OSA's Digital Library

Applied Optics

Applied Optics


  • Editor: Joseph N. Mait
  • Vol. 50, Iss. 22 — Aug. 1, 2011
  • pp: 4499–4508

Numerical modeling of field-assisted ion-exchanged channel waveguides by the explicit consideration of space-charge buildup

Piotr Mrozek  »View Author Affiliations

Applied Optics, Vol. 50, Issue 22, pp. 4499-4508 (2011)

View Full Text Article

Enhanced HTML    Acrobat PDF (1144 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



A numerical model explicitly considering the space-charge density evolved both under the mask and in the region of optical structure formation was used to predict the profiles of Ag concentration during field-assisted Ag + Na + ion exchange channel waveguide fabrication. The influence of the unequal values of diffusion constants and mobilities of incoming and outgoing ions, the value of a correlation factor (Haven ratio), and particularly space-charge density induced during the ion exchange, on the resulting profiles of Ag concentration was analyzed and discussed. It was shown that the incorporation into the numerical model of a small quantity of highly mobile ions other than exclusively Ag + and Na + may considerably affect the range and shape of calculated Ag profiles in the multicomponent glass. The Poisson equation was used to predict the electric field spread evolution in the glass substrate. The results of the numerical analysis were verified by the experimental data of Ag concentration in a channel waveguide fabricated using a field-assisted process.

© 2011 Optical Society of America

OCIS Codes
(000.4430) General : Numerical approximation and analysis
(230.7380) Optical devices : Waveguides, channeled

ToC Category:
Optical Devices

Original Manuscript: April 29, 2011
Revised Manuscript: June 13, 2011
Manuscript Accepted: June 28, 2011
Published: July 27, 2011

Piotr Mrozek, "Numerical modeling of field-assisted ion-exchanged channel waveguides by the explicit consideration of space-charge buildup," Appl. Opt. 50, 4499-4508 (2011)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. S. Honkanen, B. R. West, S. Yliniemi, P. Madasamy, M. Morrell, J. Auxier, A. Schu¨lzgen, N. Peyghambarian, J. Carriere, J. Frantz, R. Kostuk, J. Castro, and D. Geraghty, “Recent advances in ion exchanged glass waveguides and devices,” Phys. Chem. Glasses 47, 110–120 (2006).
  2. B. West, “Ion-exchanged glass waveguides,” in The Handbook of Photonics, 2nd ed., M.C.Gupta and J.Ballato, eds. (CRC Press, 2007), pp. 13.1–35.
  3. D. Cheng, J. Saarinen, H. Saarikoski, and A. Tervonen, “Simulation of field-assisted ion exchange for glass channel waveguide fabrication: effect of nonhomogeneous time-dependent electric conductivity,” Opt. Commun. 137, 233–238 (1997). [CrossRef]
  4. J. Albert and J. W. Y. Lit, “Full modeling of field-assisted ion exchange for graded index buried channel optical waveguides,” Appl. Opt. 29, 2798–2804 (1990). [CrossRef] [PubMed]
  5. B. R. West, P. Madasamy, N. Peyghambarian, and S. Honkanen, “Modeling of ion-exchanged glass waveguide structures,” J. Non-Cryst. Solids 347, 18–26 (2004). [CrossRef]
  6. A. Tervonen, “A general model for fabrication processes of channel waveguides by ion exchange,” J. Appl. Phys. 67, 2746–2752 (1990). [CrossRef]
  7. X. Prieto, R. Srivastava, J. Linares, and C. Montero, “Prediction of space-charge density and space-charge field in thermally ion-exchanged planar surface waveguides,” Opt. Mater. 5, 145–151 (1996). [CrossRef]
  8. P. Mrozek, E. Mrozek, and T. Lukaszewicz, “Side diffusion modeling by the explicit consideration of a space charge buildup under the mask during a strip waveguide formation in Ag+–Na+ field-assisted ion exchange process,” Appl. Opt. 45, 619–625 (2006). [CrossRef] [PubMed]
  9. K. M. Knowles and A. T. J. van Helvoort, “Anodic bonding,” Int. Mater. Rev. 51, 273–311 (2006). [CrossRef]
  10. U. K. Krieger and W. A. Lanford, “Field assisted transport of Na+ ions, Ca+ ions and electrons in commercial soda-lime glass I: experimental,” J. Non-Cryst. Solids 102, 50–61(1988). [CrossRef]
  11. C. M. Lepienski, J. A. Giacometti, G. F. Leal Ferreira, F. L. Freire Jr., and C. A. Achete, “Electric field distribution and near-surface modifications in soda-lime glass submitted to a dc potential,” J. Non-Cryst. Solids 159, 204–212 (1993). [CrossRef]
  12. D. E. Carlson, K. W. Hang, and G. F. Stockdale, “Electrode polarization in alkali-containing glasses,” J. Am. Ceram. Soc. 55, 337–341 (1972). [CrossRef]
  13. G. Wallis, “Direct-current polarization during field-assisted glass-metal sealing,” J. Am. Ceram. Soc. 53, 563–67 (1970). [CrossRef]
  14. D. Kapila and J. L. Plawsky, “Diffusion processes for integrated waveguide fabrication in glasses: a solid-state electrochemical approach,” Chem. Eng. Sci. 50, 2589–2600 (1995). [CrossRef]
  15. P. Mrozek, E. Mrozek, and T. Lukaszewicz, “Determination of refractive index profiles of Ag+–Na+ ion-exchange multimode strip waveguides by variable wavefront shear double-refracting interferometry microinterferometry,” Appl. Opt. 45, 756–763 (2006). [CrossRef] [PubMed]

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited