Abstract

We report on a method for the simultaneous determination of refractive index profiles and mode indices from the measured near-field intensity profiles of optical waveguides. This method has been applied to UV-written single-mode optical waveguides in ${\hbox {LiNbO}}_{3}$ for the optimization of the writing conditions. The results for the waveguides written with light of the wavelengths 275, 300.3, 302, and 305 nm for different writing powers and scan speeds reveal that for optimum writing conditions a maximum possible refractive index change of $\sim$0.0026 can be achieved at a value of 632.8 nm transmitting wavelength. The computation process used in the presented technique may also become useful to extract absolute refractive index values of any slowly varying graded index waveguide.

© 2009 IEEE

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  1. R. S. Weis, T. K. Gaylord, "Lithium niobate: Summary of physical properties and crystal structure," Appl. Phys. A 37, 191-203 (1985).
  2. S. Mailis, C. Riziotis, I. T. Wellington, P. G. R. Smith, C. B. E. Gawith, R. W. Eason, "Direct ultraviolet writing of channel waveguides in congruent lithium niobate single crystals," Opt. Lett 28, 1433-1435 (2003).
  3. K. Gallo, C. B. E. Gawith, I. T. Wellington, S. Mailis, R. W. Eason, P. G. R. Smith, D. J. Richardson, "Ultraviolet writing of channel waveguides in proton-exchanged ${\hbox {LiNbO}}_{3}$," J. Appl. Phys. 101, 014110 (2007).
  4. A. C. Muir, G. J. Daniell, C. P. Please, I. T. Wellington, S. Mailis, R. W. Eason, "Modelling the formation of optical waveguides produced in ${\hbox {LiNbO}}_{3}$ by laser induced thermal diffusion of lithium ions," Appl. Phys. A 83, 389-396 (2006).
  5. C. L. Sones, S. Mailis, V. Apostolopoulos, I. E. Barry, C. B. E. Gawith, P. G. R. Smith, R. W. Eason, "Fabrication of piezoelectric micro-cantilevers in domain engineered ${\hbox {LiNbO}}_{3}$ single crystals," J. Micromech. Microeng. 12, 53-57 (2002).
  6. 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).
  7. J. Noda, M. Minakata, S. Saito, N. Uchida, "Precise determination of refractive index and thickness in the Ti-diffused ${\hbox {LiNbO}}_{3}$ waveguide," J. Opt. Soc. Amer. 68, 1690-1693 (1978).
  8. J. Heibei, E. Voges, "Index profiles of planar optical waveguides determined from the angular dependence of reflectivity," IEEE J. Quantum Electron. QE-14, 501-506 (1978).
  9. H. M. Presby, D. Marcuse, "Direct index measurements of diffused channel waveguides," IEEE J. Quantum Electron. QE-16, 634-640 (1980).
  10. L. McCaughan, E. E. Bergman, "Index distribution of optical waveguides from their mode profile," J. Lightw. Technol. 1, 241-244 (1983).
  11. J. Helms, J. Schmidtchen, B. Schupper, K. Petermann, "Error analysis for refractive-index profile determination from near-field measurement," J. Lightw. Technol. 8, 625-633 (1990).
  12. 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).
  13. D. Brooks, S. Ruschin, "Improved near-field method for refractive index measurement of optical waveguides," IEEE Photon. Technol. Lett. 8, 254-256 (1996).
  14. F. Caccavale, F. Segato, I. Mansour, M. Gianesin, "A finite difference method for the reconstruction of refractive index profiles from near-field measurements," J. Lightw. Technol. 16, 1348-1353 (1998).
  15. N. Nikolaev, V. V. Shevchenko, "Inverse method for the reconstruction of refractive index profile and power management in graded index optical waveguides," Opt. Quantum Electron. 39, 891-902 (2007).
  16. X. Liu, F. Lu, F. Chen, Y. Tan, R. Zhang, H. Liu, L. Wang, L. Wang, "Reconstruction of extraordinary refractive index profiles of optical planar waveguides with single or double modes fabricated by ${\hbox {O}}^{2+}$ ion implantation into lithium niobate," Opt. Commun. 281, 1529-1533 (2008).
  17. R. Chakraborty, P. Ganguly, J. C. Biswas, S. K. Lahiri, "Modal profiles in ${\hbox {Ti}}:{\hbox {LiNbO}}_{3}$ two-waveguide and three-waveguide couplers by effective-index-based matrix method," Opt. Commun. 187, 155-163 (2001).
  18. I. Fatadin, D. Ives, M. Wicks, "Accurate magnified near-field measurement of optical waveguides using a calibrated CCD camera," J. Lightw. Technol. 12, 5067-5074 (2006).
  19. M. Born, E. Wolf, Principles of Optics (Pergamon, 1980).
  20. D. S. Smith, H. D. Riccius, "Refractive indices of lithium niobate," Opt. Commun. 17, 332-335 (1976).
  21. A. Rodenas, D. Jaque, C. Molpeceres, S. Lauzurica, J. L. Ocana, G. A. Torchia, F. Agullo-Rueda, "Ultra-violet nanosecond laser-assisted micro-modifications in lithium niobate monitored by ${\hbox {Nd}}^{3+}$ luminescence," Appl. Phys. A 87, 87-90 (2007).
  22. D. C. Deshpande, A. P. Malshe, E. A. Stach, V. Radmilovic, D. Alexander, D. Doerr, D. Hirt, "Investigation of femtosecond laser assisted nano and microscale modifications in lithium niobate," J. Appl. Phys. 97, (2005) 074316.
  23. J. Burghoff, C. Grebing, S. Nolte, A. Tünnermann, "Waveguides in lithium niobate fabricated by focused ultrashort laser pulses," Appl. Surf. Sci. 253, 7899-7902 (2007).
  24. D. Redfield, W. J. Burke, "Optical absorption edge of ${\hbox {LiNbO}}_{3}$," J. Appl. Phys. 45, 4566-4571 (1974).

