Abstract

A novel simple spectropolarimetric interferometer was developed based on single-mode potassium ion-exchanged (PIE) glass waveguides that generally have a large birefringence due to the compressive stress induced in the ion-exchanged layers. By using the spectropolarimetric interferometry, wavelength dependence of the modal birefringence of single-mode PIE waveguides was accurately obtained in a broad bandwidth, without need to measure individual modal indices. The modal birefringence decreases with increasing wavelength. The spectropolarimetric interferometer was demonstrated to be responsive to changes occurring within the penetration depth of the evanescent field. A refractive-index change of Δn=0.002 was easily detected in the case of a 2-cm-long interaction path length.

© 2008 Optical Society of America

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  1. R. Klein and E. Voges, “Integrated-optic ammonia sensor,” Sens. Actuators B 11, 221–225 (1993).
    [Crossref]
  2. N. Fabricius, G. Gauglitz, and J. Ingenhoff, “A gas sensor based on an integrated optical Mach-Zehnder interferometer,” Sens. Actuators B 7, 672–676 (1992).
    [Crossref]
  3. A. A. Boiarski, R. W. Ridgway, J. R. Busch, G. Turhan-Sayan, and L. S. Miller, “Integrated optical biosensor for environmental monitoring,” SPIE 1587, 114–128 (1991).
    [Crossref]
  4. Z. Qi, N. Matsuda, J. Santos, K. Itoh, A. Takatsu, and K. Kato, “A study of molecular adsorption of bromothymol blue by optical waveguide spectroscopy,” Langmuir 19, 214–217 (2003).
    [Crossref]
  5. S. E. Ross, C. J. Seliskar, and W. R. Heinenman, “Spectroelectrochemical Sensing Based on Multimode Selectivity Simultaneously Achievable in a Single Device. 9. Incorporation of Planar Waveguide Technology,” Anal. Chem. 72, 5549–5555 (2000).
    [Crossref] [PubMed]
  6. G. Zhang, S. Honkanen, A. Tervonen, C.-M. Wu, and S. I. Najafi, “Glass integrated optics circuit for 1.48/1.55- and 1.30/1.55-µm-wavelength division multiplexing and 1/8 splitting,” Appl. Opt. 33, 3371–3374 (1994).
    [Crossref] [PubMed]
  7. S. Honkanen, A. Tervonen, and M. McCourt, “Control of birefringence in ion-exchanged glass waveguides,” Appl. Opt. 26, 4710–4711 (1987).
    [Crossref] [PubMed]
  8. R. V. Ramaswamy and R. Srivastava, “Ion-exchanged glass waveguides: a review,” J. Lightwave Technol. 6, 984–1002 (1988).
    [Crossref]
  9. P. Äyräs, G. N. Conti, S. Honkanen, and N. Peyghambarian, “Birefringence Control for Ion-Exchanged Channel Glass Waveguides,” Appl. Opt. 37, 8400–8405 (1998).
    [Crossref]
  10. L. G. Yip and J. Albert, “Characterization of planar optical waveguides by K+-ion exchange in glass,” Opt. Lett. 10, 151–153 (1985).
    [Crossref] [PubMed]
  11. A. Brandenburg, “Stress in ion-exchanged glass waveguides,” J. Lightwave Technol. LT-4, 1580–1593 (1986).
    [Crossref]
  12. L. B. Glebov, N. V. Nikonorov, G. T. Petrovskii, and M. N. Filippova, “Effect of stresses on the refractive index of gradient layers in glass obtained by ion-exchange diffusion,” Sov. J. Glass Phys. Chem. 9, 477–481(1983).
  13. C. De Bernard, R. De Franceschi, C. Malvicino, S. Morasca, L. Moro, M. Morra, and A. Carnera, “Effects of potassium concentration and induced stress on the refractive index profile of K1-Na1 ion-exchanged glass waveguides,” J. Mod. Opt. 35, 907–917 (1988).
    [Crossref]
  14. Z. Qi, K. Itoh, and M. Murabayashi, “Measurement of the modal birefringence of single-mode K+ ionexchanged planar waveguides with polarimetric interferometry,” Appl. Opt. 39, 5750–5754 (2000).
    [Crossref]
  15. J. Albert and G. L. Yip, “Refractive-index profile of planar waveguides made by ion-exchange in glass,” Appl. Opt. 24, 3692–3693 (1985).
    [Crossref] [PubMed]
  16. K.. Tsutsumi, H. Hirai, and Y. Yuba, “Characteristics of swelling of sodium-potassium ion-exchanged glass waveguides,” Electron. Lett. 22, 1299–1300 (1986).
    [Crossref]
  17. J. Albert and G. L. Yip, “Stress-induced index change for K+-Na+ ion exchange in glass,” Electron. Lett 23, 738–738 (1987).
    [Crossref]
  18. S. I. Najafi, “Optical behavior of potassium ion-exchanged glass waveguides,” Appl. Opt. 27, 3728–3731 (1988).
    [Crossref] [PubMed]
  19. C. Ciminelli, A. D‘Orazio, M. D. Sario, C. Gerardi, V. Petruzzelli, and F. Prudenzano, “Effects of thermal annealing on the optical characteristics of K+-Na+ waveguides.” Appl. Opt. 37, 2346–2356 (1998).
    [Crossref]
  20. C. D. Bernardi, S. Morasca, D. Scarno, A. Carnera, and M. Morra, “Compositional and stress-optical effects in glass waveguides: comparison between K-Na and Ag-Na ion exchange,” J. Non-Cryst. Solids119, 195–204 (1990).
    [Crossref]

2003 (1)

Z. Qi, N. Matsuda, J. Santos, K. Itoh, A. Takatsu, and K. Kato, “A study of molecular adsorption of bromothymol blue by optical waveguide spectroscopy,” Langmuir 19, 214–217 (2003).
[Crossref]

2000 (2)

S. E. Ross, C. J. Seliskar, and W. R. Heinenman, “Spectroelectrochemical Sensing Based on Multimode Selectivity Simultaneously Achievable in a Single Device. 9. Incorporation of Planar Waveguide Technology,” Anal. Chem. 72, 5549–5555 (2000).
[Crossref] [PubMed]

Z. Qi, K. Itoh, and M. Murabayashi, “Measurement of the modal birefringence of single-mode K+ ionexchanged planar waveguides with polarimetric interferometry,” Appl. Opt. 39, 5750–5754 (2000).
[Crossref]

1998 (2)

1994 (1)

1993 (1)

R. Klein and E. Voges, “Integrated-optic ammonia sensor,” Sens. Actuators B 11, 221–225 (1993).
[Crossref]

1992 (1)

N. Fabricius, G. Gauglitz, and J. Ingenhoff, “A gas sensor based on an integrated optical Mach-Zehnder interferometer,” Sens. Actuators B 7, 672–676 (1992).
[Crossref]

1991 (1)

A. A. Boiarski, R. W. Ridgway, J. R. Busch, G. Turhan-Sayan, and L. S. Miller, “Integrated optical biosensor for environmental monitoring,” SPIE 1587, 114–128 (1991).
[Crossref]

1988 (3)

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

C. De Bernard, R. De Franceschi, C. Malvicino, S. Morasca, L. Moro, M. Morra, and A. Carnera, “Effects of potassium concentration and induced stress on the refractive index profile of K1-Na1 ion-exchanged glass waveguides,” J. Mod. Opt. 35, 907–917 (1988).
[Crossref]

S. I. Najafi, “Optical behavior of potassium ion-exchanged glass waveguides,” Appl. Opt. 27, 3728–3731 (1988).
[Crossref] [PubMed]

1987 (2)

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

S. Honkanen, A. Tervonen, and M. McCourt, “Control of birefringence in ion-exchanged glass waveguides,” Appl. Opt. 26, 4710–4711 (1987).
[Crossref] [PubMed]

1986 (2)

K.. Tsutsumi, H. Hirai, and Y. Yuba, “Characteristics of swelling of sodium-potassium ion-exchanged glass waveguides,” Electron. Lett. 22, 1299–1300 (1986).
[Crossref]

A. Brandenburg, “Stress in ion-exchanged glass waveguides,” J. Lightwave Technol. LT-4, 1580–1593 (1986).
[Crossref]

1985 (2)

1983 (1)

L. B. Glebov, N. V. Nikonorov, G. T. Petrovskii, and M. N. Filippova, “Effect of stresses on the refractive index of gradient layers in glass obtained by ion-exchange diffusion,” Sov. J. Glass Phys. Chem. 9, 477–481(1983).

Albert, J.

Äyräs, P.

Bernardi, C. D.

C. D. Bernardi, S. Morasca, D. Scarno, A. Carnera, and M. Morra, “Compositional and stress-optical effects in glass waveguides: comparison between K-Na and Ag-Na ion exchange,” J. Non-Cryst. Solids119, 195–204 (1990).
[Crossref]

Boiarski, A. A.

A. A. Boiarski, R. W. Ridgway, J. R. Busch, G. Turhan-Sayan, and L. S. Miller, “Integrated optical biosensor for environmental monitoring,” SPIE 1587, 114–128 (1991).
[Crossref]

Brandenburg, A.

A. Brandenburg, “Stress in ion-exchanged glass waveguides,” J. Lightwave Technol. LT-4, 1580–1593 (1986).
[Crossref]

Busch, J. R.

A. A. Boiarski, R. W. Ridgway, J. R. Busch, G. Turhan-Sayan, and L. S. Miller, “Integrated optical biosensor for environmental monitoring,” SPIE 1587, 114–128 (1991).
[Crossref]

Carnera, A.

C. De Bernard, R. De Franceschi, C. Malvicino, S. Morasca, L. Moro, M. Morra, and A. Carnera, “Effects of potassium concentration and induced stress on the refractive index profile of K1-Na1 ion-exchanged glass waveguides,” J. Mod. Opt. 35, 907–917 (1988).
[Crossref]

C. D. Bernardi, S. Morasca, D. Scarno, A. Carnera, and M. Morra, “Compositional and stress-optical effects in glass waveguides: comparison between K-Na and Ag-Na ion exchange,” J. Non-Cryst. Solids119, 195–204 (1990).
[Crossref]

Ciminelli, C.

Conti, G. N.

D‘Orazio, A.

De Bernard, C.

C. De Bernard, R. De Franceschi, C. Malvicino, S. Morasca, L. Moro, M. Morra, and A. Carnera, “Effects of potassium concentration and induced stress on the refractive index profile of K1-Na1 ion-exchanged glass waveguides,” J. Mod. Opt. 35, 907–917 (1988).
[Crossref]

De Franceschi, R.

C. De Bernard, R. De Franceschi, C. Malvicino, S. Morasca, L. Moro, M. Morra, and A. Carnera, “Effects of potassium concentration and induced stress on the refractive index profile of K1-Na1 ion-exchanged glass waveguides,” J. Mod. Opt. 35, 907–917 (1988).
[Crossref]

Fabricius, N.

N. Fabricius, G. Gauglitz, and J. Ingenhoff, “A gas sensor based on an integrated optical Mach-Zehnder interferometer,” Sens. Actuators B 7, 672–676 (1992).
[Crossref]

Filippova, M. N.

L. B. Glebov, N. V. Nikonorov, G. T. Petrovskii, and M. N. Filippova, “Effect of stresses on the refractive index of gradient layers in glass obtained by ion-exchange diffusion,” Sov. J. Glass Phys. Chem. 9, 477–481(1983).

Gauglitz, G.

N. Fabricius, G. Gauglitz, and J. Ingenhoff, “A gas sensor based on an integrated optical Mach-Zehnder interferometer,” Sens. Actuators B 7, 672–676 (1992).
[Crossref]

Gerardi, C.

Glebov, L. B.

L. B. Glebov, N. V. Nikonorov, G. T. Petrovskii, and M. N. Filippova, “Effect of stresses on the refractive index of gradient layers in glass obtained by ion-exchange diffusion,” Sov. J. Glass Phys. Chem. 9, 477–481(1983).

Heinenman, W. R.

S. E. Ross, C. J. Seliskar, and W. R. Heinenman, “Spectroelectrochemical Sensing Based on Multimode Selectivity Simultaneously Achievable in a Single Device. 9. Incorporation of Planar Waveguide Technology,” Anal. Chem. 72, 5549–5555 (2000).
[Crossref] [PubMed]

Hirai, H.

K.. Tsutsumi, H. Hirai, and Y. Yuba, “Characteristics of swelling of sodium-potassium ion-exchanged glass waveguides,” Electron. Lett. 22, 1299–1300 (1986).
[Crossref]

Honkanen, S.

Ingenhoff, J.

N. Fabricius, G. Gauglitz, and J. Ingenhoff, “A gas sensor based on an integrated optical Mach-Zehnder interferometer,” Sens. Actuators B 7, 672–676 (1992).
[Crossref]

Itoh, K.

Z. Qi, N. Matsuda, J. Santos, K. Itoh, A. Takatsu, and K. Kato, “A study of molecular adsorption of bromothymol blue by optical waveguide spectroscopy,” Langmuir 19, 214–217 (2003).
[Crossref]

Z. Qi, K. Itoh, and M. Murabayashi, “Measurement of the modal birefringence of single-mode K+ ionexchanged planar waveguides with polarimetric interferometry,” Appl. Opt. 39, 5750–5754 (2000).
[Crossref]

Kato, K.

Z. Qi, N. Matsuda, J. Santos, K. Itoh, A. Takatsu, and K. Kato, “A study of molecular adsorption of bromothymol blue by optical waveguide spectroscopy,” Langmuir 19, 214–217 (2003).
[Crossref]

Klein, R.

R. Klein and E. Voges, “Integrated-optic ammonia sensor,” Sens. Actuators B 11, 221–225 (1993).
[Crossref]

Malvicino, C.

C. De Bernard, R. De Franceschi, C. Malvicino, S. Morasca, L. Moro, M. Morra, and A. Carnera, “Effects of potassium concentration and induced stress on the refractive index profile of K1-Na1 ion-exchanged glass waveguides,” J. Mod. Opt. 35, 907–917 (1988).
[Crossref]

Matsuda, N.

Z. Qi, N. Matsuda, J. Santos, K. Itoh, A. Takatsu, and K. Kato, “A study of molecular adsorption of bromothymol blue by optical waveguide spectroscopy,” Langmuir 19, 214–217 (2003).
[Crossref]

McCourt, M.

Miller, L. S.

A. A. Boiarski, R. W. Ridgway, J. R. Busch, G. Turhan-Sayan, and L. S. Miller, “Integrated optical biosensor for environmental monitoring,” SPIE 1587, 114–128 (1991).
[Crossref]

Morasca, S.

C. De Bernard, R. De Franceschi, C. Malvicino, S. Morasca, L. Moro, M. Morra, and A. Carnera, “Effects of potassium concentration and induced stress on the refractive index profile of K1-Na1 ion-exchanged glass waveguides,” J. Mod. Opt. 35, 907–917 (1988).
[Crossref]

C. D. Bernardi, S. Morasca, D. Scarno, A. Carnera, and M. Morra, “Compositional and stress-optical effects in glass waveguides: comparison between K-Na and Ag-Na ion exchange,” J. Non-Cryst. Solids119, 195–204 (1990).
[Crossref]

Moro, L.

C. De Bernard, R. De Franceschi, C. Malvicino, S. Morasca, L. Moro, M. Morra, and A. Carnera, “Effects of potassium concentration and induced stress on the refractive index profile of K1-Na1 ion-exchanged glass waveguides,” J. Mod. Opt. 35, 907–917 (1988).
[Crossref]

Morra, M.

C. De Bernard, R. De Franceschi, C. Malvicino, S. Morasca, L. Moro, M. Morra, and A. Carnera, “Effects of potassium concentration and induced stress on the refractive index profile of K1-Na1 ion-exchanged glass waveguides,” J. Mod. Opt. 35, 907–917 (1988).
[Crossref]

C. D. Bernardi, S. Morasca, D. Scarno, A. Carnera, and M. Morra, “Compositional and stress-optical effects in glass waveguides: comparison between K-Na and Ag-Na ion exchange,” J. Non-Cryst. Solids119, 195–204 (1990).
[Crossref]

Murabayashi, M.

Najafi, S. I.

Nikonorov, N. V.

L. B. Glebov, N. V. Nikonorov, G. T. Petrovskii, and M. N. Filippova, “Effect of stresses on the refractive index of gradient layers in glass obtained by ion-exchange diffusion,” Sov. J. Glass Phys. Chem. 9, 477–481(1983).

Petrovskii, G. T.

L. B. Glebov, N. V. Nikonorov, G. T. Petrovskii, and M. N. Filippova, “Effect of stresses on the refractive index of gradient layers in glass obtained by ion-exchange diffusion,” Sov. J. Glass Phys. Chem. 9, 477–481(1983).

Petruzzelli, V.

Peyghambarian, N.

Prudenzano, F.

Qi, Z.

Z. Qi, N. Matsuda, J. Santos, K. Itoh, A. Takatsu, and K. Kato, “A study of molecular adsorption of bromothymol blue by optical waveguide spectroscopy,” Langmuir 19, 214–217 (2003).
[Crossref]

Z. Qi, K. Itoh, and M. Murabayashi, “Measurement of the modal birefringence of single-mode K+ ionexchanged planar waveguides with polarimetric interferometry,” Appl. Opt. 39, 5750–5754 (2000).
[Crossref]

Ramaswamy, R. V.

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

Ridgway, R. W.

A. A. Boiarski, R. W. Ridgway, J. R. Busch, G. Turhan-Sayan, and L. S. Miller, “Integrated optical biosensor for environmental monitoring,” SPIE 1587, 114–128 (1991).
[Crossref]

Ross, S. E.

S. E. Ross, C. J. Seliskar, and W. R. Heinenman, “Spectroelectrochemical Sensing Based on Multimode Selectivity Simultaneously Achievable in a Single Device. 9. Incorporation of Planar Waveguide Technology,” Anal. Chem. 72, 5549–5555 (2000).
[Crossref] [PubMed]

Santos, J.

Z. Qi, N. Matsuda, J. Santos, K. Itoh, A. Takatsu, and K. Kato, “A study of molecular adsorption of bromothymol blue by optical waveguide spectroscopy,” Langmuir 19, 214–217 (2003).
[Crossref]

Sario, M. D.

Scarno, D.

C. D. Bernardi, S. Morasca, D. Scarno, A. Carnera, and M. Morra, “Compositional and stress-optical effects in glass waveguides: comparison between K-Na and Ag-Na ion exchange,” J. Non-Cryst. Solids119, 195–204 (1990).
[Crossref]

Seliskar, C. J.

S. E. Ross, C. J. Seliskar, and W. R. Heinenman, “Spectroelectrochemical Sensing Based on Multimode Selectivity Simultaneously Achievable in a Single Device. 9. Incorporation of Planar Waveguide Technology,” Anal. Chem. 72, 5549–5555 (2000).
[Crossref] [PubMed]

Srivastava, R.

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

Takatsu, A.

Z. Qi, N. Matsuda, J. Santos, K. Itoh, A. Takatsu, and K. Kato, “A study of molecular adsorption of bromothymol blue by optical waveguide spectroscopy,” Langmuir 19, 214–217 (2003).
[Crossref]

Tervonen, A.

Tsutsumi, K..

K.. Tsutsumi, H. Hirai, and Y. Yuba, “Characteristics of swelling of sodium-potassium ion-exchanged glass waveguides,” Electron. Lett. 22, 1299–1300 (1986).
[Crossref]

Turhan-Sayan, G.

A. A. Boiarski, R. W. Ridgway, J. R. Busch, G. Turhan-Sayan, and L. S. Miller, “Integrated optical biosensor for environmental monitoring,” SPIE 1587, 114–128 (1991).
[Crossref]

Voges, E.

R. Klein and E. Voges, “Integrated-optic ammonia sensor,” Sens. Actuators B 11, 221–225 (1993).
[Crossref]

Wu, C.-M.

Yip, G. L.

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

J. Albert and G. L. Yip, “Refractive-index profile of planar waveguides made by ion-exchange in glass,” Appl. Opt. 24, 3692–3693 (1985).
[Crossref] [PubMed]

Yip, L. G.

Yuba, Y.

K.. Tsutsumi, H. Hirai, and Y. Yuba, “Characteristics of swelling of sodium-potassium ion-exchanged glass waveguides,” Electron. Lett. 22, 1299–1300 (1986).
[Crossref]

Zhang, G.

