Abstract

Optimal performances of integrated optical devices are obtained by the use of an accurate and reliable characterization method. The parameters of interest, i.e., optical indices and thickness of the waveguide structure, are calculated from effective indices by means of an inversion procedure. We demonstrate how an artificial neural network can achieve such a process. The artificial neural network used is a multilayer perceptron. The first result concerns a simulated anisotropic waveguide. The accuracy in the determination of optical indices and waveguide thickness is 5×105 and 4  nm, respectively. Then an experimental application on a silica–titania thin film is performed. In addition, effective indices are measured by m-lines spectroscopy. Finally, a comparison with a classical optimization algorithm demonstrates the robustness of the neural method.

© 2007 Optical Society of America

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References

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  1. S. I. Hosain, J. P. Meunier, E. Bourillot, F. de Fornel, and J. P. Goudonnet, "Review of the basic methods for characterizing integrated-optic waveguides," Fiber Integr. Opt. 44, 89-107 (1995).
  2. F. Royer, H. Roux, D. Jamon, J. J. Rousseau, D. Zins, V. Cabuil, and C. Bovier, "New technological approach in phase-matched magneto-optic planar waveguide realization," in Advances in Optical Thin Films, C. Amra, N. Kaiser, and H. A. Macleod, eds., Proc. SPIE 5250, 72-80 (2004).
    [CrossRef]
  3. W. Zaets and K. Ando, "Magneto-optical mode conversion in Cd1-xMnxTe waveguide on GaAs substrate," Appl. Phys. Lett. 77, 1593-1595 (2000).
    [CrossRef]
  4. R. M. A. Azzam and N. M. Bashara, Ellipsometry and Polarized Light, 2nd ed. (North Holland Press, 1987).
  5. H. Touir, M. Stchakovsky, R. Ossikovski, and M. Warenghem, "Coherent and incoherent interference modeling and measurement of anisotropic multilayer stacks using conventional ellipsometry," Thin Solid Films 455-456, 628-631 (2003).
    [CrossRef]
  6. V. Tkachenko, A. Marino, F. Vita, F. D'Amore, L. De Stefano, M. Malinconico, M. Rippa, and G. Abbate, "Spectroscopic ellipsometry study of liquid crystal and polymeric thin films in visible and near infrared," Eur. Phys. J. E 14, 185-192 (2004).
    [CrossRef] [PubMed]
  7. P. K. Tien, R. Ulrich, and R. J. Martin, "Modes of propagating light waves in thin deposited semiconductor films," Appl. Phys. Lett. 14, 291-294 (1969).
    [CrossRef]
  8. J. S. Wei and W. D. Westwood, "A new method for determining thin-film refractive index and thickness using guided optical waves," Appl. Phys. Lett. 32, 819-821 (1978).
    [CrossRef]
  9. R. Ulrich and R. Torge, "Measurement of thin-film parameters with a prism coupler," Appl. Opt. 12, 2901-2908 (1973).
    [CrossRef] [PubMed]
  10. C. M. Bishop, Neural Networks for Pattern Recognition (Oxford U. Press, 1995).
  11. S. Robert, A. Mure-Ravaud, S. Reynaud, S. Fourment, F. Carcenac, and P. Arguel, "Experimental characterization of subwavelength diffraction gratings by an inverse-scattering neural method," J. Opt. Soc. Am. A 19, 2394-2402 (2002).
    [CrossRef]
  12. S. Lek, M. Delacoste, P. Baran, I. Dimopoulos, J. Lauga, and S. Aulagnier, "Application of neural networks to modeling nonlinear relationships in ecology," Ecol. Modell. 90, 39-52 (1996).
    [CrossRef]
  13. F. K. Urban III, D. Barton, and N. I. Boudani, "Extremely fast ellipsometry solutions using cascaded neural networks alone," Thin Solid Films 332, 50-55 (1998).
    [CrossRef]
  14. C. Yildiz and M. Turkmen, "Very accurate and simple CAD models based on neural networks for coplanar waveguide synthesis," Int. J. RF Microwave Comput.-Aided Eng. 15, 218-222 (2005).
    [CrossRef]
  15. Y.-S. Ma, X. Liu, P.-F. Gu, and J.-F. Tang, "Estimation of optical constants of thin film by the use of artificial neural networks," Appl. Opt. 35, 5035-5039 (1996).
    [CrossRef] [PubMed]
  16. M. F. Tabet and W. A. McGahan, "Use of artificial neural networks to predict thickness and optical constants of thin films from reflectance data," Thin Solid Films 370, 122-127 (2000).
    [CrossRef]
  17. K. I. Funahashi, "On the approximate realization of continuous mappings by neural networks," Neural Networks 2, 183-192 (1989).
    [CrossRef]
  18. D. Nix and A. Weigend, "Learning local error bars for nonlinear regression," in Proceedings of Advances in Neural Information Processing Systems, G. Tesauro, D. Touretzky, and T. Leen, eds, (MIT Press, 1995), pp. 489-496.
  19. K. Levenberg, "A method for the solution of certain problems in least squares," Quart. Appl. Math. 2, 164-168 (1944).
  20. D. Marquardt, "An algorithm for least-squares estimation of nonlinear parameters," J. Appl. Math. 11, 431-441 (1963).