2008 (1)

X. Liu, F. Lu, F. Chen, Y. Tan, R. Zhang, H. Liu, L. Wang, L. Wang, "Reconstruction of extraordinary refractive index profiles of optical planar waveguides with single or double modes fabricated by ${\hbox {O}}^{2+}$ ion implantation into lithium niobate," Opt. Commun. 281, 1529-1533 (2008).

2007 (4)

K. Gallo, C. B. E. Gawith, I. T. Wellington, S. Mailis, R. W. Eason, P. G. R. Smith, D. J. Richardson, "Ultraviolet writing of channel waveguides in proton-exchanged ${\hbox {LiNbO}}_{3}$," J. Appl. Phys. 101, 014110 (2007).

A. Rodenas, D. Jaque, C. Molpeceres, S. Lauzurica, J. L. Ocana, G. A. Torchia, F. Agullo-Rueda, "Ultra-violet nanosecond laser-assisted micro-modifications in lithium niobate monitored by ${\hbox {Nd}}^{3+}$ luminescence," Appl. Phys. A 87, 87-90 (2007).

J. Burghoff, C. Grebing, S. Nolte, A. Tünnermann, "Waveguides in lithium niobate fabricated by focused ultrashort laser pulses," Appl. Surf. Sci. 253, 7899-7902 (2007).

N. Nikolaev, V. V. Shevchenko, "Inverse method for the reconstruction of refractive index profile and power management in graded index optical waveguides," Opt. Quantum Electron. 39, 891-902 (2007).

2006 (2)

I. Fatadin, D. Ives, M. Wicks, "Accurate magnified near-field measurement of optical waveguides using a calibrated CCD camera," J. Lightw. Technol. 12, 5067-5074 (2006).

A. C. Muir, G. J. Daniell, C. P. Please, I. T. Wellington, S. Mailis, R. W. Eason, "Modelling the formation of optical waveguides produced in ${\hbox {LiNbO}}_{3}$ by laser induced thermal diffusion of lithium ions," Appl. Phys. A 83, 389-396 (2006).

2005 (1)

D. C. Deshpande, A. P. Malshe, E. A. Stach, V. Radmilovic, D. Alexander, D. Doerr, D. Hirt, "Investigation of femtosecond laser assisted nano and microscale modifications in lithium niobate," J. Appl. Phys. 97, (2005) 074316.