Anal. Chem. (1)

S. E. Ross, C. J. Seliskar, and W. R. Heinenman, “Spectroelectrochemical Sensing Based on Multimode Selectivity Simultaneously Achievable in a Single Device. 9. Incorporation of Planar Waveguide Technology,” Anal. Chem. 72, 5549–5555 (2000).
[Crossref] [PubMed]

Appl. Opt. (7)

Electron. Lett (1)

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

Electron. Lett. (1)

K.. Tsutsumi, H. Hirai, and Y. Yuba, “Characteristics of swelling of sodium-potassium ion-exchanged glass waveguides,” Electron. Lett. 22, 1299–1300 (1986).
[Crossref]

J. Lightwave Technol. (2)

A. Brandenburg, “Stress in ion-exchanged glass waveguides,” J. Lightwave Technol. LT-4, 1580–1593 (1986).
[Crossref]

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

J. Mod. Opt. (1)

C. De Bernard, R. De Franceschi, C. Malvicino, S. Morasca, L. Moro, M. Morra, and A. Carnera, “Effects of potassium concentration and induced stress on the refractive index profile of K1-Na1 ion-exchanged glass waveguides,” J. Mod. Opt. 35, 907–917 (1988).
[Crossref]

Langmuir (1)

Z. Qi, N. Matsuda, J. Santos, K. Itoh, A. Takatsu, and K. Kato, “A study of molecular adsorption of bromothymol blue by optical waveguide spectroscopy,” Langmuir 19, 214–217 (2003).
[Crossref]

Opt. Lett. (1)

Sens. Actuators B (2)

R. Klein and E. Voges, “Integrated-optic ammonia sensor,” Sens. Actuators B 11, 221–225 (1993).
[Crossref]

N. Fabricius, G. Gauglitz, and J. Ingenhoff, “A gas sensor based on an integrated optical Mach-Zehnder interferometer,” Sens. Actuators B 7, 672–676 (1992).
[Crossref]

Sov. J. Glass Phys. Chem. (1)

L. B. Glebov, N. V. Nikonorov, G. T. Petrovskii, and M. N. Filippova, “Effect of stresses on the refractive index of gradient layers in glass obtained by ion-exchange diffusion,” Sov. J. Glass Phys. Chem. 9, 477–481(1983).

SPIE (1)

A. A. Boiarski, R. W. Ridgway, J. R. Busch, G. Turhan-Sayan, and L. S. Miller, “Integrated optical biosensor for environmental monitoring,” SPIE 1587, 114–128 (1991).
[Crossref]

Other (1)

C. D. Bernardi, S. Morasca, D. Scarno, A. Carnera, and M. Morra, “Compositional and stress-optical effects in glass waveguides: comparison between K-Na and Ag-Na ion exchange,” J. Non-Cryst. Solids119, 195–204 (1990).
[Crossref]

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Figures (5)

Fig. 1.
Fig. 1.

Schematic diagram of the spectropolarimetric interferometer (1. single-mode PIE waveguide; 2. supporter; 3. xenon lamp; 4. quartz fiber; 5. lens; 6. polarizer; 7. prism; 8. chamber; 9 polarization analyzer; 10. CCD spectrometer; 11. computer).

Fig. 2.
Fig. 2.

(a) Waveguide transmission spectra for the TE and TM polarizations; (b) Interference patterns measured and calculated; (c) the best-fit dispersion of the modal birefringence.

Fig. 3.
Fig. 3.

Modal indices and modal birefringences of the single-mode PIE waveguide calculated at λ=633 nm as a function of refractive index of the cladding layer.

Fig. 4.
Fig. 4.

(a) Interference patterns measured with water and ethanol in the measuring chamber; (b) the difference between two patterns.

Fig. 5.
Fig. 5.

(a) Interference patterns measured with toluene and benzene in the measuring chamber; (b) the difference between two patterns

Equations (7)

Equations on this page are rendered with MathJax. Learn more.

Δ ϕ = 2 π λ L ( N TM N TE )
I = I TE 2 + I TM 2 + γ I TE I TM cos ( Δ ϕ )
n ( x ) = n s + Δ n exp ( x 2 d 2 )
n TM = n 0 + c 1 σ x + c 2 ( σ y + σ z )
n TE = n 0 + c 1 σ y + c 2 ( σ x + σ z )
n TM n TE = ( c 2 c 1 ) ( σ σ x )
N TM N TE = α ( n TM n TE ) = α ( c 2 c 1 ) ( σ σ x )

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