2005

C. Yildiz and M. Turkmen, "Very accurate and simple CAD models based on neural networks for coplanar waveguide synthesis," Int. J. RF Microwave Comput.-Aided Eng. 15, 218-222 (2005).
[CrossRef]

2004

F. Royer, H. Roux, D. Jamon, J. J. Rousseau, D. Zins, V. Cabuil, and C. Bovier, "New technological approach in phase-matched magneto-optic planar waveguide realization," in Advances in Optical Thin Films, C. Amra, N. Kaiser, and H. A. Macleod, eds., Proc. SPIE 5250, 72-80 (2004).
[CrossRef]

V. Tkachenko, A. Marino, F. Vita, F. D'Amore, L. De Stefano, M. Malinconico, M. Rippa, and G. Abbate, "Spectroscopic ellipsometry study of liquid crystal and polymeric thin films in visible and near infrared," Eur. Phys. J. E 14, 185-192 (2004).
[CrossRef] [PubMed]

2003

H. Touir, M. Stchakovsky, R. Ossikovski, and M. Warenghem, "Coherent and incoherent interference modeling and measurement of anisotropic multilayer stacks using conventional ellipsometry," Thin Solid Films 455-456, 628-631 (2003).
[CrossRef]

2002

2000

M. F. Tabet and W. A. McGahan, "Use of artificial neural networks to predict thickness and optical constants of thin films from reflectance data," Thin Solid Films 370, 122-127 (2000).
[CrossRef]

W. Zaets and K. Ando, "Magneto-optical mode conversion in Cd1-xMnxTe waveguide on GaAs substrate," Appl. Phys. Lett. 77, 1593-1595 (2000).
[CrossRef]

1998

F. K. Urban III, D. Barton, and N. I. Boudani, "Extremely fast ellipsometry solutions using cascaded neural networks alone," Thin Solid Films 332, 50-55 (1998).
[CrossRef]

1996

S. Lek, M. Delacoste, P. Baran, I. Dimopoulos, J. Lauga, and S. Aulagnier, "Application of neural networks to modeling nonlinear relationships in ecology," Ecol. Modell. 90, 39-52 (1996).
[CrossRef]

Y.-S. Ma, X. Liu, P.-F. Gu, and J.-F. Tang, "Estimation of optical constants of thin film by the use of artificial neural networks," Appl. Opt. 35, 5035-5039 (1996).
[CrossRef] [PubMed]

1995

S. I. Hosain, J. P. Meunier, E. Bourillot, F. de Fornel, and J. P. Goudonnet, "Review of the basic methods for characterizing integrated-optic waveguides," Fiber Integr. Opt. 44, 89-107 (1995).

1989

K. I. Funahashi, "On the approximate realization of continuous mappings by neural networks," Neural Networks 2, 183-192 (1989).
[CrossRef]

1978

J. S. Wei and W. D. Westwood, "A new method for determining thin-film refractive index and thickness using guided optical waves," Appl. Phys. Lett. 32, 819-821 (1978).
[CrossRef]

1973

1969

P. K. Tien, R. Ulrich, and R. J. Martin, "Modes of propagating light waves in thin deposited semiconductor films," Appl. Phys. Lett. 14, 291-294 (1969).
[CrossRef]

1963

D. Marquardt, "An algorithm for least-squares estimation of nonlinear parameters," J. Appl. Math. 11, 431-441 (1963).

1944

K. Levenberg, "A method for the solution of certain problems in least squares," Quart. Appl. Math. 2, 164-168 (1944).

Abbate, G.

V. Tkachenko, A. Marino, F. Vita, F. D'Amore, L. De Stefano, M. Malinconico, M. Rippa, and G. Abbate, "Spectroscopic ellipsometry study of liquid crystal and polymeric thin films in visible and near infrared," Eur. Phys. J. E 14, 185-192 (2004).
[CrossRef] [PubMed]

Ando, K.

W. Zaets and K. Ando, "Magneto-optical mode conversion in Cd1-xMnxTe waveguide on GaAs substrate," Appl. Phys. Lett. 77, 1593-1595 (2000).
[CrossRef]

Arguel, P.

Aulagnier, S.

S. Lek, M. Delacoste, P. Baran, I. Dimopoulos, J. Lauga, and S. Aulagnier, "Application of neural networks to modeling nonlinear relationships in ecology," Ecol. Modell. 90, 39-52 (1996).
[CrossRef]

Azzam, R. M. A.

R. M. A. Azzam and N. M. Bashara, Ellipsometry and Polarized Light, 2nd ed. (North Holland Press, 1987).

Baran, P.

S. Lek, M. Delacoste, P. Baran, I. Dimopoulos, J. Lauga, and S. Aulagnier, "Application of neural networks to modeling nonlinear relationships in ecology," Ecol. Modell. 90, 39-52 (1996).
[CrossRef]

Barton, D.

F. K. Urban III, D. Barton, and N. I. Boudani, "Extremely fast ellipsometry solutions using cascaded neural networks alone," Thin Solid Films 332, 50-55 (1998).
[CrossRef]

Bashara, N. M.

R. M. A. Azzam and N. M. Bashara, Ellipsometry and Polarized Light, 2nd ed. (North Holland Press, 1987).

Bishop, C. M.

C. M. Bishop, Neural Networks for Pattern Recognition (Oxford U. Press, 1995).

Boudani, N. I.

F. K. Urban III, D. Barton, and N. I. Boudani, "Extremely fast ellipsometry solutions using cascaded neural networks alone," Thin Solid Films 332, 50-55 (1998).
[CrossRef]

Bourillot, E.

S. I. Hosain, J. P. Meunier, E. Bourillot, F. de Fornel, and J. P. Goudonnet, "Review of the basic methods for characterizing integrated-optic waveguides," Fiber Integr. Opt. 44, 89-107 (1995).

Bovier, C.

F. Royer, H. Roux, D. Jamon, J. J. Rousseau, D. Zins, V. Cabuil, and C. Bovier, "New technological approach in phase-matched magneto-optic planar waveguide realization," in Advances in Optical Thin Films, C. Amra, N. Kaiser, and H. A. Macleod, eds., Proc. SPIE 5250, 72-80 (2004).
[CrossRef]

Cabuil, V.

F. Royer, H. Roux, D. Jamon, J. J. Rousseau, D. Zins, V. Cabuil, and C. Bovier, "New technological approach in phase-matched magneto-optic planar waveguide realization," in Advances in Optical Thin Films, C. Amra, N. Kaiser, and H. A. Macleod, eds., Proc. SPIE 5250, 72-80 (2004).
[CrossRef]

Carcenac, F.

D'Amore, F.

V. Tkachenko, A. Marino, F. Vita, F. D'Amore, L. De Stefano, M. Malinconico, M. Rippa, and G. Abbate, "Spectroscopic ellipsometry study of liquid crystal and polymeric thin films in visible and near infrared," Eur. Phys. J. E 14, 185-192 (2004).
[CrossRef] [PubMed]

de Fornel, F.

S. I. Hosain, J. P. Meunier, E. Bourillot, F. de Fornel, and J. P. Goudonnet, "Review of the basic methods for characterizing integrated-optic waveguides," Fiber Integr. Opt. 44, 89-107 (1995).

De Stefano, L.

V. Tkachenko, A. Marino, F. Vita, F. D'Amore, L. De Stefano, M. Malinconico, M. Rippa, and G. Abbate, "Spectroscopic ellipsometry study of liquid crystal and polymeric thin films in visible and near infrared," Eur. Phys. J. E 14, 185-192 (2004).
[CrossRef] [PubMed]

Delacoste, M.

S. Lek, M. Delacoste, P. Baran, I. Dimopoulos, J. Lauga, and S. Aulagnier, "Application of neural networks to modeling nonlinear relationships in ecology," Ecol. Modell. 90, 39-52 (1996).
[CrossRef]

Dimopoulos, I.

S. Lek, M. Delacoste, P. Baran, I. Dimopoulos, J. Lauga, and S. Aulagnier, "Application of neural networks to modeling nonlinear relationships in ecology," Ecol. Modell. 90, 39-52 (1996).
[CrossRef]

Fourment, S.

Funahashi, K. I.

K. I. Funahashi, "On the approximate realization of continuous mappings by neural networks," Neural Networks 2, 183-192 (1989).
[CrossRef]

Goudonnet, J. P.

S. I. Hosain, J. P. Meunier, E. Bourillot, F. de Fornel, and J. P. Goudonnet, "Review of the basic methods for characterizing integrated-optic waveguides," Fiber Integr. Opt. 44, 89-107 (1995).

Gu, P.-F.

Hosain, S. I.

S. I. Hosain, J. P. Meunier, E. Bourillot, F. de Fornel, and J. P. Goudonnet, "Review of the basic methods for characterizing integrated-optic waveguides," Fiber Integr. Opt. 44, 89-107 (1995).

Jamon, D.

F. Royer, H. Roux, D. Jamon, J. J. Rousseau, D. Zins, V. Cabuil, and C. Bovier, "New technological approach in phase-matched magneto-optic planar waveguide realization," in Advances in Optical Thin Films, C. Amra, N. Kaiser, and H. A. Macleod, eds., Proc. SPIE 5250, 72-80 (2004).
[CrossRef]

Lauga, J.

S. Lek, M. Delacoste, P. Baran, I. Dimopoulos, J. Lauga, and S. Aulagnier, "Application of neural networks to modeling nonlinear relationships in ecology," Ecol. Modell. 90, 39-52 (1996).
[CrossRef]

Lek, S.

S. Lek, M. Delacoste, P. Baran, I. Dimopoulos, J. Lauga, and S. Aulagnier, "Application of neural networks to modeling nonlinear relationships in ecology," Ecol. Modell. 90, 39-52 (1996).
[CrossRef]

Levenberg, K.

K. Levenberg, "A method for the solution of certain problems in least squares," Quart. Appl. Math. 2, 164-168 (1944).

Liu, X.

Ma, Y.-S.

Malinconico, M.

V. Tkachenko, A. Marino, F. Vita, F. D'Amore, L. De Stefano, M. Malinconico, M. Rippa, and G. Abbate, "Spectroscopic ellipsometry study of liquid crystal and polymeric thin films in visible and near infrared," Eur. Phys. J. E 14, 185-192 (2004).
[CrossRef] [PubMed]

Marino, A.

V. Tkachenko, A. Marino, F. Vita, F. D'Amore, L. De Stefano, M. Malinconico, M. Rippa, and G. Abbate, "Spectroscopic ellipsometry study of liquid crystal and polymeric thin films in visible and near infrared," Eur. Phys. J. E 14, 185-192 (2004).
[CrossRef] [PubMed]

Marquardt, D.

D. Marquardt, "An algorithm for least-squares estimation of nonlinear parameters," J. Appl. Math. 11, 431-441 (1963).

Martin, R. J.

P. K. Tien, R. Ulrich, and R. J. Martin, "Modes of propagating light waves in thin deposited semiconductor films," Appl. Phys. Lett. 14, 291-294 (1969).
[CrossRef]

McGahan, W. A.

M. F. Tabet and W. A. McGahan, "Use of artificial neural networks to predict thickness and optical constants of thin films from reflectance data," Thin Solid Films 370, 122-127 (2000).
[CrossRef]

Meunier, J. P.

S. I. Hosain, J. P. Meunier, E. Bourillot, F. de Fornel, and J. P. Goudonnet, "Review of the basic methods for characterizing integrated-optic waveguides," Fiber Integr. Opt. 44, 89-107 (1995).