2003 (1)

S. Mailis, C. Riziotis, I. T. Wellington, P. G. R. Smith, C. B. E. Gawith, R. W. Eason, "Direct ultraviolet writing of channel waveguides in congruent lithium niobate single crystals," Opt. Lett 28, 1433-1435 (2003).

2002 (1)

C. L. Sones, S. Mailis, V. Apostolopoulos, I. E. Barry, C. B. E. Gawith, P. G. R. Smith, R. W. Eason, "Fabrication of piezoelectric micro-cantilevers in domain engineered ${\hbox {LiNbO}}_{3}$ single crystals," J. Micromech. Microeng. 12, 53-57 (2002).

2001 (1)

R. Chakraborty, P. Ganguly, J. C. Biswas, S. K. Lahiri, "Modal profiles in ${\hbox {Ti}}:{\hbox {LiNbO}}_{3}$ two-waveguide and three-waveguide couplers by effective-index-based matrix method," Opt. Commun. 187, 155-163 (2001).

1998 (1)

F. Caccavale, F. Segato, I. Mansour, M. Gianesin, "A finite difference method for the reconstruction of refractive index profiles from near-field measurements," J. Lightw. Technol. 16, 1348-1353 (1998).

1996 (2)

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).

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

1990 (1)

J. Helms, J. Schmidtchen, B. Schupper, K. Petermann, "Error analysis for refractive-index profile determination from near-field measurement," J. Lightw. Technol. 8, 625-633 (1990).

1985 (1)

R. S. Weis, T. K. Gaylord, "Lithium niobate: Summary of physical properties and crystal structure," Appl. Phys. A 37, 191-203 (1985).

1983 (1)

L. McCaughan, E. E. Bergman, "Index distribution of optical waveguides from their mode profile," J. Lightw. Technol. 1, 241-244 (1983).

1980 (1)

H. M. Presby, D. Marcuse, "Direct index measurements of diffused channel waveguides," IEEE J. Quantum Electron. QE-16, 634-640 (1980).

1978 (2)

J. Noda, M. Minakata, S. Saito, N. Uchida, "Precise determination of refractive index and thickness in the Ti-diffused ${\hbox {LiNbO}}_{3}$ waveguide," J. Opt. Soc. Amer. 68, 1690-1693 (1978).

J. Heibei, E. Voges, "Index profiles of planar optical waveguides determined from the angular dependence of reflectivity," IEEE J. Quantum Electron. QE-14, 501-506 (1978).

1976 (2)

1974 (1)

D. Redfield, W. J. Burke, "Optical absorption edge of ${\hbox {LiNbO}}_{3}$," J. Appl. Phys. 45, 4566-4571 (1974).

Appl. Opt. (1)

Appl. Phys. A (3)

R. S. Weis, T. K. Gaylord, "Lithium niobate: Summary of physical properties and crystal structure," Appl. Phys. A 37, 191-203 (1985).

A. C. Muir, G. J. Daniell, C. P. Please, I. T. Wellington, S. Mailis, R. W. Eason, "Modelling the formation of optical waveguides produced in ${\hbox {LiNbO}}_{3}$ by laser induced thermal diffusion of lithium ions," Appl. Phys. A 83, 389-396 (2006).

A. Rodenas, D. Jaque, C. Molpeceres, S. Lauzurica, J. L. Ocana, G. A. Torchia, F. Agullo-Rueda, "Ultra-violet nanosecond laser-assisted micro-modifications in lithium niobate monitored by ${\hbox {Nd}}^{3+}$ luminescence," Appl. Phys. A 87, 87-90 (2007).

Appl. Surf. Sci. (1)

J. Burghoff, C. Grebing, S. Nolte, A. Tünnermann, "Waveguides in lithium niobate fabricated by focused ultrashort laser pulses," Appl. Surf. Sci. 253, 7899-7902 (2007).

IEEE J. Quantum Electron. (2)

J. Heibei, E. Voges, "Index profiles of planar optical waveguides determined from the angular dependence of reflectivity," IEEE J. Quantum Electron. QE-14, 501-506 (1978).

