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  1. R. V. Ramaswamy, R. Srivastava, “Ion-exchanged waveguides: a review,” J. Lightwave Technol. 6, 984–1002 (1988).
    [CrossRef]
  2. S. N. Houde-Walter, D. T. Moore, “Delta-n control in GRIN glass by additives in AgCl diffusion baths,” Appl. Opt. 25, 3373–3378 (1986).
    [CrossRef] [PubMed]
  3. J. Albert, G. L. Yip, “Stress induced index change for K+–Na+ ion exchange in glass,” Electron. Lett. 23, 737–738 (1987).
    [CrossRef]
  4. J. M. White, P. F. Heidrich, “Optical waveguide refractive index profiles determined from measurement of mode indices: a simple analysis,” Appl. Opt. 15, 151–155 (1976).
    [CrossRef] [PubMed]
  5. R. Srivastava, C. K. Kao, R. V. Ramaswamy, “WKB analysis of planar surface waveguides with truncated index profiles,” J. Lightwave Technol. LT-5, 1605–1609 (1987).
    [CrossRef]
  6. B. X. Chen, H. Hamanaka, K. Iwamura, “Recovery of refractive index profiles of planar graded-index waveguides from measured mode indices: an iteration method,” J. Opt. Soc. Am. A 9, 1301–1305 (1992).
    [CrossRef]
  7. J. Steffen, A. Neyer, E. Voges, “Direct measurement of refractive index profiles of Ti:LiNbO3 planar and stripe waveguides by reflectivity profiling,” in Integrated Guided Wave Optics, Vol. 4 of 1989 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1989), pp. 121–124.
  8. S. Ruschin, J.-Y. Xu, H. Chung, W. S. C. Chang, “A filtered-transform scanning microscopic method for refractive-index profiling of optical waveguide and surface profiling,” J. Lightwave Technol. 8, 1703–1708 (1990).
    [CrossRef]
  9. R. Goring, M. Rothhardt, “Application of the refracted near field technique to multimode planar and channel waveguides in glass,” J. Opt. Commun. 7, 82–85 (1986).
    [CrossRef]
  10. D. Jestel, E. Voges, “Refracted near field characterization of ion exchange glass waveguides and device simulation,” in Fifth European Conference on Integrated Optics: ECIO ’89, A. Carenco, D. B. Ostrowsky, M. R. Papuchon, eds., Proc. Soc. Photo-Opt. Instrum. Eng. 1141, 185–190 (1989).
  11. R. Göring, T. Possner, “Accurate and effective method for measuring one- and two-dimensional refractive index gradients,” in Proceedings of the Tenth Topical Meeting on Gradient Index Optical Elements and Systems (University Publishers, Santiago de Composela, Spain, 1992), pp. 201–204.
  12. M. Sochacka, “Phase-stepping approach for data acquisition for refractive index profiling of optical fibers,” J. Lightwave Technol. (to be published).
  13. M. Sochacka, Z. Jaroszewicz, “Refractive index profiling of the GRIN slab waveguides by phase measuring interferometry,” in Proceedings of the Tenth Topical Meeting on Gradient Index Optical Elements and Systems (University Publishers, Santiago de Composela, Spain, 1992), postdeadline paper 5.
  14. Instrument made by Logitech, Materials Technologists and Engineers, Glasgow, Scotland, U.K.
  15. Instrument made by Polish Optical Works, Warsaw, Poland.
  16. M. Pluta, “A double refracting interference microscope with variable image duplication and half-shade eyepiece,” J. Phys. E 2, 685–690 (1969).
    [CrossRef]
  17. M. Pluta, “A double refracting interference microscope with continuously variable amount and direction of wavefront shear,” Opt. Acta 18, 661–675 (1971).
    [CrossRef]
  18. M. Pluta, Advanced Light Microscopy (Polish Scientific, Warsaw, 1989), Vol. 2, Chap. 7.4, pp. 183–197.
  19. R. Gonzalez, P. Wintz, Digital Image Processing (Addison-Wesley, Reading, Mass., 1987), Chap. 4, pp. 139–201.
  20. J. H. Bruning, D. R. Herriott, J. E. Gallagher, D. P. Rosenfeld, A. D. White, D. J. Brangaccio, “Digital wavefront measuring interferometer for testing surfaces and lenses,” Appl. Opt. 13, 2693–2703 (1974).
    [CrossRef] [PubMed]
  21. K. Creath, “Phase-measurement interferometry techniques,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1988), Vol. 26, pp. 349–393.
    [CrossRef]
  22. M. Sochacka, F. Le Provost, “Microscopic implementation of phase-stepping interferometry for dielectric surface evaluation in transmitted light,” Opt. Appl. (to be published).
  23. J. Schwider, R. Burow, K.-E. Elssner, J. Grzanna, R. Spolaczyk, K. Merkel, “Digital wave-front measuring interferometry: some systematic error sources,” Appl. Opt. 22, 3421–3432 (1983).
    [CrossRef] [PubMed]
  24. R. Pawluczyk, “Coherent noise elimination in holographic microscope,” Opt. Commun. 7, 366–370 (1973).
    [CrossRef]

1992 (1)

1990 (1)

S. Ruschin, J.-Y. Xu, H. Chung, W. S. C. Chang, “A filtered-transform scanning microscopic method for refractive-index profiling of optical waveguide and surface profiling,” J. Lightwave Technol. 8, 1703–1708 (1990).
[CrossRef]

1988 (1)

R. V. Ramaswamy, R. Srivastava, “Ion-exchanged waveguides: a review,” J. Lightwave Technol. 6, 984–1002 (1988).
[CrossRef]

1987 (2)

J. Albert, G. L. Yip, “Stress induced index change for K+–Na+ ion exchange in glass,” Electron. Lett. 23, 737–738 (1987).
[CrossRef]

R. Srivastava, C. K. Kao, R. V. Ramaswamy, “WKB analysis of planar surface waveguides with truncated index profiles,” J. Lightwave Technol. LT-5, 1605–1609 (1987).
[CrossRef]

1986 (2)

S. N. Houde-Walter, D. T. Moore, “Delta-n control in GRIN glass by additives in AgCl diffusion baths,” Appl. Opt. 25, 3373–3378 (1986).
[CrossRef] [PubMed]

R. Goring, M. Rothhardt, “Application of the refracted near field technique to multimode planar and channel waveguides in glass,” J. Opt. Commun. 7, 82–85 (1986).
[CrossRef]

1983 (1)

1976 (1)

1974 (1)

1973 (1)

R. Pawluczyk, “Coherent noise elimination in holographic microscope,” Opt. Commun. 7, 366–370 (1973).
[CrossRef]

1971 (1)

M. Pluta, “A double refracting interference microscope with continuously variable amount and direction of wavefront shear,” Opt. Acta 18, 661–675 (1971).
[CrossRef]

1969 (1)

M. Pluta, “A double refracting interference microscope with variable image duplication and half-shade eyepiece,” J. Phys. E 2, 685–690 (1969).
[CrossRef]

Albert, J.

J. Albert, G. L. Yip, “Stress induced index change for K+–Na+ ion exchange in glass,” Electron. Lett. 23, 737–738 (1987).
[CrossRef]

Brangaccio, D. J.

Bruning, J. H.

Burow, R.

Chang, W. S. C.

S. Ruschin, J.-Y. Xu, H. Chung, W. S. C. Chang, “A filtered-transform scanning microscopic method for refractive-index profiling of optical waveguide and surface profiling,” J. Lightwave Technol. 8, 1703–1708 (1990).
[CrossRef]

Chen, B. X.

Chung, H.