Mure-Ravaud, A.

Nix, D.

D. Nix and A. Weigend, "Learning local error bars for nonlinear regression," in Proceedings of Advances in Neural Information Processing Systems, G. Tesauro, D. Touretzky, and T. Leen, eds, (MIT Press, 1995), pp. 489-496.

Ossikovski, R.

H. Touir, M. Stchakovsky, R. Ossikovski, and M. Warenghem, "Coherent and incoherent interference modeling and measurement of anisotropic multilayer stacks using conventional ellipsometry," Thin Solid Films 455-456, 628-631 (2003).
[CrossRef]

Reynaud, S.

Rippa, M.

V. Tkachenko, A. Marino, F. Vita, F. D'Amore, L. De Stefano, M. Malinconico, M. Rippa, and G. Abbate, "Spectroscopic ellipsometry study of liquid crystal and polymeric thin films in visible and near infrared," Eur. Phys. J. E 14, 185-192 (2004).
[CrossRef] [PubMed]

Robert, S.

Rousseau, J. J.

F. Royer, H. Roux, D. Jamon, J. J. Rousseau, D. Zins, V. Cabuil, and C. Bovier, "New technological approach in phase-matched magneto-optic planar waveguide realization," in Advances in Optical Thin Films, C. Amra, N. Kaiser, and H. A. Macleod, eds., Proc. SPIE 5250, 72-80 (2004).
[CrossRef]

Roux, H.

F. Royer, H. Roux, D. Jamon, J. J. Rousseau, D. Zins, V. Cabuil, and C. Bovier, "New technological approach in phase-matched magneto-optic planar waveguide realization," in Advances in Optical Thin Films, C. Amra, N. Kaiser, and H. A. Macleod, eds., Proc. SPIE 5250, 72-80 (2004).
[CrossRef]

Royer, F.

F. Royer, H. Roux, D. Jamon, J. J. Rousseau, D. Zins, V. Cabuil, and C. Bovier, "New technological approach in phase-matched magneto-optic planar waveguide realization," in Advances in Optical Thin Films, C. Amra, N. Kaiser, and H. A. Macleod, eds., Proc. SPIE 5250, 72-80 (2004).
[CrossRef]

Stchakovsky, M.

H. Touir, M. Stchakovsky, R. Ossikovski, and M. Warenghem, "Coherent and incoherent interference modeling and measurement of anisotropic multilayer stacks using conventional ellipsometry," Thin Solid Films 455-456, 628-631 (2003).
[CrossRef]

Tabet, M. F.

M. F. Tabet and W. A. McGahan, "Use of artificial neural networks to predict thickness and optical constants of thin films from reflectance data," Thin Solid Films 370, 122-127 (2000).
[CrossRef]

Tang, J.-F.

Tien, P. K.

P. K. Tien, R. Ulrich, and R. J. Martin, "Modes of propagating light waves in thin deposited semiconductor films," Appl. Phys. Lett. 14, 291-294 (1969).
[CrossRef]

Tkachenko, V.

V. Tkachenko, A. Marino, F. Vita, F. D'Amore, L. De Stefano, M. Malinconico, M. Rippa, and G. Abbate, "Spectroscopic ellipsometry study of liquid crystal and polymeric thin films in visible and near infrared," Eur. Phys. J. E 14, 185-192 (2004).
[CrossRef] [PubMed]

Torge, R.

Touir, H.

H. Touir, M. Stchakovsky, R. Ossikovski, and M. Warenghem, "Coherent and incoherent interference modeling and measurement of anisotropic multilayer stacks using conventional ellipsometry," Thin Solid Films 455-456, 628-631 (2003).
[CrossRef]

Turkmen, M.

C. Yildiz and M. Turkmen, "Very accurate and simple CAD models based on neural networks for coplanar waveguide synthesis," Int. J. RF Microwave Comput.-Aided Eng. 15, 218-222 (2005).
[CrossRef]

Ulrich, R.

R. Ulrich and R. Torge, "Measurement of thin-film parameters with a prism coupler," Appl. Opt. 12, 2901-2908 (1973).
[CrossRef] [PubMed]

P. K. Tien, R. Ulrich, and R. J. Martin, "Modes of propagating light waves in thin deposited semiconductor films," Appl. Phys. Lett. 14, 291-294 (1969).
[CrossRef]

Urban, F. K.

