Abstract

We propose a modified inverse regularization algorithm for computing the 2-D refractive index profiles of integrated-optic waveguides from measured near-field data. The algorithm involves embedding of a spatial mean filter to remove impulses and high frequency noises from the near-field intensity as well as from its second derivative. The proposed filtering scheme is built-in to the inverse algorithm and does not require extra computation for filtering. The effectiveness of the proposed method is demonstrated by reconstructing the Refractive index profile of a single mode lithium niobate channel waveguide from the propagating mode near-field intensity pattern.

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  1. F. Cacavale, P. Chakraborty, A. Quanranta, I. Mansour, G. Gianello, S. Bosso, R. Corsini, G. Mussi, "Secondary ion mass spectroscopy and near field studies of ${\rm Ti}:{\rm LiNbO}_{3}$ optical waveguides," J. Appl. Phys. 78, 5345-5350 (1995).
  2. P. Kaminow, J. R. Carruthers, "Optical waveguide layers in ${\rm LiNbO}_{3}$ and ${\rm LiTaO}_{3}$," J. Appl. Phys. 22, 326-328 (1973).
  3. J. M. White, Heidrich, "Optical waveguide refractive index profile determined from measurement of mode indices: A simple analysis," Appl. Opt. 15, 151-155 (1976).
  4. K. S. Chiang, "Construction of refractive index profile of planar dielectric waveguide from the distribution of effective indexes," J. Lightw. Technol. LT-3, 385-391 (1985).
  5. G. L. Yip, P. C. Noutsios, L. Chen, "Improved propagation mode near-field method for refractive index profiling of optical waveguides," Appl. Opt. 35, 2060-2068 (1996).
  6. F. Caccavale, F. Segato, I. Mansour, M. Gianesin, "A finite differences method for the reconstruction of refractive index profiles from near-field measurements," J. Lightw. Technol. 16, 1348-1352 (1998).
  7. D. Brooks, S. Ruschin, "Improved near-field method for refractive index measurement of optical waveguides," J. Photon. Technol, Lett. 8, 254-256 (1996).
  8. I. Mansour, F. Caccavale, "An improved procedure to calculate the refractive index profile from the measured near-field intensity," J. Lightw. Technol. 14, 423-428 (1996).
  9. K. Morishita, "Index profiling of three-dimensional optical waveguide by the propagation mode near-field mrthod," J. Lightw. Technol. 4, 1120-1124 (1986).
  10. M. Artiglia, M. Calzavara, P. D. Vita, A. Sharma, "A new procedure for the analysis of single mode-fiber far-field data," Fiber Integrat. Opt. 9, 37-42 (1989).
  11. A. Sharma, P. Bindal, "Analysis of near field data of diffused channel waveguides: An accurate method to obtain $\Delta n$ and index profile," SPIE (1994) pp. 152-163.
  12. G. G. Lin, C. K. Chen, "An inverse algorithm to calculate the refractive indeed profiles of periodically segmented waveguides from the measured near-field intensities," J. Lightw. Technol. 20, 58-64 (2002).
  13. R. C. Gonzalez, R. E. Woods, Digital Image Processing (Pearson Prentice Hall, 2006).
  14. A. Tarantola, Inverse Problems Theory and Methods for Model Parameter Estimation (SIAM, 2005).
  15. J. V. Beck, K. L. Amold, Parameter Estimation in Engineering and Science (Wiley, 1977).
  16. R. L. Gallawa, I. C. Goyal, Y. Tu, A. K. Ghatak, "Optical waveguide modes: An approximate solution using Galerkin's method with Hermite-Gauss basis functions," IEEE J. Quantum Electron. 27, 518-522 (1991).
  17. A. Sharma, P. Bindal, "Analysis of diffused planar and channel waveguides," J. Quantum Electron. 29, 150-153 (1993).
  18. K. Nassau, H. Levinstien, "Growth and properties of lithium niobate," J. Quantum Electron. 2, 128-128 (1966).
  19. J. Helms, J. Schmidtchen, B. Schuppert, K. Peterman, "Error analysis for refractive-index profile determination form near-field measurements," J. Lightw. Technol. 8, 625-633 (1990).
  20. A. D. Lallo, A. Cino, C. Conti, G. Assanto, "Second harmonic generation in reverse proton exchanged lithium niobate waveguides," Opt. Expr. 8, 232-237 (2001).

2002 (1)

G. G. Lin, C. K. Chen, "An inverse algorithm to calculate the refractive indeed profiles of periodically segmented waveguides from the measured near-field intensities," J. Lightw. Technol. 20, 58-64 (2002).

2001 (1)

A. D. Lallo, A. Cino, C. Conti, G. Assanto, "Second harmonic generation in reverse proton exchanged lithium niobate waveguides," Opt. Expr. 8, 232-237 (2001).

1998 (1)

F. Caccavale, F. Segato, I. Mansour, M. Gianesin, "A finite differences method for the reconstruction of refractive index profiles from near-field measurements," J. Lightw. Technol. 16, 1348-1352 (1998).

1996 (3)

D. Brooks, S. Ruschin, "Improved near-field method for refractive index measurement of optical waveguides," J. Photon. Technol, Lett. 8, 254-256 (1996).

I. Mansour, F. Caccavale, "An improved procedure to calculate the refractive index profile from the measured near-field intensity," J. Lightw. Technol. 14, 423-428 (1996).

G. L. Yip, P. C. Noutsios, L. Chen, "Improved propagation mode near-field method for refractive index profiling of optical waveguides," Appl. Opt. 35, 2060-2068 (1996).

1995 (1)

F. Cacavale, P. Chakraborty, A. Quanranta, I. Mansour, G. Gianello, S. Bosso, R. Corsini, G. Mussi, "Secondary ion mass spectroscopy and near field studies of ${\rm Ti}:{\rm LiNbO}_{3}$ optical waveguides," J. Appl. Phys. 78, 5345-5350 (1995).

1993 (1)

A. Sharma, P. Bindal, "Analysis of diffused planar and channel waveguides," J. Quantum Electron. 29, 150-153 (1993).

1991 (1)

R. L. Gallawa, I. C. Goyal, Y. Tu, A. K. Ghatak, "Optical waveguide modes: An approximate solution using Galerkin's method with Hermite-Gauss basis functions," IEEE J. Quantum Electron. 27, 518-522 (1991).

1990 (1)

J. Helms, J. Schmidtchen, B. Schuppert, K. Peterman, "Error analysis for refractive-index profile determination form near-field measurements," J. Lightw. Technol. 8, 625-633 (1990).

1989 (1)

M. Artiglia, M. Calzavara, P. D. Vita, A. Sharma, "A new procedure for the analysis of single mode-fiber far-field data," Fiber Integrat. Opt. 9, 37-42 (1989).

1986 (1)

K. Morishita, "Index profiling of three-dimensional optical waveguide by the propagation mode near-field mrthod," J. Lightw. Technol. 4, 1120-1124 (1986).

1985 (1)

K. S. Chiang, "Construction of refractive index profile of planar dielectric waveguide from the distribution of effective indexes," J. Lightw. Technol. LT-3, 385-391 (1985).

1976 (1)

1973 (1)

P. Kaminow, J. R. Carruthers, "Optical waveguide layers in ${\rm LiNbO}_{3}$ and ${\rm LiTaO}_{3}$," J. Appl. Phys. 22, 326-328 (1973).

1966 (1)

K. Nassau, H. Levinstien, "Growth and properties of lithium niobate," J. Quantum Electron. 2, 128-128 (1966).

Appl. Opt. (1)

G. L. Yip, P. C. Noutsios, L. Chen, "Improved propagation mode near-field method for refractive index profiling of optical waveguides," Appl. Opt. 35, 2060-2068 (1996).

Appl. Opt. (1)

Fiber Integrat. Opt. (1)

M. Artiglia, M. Calzavara, P. D. Vita, A. Sharma, "A new procedure for the analysis of single mode-fiber far-field data," Fiber Integrat. Opt. 9, 37-42 (1989).

IEEE J. Quantum Electron. (1)

R. L. Gallawa, I. C. Goyal, Y. Tu, A. K. Ghatak, "Optical waveguide modes: An approximate solution using Galerkin's method with Hermite-Gauss basis functions," IEEE J. Quantum Electron. 27, 518-522 (1991).

J. Lightw. Technol. (1)

J. Helms, J. Schmidtchen, B. Schuppert, K. Peterman, "Error analysis for refractive-index profile determination form near-field measurements," J. Lightw. Technol. 8, 625-633 (1990).

J. Appl. Phys. (2)

F. Cacavale, P. Chakraborty, A. Quanranta, I. Mansour, G. Gianello, S. Bosso, R. Corsini, G. Mussi, "Secondary ion mass spectroscopy and near field studies of ${\rm Ti}:{\rm LiNbO}_{3}$ optical waveguides," J. Appl. Phys. 78, 5345-5350 (1995).

P. Kaminow, J. R. Carruthers, "Optical waveguide layers in ${\rm LiNbO}_{3}$ and ${\rm LiTaO}_{3}$," J. Appl. Phys. 22, 326-328 (1973).

J. Lightw. Technol. (1)

G. G. Lin, C. K. Chen, "An inverse algorithm to calculate the refractive indeed profiles of periodically segmented waveguides from the measured near-field intensities," J. Lightw. Technol. 20, 58-64 (2002).

J. Lightw. Technol. (4)

K. S. Chiang, "Construction of refractive index profile of planar dielectric waveguide from the distribution of effective indexes," J. Lightw. Technol. LT-3, 385-391 (1985).

F. Caccavale, F. Segato, I. Mansour, M. Gianesin, "A finite differences method for the reconstruction of refractive index profiles from near-field measurements," J. Lightw. Technol. 16, 1348-1352 (1998).

I. Mansour, F. Caccavale, "An improved procedure to calculate the refractive index profile from the measured near-field intensity," J. Lightw. Technol. 14, 423-428 (1996).

K. Morishita, "Index profiling of three-dimensional optical waveguide by the propagation mode near-field mrthod," J. Lightw. Technol. 4, 1120-1124 (1986).

J. Photon. Technol, Lett. (1)

D. Brooks, S. Ruschin, "Improved near-field method for refractive index measurement of optical waveguides," J. Photon. Technol, Lett. 8, 254-256 (1996).

J. Quantum Electron. (2)

A. Sharma, P. Bindal, "Analysis of diffused planar and channel waveguides," J. Quantum Electron. 29, 150-153 (1993).

K. Nassau, H. Levinstien, "Growth and properties of lithium niobate," J. Quantum Electron. 2, 128-128 (1966).

Opt. Expr. (1)

A. D. Lallo, A. Cino, C. Conti, G. Assanto, "Second harmonic generation in reverse proton exchanged lithium niobate waveguides," Opt. Expr. 8, 232-237 (2001).

Other (4)

A. Sharma, P. Bindal, "Analysis of near field data of diffused channel waveguides: An accurate method to obtain $\Delta n$ and index profile," SPIE (1994) pp. 152-163.

R. C. Gonzalez, R. E. Woods, Digital Image Processing (Pearson Prentice Hall, 2006).

A. Tarantola, Inverse Problems Theory and Methods for Model Parameter Estimation (SIAM, 2005).

J. V. Beck, K. L. Amold, Parameter Estimation in Engineering and Science (Wiley, 1977).

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