H. M. Presby, D. Marcuse, "Direct index measurements of diffused channel waveguides," IEEE J. Quantum Electron. QE-16, 634-640 (1980).

IEEE Photon. Technol. Lett. (1)

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

J. Appl. Phys. (3)

D. Redfield, W. J. Burke, "Optical absorption edge of ${\hbox {LiNbO}}_{3}$," J. Appl. Phys. 45, 4566-4571 (1974).

D. C. Deshpande, A. P. Malshe, E. A. Stach, V. Radmilovic, D. Alexander, D. Doerr, D. Hirt, "Investigation of femtosecond laser assisted nano and microscale modifications in lithium niobate," J. Appl. Phys. 97, (2005) 074316.

K. Gallo, C. B. E. Gawith, I. T. Wellington, S. Mailis, R. W. Eason, P. G. R. Smith, D. J. Richardson, "Ultraviolet writing of channel waveguides in proton-exchanged ${\hbox {LiNbO}}_{3}$," J. Appl. Phys. 101, 014110 (2007).

J. Lightw. Technol. (5)

F. Caccavale, F. Segato, I. Mansour, M. Gianesin, "A finite difference method for the reconstruction of refractive index profiles from near-field measurements," J. Lightw. Technol. 16, 1348-1353 (1998).

I. Fatadin, D. Ives, M. Wicks, "Accurate magnified near-field measurement of optical waveguides using a calibrated CCD camera," J. Lightw. Technol. 12, 5067-5074 (2006).

L. McCaughan, E. E. Bergman, "Index distribution of optical waveguides from their mode profile," J. Lightw. Technol. 1, 241-244 (1983).

J. Helms, J. Schmidtchen, B. Schupper, K. Petermann, "Error analysis for refractive-index profile determination from near-field measurement," J. Lightw. Technol. 8, 625-633 (1990).

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).

J. Micromech. Microeng. (1)

C. L. Sones, S. Mailis, V. Apostolopoulos, I. E. Barry, C. B. E. Gawith, P. G. R. Smith, R. W. Eason, "Fabrication of piezoelectric micro-cantilevers in domain engineered ${\hbox {LiNbO}}_{3}$ single crystals," J. Micromech. Microeng. 12, 53-57 (2002).

J. Opt. Soc. Amer. (1)

J. Noda, M. Minakata, S. Saito, N. Uchida, "Precise determination of refractive index and thickness in the Ti-diffused ${\hbox {LiNbO}}_{3}$ waveguide," J. Opt. Soc. Amer. 68, 1690-1693 (1978).

Opt. Commun. (3)

X. Liu, F. Lu, F. Chen, Y. Tan, R. Zhang, H. Liu, L. Wang, L. Wang, "Reconstruction of extraordinary refractive index profiles of optical planar waveguides with single or double modes fabricated by ${\hbox {O}}^{2+}$ ion implantation into lithium niobate," Opt. Commun. 281, 1529-1533 (2008).

R. Chakraborty, P. Ganguly, J. C. Biswas, S. K. Lahiri, "Modal profiles in ${\hbox {Ti}}:{\hbox {LiNbO}}_{3}$ two-waveguide and three-waveguide couplers by effective-index-based matrix method," Opt. Commun. 187, 155-163 (2001).

D. S. Smith, H. D. Riccius, "Refractive indices of lithium niobate," Opt. Commun. 17, 332-335 (1976).

Opt. Lett (1)

S. Mailis, C. Riziotis, I. T. Wellington, P. G. R. Smith, C. B. E. Gawith, R. W. Eason, "Direct ultraviolet writing of channel waveguides in congruent lithium niobate single crystals," Opt. Lett 28, 1433-1435 (2003).

Opt. Quantum Electron. (1)

N. Nikolaev, V. V. Shevchenko, "Inverse method for the reconstruction of refractive index profile and power management in graded index optical waveguides," Opt. Quantum Electron. 39, 891-902 (2007).

Other (1)

M. Born, E. Wolf, Principles of Optics (Pergamon, 1980).

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