F. K. Urban III, D. Barton, and N. I. Boudani, "Extremely fast ellipsometry solutions using cascaded neural networks alone," Thin Solid Films 332, 50-55 (1998).
[CrossRef]

Vita, F.

V. Tkachenko, A. Marino, F. Vita, F. D'Amore, L. De Stefano, M. Malinconico, M. Rippa, and G. Abbate, "Spectroscopic ellipsometry study of liquid crystal and polymeric thin films in visible and near infrared," Eur. Phys. J. E 14, 185-192 (2004).
[CrossRef] [PubMed]

Warenghem, M.

H. Touir, M. Stchakovsky, R. Ossikovski, and M. Warenghem, "Coherent and incoherent interference modeling and measurement of anisotropic multilayer stacks using conventional ellipsometry," Thin Solid Films 455-456, 628-631 (2003).
[CrossRef]

Wei, J. S.

J. S. Wei and W. D. Westwood, "A new method for determining thin-film refractive index and thickness using guided optical waves," Appl. Phys. Lett. 32, 819-821 (1978).
[CrossRef]

Weigend, A.

D. Nix and A. Weigend, "Learning local error bars for nonlinear regression," in Proceedings of Advances in Neural Information Processing Systems, G. Tesauro, D. Touretzky, and T. Leen, eds, (MIT Press, 1995), pp. 489-496.

Westwood, W. D.

J. S. Wei and W. D. Westwood, "A new method for determining thin-film refractive index and thickness using guided optical waves," Appl. Phys. Lett. 32, 819-821 (1978).
[CrossRef]

Yildiz, C.

C. Yildiz and M. Turkmen, "Very accurate and simple CAD models based on neural networks for coplanar waveguide synthesis," Int. J. RF Microwave Comput.-Aided Eng. 15, 218-222 (2005).
[CrossRef]

Zaets, W.

W. Zaets and K. Ando, "Magneto-optical mode conversion in Cd1-xMnxTe waveguide on GaAs substrate," Appl. Phys. Lett. 77, 1593-1595 (2000).
[CrossRef]

Zins, D.

F. Royer, H. Roux, D. Jamon, J. J. Rousseau, D. Zins, V. Cabuil, and C. Bovier, "New technological approach in phase-matched magneto-optic planar waveguide realization," in Advances in Optical Thin Films, C. Amra, N. Kaiser, and H. A. Macleod, eds., Proc. SPIE 5250, 72-80 (2004).
[CrossRef]

Appl. Opt.

Appl. Phys. Lett.

W. Zaets and K. Ando, "Magneto-optical mode conversion in Cd1-xMnxTe waveguide on GaAs substrate," Appl. Phys. Lett. 77, 1593-1595 (2000).
[CrossRef]

P. K. Tien, R. Ulrich, and R. J. Martin, "Modes of propagating light waves in thin deposited semiconductor films," Appl. Phys. Lett. 14, 291-294 (1969).
[CrossRef]

J. S. Wei and W. D. Westwood, "A new method for determining thin-film refractive index and thickness using guided optical waves," Appl. Phys. Lett. 32, 819-821 (1978).
[CrossRef]

Ecol. Modell.

S. Lek, M. Delacoste, P. Baran, I. Dimopoulos, J. Lauga, and S. Aulagnier, "Application of neural networks to modeling nonlinear relationships in ecology," Ecol. Modell. 90, 39-52 (1996).
[CrossRef]

Eur. Phys. J. E

V. Tkachenko, A. Marino, F. Vita, F. D'Amore, L. De Stefano, M. Malinconico, M. Rippa, and G. Abbate, "Spectroscopic ellipsometry study of liquid crystal and polymeric thin films in visible and near infrared," Eur. Phys. J. E 14, 185-192 (2004).
[CrossRef] [PubMed]

Fiber Integr. Opt.

S. I. Hosain, J. P. Meunier, E. Bourillot, F. de Fornel, and J. P. Goudonnet, "Review of the basic methods for characterizing integrated-optic waveguides," Fiber Integr. Opt. 44, 89-107 (1995).

Int. J. RF Microwave Comput.-Aided Eng.