S. Ruschin, J.-Y. Xu, H. Chung, W. S. C. Chang, “A filtered-transform scanning microscopic method for refractive-index profiling of optical waveguide and surface profiling,” J. Lightwave Technol. 8, 1703–1708 (1990).
[CrossRef]

Creath, K.

K. Creath, “Phase-measurement interferometry techniques,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1988), Vol. 26, pp. 349–393.
[CrossRef]

Elssner, K.-E.

Gallagher, J. E.

Gonzalez, R.

R. Gonzalez, P. Wintz, Digital Image Processing (Addison-Wesley, Reading, Mass., 1987), Chap. 4, pp. 139–201.

Goring, R.

R. Goring, M. Rothhardt, “Application of the refracted near field technique to multimode planar and channel waveguides in glass,” J. Opt. Commun. 7, 82–85 (1986).
[CrossRef]

Göring, R.

R. Göring, T. Possner, “Accurate and effective method for measuring one- and two-dimensional refractive index gradients,” in Proceedings of the Tenth Topical Meeting on Gradient Index Optical Elements and Systems (University Publishers, Santiago de Composela, Spain, 1992), pp. 201–204.

Grzanna, J.

Hamanaka, H.

Heidrich, P. F.

Herriott, D. R.

Houde-Walter, S. N.

Iwamura, K.

Jaroszewicz, Z.

M. Sochacka, Z. Jaroszewicz, “Refractive index profiling of the GRIN slab waveguides by phase measuring interferometry,” in Proceedings of the Tenth Topical Meeting on Gradient Index Optical Elements and Systems (University Publishers, Santiago de Composela, Spain, 1992), postdeadline paper 5.

Jestel, D.

D. Jestel, E. Voges, “Refracted near field characterization of ion exchange glass waveguides and device simulation,” in Fifth European Conference on Integrated Optics: ECIO ’89, A. Carenco, D. B. Ostrowsky, M. R. Papuchon, eds., Proc. Soc. Photo-Opt. Instrum. Eng. 1141, 185–190 (1989).

Kao, C. K.

R. Srivastava, C. K. Kao, R. V. Ramaswamy, “WKB analysis of planar surface waveguides with truncated index profiles,” J. Lightwave Technol. LT-5, 1605–1609 (1987).
[CrossRef]

Le Provost, F.

M. Sochacka, F. Le Provost, “Microscopic implementation of phase-stepping interferometry for dielectric surface evaluation in transmitted light,” Opt. Appl. (to be published).

Merkel, K.

Moore, D. T.

Neyer, A.

J. Steffen, A. Neyer, E. Voges, “Direct measurement of refractive index profiles of Ti:LiNbO3 planar and stripe waveguides by reflectivity profiling,” in Integrated Guided Wave Optics, Vol. 4 of 1989 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1989), pp. 121–124.

Pawluczyk, R.

R. Pawluczyk, “Coherent noise elimination in holographic microscope,” Opt. Commun. 7, 366–370 (1973).
[CrossRef]

Pluta, M.

M. Pluta, “A double refracting interference microscope with continuously variable amount and direction of wavefront shear,” Opt. Acta 18, 661–675 (1971).
[CrossRef]

M. Pluta, “A double refracting interference microscope with variable image duplication and half-shade eyepiece,” J. Phys. E 2, 685–690 (1969).
[CrossRef]

M. Pluta, Advanced Light Microscopy (Polish Scientific, Warsaw, 1989), Vol. 2, Chap. 7.4, pp. 183–197.

Possner, T.

R. Göring, T. Possner, “Accurate and effective method for measuring one- and two-dimensional refractive index gradients,” in Proceedings of the Tenth Topical Meeting on Gradient Index Optical Elements and Systems (University Publishers, Santiago de Composela, Spain, 1992), pp. 201–204.

Ramaswamy, R. V.

