Advertisement

Applied Physics B

, Volume 81, Issue 1, pp 65–73 | Cite as

Analytical and numerical study on grating depth effects in grating coupled waveguide sensors

  • R. Horvath
  • L. C. Wilcox
  • H. C. Pedersen
  • N. Skivesen
  • J. S. Hesthaven
  • P. M. Johansen
Article

Abstract

The in-coupling process for grating-coupled planar optical waveguide sensors is investigated in the case of TE waves. A simple analytical model based on the Rayleigh–Fourier–Kiselev method is applied to take into account the depth of the grating coupler, which is usually neglected in the modeling. Analytical expressions are derived both for the position and width of the in-coupling peaks to illustrate the effects of grating depth on the guided mode resonances in grating coupled waveguide sensors. Numerical computations verify the model for shallow gratings both in terms of peak shape and position and provide the limitations for the analytical formulas.

PACS

42.82.Et 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    O. Parriaux, V.A. Sychugov, A.V. Tishchenko, Pure Appl. Opt. 5, 453 (1996)CrossRefGoogle Scholar
  2. 2.
    W. Lukosz, K. Tiefenthaler, Opt. Lett. 10, 137 (1984)Google Scholar
  3. 3.
    K. Tiefenthaler, W. Lukosz, J. Opt. Soc. Am. B 6, 209 (1989)Google Scholar
  4. 4.
    W. Lukosz, Biosens. Bioelectron. 6, 215 (1991)CrossRefGoogle Scholar
  5. 5.
    W. Lukosz, Sens. Actuators 29, 37 (1995)CrossRefGoogle Scholar
  6. 6.
    K. Tiefenthaler, W. Lukosz, Thin Solid Films 126, 205 (1985)CrossRefGoogle Scholar
  7. 7.
    K. Tiefenthaler, Adv. Biosens. 2, 261 (1992)Google Scholar
  8. 8.
    O. Parriaux, P. Sixt, Sens. Actuators, B 29, 289 (1995)Google Scholar
  9. 9.
    R. Horvath, L.R. Lindvold, N.B. Larsen, Appl. Phys. B 74, 383 (2002)CrossRefGoogle Scholar
  10. 10.
    J. Voros, J.J. Ramsden, G. Csucs, I. Szendro, S.M. de Paul, M. Textor, N.D. Spencer, Biomaterials 23, 3699 (2002)CrossRefPubMedGoogle Scholar
  11. 11.
    J.J. Ramsden, J. Stat. Phys. 73, 853 (1993)CrossRefGoogle Scholar
  12. 12.
    J.J. Ramsden, J. Phys. Chem. 97, 4479 (1993)CrossRefGoogle Scholar
  13. 13.
    J.J. Ramsden, S.-Y. Li, J.E. Prenosil, E. Heinzle, Biotechnol. Bioeng. 43, 939 (1994)CrossRefGoogle Scholar
  14. 14.
    R. Horvath, J. Voros, R. Graf, G. Fricsovszky, M. Textor, L.R. Lindvold, N.D. Spencer, E. Papp, Appl. Phys. B 72, 441 (2001)Google Scholar
  15. 15.
    R. Horvath, G. Fricsovszky, E. Papp, Biosens. Bioelectron. 18, 415 (2003)CrossRefGoogle Scholar
  16. 16.
    R.E. Kunz, J. Dubendorfer, R.H. Morf, Biosens. Bioelectron. 11, 653 (1996)CrossRefGoogle Scholar
  17. 17.
    D. Marcuse, Theory of Dielectric Optical Waveguides (Academic, New York, 1974)Google Scholar
  18. 18.
    R. Petit (ed.), Electromagnetic Theory of Gratings (Springer, Berlin Heidelberg New York, 1980)Google Scholar
  19. 19.
    D. Maystre, Progress in Optics, vol. 21, ed. by E. Wolf (Amsterdam: North-Holland, 1984)Google Scholar
  20. 20.
    T. Tamir, S.T. Peng, Appl. Phys. 14, 235 (1977)CrossRefGoogle Scholar
  21. 21.
    Lord Rayleigh, Proc. R. Soc. A 79, 399 (1907)Google Scholar
  22. 22.
    V.A. Kiselev, Sov. J. Quant. Electron. 4, 872 (1975)Google Scholar
  23. 23.
    M.O. Shopin, Opt. Spectros. 77(1), 65 (1994)Google Scholar
  24. 24.
    V.A. Sychugov, A.V. Tishchenko, N.M. Lyndin, O. Parriaux, Sens. Actuators, B 38–39, 360 (1997)Google Scholar
  25. 25.
    V. Kochergin, I. Avrutsky, Y. Zhao, Biosens. Bioelectron. 15, 283 (2000)CrossRefGoogle Scholar
  26. 26.
    In Proceedings of IOFAN (Institute of General Physics of the Academy of Sciences of the Soviet Union) ISSN 0233-9390, Tom 34 (1991) (in Russian)Google Scholar
  27. 27.
    O.P. Bruno, F. Reitich, J. Opt. Soc. Am. A 10, 1168 (1993)Google Scholar
  28. 28.
    O.P. Bruno, F. Reitich, J. Opt. Soc. Am. A 10, 2307 (1993)Google Scholar
  29. 29.
    L.C. Wilcox, P.G. Dinesen, J.S. Hesthaven, J. Opt. Soc. Am. A 21(5), 757 (2004)CrossRefGoogle Scholar
  30. 30.
    P.K. Tien, Rev. Modern Phys. 49, 361 (1977)CrossRefGoogle Scholar
  31. 31.
    H. Kogelnik, H.P. Weber, J. Opt. Soc. Am. 64, 174 (1974)Google Scholar
  32. 32.
    R. Horvath, H.C. Pedersen, N.B. Larsen, Appl. Phys. Lett. 81, 2166 (2002)CrossRefGoogle Scholar
  33. 33.
    R. Horvath, H.C. Pedersen, N. Skivesen, D. Selmeczi, N.B. Larsen, Opt. Lett. 28, 1233 (2003)PubMedGoogle Scholar
  34. 34.
    A.K. Ghadak, K. Thyagaranjan, M.R. Shenoy, IEEE J. Lightwave Technol. LT-5, 660 (1987)Google Scholar
  35. 35.
    M.R. Ramadas, E. Garmire, A.K. Ghatak, K. Thyagaranjan, M.R. Shenoy, Opt. Lett. 14, 376 (1989)Google Scholar
  36. 36.
    N.M. Lyndin, O. Parriaux, V.A. Sychugov, Sens. Actuators, B 41, 23 (1997)Google Scholar

Copyright information

© Springer-Verlag 2005

Authors and Affiliations

  • R. Horvath
    • 1
  • L. C. Wilcox
    • 2
  • H. C. Pedersen
    • 1
  • N. Skivesen
    • 1
  • J. S. Hesthaven
    • 2
  • P. M. Johansen
    • 1
  1. 1.Optics and Plasma Research DepartmentRisø National LaboratoryRoskildeDenmark
  2. 2.Division of Applied MathematicsBrown UniversityProvidenceUSA

Personalised recommendations