C. Yildiz and M. Turkmen, "Very accurate and simple CAD models based on neural networks for coplanar waveguide synthesis," Int. J. RF Microwave Comput.-Aided Eng. 15, 218-222 (2005).
[CrossRef]

J. Appl. Math.

D. Marquardt, "An algorithm for least-squares estimation of nonlinear parameters," J. Appl. Math. 11, 431-441 (1963).

J. Opt. Soc. Am. A

Neural Networks

K. I. Funahashi, "On the approximate realization of continuous mappings by neural networks," Neural Networks 2, 183-192 (1989).
[CrossRef]

Proc. SPIE

F. Royer, H. Roux, D. Jamon, J. J. Rousseau, D. Zins, V. Cabuil, and C. Bovier, "New technological approach in phase-matched magneto-optic planar waveguide realization," in Advances in Optical Thin Films, C. Amra, N. Kaiser, and H. A. Macleod, eds., Proc. SPIE 5250, 72-80 (2004).
[CrossRef]

Quart. Appl. Math.

K. Levenberg, "A method for the solution of certain problems in least squares," Quart. Appl. Math. 2, 164-168 (1944).

Thin Solid Films

H. Touir, M. Stchakovsky, R. Ossikovski, and M. Warenghem, "Coherent and incoherent interference modeling and measurement of anisotropic multilayer stacks using conventional ellipsometry," Thin Solid Films 455-456, 628-631 (2003).
[CrossRef]

M. F. Tabet and W. A. McGahan, "Use of artificial neural networks to predict thickness and optical constants of thin films from reflectance data," Thin Solid Films 370, 122-127 (2000).
[CrossRef]

F. K. Urban III, D. Barton, and N. I. Boudani, "Extremely fast ellipsometry solutions using cascaded neural networks alone," Thin Solid Films 332, 50-55 (1998).
[CrossRef]

Other

C. M. Bishop, Neural Networks for Pattern Recognition (Oxford U. Press, 1995).

R. M. A. Azzam and N. M. Bashara, Ellipsometry and Polarized Light, 2nd ed. (North Holland Press, 1987).

D. Nix and A. Weigend, "Learning local error bars for nonlinear regression," in Proceedings of Advances in Neural Information Processing Systems, G. Tesauro, D. Touretzky, and T. Leen, eds, (MIT Press, 1995), pp. 489-496.

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Figures (3)

Fig. 1
Fig. 1

Representation of a step-index planar waveguide defined by a thin anisotropic film of thickness h located between a dielectric substrate of refractive index n s and a dielectric cover formed by the air.

Fig. 2
Fig. 2

Structure of a multilayer perceptron with one hidden layer composed of 15 neurons. The input vector N contains the different measured effective indices, and the output vector X represents the estimation of the corresponding optogeometrical parameters ( n x , n y , and h) characterizing the waveguide structure.

Fig. 3
Fig. 3

The m-lines setup that allows measurement of the effective indices from an optical waveguide.

Tables (4)

Tables Icon

Table 1 Results and Error Bars for Two Standard Deviations (σ and 2σ) Calculated by the NN Concerning a Simulated Optical Anisotropic Waveguide

Tables Icon

Table 2 NN Results Concerning Experimental Characterization of a Silica–Titania Thin Film

Tables Icon

Table 3 Results Obtained on the Silica–Titania Thin Film by Means of the Classical Levenberg–Marquardt (LM) Algorithm with Different Initial Guesses

Tables Icon

Table 4 CPU Times for the Different Stages of the Neural Characterization

Equations (6)

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h k n y 2 N m T E 2 arctan ( N m T E 2 1 n y 2 N m T E 2 ) arctan ( N m T E 2 n s 2 n y 2 N m T E 2 ) = m π ,
h k n y n x n x 2 N m T M 2 arctan ( n x n y N m T M 2 1 n x 2 N m T M 2 ) arctan ( n x n y n s 2 N m T M 2 n s 2 n x 2 N m T M 2 ) = m π ,
f ( X ) = N ,
o i = g ( j w i,j N j ) ,
E = [ 1 n t e s t n t e s t ( X t e s t X ) 2 ] 1 / 2 ,
N i n = n p   sin ( A p + arcsin ( sin   θ i n n p ) ) ,

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