R. V. Ramaswamy, R. Srivastava, “Ion-exchanged waveguides: a review,” J. Lightwave Technol. 6, 984–1002 (1988).
[CrossRef]

R. Srivastava, C. K. Kao, R. V. Ramaswamy, “WKB analysis of planar surface waveguides with truncated index profiles,” J. Lightwave Technol. LT-5, 1605–1609 (1987).
[CrossRef]

Rosenfeld, D. P.

Rothhardt, M.

R. Goring, M. Rothhardt, “Application of the refracted near field technique to multimode planar and channel waveguides in glass,” J. Opt. Commun. 7, 82–85 (1986).
[CrossRef]

Ruschin, S.

S. Ruschin, J.-Y. Xu, H. Chung, W. S. C. Chang, “A filtered-transform scanning microscopic method for refractive-index profiling of optical waveguide and surface profiling,” J. Lightwave Technol. 8, 1703–1708 (1990).
[CrossRef]

Schwider, J.

Sochacka, M.

M. Sochacka, F. Le Provost, “Microscopic implementation of phase-stepping interferometry for dielectric surface evaluation in transmitted light,” Opt. Appl. (to be published).

M. Sochacka, “Phase-stepping approach for data acquisition for refractive index profiling of optical fibers,” J. Lightwave Technol. (to be published).

M. Sochacka, Z. Jaroszewicz, “Refractive index profiling of the GRIN slab waveguides by phase measuring interferometry,” in Proceedings of the Tenth Topical Meeting on Gradient Index Optical Elements and Systems (University Publishers, Santiago de Composela, Spain, 1992), postdeadline paper 5.

Spolaczyk, R.

Srivastava, R.

R. V. Ramaswamy, R. Srivastava, “Ion-exchanged waveguides: a review,” J. Lightwave Technol. 6, 984–1002 (1988).
[CrossRef]

R. Srivastava, C. K. Kao, R. V. Ramaswamy, “WKB analysis of planar surface waveguides with truncated index profiles,” J. Lightwave Technol. LT-5, 1605–1609 (1987).
[CrossRef]

Steffen, J.

J. Steffen, A. Neyer, E. Voges, “Direct measurement of refractive index profiles of Ti:LiNbO3 planar and stripe waveguides by reflectivity profiling,” in Integrated Guided Wave Optics, Vol. 4 of 1989 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1989), pp. 121–124.

Voges, E.

J. Steffen, A. Neyer, E. Voges, “Direct measurement of refractive index profiles of Ti:LiNbO3 planar and stripe waveguides by reflectivity profiling,” in Integrated Guided Wave Optics, Vol. 4 of 1989 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1989), pp. 121–124.

D. Jestel, E. Voges, “Refracted near field characterization of ion exchange glass waveguides and device simulation,” in Fifth European Conference on Integrated Optics: ECIO ’89, A. Carenco, D. B. Ostrowsky, M. R. Papuchon, eds., Proc. Soc. Photo-Opt. Instrum. Eng. 1141, 185–190 (1989).

White, A. D.

White, J. M.

Wintz, P.

R. Gonzalez, P. Wintz, Digital Image Processing (Addison-Wesley, Reading, Mass., 1987), Chap. 4, pp. 139–201.

Xu, J.-Y.

S. Ruschin, J.-Y. Xu, H. Chung, W. S. C. Chang, “A filtered-transform scanning microscopic method for refractive-index profiling of optical waveguide and surface profiling,” J. Lightwave Technol. 8, 1703–1708 (1990).
[CrossRef]

Yip, G. L.

J. Albert, G. L. Yip, “Stress induced index change for K+–Na+ ion exchange in glass,” Electron. Lett. 23, 737–738 (1987).
[CrossRef]

Appl. Opt. (4)

Electron. Lett. (1)

J. Albert, G. L. Yip, “Stress induced index change for K+–Na+ ion exchange in glass,” Electron. Lett. 23, 737–738 (1987).
[CrossRef]

J. Lightwave Technol. (3)

R. V. Ramaswamy, R. Srivastava, “Ion-exchanged waveguides: a review,” J. Lightwave Technol. 6, 984–1002 (1988).
[CrossRef]

R. Srivastava, C. K. Kao, R. V. Ramaswamy, “WKB analysis of planar surface waveguides with truncated index profiles,” J. Lightwave Technol. LT-5, 1605–1609 (1987).
[CrossRef]

S. Ruschin, J.-Y. Xu, H. Chung, W. S. C. Chang, “A filtered-transform scanning microscopic method for refractive-index profiling of optical waveguide and surface profiling,” J. Lightwave Technol. 8, 1703–1708 (1990).
[CrossRef]

J. Opt. Commun. (1)

R. Goring, M. Rothhardt, “Application of the refracted near field technique to multimode planar and channel waveguides in glass,” J. Opt. Commun. 7, 82–85 (1986).
[CrossRef]

J. Opt. Soc. Am. A (1)

J. Phys. E (1)

M. Pluta, “A double refracting interference microscope with variable image duplication and half-shade eyepiece,” J. Phys. E 2, 685–690 (1969).
[CrossRef]

Opt. Acta (1)

M. Pluta, “A double refracting interference microscope with continuously variable amount and direction of wavefront shear,” Opt. Acta 18, 661–675 (1971).
[CrossRef]

Opt. Commun. (1)

R. Pawluczyk, “Coherent noise elimination in holographic microscope,” Opt. Commun. 7, 366–370 (1973).
[CrossRef]

Other (11)

K. Creath, “Phase-measurement interferometry techniques,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1988), Vol. 26, pp. 349–393.
[CrossRef]

M. Sochacka, F. Le Provost, “Microscopic implementation of phase-stepping interferometry for dielectric surface evaluation in transmitted light,” Opt. Appl. (to be published).

M. Pluta, Advanced Light Microscopy (Polish Scientific, Warsaw, 1989), Vol. 2, Chap. 7.4, pp. 183–197.

R. Gonzalez, P. Wintz, Digital Image Processing (Addison-Wesley, Reading, Mass., 1987), Chap. 4, pp. 139–201.

J. Steffen, A. Neyer, E. Voges, “Direct measurement of refractive index profiles of Ti:LiNbO3 planar and stripe waveguides by reflectivity profiling,” in Integrated Guided Wave Optics, Vol. 4 of 1989 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1989), pp. 121–124.

D. Jestel, E. Voges, “Refracted near field characterization of ion exchange glass waveguides and device simulation,” in Fifth European Conference on Integrated Optics: ECIO ’89, A. Carenco, D. B. Ostrowsky, M. R. Papuchon, eds., Proc. Soc. Photo-Opt. Instrum. Eng. 1141, 185–190 (1989).

R. Göring, T. Possner, “Accurate and effective method for measuring one- and two-dimensional refractive index gradients,” in Proceedings of the Tenth Topical Meeting on Gradient Index Optical Elements and Systems (University Publishers, Santiago de Composela, Spain, 1992), pp. 201–204.

M. Sochacka, “Phase-stepping approach for data acquisition for refractive index profiling of optical fibers,” J. Lightwave Technol. (to be published).

M. Sochacka, Z. Jaroszewicz, “Refractive index profiling of the GRIN slab waveguides by phase measuring interferometry,” in Proceedings of the Tenth Topical Meeting on Gradient Index Optical Elements and Systems (University Publishers, Santiago de Composela, Spain, 1992), postdeadline paper 5.

Instrument made by Logitech, Materials Technologists and Engineers, Glasgow, Scotland, U.K.

Instrument made by Polish Optical Works, Warsaw, Poland.

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Figures (8)

Fig. 1
Fig. 1

Wedge-shaped sample of the slab gradient-index waveguide.

Fig. 2
Fig. 2

Optical schematic of the microinterferometer Biolar PI: P, polarizer; D, regulable slit diaphragm; W1, rotatable Wollaston prism; W2, tube Wollaston prism (with the possibility of horizontal and vertical translations); A, analyzer.

Fig. 3
Fig. 3

Double image of the upper edge of the waveguide sample as seen in the interferometer field of view and the coordinate system. The zones of different interference effects are indicated by the arrows.

Fig. 4
Fig. 4

Four homogeneous field interferograms of a planar waveguide sample (as in Fig. 1) taken with phase biases ϕ B of 0, π/2, π, and 3π/2. The total shearing technique was applied, and the horizontal image shear in the object plane was 44.5 μm.

Fig. 5
Fig. 5

Four homogeneous field interferograms of a planar waveguide sample (as in Fig. 1) taken with phase biases ϕ B of 0, π/2, π, and 3π/2. The differential shearing technique was applied, and the horizontal image shear in the object plane was 1.84 μm.

Fig. 6
Fig. 6

Refractive-index profiles of the investigated waveguides retrieved from the phase data according to Eq. (3) (total shearing technique) and mapped in the y direction with the help of relation y = −tan(α)x. The waveguides were obtained by Ag+–Na+ ion interchange made in a bath of 5% AgNO3 solution in NaNO3 at 340°C. The number of modes was equal to 16 (solid curve), 15 (long-dashed curve), and 11 (short-dashed curve), for λHe–Ne = 0.633 μm introduced into the layer. The wedge angles measured for the samples were 24.86°, 24.71°, and 39.10°, respectively.

Fig. 7
Fig. 7

Refractive-index profiles reconstructed from phase data according to Eq. (11) (the differential shearing technique) and mapped in the y direction with the help of the relation y = −tan(α)x. The waveguides were obtained by a Ag+–Na+-ion interchange made in a bath of 5% AgNO3 solution in NaNO3 (solid and short-dashed curves) and in a bath of 1% AgNO3 solution in NaNO3 (long-dashed curve), all at 340 °C. The number of modes was equal to 16 (solid curve), 27 (long-dashed curve), and 37 (short-dashed curve) for λHe–NE = 0.633 μm introduced into the layer. The wedge angles measured for the samples were 39.10°, 45.32°, and 45.66°, respectively.

Fig. 8
Fig. 8

Refractive-index profiles reconstructed from phase data according to Eq. (11) (the differential shearing technique) and mapped in the y direction with the help of the relation y = −tan(α)x. The waveguides were obtained by a K+–Na+-ion inter-change made in a bath of KNO3 at 400 °C (solid curve) and 450 °C (dashed curve). The number of modes was equal to 6 (solid curve) and 3 (dashed curve) for λHe–Ne = 0.633 μm introduced into the layer. The wedge angles measured for the samples were 45,32° and 45.90°, respectively.

Equations (12)

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Φ 2 ( x ) = k { y ( x ) d n ( y ) d y - n i [ d - y ( x ) ] } ,
Φ 3 ( x ) = k { 0 d n ( y ) d y - n s y ( x ) - n i [ d - y ( x ) ] } .
Φ 4 ( x ) = k [ 0 y ( x - s ) n ( y ) d y - n i s tan ( α ) - n s y ( x ) ] .
Φ 5 ( x ) = k s ( n s - n i ) tan ( α ) .
n ( y ) = n i + 1 k tan ( α ) d Φ 2 d x ,
n ( y ) = n s - 1 k tan ( α ) d Φ 4 d x ,
α = arctan [ Φ 5 k s ( n i - n s ) ] ,
α = arctan [ 1 k ( n s - n i ) d Φ 3 d x ] .
Φ ( x ) = k { y ( x - s ) y ( x ) n ( y ) d y + n i [ y ( x - s ) - y ( x ) ] } .
n ( y ) = n i - Φ ( x ) / k s tan ( α ) .
n ( y ) = n i - n s - n i Φ 5 Φ ( x ) .
ϕ ( x , z ) = arctan [ I 2 ( x , z ) - I 4 ( x , z ) I 3 ( x , z ) - I 1 ( x , z ) ] ,

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